id	sid	tid	token	lemma	pos
cana-1759	1	1	communications	communication	NOUN
cana-1759	1	2	on	on	ADP
cana-1759	1	3	applied	apply	VERB
cana-1759	1	4	nonlinear	nonlinear	ADJ
cana-1759	1	5	analysis	analysis	NOUN
cana-1759	1	6	issn	issn	NOUN
cana-1759	1	7	:	:	PUNCT
cana-1759	1	8	1074	1074	NUM
cana-1759	1	9	-	-	PUNCT
cana-1759	1	10	133x	133x	NUM
cana-1759	1	11	vol	vol	NOUN
cana-1759	1	12	32	32	NUM
cana-1759	1	13	no	no	NOUN
cana-1759	1	14	.	.	NOUN
cana-1759	1	15	2	2	NUM
cana-1759	1	16	(	(	PUNCT
cana-1759	1	17	2025	2025	NUM
cana-1759	1	18	)	)	PUNCT
cana-1759	2	1	471	471	NUM
cana-1759	2	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	2	3	revolutionizing	revolutionize	VERB
cana-1759	2	4	heat	heat	NOUN
cana-1759	2	5	transfer	transfer	NOUN
cana-1759	2	6	and	and	CCONJ
cana-1759	2	7	fluid	fluid	ADJ
cana-1759	2	8	flow	flow	NOUN
cana-1759	2	9	models	model	NOUN
cana-1759	2	10	:	:	PUNCT
cana-1759	2	11	fractional	fractional	ADJ
cana-1759	2	12	calculus	calculus	NOUN
cana-1759	2	13	and	and	CCONJ
cana-1759	2	14	non	non	ADJ
cana-1759	2	15	-	-	ADJ
cana-1759	2	16	newtonian	newtonian	ADJ
cana-1759	2	17	dynamics	dynamic	NOUN
cana-1759	2	18	meet	meet	VERB
cana-1759	2	19	advanced	advanced	ADJ
cana-1759	2	20	numerical	numerical	ADJ
cana-1759	2	21	methods	method	NOUN
cana-1759	2	22	prabhat	prabhat	PROPN
cana-1759	2	23	kumar1	kumar1	PROPN
cana-1759	2	24	,	,	PUNCT
cana-1759	2	25	m.m	m.m	PROPN
cana-1759	2	26	.	.	PROPN
cana-1759	2	27	dixit2	dixit2	PROPN
cana-1759	2	28	,	,	PUNCT
cana-1759	2	29	dr	dr	PROPN
cana-1759	2	30	.	.	PROPN
cana-1759	2	31	neha	neha	PROPN
cana-1759	2	32	verma3	verma3	PROPN
cana-1759	2	33	,	,	PUNCT
cana-1759	2	34	dr.j.pandima	dr.j.pandima	PROPN
cana-1759	2	35	devi4	devi4	PROPN
cana-1759	2	36	,	,	PUNCT
cana-1759	2	37	dr.p.rani5	dr.p.rani5	PROPN
cana-1759	2	38	,	,	PUNCT
cana-1759	2	39	dr	dr	PROPN
cana-1759	2	40	.	.	PROPN
cana-1759	2	41	vijay	vijay	PROPN
cana-1759	2	42	kumar	kumar	PROPN
cana-1759	2	43	dwivedi6	dwivedi6	PROPN
cana-1759	2	44	,	,	PUNCT
cana-1759	2	45	kanchan	kanchan	PROPN
cana-1759	2	46	yadav7	yadav7	PROPN
cana-1759	3	1	1department	1department	NUM
cana-1759	3	2	of	of	ADP
cana-1759	3	3	applied	apply	VERB
cana-1759	3	4	sciences	sciences	PROPN
cana-1759	3	5	&	&	CCONJ
cana-1759	3	6	humanities	humanity	NOUN
cana-1759	3	7	,	,	PUNCT
cana-1759	3	8	nerist	nerist	NOUN
cana-1759	3	9	,	,	PUNCT
cana-1759	3	10	nirjuli	nirjuli	NOUN
cana-1759	3	11	,	,	PUNCT
cana-1759	3	12	department	department	NOUN
cana-1759	3	13	of	of	ADP
cana-1759	3	14	mathematics	mathematics	PROPN
cana-1759	3	15	,	,	PUNCT
cana-1759	3	16	a.p	a.p	PROPN
cana-1759	3	17	..	..	PROPN
cana-1759	3	18	india-prabhats1718@gmail.com	india-prabhats1718@gmail.com	PROPN
cana-1759	4	1	2department	2department	NUM
cana-1759	4	2	of	of	ADP
cana-1759	4	3	applied	apply	VERB
cana-1759	4	4	sciences	sciences	PROPN
cana-1759	4	5	&	&	CCONJ
cana-1759	4	6	humanities	humanity	NOUN
cana-1759	4	7	,	,	PUNCT
cana-1759	4	8	nerist	nerist	NOUN
cana-1759	4	9	,	,	PUNCT
cana-1759	4	10	nirjuli	nirjuli	NOUN
cana-1759	4	11	,	,	PUNCT
cana-1759	4	12	department	department	NOUN
cana-1759	4	13	of	of	ADP
cana-1759	4	14	mathematics	mathematics	PROPN
cana-1759	4	15	,	,	PUNCT
cana-1759	4	16	a.p	a.p	PROPN
cana-1759	4	17	.	.	PROPN
cana-1759	4	18	india.-mmdixixt79@gmail.com	india.-mmdixixt79@gmail.com	PROPN
cana-1759	4	19	3department	3department	NUM
cana-1759	4	20	of	of	ADP
cana-1759	4	21	mechanical	mechanical	ADJ
cana-1759	4	22	engineering	engineering	NOUN
cana-1759	4	23	,	,	PUNCT
cana-1759	4	24	shri	shri	PROPN
cana-1759	4	25	shankaracharya	shankaracharya	PROPN
cana-1759	4	26	institute	institute	PROPN
cana-1759	4	27	of	of	ADP
cana-1759	4	28	professional	professional	PROPN
cana-1759	4	29	management	management	NOUN
cana-1759	4	30	and	and	CCONJ
cana-1759	4	31	technology	technology	NOUN
cana-1759	4	32	,	,	PUNCT
cana-1759	4	33	raipur	raipur	NOUN
cana-1759	4	34	,	,	PUNCT
cana-1759	4	35	chhattisgarh	chhattisgarh	NOUN
cana-1759	4	36	492013	492013	NUM
cana-1759	4	37	,	,	PUNCT
cana-1759	4	38	india	india	PROPN
cana-1759	4	39	.	.	PUNCT
cana-1759	5	1	n.verma@ssipmt.com	n.verma@ssipmt.com	PROPN
cana-1759	5	2	4assistant	4assistant	NUM
cana-1759	5	3	professor	professor	NOUN
cana-1759	5	4	,	,	PUNCT
cana-1759	5	5	department	department	NOUN
cana-1759	5	6	of	of	ADP
cana-1759	5	7	mathematics	mathematics	PROPN
cana-1759	5	8	,	,	PUNCT
cana-1759	5	9	npr	npr	PROPN
cana-1759	5	10	college	college	PROPN
cana-1759	5	11	of	of	ADP
cana-1759	5	12	engineering	engineering	PROPN
cana-1759	5	13	&	&	CCONJ
cana-1759	5	14	technology	technology	PROPN
cana-1759	5	15	,	,	PUNCT
cana-1759	5	16	natham	natham	PROPN
cana-1759	5	17	,	,	PUNCT
cana-1759	5	18	dindigul	dindigul	ADJ
cana-1759	5	19	sabarimadhu84@gmail.com	sabarimadhu84@gmail.com	X
cana-1759	6	1	5associate	5associate	NUM
cana-1759	6	2	professor	professor	NOUN
cana-1759	6	3	,	,	PUNCT
cana-1759	6	4	department	department	NOUN
cana-1759	6	5	of	of	ADP
cana-1759	6	6	mathematics	mathematics	PROPN
cana-1759	6	7	,	,	PUNCT
cana-1759	6	8	npr	npr	PROPN
cana-1759	6	9	college	college	PROPN
cana-1759	6	10	of	of	ADP
cana-1759	6	11	engineering	engineering	PROPN
cana-1759	6	12	&	&	CCONJ
cana-1759	6	13	technology	technology	PROPN
cana-1759	6	14	,	,	PUNCT
cana-1759	6	15	natham	natham	PROPN
cana-1759	6	16	,	,	PUNCT
cana-1759	6	17	dindigul	dindigul	NOUN
cana-1759	6	18	ranikathir@gmail.com	ranikathir@gmail.com	X
cana-1759	7	1	6assistant	6assistant	NUM
cana-1759	7	2	professor	professor	NOUN
cana-1759	7	3	,	,	PUNCT
cana-1759	7	4	department	department	NOUN
cana-1759	7	5	of	of	ADP
cana-1759	7	6	mathematics	mathematic	NOUN
cana-1759	7	7	,	,	PUNCT
cana-1759	7	8	vishwavidyalaya	vishwavidyalaya	NOUN
cana-1759	7	9	engineering	engineering	NOUN
cana-1759	7	10	college	college	NOUN
cana-1759	7	11	,	,	PUNCT
cana-1759	7	12	ambikapur	ambikapur	NOUN
cana-1759	7	13	(	(	PUNCT
cana-1759	7	14	c.g	c.g	PROPN
cana-1759	7	15	.	.	PROPN
cana-1759	7	16	)	)	PUNCT
cana-1759	8	1	497001	497001	NUM
cana-1759	8	2	dwivedi.vk69@gmail.com	dwivedi.vk69@gmail.com	X
cana-1759	9	1	7department	7department	NUM
cana-1759	9	2	of	of	ADP
cana-1759	9	3	electrical	electrical	ADJ
cana-1759	9	4	engineering	engineering	NOUN
cana-1759	9	5	,	,	PUNCT
cana-1759	9	6	gla	gla	PROPN
cana-1759	9	7	university	university	PROPN
cana-1759	9	8	,	,	PUNCT
cana-1759	9	9	mathura	mathura	PROPN
cana-1759	9	10	,	,	PUNCT
cana-1759	9	11	india	india	PROPN
cana-1759	9	12	.	.	PUNCT
cana-1759	10	1	kanchan.yadav@gla.ac.in	kanchan.yadav@gla.ac.in	PROPN
cana-1759	10	2	article	article	PROPN
cana-1759	10	3	history	history	NOUN
cana-1759	10	4	:	:	PUNCT
cana-1759	10	5	received	receive	VERB
cana-1759	10	6	:	:	PUNCT
cana-1759	10	7	05	05	NUM
cana-1759	10	8	-	-	SYM
cana-1759	10	9	08	08	NUM
cana-1759	10	10	-	-	PUNCT
cana-1759	10	11	2024	2024	NUM
cana-1759	10	12	revised	revise	VERB
cana-1759	10	13	:	:	PUNCT
cana-1759	10	14	10	10	NUM
cana-1759	10	15	-	-	SYM
cana-1759	10	16	09	09	NUM
cana-1759	10	17	-	-	PUNCT
cana-1759	10	18	2024	2024	NUM
cana-1759	10	19	accepted	accept	VERB
cana-1759	10	20	:	:	PUNCT
cana-1759	10	21	21	21	NUM
cana-1759	10	22	-	-	SYM
cana-1759	10	23	09	09	NUM
cana-1759	10	24	-	-	PUNCT
cana-1759	10	25	2024	2024	NUM
cana-1759	10	26	abstract	abstract	NOUN
cana-1759	10	27	:	:	PUNCT
cana-1759	10	28	this	this	DET
cana-1759	10	29	research	research	NOUN
cana-1759	10	30	explores	explore	VERB
cana-1759	10	31	the	the	DET
cana-1759	10	32	recent	recent	ADJ
cana-1759	10	33	advancements	advancement	NOUN
cana-1759	10	34	in	in	ADP
cana-1759	10	35	mathematical	mathematical	ADJ
cana-1759	10	36	modelling	modelling	NOUN
cana-1759	10	37	of	of	ADP
cana-1759	10	38	heat	heat	NOUN
cana-1759	10	39	transfer	transfer	NOUN
cana-1759	10	40	and	and	CCONJ
cana-1759	10	41	fluid	fluid	ADJ
cana-1759	10	42	flows	flow	NOUN
cana-1759	10	43	,	,	PUNCT
cana-1759	10	44	emphasizing	emphasize	VERB
cana-1759	10	45	fractional	fractional	ADJ
cana-1759	10	46	calculus	calculus	NOUN
cana-1759	10	47	,	,	PUNCT
cana-1759	10	48	non	non	ADJ
cana-1759	10	49	-	-	ADJ
cana-1759	10	50	newtonian	newtonian	ADJ
cana-1759	10	51	fluid	fluid	ADJ
cana-1759	10	52	dynamics	dynamic	NOUN
cana-1759	10	53	,	,	PUNCT
cana-1759	10	54	and	and	CCONJ
cana-1759	10	55	nanofluid	nanofluid	ADJ
cana-1759	10	56	models	model	NOUN
cana-1759	10	57	.	.	PUNCT
cana-1759	11	1	we	we	PRON
cana-1759	11	2	discuss	discuss	VERB
cana-1759	11	3	the	the	DET
cana-1759	11	4	use	use	NOUN
cana-1759	11	5	of	of	ADP
cana-1759	11	6	fractional	fractional	ADJ
cana-1759	11	7	derivatives	derivative	NOUN
cana-1759	11	8	in	in	ADP
cana-1759	11	9	modelling	model	VERB
cana-1759	11	10	complex	complex	ADJ
cana-1759	11	11	thermal	thermal	ADJ
cana-1759	11	12	and	and	CCONJ
cana-1759	11	13	flow	flow	NOUN
cana-1759	11	14	behaviours	behaviour	NOUN
cana-1759	11	15	in	in	ADP
cana-1759	11	16	various	various	ADJ
cana-1759	11	17	engineering	engineering	NOUN
cana-1759	11	18	contexts	contexts	NOUN
cana-1759	11	19	,	,	PUNCT
cana-1759	11	20	including	include	VERB
cana-1759	11	21	permeable	permeable	ADJ
cana-1759	11	22	surfaces	surface	NOUN
cana-1759	11	23	and	and	CCONJ
cana-1759	11	24	porous	porous	ADJ
cana-1759	11	25	media	medium	NOUN
cana-1759	11	26	.	.	PUNCT
cana-1759	12	1	applications	application	NOUN
cana-1759	12	2	range	range	VERB
cana-1759	12	3	from	from	ADP
cana-1759	12	4	industrial	industrial	ADJ
cana-1759	12	5	heat	heat	NOUN
cana-1759	12	6	exchangers	exchanger	NOUN
cana-1759	12	7	to	to	ADP
cana-1759	12	8	biomedical	biomedical	ADJ
cana-1759	12	9	devices	device	NOUN
cana-1759	12	10	.	.	PUNCT
cana-1759	13	1	numerical	numerical	ADJ
cana-1759	13	2	methods	method	NOUN
cana-1759	13	3	such	such	ADJ
cana-1759	13	4	as	as	ADP
cana-1759	13	5	the	the	DET
cana-1759	13	6	iterative	iterative	NOUN
cana-1759	13	7	power	power	NOUN
cana-1759	13	8	series	series	NOUN
cana-1759	13	9	(	(	PUNCT
cana-1759	13	10	ips	ips	NOUN
cana-1759	13	11	)	)	PUNCT
cana-1759	13	12	technique	technique	NOUN
cana-1759	13	13	and	and	CCONJ
cana-1759	13	14	finite	finite	ADJ
cana-1759	13	15	element	element	NOUN
cana-1759	13	16	methods	method	NOUN
cana-1759	13	17	(	(	PUNCT
cana-1759	13	18	fem	fem	NOUN
cana-1759	13	19	)	)	PUNCT
cana-1759	13	20	are	be	AUX
cana-1759	13	21	employed	employ	VERB
cana-1759	13	22	to	to	PART
cana-1759	13	23	solve	solve	VERB
cana-1759	13	24	the	the	DET
cana-1759	13	25	nonlinear	nonlinear	ADJ
cana-1759	13	26	equations	equation	NOUN
cana-1759	13	27	governing	govern	VERB
cana-1759	13	28	these	these	DET
cana-1759	13	29	phenomena	phenomenon	NOUN
cana-1759	13	30	.	.	PUNCT
cana-1759	14	1	a	a	DET
cana-1759	14	2	comprehensive	comprehensive	ADJ
cana-1759	14	3	comparison	comparison	NOUN
cana-1759	14	4	of	of	ADP
cana-1759	14	5	these	these	DET
cana-1759	14	6	methods	method	NOUN
cana-1759	14	7	highlights	highlight	VERB
cana-1759	14	8	their	their	PRON
cana-1759	14	9	strengths	strength	NOUN
cana-1759	14	10	and	and	CCONJ
cana-1759	14	11	limitations	limitation	NOUN
cana-1759	14	12	in	in	ADP
cana-1759	14	13	terms	term	NOUN
cana-1759	14	14	of	of	ADP
cana-1759	14	15	accuracy	accuracy	NOUN
cana-1759	14	16	,	,	PUNCT
cana-1759	14	17	convergence	convergence	NOUN
cana-1759	14	18	,	,	PUNCT
cana-1759	14	19	and	and	CCONJ
cana-1759	14	20	computational	computational	ADJ
cana-1759	14	21	efficiency	efficiency	NOUN
cana-1759	14	22	.	.	PUNCT
cana-1759	15	1	the	the	DET
cana-1759	15	2	results	result	NOUN
cana-1759	15	3	reveal	reveal	VERB
cana-1759	15	4	significant	significant	ADJ
cana-1759	15	5	insights	insight	NOUN
cana-1759	15	6	into	into	ADP
cana-1759	15	7	the	the	DET
cana-1759	15	8	optimization	optimization	NOUN
cana-1759	15	9	of	of	ADP
cana-1759	15	10	thermal	thermal	ADJ
cana-1759	15	11	systems	system	NOUN
cana-1759	15	12	,	,	PUNCT
cana-1759	15	13	with	with	ADP
cana-1759	15	14	fractional	fractional	ADJ
cana-1759	15	15	models	model	NOUN
cana-1759	15	16	demonstrating	demonstrate	VERB
cana-1759	15	17	superior	superior	ADJ
cana-1759	15	18	adaptability	adaptability	NOUN
cana-1759	15	19	to	to	ADP
cana-1759	15	20	anomalous	anomalous	ADJ
cana-1759	15	21	flow	flow	NOUN
cana-1759	15	22	and	and	CCONJ
cana-1759	15	23	heat	heat	NOUN
cana-1759	15	24	transfer	transfer	NOUN
cana-1759	15	25	conditions	condition	NOUN
cana-1759	15	26	.	.	PUNCT
cana-1759	16	1	the	the	DET
cana-1759	16	2	findings	finding	NOUN
cana-1759	16	3	contribute	contribute	VERB
cana-1759	16	4	to	to	ADP
cana-1759	16	5	the	the	DET
cana-1759	16	6	development	development	NOUN
cana-1759	16	7	of	of	ADP
cana-1759	16	8	more	more	ADV
cana-1759	16	9	efficient	efficient	ADJ
cana-1759	16	10	and	and	CCONJ
cana-1759	16	11	effective	effective	ADJ
cana-1759	16	12	engineering	engineering	NOUN
cana-1759	16	13	designs	design	NOUN
cana-1759	16	14	,	,	PUNCT
cana-1759	16	15	and	and	CCONJ
cana-1759	16	16	the	the	DET
cana-1759	16	17	study	study	NOUN
cana-1759	16	18	suggests	suggest	VERB
cana-1759	16	19	directions	direction	NOUN
cana-1759	16	20	for	for	ADP
cana-1759	16	21	future	future	ADJ
cana-1759	16	22	research	research	NOUN
cana-1759	16	23	in	in	ADP
cana-1759	16	24	this	this	DET
cana-1759	16	25	field	field	NOUN
cana-1759	16	26	.	.	PUNCT
cana-1759	17	1	keywords	keyword	NOUN
cana-1759	17	2	:	:	PUNCT
cana-1759	17	3	fractional	fractional	ADJ
cana-1759	17	4	calculus	calculus	NOUN
cana-1759	17	5	,	,	PUNCT
cana-1759	17	6	heat	heat	NOUN
cana-1759	17	7	transfer	transfer	NOUN
cana-1759	17	8	,	,	PUNCT
cana-1759	17	9	fluid	fluid	ADJ
cana-1759	17	10	flows	flow	NOUN
cana-1759	17	11	,	,	PUNCT
cana-1759	17	12	non	non	ADJ
cana-1759	17	13	-	-	ADJ
cana-1759	17	14	newtonian	newtonian	ADJ
cana-1759	17	15	fluids	fluid	NOUN
cana-1759	17	16	,	,	PUNCT
cana-1759	17	17	nanofluids	nanofluid	NOUN
cana-1759	17	18	,	,	PUNCT
cana-1759	17	19	numerical	numerical	ADJ
cana-1759	17	20	methods	method	NOUN
cana-1759	17	21	,	,	PUNCT
cana-1759	17	22	iterative	iterative	ADJ
cana-1759	17	23	power	power	NOUN
cana-1759	17	24	series	series	NOUN
cana-1759	17	25	,	,	PUNCT
cana-1759	17	26	finite	finite	PROPN
cana-1759	17	27	element	element	NOUN
cana-1759	17	28	method	method	NOUN
cana-1759	17	29	,	,	PUNCT
cana-1759	17	30	permeable	permeable	ADJ
cana-1759	17	31	surfaces	surface	NOUN
cana-1759	17	32	,	,	PUNCT
cana-1759	17	33	porous	porous	ADJ
cana-1759	17	34	media	medium	NOUN
cana-1759	17	35	.	.	PUNCT
cana-1759	18	1	1	1	X
cana-1759	18	2	.	.	X
cana-1759	18	3	introduction	introduction	NOUN
cana-1759	18	4	heat	heat	NOUN
cana-1759	18	5	transfer	transfer	NOUN
cana-1759	18	6	and	and	CCONJ
cana-1759	18	7	fluid	fluid	ADJ
cana-1759	18	8	flow	flow	NOUN
cana-1759	18	9	are	be	AUX
cana-1759	18	10	fundamental	fundamental	ADJ
cana-1759	18	11	physical	physical	ADJ
cana-1759	18	12	phenomena	phenomenon	NOUN
cana-1759	18	13	that	that	PRON
cana-1759	18	14	play	play	VERB
cana-1759	18	15	critical	critical	ADJ
cana-1759	18	16	roles	role	NOUN
cana-1759	18	17	in	in	ADP
cana-1759	18	18	a	a	DET
cana-1759	18	19	wide	wide	ADJ
cana-1759	18	20	range	range	NOUN
cana-1759	18	21	of	of	ADP
cana-1759	18	22	engineering	engineering	NOUN
cana-1759	18	23	and	and	CCONJ
cana-1759	18	24	scientific	scientific	ADJ
cana-1759	18	25	applications	application	NOUN
cana-1759	18	26	.	.	PUNCT
cana-1759	19	1	these	these	DET
cana-1759	19	2	phenomena	phenomenon	NOUN
cana-1759	19	3	are	be	AUX
cana-1759	19	4	pivotal	pivotal	ADJ
cana-1759	19	5	in	in	ADP
cana-1759	19	6	processes	process	NOUN
cana-1759	19	7	such	such	ADJ
cana-1759	19	8	as	as	ADP
cana-1759	19	9	energy	energy	NOUN
cana-1759	19	10	conversion	conversion	NOUN
cana-1759	19	11	,	,	PUNCT
cana-1759	19	12	chemical	chemical	NOUN
cana-1759	19	13	processing	processing	NOUN
cana-1759	19	14	,	,	PUNCT
cana-1759	19	15	environmental	environmental	ADJ
cana-1759	19	16	control	control	NOUN
cana-1759	19	17	,	,	PUNCT
cana-1759	19	18	and	and	CCONJ
cana-1759	19	19	biomedical	biomedical	ADJ
cana-1759	19	20	engineering	engineering	NOUN
cana-1759	19	21	.	.	PUNCT
cana-1759	20	1	mailto:india-prabhats1718@gmail.com	mailto:india-prabhats1718@gmail.com	X
cana-1759	20	2	mailto:india.-mmdixixt79@gmail.com	mailto:india.-mmdixixt79@gmail.com	X
cana-1759	21	1	mailto:n.verma@ssipmt.com	mailto:n.verma@ssipmt.com	X
cana-1759	21	2	mailto:sabarimadhu84@gmail.com	mailto:sabarimadhu84@gmail.com	PROPN
cana-1759	21	3	mailto:ranikathir@gmail.com	mailto:ranikathir@gmail.com	PROPN
cana-1759	22	1	mailto:dwivedi.vk69@gmail.com	mailto:dwivedi.vk69@gmail.com	PROPN
cana-1759	23	1	mailto:kanchan.yadav@gla.ac.in	mailto:kanchan.yadav@gla.ac.in	PROPN
cana-1759	23	2	communications	communication	NOUN
cana-1759	23	3	on	on	ADP
cana-1759	23	4	applied	apply	VERB
cana-1759	23	5	nonlinear	nonlinear	ADJ
cana-1759	23	6	analysis	analysis	NOUN
cana-1759	23	7	issn	issn	NOUN
cana-1759	23	8	:	:	PUNCT
cana-1759	23	9	1074	1074	NUM
cana-1759	23	10	-	-	PUNCT
cana-1759	23	11	133x	133x	NUM
cana-1759	23	12	vol	vol	NOUN
cana-1759	23	13	32	32	NUM
cana-1759	23	14	no	no	NOUN
cana-1759	23	15	.	.	NOUN
cana-1759	23	16	2	2	NUM
cana-1759	23	17	(	(	PUNCT
cana-1759	23	18	2025	2025	NUM
cana-1759	23	19	)	)	PUNCT
cana-1759	23	20	472	472	NUM
cana-1759	23	21	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	23	22	traditional	traditional	ADJ
cana-1759	23	23	modelling	modelling	NOUN
cana-1759	23	24	approaches	approach	NOUN
cana-1759	23	25	,	,	PUNCT
cana-1759	23	26	primarily	primarily	ADV
cana-1759	23	27	based	base	VERB
cana-1759	23	28	on	on	ADP
cana-1759	23	29	classical	classical	ADJ
cana-1759	23	30	calculus	calculus	NOUN
cana-1759	23	31	and	and	CCONJ
cana-1759	23	32	integer	integer	NOUN
cana-1759	23	33	-	-	PUNCT
cana-1759	23	34	order	order	NOUN
cana-1759	23	35	differential	differential	ADJ
cana-1759	23	36	equations	equation	NOUN
cana-1759	23	37	,	,	PUNCT
cana-1759	23	38	have	have	AUX
cana-1759	23	39	provided	provide	VERB
cana-1759	23	40	substantial	substantial	ADJ
cana-1759	23	41	insights	insight	NOUN
cana-1759	23	42	into	into	ADP
cana-1759	23	43	understanding	understand	VERB
cana-1759	23	44	these	these	DET
cana-1759	23	45	processes	process	NOUN
cana-1759	23	46	.	.	PUNCT
cana-1759	24	1	however	however	ADV
cana-1759	24	2	,	,	PUNCT
cana-1759	24	3	they	they	PRON
cana-1759	24	4	often	often	ADV
cana-1759	24	5	fall	fall	VERB
cana-1759	24	6	short	short	ADJ
cana-1759	24	7	in	in	ADP
cana-1759	24	8	accurately	accurately	ADV
cana-1759	24	9	capturing	capture	VERB
cana-1759	24	10	the	the	DET
cana-1759	24	11	complexities	complexity	NOUN
cana-1759	24	12	observed	observe	VERB
cana-1759	24	13	in	in	ADP
cana-1759	24	14	real	real	ADJ
cana-1759	24	15	-	-	PUNCT
cana-1759	24	16	world	world	NOUN
cana-1759	24	17	systems	system	NOUN
cana-1759	24	18	,	,	PUNCT
cana-1759	24	19	particularly	particularly	ADV
cana-1759	24	20	those	those	PRON
cana-1759	24	21	involving	involve	VERB
cana-1759	24	22	anomalous	anomalous	ADJ
cana-1759	24	23	diffusion	diffusion	NOUN
cana-1759	24	24	,	,	PUNCT
cana-1759	24	25	non	non	ADJ
cana-1759	24	26	-	-	ADJ
cana-1759	24	27	newtonian	newtonian	ADJ
cana-1759	24	28	fluids	fluid	NOUN
cana-1759	24	29	,	,	PUNCT
cana-1759	24	30	and	and	CCONJ
cana-1759	24	31	nanofluids	nanofluid	NOUN
cana-1759	24	32	.	.	PUNCT
cana-1759	25	1	background	background	NOUN
cana-1759	25	2	and	and	CCONJ
cana-1759	25	3	significance	significance	NOUN
cana-1759	25	4	in	in	ADP
cana-1759	25	5	recent	recent	ADJ
cana-1759	25	6	years	year	NOUN
cana-1759	25	7	,	,	PUNCT
cana-1759	25	8	there	there	PRON
cana-1759	25	9	has	have	AUX
cana-1759	25	10	been	be	AUX
cana-1759	25	11	a	a	DET
cana-1759	25	12	significant	significant	ADJ
cana-1759	25	13	shift	shift	NOUN
cana-1759	25	14	towards	towards	ADP
cana-1759	25	15	more	more	ADV
cana-1759	25	16	advanced	advanced	ADJ
cana-1759	25	17	mathematical	mathematical	ADJ
cana-1759	25	18	modelling	modelling	NOUN
cana-1759	25	19	techniques	technique	NOUN
cana-1759	25	20	to	to	PART
cana-1759	25	21	better	well	ADV
cana-1759	25	22	understand	understand	VERB
cana-1759	25	23	and	and	CCONJ
cana-1759	25	24	optimize	optimize	VERB
cana-1759	25	25	heat	heat	NOUN
cana-1759	25	26	transfer	transfer	NOUN
cana-1759	25	27	and	and	CCONJ
cana-1759	25	28	fluid	fluid	ADJ
cana-1759	25	29	flow	flow	NOUN
cana-1759	25	30	processes	process	NOUN
cana-1759	25	31	.	.	PUNCT
cana-1759	26	1	this	this	DET
cana-1759	26	2	shift	shift	NOUN
cana-1759	26	3	is	be	AUX
cana-1759	26	4	driven	drive	VERB
cana-1759	26	5	by	by	ADP
cana-1759	26	6	the	the	DET
cana-1759	26	7	increasing	increase	VERB
cana-1759	26	8	complexity	complexity	NOUN
cana-1759	26	9	of	of	ADP
cana-1759	26	10	industrial	industrial	ADJ
cana-1759	26	11	and	and	CCONJ
cana-1759	26	12	environmental	environmental	ADJ
cana-1759	26	13	applications	application	NOUN
cana-1759	26	14	that	that	PRON
cana-1759	26	15	demand	demand	VERB
cana-1759	26	16	more	more	ADV
cana-1759	26	17	precise	precise	ADJ
cana-1759	26	18	and	and	CCONJ
cana-1759	26	19	accurate	accurate	ADJ
cana-1759	26	20	predictive	predictive	ADJ
cana-1759	26	21	capabilities	capability	NOUN
cana-1759	26	22	.	.	PUNCT
cana-1759	27	1	traditional	traditional	ADJ
cana-1759	27	2	models	model	NOUN
cana-1759	27	3	based	base	VERB
cana-1759	27	4	on	on	ADP
cana-1759	27	5	newtonian	newtonian	ADJ
cana-1759	27	6	fluid	fluid	ADJ
cana-1759	27	7	assumptions	assumption	NOUN
cana-1759	27	8	and	and	CCONJ
cana-1759	27	9	simple	simple	ADJ
cana-1759	27	10	boundary	boundary	ADJ
cana-1759	27	11	conditions	condition	NOUN
cana-1759	27	12	are	be	AUX
cana-1759	27	13	often	often	ADV
cana-1759	27	14	inadequate	inadequate	ADJ
cana-1759	27	15	for	for	ADP
cana-1759	27	16	capturing	capture	VERB
cana-1759	27	17	the	the	DET
cana-1759	27	18	intricate	intricate	ADJ
cana-1759	27	19	interactions	interaction	NOUN
cana-1759	27	20	and	and	CCONJ
cana-1759	27	21	nonlinearities	nonlinearitie	NOUN
cana-1759	27	22	present	present	ADJ
cana-1759	27	23	in	in	ADP
cana-1759	27	24	practical	practical	ADJ
cana-1759	27	25	scenarios	scenario	NOUN
cana-1759	27	26	.	.	PUNCT
cana-1759	28	1	this	this	PRON
cana-1759	28	2	has	have	AUX
cana-1759	28	3	led	lead	VERB
cana-1759	28	4	to	to	ADP
cana-1759	28	5	the	the	DET
cana-1759	28	6	exploration	exploration	NOUN
cana-1759	28	7	of	of	ADP
cana-1759	28	8	more	more	ADV
cana-1759	28	9	sophisticated	sophisticated	ADJ
cana-1759	28	10	approaches	approach	NOUN
cana-1759	28	11	,	,	PUNCT
cana-1759	28	12	including	include	VERB
cana-1759	28	13	the	the	DET
cana-1759	28	14	use	use	NOUN
cana-1759	28	15	of	of	ADP
cana-1759	28	16	fractional	fractional	ADJ
cana-1759	28	17	calculus	calculus	NOUN
cana-1759	28	18	,	,	PUNCT
cana-1759	28	19	non	non	ADJ
cana-1759	28	20	-	-	ADJ
cana-1759	28	21	newtonian	newtonian	ADJ
cana-1759	28	22	fluid	fluid	ADJ
cana-1759	28	23	dynamics	dynamic	NOUN
cana-1759	28	24	,	,	PUNCT
cana-1759	28	25	and	and	CCONJ
cana-1759	28	26	nanofluid	nanofluid	ADJ
cana-1759	28	27	models	model	NOUN
cana-1759	28	28	.	.	PUNCT
cana-1759	29	1	fractional	fractional	ADJ
cana-1759	29	2	calculus	calculus	NOUN
cana-1759	29	3	has	have	AUX
cana-1759	29	4	emerged	emerge	VERB
cana-1759	29	5	as	as	ADP
cana-1759	29	6	a	a	DET
cana-1759	29	7	powerful	powerful	ADJ
cana-1759	29	8	tool	tool	NOUN
cana-1759	29	9	in	in	ADP
cana-1759	29	10	this	this	DET
cana-1759	29	11	context	context	NOUN
cana-1759	29	12	.	.	PUNCT
cana-1759	30	1	unlike	unlike	ADP
cana-1759	30	2	classical	classical	ADJ
cana-1759	30	3	calculus	calculus	NOUN
cana-1759	30	4	,	,	PUNCT
cana-1759	30	5	which	which	PRON
cana-1759	30	6	deals	deal	VERB
cana-1759	30	7	with	with	ADP
cana-1759	30	8	integer	integer	NOUN
cana-1759	30	9	-	-	PUNCT
cana-1759	30	10	order	order	NOUN
cana-1759	30	11	differentiation	differentiation	NOUN
cana-1759	30	12	and	and	CCONJ
cana-1759	30	13	integration	integration	NOUN
cana-1759	30	14	,	,	PUNCT
cana-1759	30	15	fractional	fractional	ADJ
cana-1759	30	16	calculus	calculus	NOUN
cana-1759	30	17	extends	extend	VERB
cana-1759	30	18	these	these	DET
cana-1759	30	19	operations	operation	NOUN
cana-1759	30	20	to	to	ADP
cana-1759	30	21	non	non	ADJ
cana-1759	30	22	-	-	ADJ
cana-1759	30	23	integer	integer	ADJ
cana-1759	30	24	orders	order	NOUN
cana-1759	30	25	.	.	PUNCT
cana-1759	31	1	this	this	DET
cana-1759	31	2	extension	extension	NOUN
cana-1759	31	3	provides	provide	VERB
cana-1759	31	4	a	a	DET
cana-1759	31	5	more	more	ADV
cana-1759	31	6	flexible	flexible	ADJ
cana-1759	31	7	framework	framework	NOUN
cana-1759	31	8	for	for	ADP
cana-1759	31	9	modelling	model	VERB
cana-1759	31	10	phenomena	phenomenon	NOUN
cana-1759	31	11	characterized	characterize	VERB
cana-1759	31	12	by	by	ADP
cana-1759	31	13	memory	memory	NOUN
cana-1759	31	14	effects	effect	NOUN
cana-1759	31	15	and	and	CCONJ
cana-1759	31	16	non	non	ADJ
cana-1759	31	17	-	-	ADJ
cana-1759	31	18	local	local	ADJ
cana-1759	31	19	dependencies	dependency	NOUN
cana-1759	31	20	,	,	PUNCT
cana-1759	31	21	which	which	PRON
cana-1759	31	22	are	be	AUX
cana-1759	31	23	typical	typical	ADJ
cana-1759	31	24	in	in	ADP
cana-1759	31	25	complex	complex	ADJ
cana-1759	31	26	heat	heat	NOUN
cana-1759	31	27	transfer	transfer	NOUN
cana-1759	31	28	and	and	CCONJ
cana-1759	31	29	fluid	fluid	ADJ
cana-1759	31	30	flow	flow	NOUN
cana-1759	31	31	scenarios	scenario	NOUN
cana-1759	31	32	.	.	PUNCT
cana-1759	32	1	fractional	fractional	ADJ
cana-1759	32	2	derivatives	derivative	NOUN
cana-1759	32	3	,	,	PUNCT
cana-1759	32	4	such	such	ADJ
cana-1759	32	5	as	as	ADP
cana-1759	32	6	caputo	caputo	PROPN
cana-1759	32	7	,	,	PUNCT
cana-1759	32	8	atangana	atangana	PROPN
cana-1759	32	9	–	–	PUNCT
cana-1759	32	10	baleanu	baleanu	NOUN
cana-1759	32	11	,	,	PUNCT
cana-1759	32	12	and	and	CCONJ
cana-1759	32	13	conformable	conformable	ADJ
cana-1759	32	14	derivatives	derivative	NOUN
cana-1759	32	15	,	,	PUNCT
cana-1759	32	16	have	have	AUX
cana-1759	32	17	been	be	AUX
cana-1759	32	18	increasingly	increasingly	ADV
cana-1759	32	19	applied	apply	VERB
cana-1759	32	20	to	to	AUX
cana-1759	32	21	model	model	VERB
cana-1759	32	22	anomalous	anomalous	ADJ
cana-1759	32	23	diffusion	diffusion	NOUN
cana-1759	32	24	processes	process	NOUN
cana-1759	32	25	and	and	CCONJ
cana-1759	32	26	viscoelastic	viscoelastic	ADJ
cana-1759	32	27	fluid	fluid	NOUN
cana-1759	32	28	behavior	behavior	NOUN
cana-1759	32	29	,	,	PUNCT
cana-1759	32	30	offering	offer	VERB
cana-1759	32	31	more	more	ADV
cana-1759	32	32	accurate	accurate	ADJ
cana-1759	32	33	descriptions	description	NOUN
cana-1759	32	34	of	of	ADP
cana-1759	32	35	systems	system	NOUN
cana-1759	32	36	where	where	SCONJ
cana-1759	32	37	classical	classical	ADJ
cana-1759	32	38	models	model	NOUN
cana-1759	32	39	fail	fail	VERB
cana-1759	32	40	.	.	PUNCT
cana-1759	33	1	non	non	ADJ
cana-1759	33	2	-	-	ADJ
cana-1759	33	3	newtonian	newtonian	ADJ
cana-1759	33	4	fluid	fluid	NOUN
cana-1759	33	5	models	model	NOUN
cana-1759	33	6	are	be	AUX
cana-1759	33	7	another	another	DET
cana-1759	33	8	area	area	NOUN
cana-1759	33	9	of	of	ADP
cana-1759	33	10	growing	grow	VERB
cana-1759	33	11	interest	interest	NOUN
cana-1759	33	12	.	.	PUNCT
cana-1759	34	1	many	many	ADJ
cana-1759	34	2	industrial	industrial	ADJ
cana-1759	34	3	fluids	fluid	NOUN
cana-1759	34	4	,	,	PUNCT
cana-1759	34	5	such	such	ADJ
cana-1759	34	6	as	as	ADP
cana-1759	34	7	polymers	polymer	NOUN
cana-1759	34	8	,	,	PUNCT
cana-1759	34	9	slurries	slurry	NOUN
cana-1759	34	10	,	,	PUNCT
cana-1759	34	11	and	and	CCONJ
cana-1759	34	12	biological	biological	ADJ
cana-1759	34	13	fluids	fluid	NOUN
cana-1759	34	14	,	,	PUNCT
cana-1759	34	15	exhibit	exhibit	VERB
cana-1759	34	16	non	non	ADJ
cana-1759	34	17	-	-	ADJ
cana-1759	34	18	newtonian	newtonian	ADJ
cana-1759	34	19	behavior	behavior	NOUN
cana-1759	34	20	,	,	PUNCT
cana-1759	34	21	where	where	SCONJ
cana-1759	34	22	the	the	DET
cana-1759	34	23	viscosity	viscosity	NOUN
cana-1759	34	24	is	be	AUX
cana-1759	34	25	not	not	PART
cana-1759	34	26	constant	constant	ADJ
cana-1759	34	27	but	but	CCONJ
cana-1759	34	28	depends	depend	VERB
cana-1759	34	29	on	on	ADP
cana-1759	34	30	the	the	DET
cana-1759	34	31	shear	shear	NOUN
cana-1759	34	32	rate	rate	NOUN
cana-1759	34	33	or	or	CCONJ
cana-1759	34	34	shear	shear	NOUN
cana-1759	34	35	history	history	NOUN
cana-1759	34	36	.	.	PUNCT
cana-1759	35	1	traditional	traditional	ADJ
cana-1759	35	2	newtonian	newtonian	ADJ
cana-1759	35	3	models	model	NOUN
cana-1759	35	4	are	be	AUX
cana-1759	35	5	inadequate	inadequate	ADJ
cana-1759	35	6	for	for	ADP
cana-1759	35	7	such	such	ADJ
cana-1759	35	8	fluids	fluid	NOUN
cana-1759	35	9	,	,	PUNCT
cana-1759	35	10	leading	lead	VERB
cana-1759	35	11	to	to	ADP
cana-1759	35	12	the	the	DET
cana-1759	35	13	development	development	NOUN
cana-1759	35	14	of	of	ADP
cana-1759	35	15	various	various	ADJ
cana-1759	35	16	non	non	ADJ
cana-1759	35	17	-	-	ADJ
cana-1759	35	18	newtonian	newtonian	ADJ
cana-1759	35	19	models	model	NOUN
cana-1759	35	20	,	,	PUNCT
cana-1759	35	21	including	include	VERB
cana-1759	35	22	power	power	NOUN
cana-1759	35	23	-	-	PUNCT
cana-1759	35	24	law	law	NOUN
cana-1759	35	25	,	,	PUNCT
cana-1759	35	26	bingham	bingham	PROPN
cana-1759	35	27	plastic	plastic	PROPN
cana-1759	35	28	,	,	PUNCT
cana-1759	35	29	carreau	carreau	PROPN
cana-1759	35	30	,	,	PUNCT
cana-1759	35	31	and	and	CCONJ
cana-1759	35	32	eyring	eyring	NOUN
cana-1759	35	33	-	-	PUNCT
cana-1759	35	34	powell	powell	NOUN
cana-1759	35	35	models	model	NOUN
cana-1759	35	36	.	.	PUNCT
cana-1759	36	1	these	these	DET
cana-1759	36	2	models	model	NOUN
cana-1759	36	3	have	have	AUX
cana-1759	36	4	been	be	AUX
cana-1759	36	5	instrumental	instrumental	ADJ
cana-1759	36	6	in	in	ADP
cana-1759	36	7	describing	describe	VERB
cana-1759	36	8	the	the	DET
cana-1759	36	9	complex	complex	ADJ
cana-1759	36	10	rheological	rheological	ADJ
cana-1759	36	11	behavior	behavior	NOUN
cana-1759	36	12	of	of	ADP
cana-1759	36	13	non	non	ADJ
cana-1759	36	14	-	-	ADJ
cana-1759	36	15	newtonian	newtonian	ADJ
cana-1759	36	16	fluids	fluid	NOUN
cana-1759	36	17	under	under	ADP
cana-1759	36	18	different	different	ADJ
cana-1759	36	19	flow	flow	NOUN
cana-1759	36	20	conditions	condition	NOUN
cana-1759	36	21	,	,	PUNCT
cana-1759	36	22	providing	provide	VERB
cana-1759	36	23	critical	critical	ADJ
cana-1759	36	24	insights	insight	NOUN
cana-1759	36	25	for	for	ADP
cana-1759	36	26	applications	application	NOUN
cana-1759	36	27	ranging	range	VERB
cana-1759	36	28	from	from	ADP
cana-1759	36	29	polymer	polymer	NOUN
cana-1759	36	30	processing	processing	NOUN
cana-1759	36	31	to	to	ADP
cana-1759	36	32	biomedical	biomedical	ADJ
cana-1759	36	33	engineering	engineering	NOUN
cana-1759	36	34	.	.	PUNCT
cana-1759	37	1	nanofluid	nanofluid	ADJ
cana-1759	37	2	dynamics	dynamic	NOUN
cana-1759	37	3	represents	represent	VERB
cana-1759	37	4	another	another	DET
cana-1759	37	5	frontier	frontier	NOUN
cana-1759	37	6	in	in	ADP
cana-1759	37	7	heat	heat	NOUN
cana-1759	37	8	transfer	transfer	NOUN
cana-1759	37	9	enhancement	enhancement	NOUN
cana-1759	37	10	techniques	technique	NOUN
cana-1759	37	11	.	.	PUNCT
cana-1759	38	1	nanofluids	nanofluids	PROPN
cana-1759	38	2	,	,	PUNCT
cana-1759	38	3	which	which	PRON
cana-1759	38	4	are	be	AUX
cana-1759	38	5	engineered	engineer	VERB
cana-1759	38	6	colloidal	colloidal	NOUN
cana-1759	38	7	suspensions	suspension	NOUN
cana-1759	38	8	of	of	ADP
cana-1759	38	9	nanoparticles	nanoparticle	NOUN
cana-1759	38	10	in	in	ADP
cana-1759	38	11	a	a	DET
cana-1759	38	12	base	base	NOUN
cana-1759	38	13	fluid	fluid	NOUN
cana-1759	38	14	,	,	PUNCT
cana-1759	38	15	exhibit	exhibit	VERB
cana-1759	38	16	significantly	significantly	ADV
cana-1759	38	17	enhanced	enhance	VERB
cana-1759	38	18	thermal	thermal	ADJ
cana-1759	38	19	properties	property	NOUN
cana-1759	38	20	compared	compare	VERB
cana-1759	38	21	to	to	ADP
cana-1759	38	22	their	their	PRON
cana-1759	38	23	base	base	NOUN
cana-1759	38	24	fluids	fluid	NOUN
cana-1759	38	25	.	.	PUNCT
cana-1759	39	1	this	this	DET
cana-1759	39	2	enhancement	enhancement	NOUN
cana-1759	39	3	is	be	AUX
cana-1759	39	4	primarily	primarily	ADV
cana-1759	39	5	due	due	ADJ
cana-1759	39	6	to	to	ADP
cana-1759	39	7	the	the	DET
cana-1759	39	8	high	high	ADJ
cana-1759	39	9	thermal	thermal	ADJ
cana-1759	39	10	conductivity	conductivity	NOUN
cana-1759	39	11	of	of	ADP
cana-1759	39	12	nanoparticles	nanoparticle	NOUN
cana-1759	39	13	and	and	CCONJ
cana-1759	39	14	their	their	PRON
cana-1759	39	15	ability	ability	NOUN
cana-1759	39	16	to	to	PART
cana-1759	39	17	alter	alter	VERB
cana-1759	39	18	the	the	DET
cana-1759	39	19	flow	flow	NOUN
cana-1759	39	20	dynamics	dynamic	NOUN
cana-1759	39	21	of	of	ADP
cana-1759	39	22	the	the	DET
cana-1759	39	23	base	base	NOUN
cana-1759	39	24	fluid	fluid	NOUN
cana-1759	39	25	.	.	PUNCT
cana-1759	40	1	mathematical	mathematical	ADJ
cana-1759	40	2	modelling	modelling	NOUN
cana-1759	40	3	of	of	ADP
cana-1759	40	4	nanofluids	nanofluid	NOUN
cana-1759	40	5	,	,	PUNCT
cana-1759	40	6	incorporating	incorporate	VERB
cana-1759	40	7	factors	factor	NOUN
cana-1759	40	8	such	such	ADJ
cana-1759	40	9	as	as	ADP
cana-1759	40	10	brownian	brownian	ADJ
cana-1759	40	11	motion	motion	NOUN
cana-1759	40	12	and	and	CCONJ
cana-1759	40	13	thermophoresis	thermophoresis	NOUN
cana-1759	40	14	,	,	PUNCT
cana-1759	40	15	has	have	AUX
cana-1759	40	16	shown	show	VERB
cana-1759	40	17	promising	promising	ADJ
cana-1759	40	18	results	result	NOUN
cana-1759	40	19	in	in	ADP
cana-1759	40	20	predicting	predict	VERB
cana-1759	40	21	and	and	CCONJ
cana-1759	40	22	optimizing	optimize	VERB
cana-1759	40	23	heat	heat	NOUN
cana-1759	40	24	transfer	transfer	NOUN
cana-1759	40	25	rates	rate	NOUN
cana-1759	40	26	in	in	ADP
cana-1759	40	27	various	various	ADJ
cana-1759	40	28	applications	application	NOUN
cana-1759	40	29	,	,	PUNCT
cana-1759	40	30	including	include	VERB
cana-1759	40	31	cooling	cool	VERB
cana-1759	40	32	systems	system	NOUN
cana-1759	40	33	,	,	PUNCT
cana-1759	40	34	heat	heat	NOUN
cana-1759	40	35	exchangers	exchanger	NOUN
cana-1759	40	36	,	,	PUNCT
cana-1759	40	37	and	and	CCONJ
cana-1759	40	38	electronic	electronic	ADJ
cana-1759	40	39	device	device	NOUN
cana-1759	40	40	cooling	cooling	NOUN
cana-1759	40	41	.	.	PUNCT
cana-1759	41	1	the	the	DET
cana-1759	41	2	paper	paper	NOUN
cana-1759	41	3	is	be	AUX
cana-1759	41	4	organized	organize	VERB
cana-1759	41	5	as	as	SCONJ
cana-1759	41	6	follows	follow	VERB
cana-1759	41	7	:	:	PUNCT
cana-1759	41	8	section	section	NOUN
cana-1759	41	9	2	2	NUM
cana-1759	41	10	provides	provide	VERB
cana-1759	41	11	a	a	DET
cana-1759	41	12	detailed	detailed	ADJ
cana-1759	41	13	overview	overview	NOUN
cana-1759	41	14	of	of	ADP
cana-1759	41	15	the	the	DET
cana-1759	41	16	mathematical	mathematical	ADJ
cana-1759	41	17	modelling	modelling	NOUN
cana-1759	41	18	approaches	approach	NOUN
cana-1759	41	19	,	,	PUNCT
cana-1759	41	20	including	include	VERB
cana-1759	41	21	the	the	DET
cana-1759	41	22	governing	govern	VERB
cana-1759	41	23	equations	equation	NOUN
cana-1759	41	24	for	for	ADP
cana-1759	41	25	fractional	fractional	ADJ
cana-1759	41	26	calculus	calculus	NOUN
cana-1759	41	27	,	,	PUNCT
cana-1759	41	28	non	non	ADJ
cana-1759	41	29	-	-	ADJ
cana-1759	41	30	newtonian	newtonian	ADJ
cana-1759	41	31	fluid	fluid	ADJ
cana-1759	41	32	models	model	NOUN
cana-1759	41	33	,	,	PUNCT
cana-1759	41	34	and	and	CCONJ
cana-1759	41	35	nanofluid	nanofluid	ADJ
cana-1759	41	36	dynamics	dynamic	NOUN
cana-1759	41	37	.	.	PUNCT
cana-1759	42	1	section	section	NOUN
cana-1759	42	2	3	3	NUM
cana-1759	42	3	discusses	discuss	VERB
cana-1759	42	4	the	the	DET
cana-1759	42	5	numerical	numerical	ADJ
cana-1759	42	6	methods	method	NOUN
cana-1759	42	7	employed	employ	VERB
cana-1759	42	8	to	to	PART
cana-1759	42	9	solve	solve	VERB
cana-1759	42	10	these	these	DET
cana-1759	42	11	complex	complex	ADJ
cana-1759	42	12	equations	equation	NOUN
cana-1759	42	13	,	,	PUNCT
cana-1759	42	14	with	with	ADP
cana-1759	42	15	a	a	DET
cana-1759	42	16	particular	particular	ADJ
cana-1759	42	17	focus	focus	NOUN
cana-1759	42	18	on	on	ADP
cana-1759	42	19	the	the	DET
cana-1759	42	20	iterative	iterative	NOUN
cana-1759	42	21	power	power	NOUN
cana-1759	42	22	series	series	NOUN
cana-1759	42	23	(	(	PUNCT
cana-1759	42	24	ips	ips	NOUN
cana-1759	42	25	)	)	PUNCT
cana-1759	42	26	technique	technique	NOUN
cana-1759	42	27	and	and	CCONJ
cana-1759	42	28	finite	finite	ADJ
cana-1759	42	29	element	element	NOUN
cana-1759	42	30	method	method	NOUN
cana-1759	42	31	(	(	PUNCT
cana-1759	42	32	fem	fem	PROPN
cana-1759	42	33	)	)	PUNCT
cana-1759	42	34	.	.	PUNCT
cana-1759	43	1	section	section	NOUN
cana-1759	43	2	4	4	NUM
cana-1759	43	3	presents	present	VERB
cana-1759	43	4	various	various	ADJ
cana-1759	43	5	applications	application	NOUN
cana-1759	43	6	of	of	ADP
cana-1759	43	7	these	these	DET
cana-1759	43	8	models	model	NOUN
cana-1759	43	9	in	in	ADP
cana-1759	43	10	industrial	industrial	ADJ
cana-1759	43	11	,	,	PUNCT
cana-1759	43	12	biomedical	biomedical	ADJ
cana-1759	43	13	,	,	PUNCT
cana-1759	43	14	and	and	CCONJ
cana-1759	43	15	environmental	environmental	ADJ
cana-1759	43	16	engineering	engineering	NOUN
cana-1759	43	17	contexts	context	NOUN
cana-1759	43	18	.	.	PUNCT
cana-1759	44	1	section	section	NOUN
cana-1759	44	2	5	5	NUM
cana-1759	44	3	provides	provide	VERB
cana-1759	44	4	a	a	DET
cana-1759	44	5	detailed	detailed	ADJ
cana-1759	44	6	discussion	discussion	NOUN
cana-1759	44	7	of	of	ADP
cana-1759	44	8	the	the	DET
cana-1759	44	9	numerical	numerical	ADJ
cana-1759	44	10	results	result	NOUN
cana-1759	44	11	and	and	CCONJ
cana-1759	44	12	their	their	PRON
cana-1759	44	13	implications	implication	NOUN
cana-1759	44	14	,	,	PUNCT
cana-1759	44	15	while	while	SCONJ
cana-1759	44	16	section	section	NOUN
cana-1759	44	17	6	6	NUM
cana-1759	44	18	concludes	conclude	VERB
cana-1759	44	19	the	the	DET
cana-1759	44	20	paper	paper	NOUN
cana-1759	44	21	with	with	ADP
cana-1759	44	22	key	key	ADJ
cana-1759	44	23	findings	finding	NOUN
cana-1759	44	24	and	and	CCONJ
cana-1759	44	25	suggestions	suggestion	NOUN
cana-1759	44	26	for	for	ADP
cana-1759	44	27	future	future	ADJ
cana-1759	44	28	research	research	NOUN
cana-1759	44	29	directions	direction	NOUN
cana-1759	44	30	.	.	PUNCT
cana-1759	45	1	communications	communication	NOUN
cana-1759	45	2	on	on	ADP
cana-1759	45	3	applied	apply	VERB
cana-1759	45	4	nonlinear	nonlinear	ADJ
cana-1759	45	5	analysis	analysis	NOUN
cana-1759	45	6	issn	issn	NOUN
cana-1759	45	7	:	:	PUNCT
cana-1759	45	8	1074	1074	NUM
cana-1759	45	9	-	-	PUNCT
cana-1759	45	10	133x	133x	NUM
cana-1759	45	11	vol	vol	NOUN
cana-1759	45	12	32	32	NUM
cana-1759	45	13	no	no	NOUN
cana-1759	45	14	.	.	NOUN
cana-1759	45	15	2	2	NUM
cana-1759	45	16	(	(	PUNCT
cana-1759	45	17	2025	2025	NUM
cana-1759	45	18	)	)	PUNCT
cana-1759	45	19	473	473	NUM
cana-1759	45	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	45	21	2	2	X
cana-1759	45	22	.	.	X
cana-1759	45	23	literature	literature	PROPN
cana-1759	45	24	review	review	PROPN
cana-1759	45	25	:	:	PUNCT
cana-1759	45	26	the	the	DET
cana-1759	45	27	application	application	NOUN
cana-1759	45	28	of	of	ADP
cana-1759	45	29	fractional	fractional	ADJ
cana-1759	45	30	calculus	calculus	NOUN
cana-1759	45	31	in	in	ADP
cana-1759	45	32	heat	heat	NOUN
cana-1759	45	33	transfer	transfer	NOUN
cana-1759	45	34	and	and	CCONJ
cana-1759	45	35	fluid	fluid	NOUN
cana-1759	45	36	flow	flow	NOUN
cana-1759	45	37	modelling	modelling	NOUN
cana-1759	45	38	has	have	AUX
cana-1759	45	39	gained	gain	VERB
cana-1759	45	40	significant	significant	ADJ
cana-1759	45	41	attention	attention	NOUN
cana-1759	45	42	in	in	ADP
cana-1759	45	43	recent	recent	ADJ
cana-1759	45	44	years	year	NOUN
cana-1759	45	45	due	due	ADP
cana-1759	45	46	to	to	ADP
cana-1759	45	47	its	its	PRON
cana-1759	45	48	ability	ability	NOUN
cana-1759	45	49	to	to	PART
cana-1759	45	50	accurately	accurately	ADV
cana-1759	45	51	describe	describe	VERB
cana-1759	45	52	systems	system	NOUN
cana-1759	45	53	with	with	ADP
cana-1759	45	54	memory	memory	NOUN
cana-1759	45	55	effects	effect	NOUN
cana-1759	45	56	and	and	CCONJ
cana-1759	45	57	anomalous	anomalous	ADJ
cana-1759	45	58	diffusion	diffusion	NOUN
cana-1759	45	59	.	.	PUNCT
cana-1759	46	1	*	*	PUNCT
cana-1759	46	2	*	*	PUNCT
cana-1759	46	3	alharbi	alharbi	PROPN
cana-1759	46	4	et	et	PROPN
cana-1759	46	5	al	al	PROPN
cana-1759	46	6	.	.	PROPN
cana-1759	47	1	(	(	PUNCT
cana-1759	47	2	2023	2023	NUM
cana-1759	47	3	)	)	PUNCT
cana-1759	48	1	*	*	PUNCT
cana-1759	48	2	*	*	PUNCT
cana-1759	48	3	investigated	investigate	VERB
cana-1759	48	4	fractional	fractional	ADJ
cana-1759	48	5	derivative	derivative	ADJ
cana-1759	48	6	modelling	modelling	NOUN
cana-1759	48	7	in	in	ADP
cana-1759	48	8	heat	heat	NOUN
cana-1759	48	9	transfer	transfer	NOUN
cana-1759	48	10	analysis	analysis	NOUN
cana-1759	48	11	of	of	ADP
cana-1759	48	12	nanofluids	nanofluid	NOUN
cana-1759	48	13	over	over	ADP
cana-1759	48	14	a	a	DET
cana-1759	48	15	stretching	stretch	VERB
cana-1759	48	16	cylinder	cylinder	NOUN
cana-1759	48	17	,	,	PUNCT
cana-1759	48	18	showing	show	VERB
cana-1759	48	19	that	that	SCONJ
cana-1759	48	20	fractional	fractional	ADJ
cana-1759	48	21	models	model	NOUN
cana-1759	48	22	can	can	AUX
cana-1759	48	23	capture	capture	VERB
cana-1759	48	24	the	the	DET
cana-1759	48	25	complexities	complexity	NOUN
cana-1759	48	26	of	of	ADP
cana-1759	48	27	heat	heat	NOUN
cana-1759	48	28	transfer	transfer	NOUN
cana-1759	48	29	more	more	ADV
cana-1759	48	30	effectively	effectively	ADV
cana-1759	48	31	than	than	ADP
cana-1759	48	32	traditional	traditional	ADJ
cana-1759	48	33	models	model	NOUN
cana-1759	48	34	.	.	PUNCT
cana-1759	49	1	the	the	DET
cana-1759	49	2	study	study	NOUN
cana-1759	49	3	demonstrated	demonstrate	VERB
cana-1759	49	4	improved	improved	ADJ
cana-1759	49	5	thermal	thermal	ADJ
cana-1759	49	6	conductivity	conductivity	NOUN
cana-1759	49	7	and	and	CCONJ
cana-1759	49	8	heat	heat	NOUN
cana-1759	49	9	transfer	transfer	NOUN
cana-1759	49	10	rates	rate	NOUN
cana-1759	49	11	when	when	SCONJ
cana-1759	49	12	using	use	VERB
cana-1759	49	13	fractional	fractional	ADJ
cana-1759	49	14	derivatives	derivative	NOUN
cana-1759	49	15	,	,	PUNCT
cana-1759	49	16	such	such	ADJ
cana-1759	49	17	as	as	ADP
cana-1759	49	18	the	the	DET
cana-1759	49	19	caputo	caputo	PROPN
cana-1759	49	20	and	and	CCONJ
cana-1759	49	21	atangana	atangana	PROPN
cana-1759	49	22	–	–	PUNCT
cana-1759	49	23	baleanu	baleanu	ADJ
cana-1759	49	24	derivatives	derivative	NOUN
cana-1759	49	25	,	,	PUNCT
cana-1759	49	26	in	in	ADP
cana-1759	49	27	modelling	model	VERB
cana-1759	49	28	nanofluid	nanofluid	ADJ
cana-1759	49	29	dynamics	dynamic	NOUN
cana-1759	49	30	under	under	ADP
cana-1759	49	31	varying	vary	VERB
cana-1759	49	32	thermal	thermal	ADJ
cana-1759	49	33	boundary	boundary	ADJ
cana-1759	49	34	conditions	condition	NOUN
cana-1759	49	35	.	.	PUNCT
cana-1759	50	1	similarly	similarly	ADV
cana-1759	50	2	,	,	PUNCT
cana-1759	50	3	*	*	PUNCT
cana-1759	50	4	*	*	PUNCT
cana-1759	50	5	al	al	PROPN
cana-1759	50	6	-	-	PUNCT
cana-1759	50	7	mdallal	mdallal	PROPN
cana-1759	50	8	et	et	PROPN
cana-1759	50	9	al	al	PROPN
cana-1759	50	10	.	.	PROPN
cana-1759	51	1	(	(	PUNCT
cana-1759	51	2	2022	2022	NUM
cana-1759	51	3	)	)	PUNCT
cana-1759	51	4	*	*	PUNCT
cana-1759	52	1	*	*	PUNCT
cana-1759	52	2	employed	employ	VERB
cana-1759	52	3	fractional	fractional	ADJ
cana-1759	52	4	derivatives	derivative	NOUN
cana-1759	52	5	to	to	PART
cana-1759	52	6	model	model	VERB
cana-1759	52	7	magnetohydrodynamic	magnetohydrodynamic	ADJ
cana-1759	52	8	(	(	PUNCT
cana-1759	52	9	mhd	mhd	NOUN
cana-1759	52	10	)	)	PUNCT
cana-1759	52	11	nanofluid	nanofluid	NOUN
cana-1759	52	12	flow	flow	NOUN
cana-1759	52	13	over	over	ADP
cana-1759	52	14	a	a	DET
cana-1759	52	15	stretching	stretch	VERB
cana-1759	52	16	sheet	sheet	NOUN
cana-1759	52	17	with	with	ADP
cana-1759	52	18	convective	convective	ADJ
cana-1759	52	19	boundary	boundary	ADJ
cana-1759	52	20	conditions	condition	NOUN
cana-1759	52	21	.	.	PUNCT
cana-1759	53	1	their	their	PRON
cana-1759	53	2	findings	finding	NOUN
cana-1759	53	3	highlighted	highlight	VERB
cana-1759	53	4	the	the	DET
cana-1759	53	5	efficacy	efficacy	NOUN
cana-1759	53	6	of	of	ADP
cana-1759	53	7	fractional	fractional	ADJ
cana-1759	53	8	derivatives	derivative	NOUN
cana-1759	53	9	in	in	ADP
cana-1759	53	10	modelling	model	VERB
cana-1759	53	11	the	the	DET
cana-1759	53	12	non	non	ADJ
cana-1759	53	13	-	-	ADJ
cana-1759	53	14	local	local	ADJ
cana-1759	53	15	and	and	CCONJ
cana-1759	53	16	history	history	NOUN
cana-1759	53	17	-	-	PUNCT
cana-1759	53	18	dependent	dependent	ADJ
cana-1759	53	19	nature	nature	NOUN
cana-1759	53	20	of	of	ADP
cana-1759	53	21	heat	heat	NOUN
cana-1759	53	22	and	and	CCONJ
cana-1759	53	23	mass	mass	NOUN
cana-1759	53	24	transfer	transfer	NOUN
cana-1759	53	25	in	in	ADP
cana-1759	53	26	nanofluids	nanofluid	NOUN
cana-1759	53	27	,	,	PUNCT
cana-1759	53	28	which	which	PRON
cana-1759	53	29	are	be	AUX
cana-1759	53	30	not	not	PART
cana-1759	53	31	adequately	adequately	ADV
cana-1759	53	32	captured	capture	VERB
cana-1759	53	33	by	by	ADP
cana-1759	53	34	classical	classical	ADJ
cana-1759	53	35	models	model	NOUN
cana-1759	53	36	.	.	PUNCT
cana-1759	54	1	the	the	DET
cana-1759	54	2	use	use	NOUN
cana-1759	54	3	of	of	ADP
cana-1759	54	4	fractional	fractional	ADJ
cana-1759	54	5	calculus	calculus	NOUN
cana-1759	54	6	provided	provide	VERB
cana-1759	54	7	more	more	ADV
cana-1759	54	8	accurate	accurate	ADJ
cana-1759	54	9	predictions	prediction	NOUN
cana-1759	54	10	of	of	ADP
cana-1759	54	11	temperature	temperature	NOUN
cana-1759	54	12	distribution	distribution	NOUN
cana-1759	54	13	and	and	CCONJ
cana-1759	54	14	velocity	velocity	NOUN
cana-1759	54	15	profiles	profile	NOUN
cana-1759	54	16	,	,	PUNCT
cana-1759	54	17	essential	essential	ADJ
cana-1759	54	18	for	for	ADP
cana-1759	54	19	optimizing	optimize	VERB
cana-1759	54	20	industrial	industrial	ADJ
cana-1759	54	21	heat	heat	NOUN
cana-1759	54	22	exchanger	exchanger	NOUN
cana-1759	54	23	designs	design	NOUN
cana-1759	54	24	.	.	PUNCT
cana-1759	55	1	recent	recent	ADJ
cana-1759	55	2	advancements	advancement	NOUN
cana-1759	55	3	have	have	AUX
cana-1759	55	4	also	also	ADV
cana-1759	55	5	focused	focus	VERB
cana-1759	55	6	on	on	ADP
cana-1759	55	7	the	the	DET
cana-1759	55	8	comparative	comparative	ADJ
cana-1759	55	9	analysis	analysis	NOUN
cana-1759	55	10	of	of	ADP
cana-1759	55	11	different	different	ADJ
cana-1759	55	12	numerical	numerical	ADJ
cana-1759	55	13	methods	method	NOUN
cana-1759	55	14	for	for	ADP
cana-1759	55	15	solving	solve	VERB
cana-1759	55	16	fractional	fractional	ADJ
cana-1759	55	17	heat	heat	NOUN
cana-1759	55	18	transfer	transfer	NOUN
cana-1759	55	19	problems	problem	NOUN
cana-1759	55	20	.	.	PUNCT
cana-1759	56	1	*	*	PUNCT
cana-1759	56	2	*	*	PUNCT
cana-1759	56	3	ahmad	ahmad	PROPN
cana-1759	56	4	et	et	PROPN
cana-1759	56	5	al	al	PROPN
cana-1759	56	6	.	.	PROPN
cana-1759	57	1	(	(	PUNCT
cana-1759	57	2	2023	2023	NUM
cana-1759	57	3	)	)	PUNCT
cana-1759	58	1	*	*	PUNCT
cana-1759	58	2	*	*	PUNCT
cana-1759	58	3	compared	compare	VERB
cana-1759	58	4	various	various	ADJ
cana-1759	58	5	numerical	numerical	ADJ
cana-1759	58	6	techniques	technique	NOUN
cana-1759	58	7	,	,	PUNCT
cana-1759	58	8	including	include	VERB
cana-1759	58	9	the	the	DET
cana-1759	58	10	iterative	iterative	NOUN
cana-1759	58	11	power	power	NOUN
cana-1759	58	12	series	series	NOUN
cana-1759	58	13	(	(	PUNCT
cana-1759	58	14	ips	ips	PROPN
cana-1759	58	15	)	)	PUNCT
cana-1759	58	16	method	method	NOUN
cana-1759	58	17	and	and	CCONJ
cana-1759	58	18	finite	finite	ADJ
cana-1759	58	19	element	element	NOUN
cana-1759	58	20	method	method	NOUN
cana-1759	58	21	(	(	PUNCT
cana-1759	58	22	fem	fem	NOUN
cana-1759	58	23	)	)	PUNCT
cana-1759	58	24	,	,	PUNCT
cana-1759	58	25	for	for	ADP
cana-1759	58	26	solving	solve	VERB
cana-1759	58	27	fractional	fractional	ADJ
cana-1759	58	28	heat	heat	NOUN
cana-1759	58	29	transfer	transfer	NOUN
cana-1759	58	30	equations	equation	NOUN
cana-1759	58	31	in	in	ADP
cana-1759	58	32	porous	porous	ADJ
cana-1759	58	33	media	medium	NOUN
cana-1759	58	34	.	.	PUNCT
cana-1759	59	1	their	their	PRON
cana-1759	59	2	study	study	NOUN
cana-1759	59	3	concluded	conclude	VERB
cana-1759	59	4	that	that	SCONJ
cana-1759	59	5	the	the	DET
cana-1759	59	6	ips	ips	PROPN
cana-1759	59	7	method	method	NOUN
cana-1759	59	8	offers	offer	VERB
cana-1759	59	9	higher	high	ADJ
cana-1759	59	10	accuracy	accuracy	NOUN
cana-1759	59	11	and	and	CCONJ
cana-1759	59	12	faster	fast	ADJ
cana-1759	59	13	convergence	convergence	NOUN
cana-1759	59	14	rates	rate	NOUN
cana-1759	59	15	compared	compare	VERB
cana-1759	59	16	to	to	ADP
cana-1759	59	17	traditional	traditional	ADJ
cana-1759	59	18	methods	method	NOUN
cana-1759	59	19	,	,	PUNCT
cana-1759	59	20	especially	especially	ADV
cana-1759	59	21	for	for	ADP
cana-1759	59	22	fractional	fractional	ADJ
cana-1759	59	23	models	model	NOUN
cana-1759	59	24	involving	involve	VERB
cana-1759	59	25	complex	complex	ADJ
cana-1759	59	26	geometries	geometry	NOUN
cana-1759	59	27	and	and	CCONJ
cana-1759	59	28	boundary	boundary	ADJ
cana-1759	59	29	conditions	condition	NOUN
cana-1759	59	30	.	.	PUNCT
cana-1759	60	1	the	the	DET
cana-1759	60	2	findings	finding	NOUN
cana-1759	60	3	underscore	underscore	VERB
cana-1759	60	4	the	the	DET
cana-1759	60	5	importance	importance	NOUN
cana-1759	60	6	of	of	ADP
cana-1759	60	7	selecting	select	VERB
cana-1759	60	8	appropriate	appropriate	ADJ
cana-1759	60	9	numerical	numerical	ADJ
cana-1759	60	10	methods	method	NOUN
cana-1759	60	11	to	to	PART
cana-1759	60	12	ensure	ensure	VERB
cana-1759	60	13	accurate	accurate	ADJ
cana-1759	60	14	simulation	simulation	NOUN
cana-1759	60	15	results	result	NOUN
cana-1759	60	16	for	for	ADP
cana-1759	60	17	engineering	engineering	NOUN
cana-1759	60	18	applications	application	NOUN
cana-1759	60	19	.	.	PUNCT
cana-1759	61	1	in	in	ADP
cana-1759	61	2	the	the	DET
cana-1759	61	3	realm	realm	NOUN
cana-1759	61	4	of	of	ADP
cana-1759	61	5	non	non	ADJ
cana-1759	61	6	-	-	ADJ
cana-1759	61	7	newtonian	newtonian	ADJ
cana-1759	61	8	fluids	fluid	NOUN
cana-1759	61	9	,	,	PUNCT
cana-1759	61	10	*	*	PUNCT
cana-1759	61	11	*	*	PUNCT
cana-1759	61	12	das	das	PROPN
cana-1759	61	13	and	and	CCONJ
cana-1759	61	14	mandal	mandal	ADJ
cana-1759	61	15	(	(	PUNCT
cana-1759	61	16	2022	2022	NUM
cana-1759	61	17	)	)	PUNCT
cana-1759	61	18	*	*	PUNCT
cana-1759	61	19	*	*	PUNCT
cana-1759	61	20	explored	explore	VERB
cana-1759	61	21	thermal	thermal	ADJ
cana-1759	61	22	analysis	analysis	NOUN
cana-1759	61	23	of	of	ADP
cana-1759	61	24	non	non	ADJ
cana-1759	61	25	-	-	ADJ
cana-1759	61	26	newtonian	newtonian	ADJ
cana-1759	61	27	fluid	fluid	ADJ
cana-1759	61	28	flow	flow	NOUN
cana-1759	61	29	over	over	ADP
cana-1759	61	30	a	a	DET
cana-1759	61	31	stretching	stretch	VERB
cana-1759	61	32	surface	surface	NOUN
cana-1759	61	33	using	use	VERB
cana-1759	61	34	fractional	fractional	ADJ
cana-1759	61	35	derivatives	derivative	NOUN
cana-1759	61	36	.	.	PUNCT
cana-1759	62	1	their	their	PRON
cana-1759	62	2	work	work	NOUN
cana-1759	62	3	emphasized	emphasize	VERB
cana-1759	62	4	the	the	DET
cana-1759	62	5	critical	critical	ADJ
cana-1759	62	6	role	role	NOUN
cana-1759	62	7	of	of	ADP
cana-1759	62	8	non	non	ADJ
cana-1759	62	9	-	-	ADJ
cana-1759	62	10	integer	integer	ADJ
cana-1759	62	11	order	order	NOUN
cana-1759	62	12	derivatives	derivative	NOUN
cana-1759	62	13	in	in	ADP
cana-1759	62	14	capturing	capture	VERB
cana-1759	62	15	the	the	DET
cana-1759	62	16	complex	complex	ADJ
cana-1759	62	17	rheological	rheological	ADJ
cana-1759	62	18	behavior	behavior	NOUN
cana-1759	62	19	of	of	ADP
cana-1759	62	20	non	non	ADJ
cana-1759	62	21	-	-	ADJ
cana-1759	62	22	newtonian	newtonian	ADJ
cana-1759	62	23	fluids	fluid	NOUN
cana-1759	62	24	,	,	PUNCT
cana-1759	62	25	such	such	ADJ
cana-1759	62	26	as	as	ADP
cana-1759	62	27	shear	shear	NOUN
cana-1759	62	28	thinning	thinning	NOUN
cana-1759	62	29	and	and	CCONJ
cana-1759	62	30	viscoelasticity	viscoelasticity	NOUN
cana-1759	62	31	,	,	PUNCT
cana-1759	62	32	which	which	PRON
cana-1759	62	33	are	be	AUX
cana-1759	62	34	prevalent	prevalent	ADJ
cana-1759	62	35	in	in	ADP
cana-1759	62	36	many	many	ADJ
cana-1759	62	37	industrial	industrial	ADJ
cana-1759	62	38	processes	process	NOUN
cana-1759	62	39	involving	involve	VERB
cana-1759	62	40	polymers	polymer	NOUN
cana-1759	62	41	and	and	CCONJ
cana-1759	62	42	biological	biological	ADJ
cana-1759	62	43	fluids	fluid	NOUN
cana-1759	62	44	.	.	PUNCT
cana-1759	63	1	the	the	DET
cana-1759	63	2	study	study	NOUN
cana-1759	63	3	also	also	ADV
cana-1759	63	4	highlighted	highlight	VERB
cana-1759	63	5	the	the	DET
cana-1759	63	6	challenges	challenge	NOUN
cana-1759	63	7	of	of	ADP
cana-1759	63	8	implementing	implement	VERB
cana-1759	63	9	fractional	fractional	ADJ
cana-1759	63	10	models	model	NOUN
cana-1759	63	11	in	in	ADP
cana-1759	63	12	computational	computational	ADJ
cana-1759	63	13	fluid	fluid	ADJ
cana-1759	63	14	dynamics	dynamic	NOUN
cana-1759	63	15	(	(	PUNCT
cana-1759	63	16	cfd	cfd	NOUN
cana-1759	63	17	)	)	PUNCT
cana-1759	63	18	simulations	simulation	NOUN
cana-1759	63	19	due	due	ADP
cana-1759	63	20	to	to	ADP
cana-1759	63	21	their	their	PRON
cana-1759	63	22	increased	increase	VERB
cana-1759	63	23	computational	computational	ADJ
cana-1759	63	24	cost	cost	NOUN
cana-1759	63	25	and	and	CCONJ
cana-1759	63	26	complexity	complexity	NOUN
cana-1759	63	27	.	.	PUNCT
cana-1759	64	1	further	far	ADV
cana-1759	64	2	,	,	PUNCT
cana-1759	64	3	*	*	PUNCT
cana-1759	64	4	*	*	PUNCT
cana-1759	64	5	hayat	hayat	X
cana-1759	64	6	et	et	PROPN
cana-1759	64	7	al	al	PROPN
cana-1759	64	8	.	.	PROPN
cana-1759	64	9	(	(	PUNCT
cana-1759	64	10	2023	2023	NUM
cana-1759	64	11	)	)	PUNCT
cana-1759	64	12	*	*	PUNCT
cana-1759	64	13	*	*	AUX
cana-1759	64	14	conducted	conduct	VERB
cana-1759	64	15	a	a	DET
cana-1759	64	16	comparative	comparative	ADJ
cana-1759	64	17	study	study	NOUN
cana-1759	64	18	of	of	ADP
cana-1759	64	19	various	various	ADJ
cana-1759	64	20	fractional	fractional	ADJ
cana-1759	64	21	-	-	PUNCT
cana-1759	64	22	order	order	NOUN
cana-1759	64	23	models	model	NOUN
cana-1759	64	24	to	to	PART
cana-1759	64	25	enhance	enhance	VERB
cana-1759	64	26	heat	heat	NOUN
cana-1759	64	27	transfer	transfer	NOUN
cana-1759	64	28	in	in	ADP
cana-1759	64	29	nanofluids	nanofluid	NOUN
cana-1759	64	30	.	.	PUNCT
cana-1759	65	1	the	the	DET
cana-1759	65	2	research	research	NOUN
cana-1759	65	3	focused	focus	VERB
cana-1759	65	4	on	on	ADP
cana-1759	65	5	examining	examine	VERB
cana-1759	65	6	different	different	ADJ
cana-1759	65	7	fractional	fractional	ADJ
cana-1759	65	8	derivatives	derivative	NOUN
cana-1759	65	9	and	and	CCONJ
cana-1759	65	10	their	their	PRON
cana-1759	65	11	impact	impact	NOUN
cana-1759	65	12	on	on	ADP
cana-1759	65	13	heat	heat	NOUN
cana-1759	65	14	transfer	transfer	NOUN
cana-1759	65	15	efficiency	efficiency	NOUN
cana-1759	65	16	in	in	ADP
cana-1759	65	17	nanofluid	nanofluid	ADJ
cana-1759	65	18	applications	application	NOUN
cana-1759	65	19	.	.	PUNCT
cana-1759	66	1	the	the	DET
cana-1759	66	2	authors	author	NOUN
cana-1759	66	3	found	find	VERB
cana-1759	66	4	that	that	SCONJ
cana-1759	66	5	fractional	fractional	ADJ
cana-1759	66	6	models	model	NOUN
cana-1759	66	7	offer	offer	VERB
cana-1759	66	8	superior	superior	ADJ
cana-1759	66	9	adaptability	adaptability	NOUN
cana-1759	66	10	and	and	CCONJ
cana-1759	66	11	accuracy	accuracy	NOUN
cana-1759	66	12	in	in	ADP
cana-1759	66	13	predicting	predict	VERB
cana-1759	66	14	heat	heat	NOUN
cana-1759	66	15	transfer	transfer	NOUN
cana-1759	66	16	rates	rate	NOUN
cana-1759	66	17	in	in	ADP
cana-1759	66	18	nanofluids	nanofluid	NOUN
cana-1759	66	19	,	,	PUNCT
cana-1759	66	20	making	make	VERB
cana-1759	66	21	them	they	PRON
cana-1759	66	22	suitable	suitable	ADJ
cana-1759	66	23	for	for	ADP
cana-1759	66	24	a	a	DET
cana-1759	66	25	wide	wide	ADJ
cana-1759	66	26	range	range	NOUN
cana-1759	66	27	of	of	ADP
cana-1759	66	28	applications	application	NOUN
cana-1759	66	29	,	,	PUNCT
cana-1759	66	30	from	from	ADP
cana-1759	66	31	microelectronics	microelectronic	NOUN
cana-1759	66	32	cooling	cool	VERB
cana-1759	66	33	to	to	ADP
cana-1759	66	34	biomedical	biomedical	ADJ
cana-1759	66	35	devices	device	NOUN
cana-1759	66	36	.	.	PUNCT
cana-1759	67	1	studies	study	NOUN
cana-1759	67	2	on	on	ADP
cana-1759	67	3	the	the	DET
cana-1759	67	4	transient	transient	ADJ
cana-1759	67	5	heat	heat	NOUN
cana-1759	67	6	conduction	conduction	NOUN
cana-1759	67	7	in	in	ADP
cana-1759	67	8	non	non	ADJ
cana-1759	67	9	-	-	ADJ
cana-1759	67	10	homogeneous	homogeneous	ADJ
cana-1759	67	11	materials	material	NOUN
cana-1759	67	12	have	have	AUX
cana-1759	67	13	also	also	ADV
cana-1759	67	14	leveraged	leverage	VERB
cana-1759	67	15	fractional	fractional	ADJ
cana-1759	67	16	calculus	calculus	NOUN
cana-1759	67	17	.	.	PUNCT
cana-1759	68	1	*	*	PUNCT
cana-1759	68	2	*	*	PUNCT
cana-1759	68	3	javed	javed	X
cana-1759	68	4	et	et	PROPN
cana-1759	68	5	al	al	PROPN
cana-1759	68	6	.	.	PROPN
cana-1759	69	1	(	(	PUNCT
cana-1759	69	2	2022	2022	NUM
cana-1759	69	3	)	)	PUNCT
cana-1759	69	4	*	*	PUNCT
cana-1759	70	1	*	*	PUNCT
cana-1759	70	2	analyzed	analyze	VERB
cana-1759	70	3	fractional	fractional	ADJ
cana-1759	70	4	models	model	NOUN
cana-1759	70	5	for	for	ADP
cana-1759	70	6	transient	transient	ADJ
cana-1759	70	7	heat	heat	NOUN
cana-1759	70	8	conduction	conduction	NOUN
cana-1759	70	9	in	in	ADP
cana-1759	70	10	anisotropic	anisotropic	NOUN
cana-1759	70	11	materials	material	NOUN
cana-1759	70	12	,	,	PUNCT
cana-1759	70	13	employing	employ	VERB
cana-1759	70	14	caputo	caputo	PROPN
cana-1759	70	15	and	and	CCONJ
cana-1759	70	16	atangana	atangana	PROPN
cana-1759	70	17	–	–	PUNCT
cana-1759	70	18	baleanu	baleanu	ADJ
cana-1759	70	19	derivatives	derivative	NOUN
cana-1759	70	20	to	to	PART
cana-1759	70	21	describe	describe	VERB
cana-1759	70	22	the	the	DET
cana-1759	70	23	non	non	ADJ
cana-1759	70	24	-	-	ADJ
cana-1759	70	25	local	local	ADJ
cana-1759	70	26	behavior	behavior	NOUN
cana-1759	70	27	of	of	ADP
cana-1759	70	28	thermal	thermal	ADJ
cana-1759	70	29	conductivity	conductivity	NOUN
cana-1759	70	30	.	.	PUNCT
cana-1759	71	1	their	their	PRON
cana-1759	71	2	results	result	NOUN
cana-1759	71	3	showed	show	VERB
cana-1759	71	4	that	that	SCONJ
cana-1759	71	5	fractional	fractional	ADJ
cana-1759	71	6	models	model	NOUN
cana-1759	71	7	provide	provide	VERB
cana-1759	71	8	better	well	ADJ
cana-1759	71	9	fits	fit	NOUN
cana-1759	71	10	to	to	ADP
cana-1759	71	11	experimental	experimental	ADJ
cana-1759	71	12	data	datum	NOUN
cana-1759	71	13	,	,	PUNCT
cana-1759	71	14	particularly	particularly	ADV
cana-1759	71	15	in	in	ADP
cana-1759	71	16	materials	material	NOUN
cana-1759	71	17	with	with	ADP
cana-1759	71	18	complex	complex	ADJ
cana-1759	71	19	microstructures	microstructure	NOUN
cana-1759	71	20	and	and	CCONJ
cana-1759	71	21	varying	vary	VERB
cana-1759	71	22	thermal	thermal	ADJ
cana-1759	71	23	properties	property	NOUN
cana-1759	71	24	.	.	PUNCT
cana-1759	72	1	the	the	DET
cana-1759	72	2	authors	author	NOUN
cana-1759	72	3	also	also	ADV
cana-1759	72	4	noted	note	VERB
cana-1759	72	5	the	the	DET
cana-1759	72	6	need	need	NOUN
cana-1759	72	7	for	for	ADP
cana-1759	72	8	more	more	ADV
cana-1759	72	9	efficient	efficient	ADJ
cana-1759	72	10	numerical	numerical	ADJ
cana-1759	72	11	methods	method	NOUN
cana-1759	72	12	to	to	PART
cana-1759	72	13	solve	solve	VERB
cana-1759	72	14	fractional	fractional	ADJ
cana-1759	72	15	differential	differential	ADJ
cana-1759	72	16	equations	equation	NOUN
cana-1759	72	17	(	(	PUNCT
cana-1759	72	18	fdes	fde	NOUN
cana-1759	72	19	)	)	PUNCT
cana-1759	72	20	in	in	ADP
cana-1759	72	21	three	three	NUM
cana-1759	72	22	-	-	PUNCT
cana-1759	72	23	dimensional	dimensional	ADJ
cana-1759	72	24	domains	domain	NOUN
cana-1759	72	25	.	.	PUNCT
cana-1759	73	1	the	the	DET
cana-1759	73	2	impact	impact	NOUN
cana-1759	73	3	of	of	ADP
cana-1759	73	4	magnetic	magnetic	ADJ
cana-1759	73	5	fields	field	NOUN
cana-1759	73	6	and	and	CCONJ
cana-1759	73	7	thermal	thermal	ADJ
cana-1759	73	8	communications	communication	NOUN
cana-1759	73	9	on	on	ADP
cana-1759	73	10	applied	apply	VERB
cana-1759	73	11	nonlinear	nonlinear	ADJ
cana-1759	73	12	analysis	analysis	NOUN
cana-1759	73	13	issn	issn	NOUN
cana-1759	73	14	:	:	PUNCT
cana-1759	73	15	1074	1074	NUM
cana-1759	73	16	-	-	PUNCT
cana-1759	73	17	133x	133x	NUM
cana-1759	73	18	vol	vol	NOUN
cana-1759	73	19	32	32	NUM
cana-1759	73	20	no	no	NOUN
cana-1759	73	21	.	.	NOUN
cana-1759	73	22	2	2	NUM
cana-1759	73	23	(	(	PUNCT
cana-1759	73	24	2025	2025	NUM
cana-1759	73	25	)	)	PUNCT
cana-1759	74	1	474	474	NUM
cana-1759	74	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	75	1	radiation	radiation	NOUN
cana-1759	75	2	on	on	ADP
cana-1759	75	3	non	non	ADJ
cana-1759	75	4	-	-	ADJ
cana-1759	75	5	newtonian	newtonian	ADJ
cana-1759	75	6	nanofluid	nanofluid	ADJ
cana-1759	75	7	flows	flow	NOUN
cana-1759	75	8	has	have	AUX
cana-1759	75	9	been	be	AUX
cana-1759	75	10	another	another	DET
cana-1759	75	11	area	area	NOUN
cana-1759	75	12	of	of	ADP
cana-1759	75	13	significant	significant	ADJ
cana-1759	75	14	research	research	NOUN
cana-1759	75	15	.	.	PUNCT
cana-1759	76	1	*	*	PUNCT
cana-1759	76	2	*	*	PUNCT
cana-1759	76	3	nadeem	nadeem	ADJ
cana-1759	76	4	and	and	CCONJ
cana-1759	76	5	hussain	hussain	PROPN
cana-1759	76	6	(	(	PUNCT
cana-1759	76	7	2022	2022	NUM
cana-1759	76	8	)	)	PUNCT
cana-1759	77	1	*	*	PUNCT
cana-1759	77	2	*	*	PUNCT
cana-1759	77	3	explored	explore	VERB
cana-1759	77	4	the	the	DET
cana-1759	77	5	effects	effect	NOUN
cana-1759	77	6	of	of	ADP
cana-1759	77	7	magnetic	magnetic	ADJ
cana-1759	77	8	fields	field	NOUN
cana-1759	77	9	and	and	CCONJ
cana-1759	77	10	thermal	thermal	ADJ
cana-1759	77	11	radiation	radiation	NOUN
cana-1759	77	12	on	on	ADP
cana-1759	77	13	casson	casson	PROPN
cana-1759	77	14	nanofluid	nanofluid	PROPN
cana-1759	77	15	flow	flow	NOUN
cana-1759	77	16	over	over	ADP
cana-1759	77	17	a	a	DET
cana-1759	77	18	stretching	stretch	VERB
cana-1759	77	19	sheet	sheet	NOUN
cana-1759	77	20	using	use	VERB
cana-1759	77	21	fractional	fractional	ADJ
cana-1759	77	22	derivatives	derivative	NOUN
cana-1759	77	23	.	.	PUNCT
cana-1759	78	1	the	the	DET
cana-1759	78	2	study	study	NOUN
cana-1759	78	3	provided	provide	VERB
cana-1759	78	4	insights	insight	NOUN
cana-1759	78	5	into	into	ADP
cana-1759	78	6	the	the	DET
cana-1759	78	7	interaction	interaction	NOUN
cana-1759	78	8	between	between	ADP
cana-1759	78	9	electromagnetic	electromagnetic	ADJ
cana-1759	78	10	forces	force	NOUN
cana-1759	78	11	and	and	CCONJ
cana-1759	78	12	fractional	fractional	ADJ
cana-1759	78	13	-	-	PUNCT
cana-1759	78	14	order	order	NOUN
cana-1759	78	15	heat	heat	NOUN
cana-1759	78	16	transfer	transfer	NOUN
cana-1759	78	17	processes	process	NOUN
cana-1759	78	18	,	,	PUNCT
cana-1759	78	19	revealing	reveal	VERB
cana-1759	78	20	that	that	SCONJ
cana-1759	78	21	fractional	fractional	ADJ
cana-1759	78	22	models	model	NOUN
cana-1759	78	23	are	be	AUX
cana-1759	78	24	crucial	crucial	ADJ
cana-1759	78	25	for	for	ADP
cana-1759	78	26	accurately	accurately	ADV
cana-1759	78	27	predicting	predict	VERB
cana-1759	78	28	the	the	DET
cana-1759	78	29	behavior	behavior	NOUN
cana-1759	78	30	of	of	ADP
cana-1759	78	31	electrically	electrically	ADV
cana-1759	78	32	conducting	conduct	VERB
cana-1759	78	33	fluids	fluid	NOUN
cana-1759	78	34	under	under	ADP
cana-1759	78	35	magnetic	magnetic	ADJ
cana-1759	78	36	influence	influence	NOUN
cana-1759	78	37	.	.	PUNCT
cana-1759	79	1	in	in	ADP
cana-1759	79	2	terms	term	NOUN
cana-1759	79	3	of	of	ADP
cana-1759	79	4	numerical	numerical	ADJ
cana-1759	79	5	simulations	simulation	NOUN
cana-1759	79	6	,	,	PUNCT
cana-1759	79	7	*	*	PUNCT
cana-1759	79	8	*	*	PUNCT
cana-1759	79	9	prasad	prasad	PROPN
cana-1759	79	10	et	et	PROPN
cana-1759	79	11	al	al	PROPN
cana-1759	79	12	.	.	PROPN
cana-1759	79	13	(	(	PUNCT
cana-1759	79	14	2023	2023	NUM
cana-1759	79	15	)	)	PUNCT
cana-1759	79	16	*	*	PUNCT
cana-1759	80	1	*	*	PUNCT
cana-1759	80	2	utilized	utilize	VERB
cana-1759	80	3	a	a	DET
cana-1759	80	4	fractional	fractional	ADJ
cana-1759	80	5	modelling	modelling	NOUN
cana-1759	80	6	approach	approach	NOUN
cana-1759	80	7	to	to	PART
cana-1759	80	8	study	study	VERB
cana-1759	80	9	mhd	mhd	PROPN
cana-1759	80	10	viscoelastic	viscoelastic	ADJ
cana-1759	80	11	fluid	fluid	NOUN
cana-1759	80	12	flow	flow	NOUN
cana-1759	80	13	and	and	CCONJ
cana-1759	80	14	heat	heat	NOUN
cana-1759	80	15	transfer	transfer	NOUN
cana-1759	80	16	over	over	ADP
cana-1759	80	17	a	a	DET
cana-1759	80	18	stretching	stretch	VERB
cana-1759	80	19	sheet	sheet	NOUN
cana-1759	80	20	.	.	PUNCT
cana-1759	81	1	their	their	PRON
cana-1759	81	2	study	study	NOUN
cana-1759	81	3	demonstrated	demonstrate	VERB
cana-1759	81	4	the	the	DET
cana-1759	81	5	potential	potential	NOUN
cana-1759	81	6	of	of	ADP
cana-1759	81	7	fractional	fractional	ADJ
cana-1759	81	8	derivatives	derivative	NOUN
cana-1759	81	9	in	in	ADP
cana-1759	81	10	capturing	capture	VERB
cana-1759	81	11	the	the	DET
cana-1759	81	12	viscoelastic	viscoelastic	ADJ
cana-1759	81	13	nature	nature	NOUN
cana-1759	81	14	of	of	ADP
cana-1759	81	15	the	the	DET
cana-1759	81	16	fluid	fluid	NOUN
cana-1759	81	17	and	and	CCONJ
cana-1759	81	18	its	its	PRON
cana-1759	81	19	impact	impact	NOUN
cana-1759	81	20	on	on	ADP
cana-1759	81	21	heat	heat	NOUN
cana-1759	81	22	transfer	transfer	NOUN
cana-1759	81	23	rates	rate	NOUN
cana-1759	81	24	.	.	PUNCT
cana-1759	82	1	the	the	DET
cana-1759	82	2	authors	author	NOUN
cana-1759	82	3	employed	employ	VERB
cana-1759	82	4	a	a	DET
cana-1759	82	5	numerical	numerical	ADJ
cana-1759	82	6	method	method	NOUN
cana-1759	82	7	that	that	PRON
cana-1759	82	8	combines	combine	VERB
cana-1759	82	9	the	the	DET
cana-1759	82	10	fractional	fractional	PROPN
cana-1759	82	11	caputo	caputo	PROPN
cana-1759	82	12	-	-	PUNCT
cana-1759	82	13	fabrizio	fabrizio	PROPN
cana-1759	82	14	derivative	derivative	NOUN
cana-1759	82	15	with	with	ADP
cana-1759	82	16	spectral	spectral	ADJ
cana-1759	82	17	methods	method	NOUN
cana-1759	82	18	to	to	PART
cana-1759	82	19	achieve	achieve	VERB
cana-1759	82	20	high	high	ADJ
cana-1759	82	21	accuracy	accuracy	NOUN
cana-1759	82	22	and	and	CCONJ
cana-1759	82	23	computational	computational	ADJ
cana-1759	82	24	efficiency	efficiency	NOUN
cana-1759	82	25	in	in	ADP
cana-1759	82	26	solving	solve	VERB
cana-1759	82	27	the	the	DET
cana-1759	82	28	governing	govern	VERB
cana-1759	82	29	equations	equation	NOUN
cana-1759	82	30	.	.	PUNCT
cana-1759	83	1	the	the	DET
cana-1759	83	2	unsteady	unsteady	ADJ
cana-1759	83	3	mhd	mhd	NOUN
cana-1759	83	4	flow	flow	NOUN
cana-1759	83	5	of	of	ADP
cana-1759	83	6	nanofluids	nanofluid	NOUN
cana-1759	83	7	over	over	ADP
cana-1759	83	8	permeable	permeable	ADJ
cana-1759	83	9	stretching	stretch	VERB
cana-1759	83	10	sheets	sheet	NOUN
cana-1759	83	11	has	have	AUX
cana-1759	83	12	also	also	ADV
cana-1759	83	13	been	be	AUX
cana-1759	83	14	extensively	extensively	ADV
cana-1759	83	15	studied	study	VERB
cana-1759	83	16	using	use	VERB
cana-1759	83	17	fractional	fractional	ADJ
cana-1759	83	18	calculus	calculus	NOUN
cana-1759	83	19	.	.	PUNCT
cana-1759	84	1	*	*	PUNCT
cana-1759	84	2	*	*	PUNCT
cana-1759	84	3	ramesh	ramesh	PROPN
cana-1759	84	4	and	and	CCONJ
cana-1759	84	5	reddy	reddy	PROPN
cana-1759	84	6	(	(	PUNCT
cana-1759	84	7	2022	2022	NUM
cana-1759	84	8	)	)	PUNCT
cana-1759	85	1	*	*	PUNCT
cana-1759	85	2	*	*	PUNCT
cana-1759	85	3	investigated	investigate	VERB
cana-1759	85	4	the	the	DET
cana-1759	85	5	use	use	NOUN
cana-1759	85	6	of	of	ADP
cana-1759	85	7	caputofabrizio	caputofabrizio	NOUN
cana-1759	85	8	fractional	fractional	ADJ
cana-1759	85	9	derivatives	derivative	NOUN
cana-1759	85	10	to	to	PART
cana-1759	85	11	model	model	VERB
cana-1759	85	12	the	the	DET
cana-1759	85	13	thermal	thermal	ADJ
cana-1759	85	14	conductivity	conductivity	NOUN
cana-1759	85	15	variations	variation	NOUN
cana-1759	85	16	and	and	CCONJ
cana-1759	85	17	their	their	PRON
cana-1759	85	18	effects	effect	NOUN
cana-1759	85	19	on	on	ADP
cana-1759	85	20	nanofluid	nanofluid	PROPN
cana-1759	85	21	flows	flow	NOUN
cana-1759	85	22	.	.	PUNCT
cana-1759	86	1	the	the	DET
cana-1759	86	2	study	study	NOUN
cana-1759	86	3	's	's	PART
cana-1759	86	4	findings	finding	NOUN
cana-1759	86	5	indicated	indicate	VERB
cana-1759	86	6	that	that	SCONJ
cana-1759	86	7	fractional	fractional	ADJ
cana-1759	86	8	derivatives	derivative	NOUN
cana-1759	86	9	could	could	AUX
cana-1759	86	10	effectively	effectively	ADV
cana-1759	86	11	describe	describe	VERB
cana-1759	86	12	the	the	DET
cana-1759	86	13	transient	transient	ADJ
cana-1759	86	14	behavior	behavior	NOUN
cana-1759	86	15	of	of	ADP
cana-1759	86	16	nanofluids	nanofluid	NOUN
cana-1759	86	17	in	in	ADP
cana-1759	86	18	porous	porous	ADJ
cana-1759	86	19	media	medium	NOUN
cana-1759	86	20	,	,	PUNCT
cana-1759	86	21	providing	provide	VERB
cana-1759	86	22	a	a	DET
cana-1759	86	23	better	well	ADJ
cana-1759	86	24	understanding	understanding	NOUN
cana-1759	86	25	of	of	ADP
cana-1759	86	26	the	the	DET
cana-1759	86	27	heat	heat	NOUN
cana-1759	86	28	transfer	transfer	NOUN
cana-1759	86	29	mechanisms	mechanism	NOUN
cana-1759	86	30	involved	involve	VERB
cana-1759	86	31	.	.	PUNCT
cana-1759	87	1	additionally	additionally	ADV
cana-1759	87	2	,	,	PUNCT
cana-1759	87	3	*	*	PUNCT
cana-1759	87	4	*	*	PUNCT
cana-1759	87	5	sadeghy	sadeghy	NOUN
cana-1759	87	6	and	and	CCONJ
cana-1759	87	7	kazemi	kazemi	PROPN
cana-1759	87	8	(	(	PUNCT
cana-1759	87	9	2023	2023	NUM
cana-1759	87	10	)	)	PUNCT
cana-1759	87	11	*	*	PUNCT
cana-1759	87	12	*	*	PUNCT
cana-1759	87	13	explored	explore	VERB
cana-1759	87	14	numerical	numerical	ADJ
cana-1759	87	15	simulations	simulation	NOUN
cana-1759	87	16	of	of	ADP
cana-1759	87	17	natural	natural	ADJ
cana-1759	87	18	convection	convection	NOUN
cana-1759	87	19	heat	heat	NOUN
cana-1759	87	20	transfer	transfer	NOUN
cana-1759	87	21	of	of	ADP
cana-1759	87	22	nanofluids	nanofluid	NOUN
cana-1759	87	23	using	use	VERB
cana-1759	87	24	a	a	DET
cana-1759	87	25	modified	modify	VERB
cana-1759	87	26	lattice	lattice	NOUN
cana-1759	87	27	boltzmann	boltzmann	PROPN
cana-1759	87	28	method	method	NOUN
cana-1759	87	29	(	(	PUNCT
cana-1759	87	30	lbm	lbm	NOUN
cana-1759	87	31	)	)	PUNCT
cana-1759	87	32	.	.	PUNCT
cana-1759	88	1	they	they	PRON
cana-1759	88	2	introduced	introduce	VERB
cana-1759	88	3	a	a	DET
cana-1759	88	4	fractional	fractional	ADJ
cana-1759	88	5	model	model	NOUN
cana-1759	88	6	to	to	PART
cana-1759	88	7	account	account	VERB
cana-1759	88	8	for	for	ADP
cana-1759	88	9	the	the	DET
cana-1759	88	10	non	non	ADJ
cana-1759	88	11	-	-	ADJ
cana-1759	88	12	local	local	ADJ
cana-1759	88	13	thermal	thermal	ADJ
cana-1759	88	14	effects	effect	NOUN
cana-1759	88	15	in	in	ADP
cana-1759	88	16	nanofluids	nanofluid	NOUN
cana-1759	88	17	,	,	PUNCT
cana-1759	88	18	demonstrating	demonstrate	VERB
cana-1759	88	19	that	that	SCONJ
cana-1759	88	20	fractional	fractional	ADJ
cana-1759	88	21	derivatives	derivative	NOUN
cana-1759	88	22	can	can	AUX
cana-1759	88	23	significantly	significantly	ADV
cana-1759	88	24	enhance	enhance	VERB
cana-1759	88	25	the	the	DET
cana-1759	88	26	accuracy	accuracy	NOUN
cana-1759	88	27	of	of	ADP
cana-1759	88	28	lbm	lbm	NOUN
cana-1759	88	29	simulations	simulation	NOUN
cana-1759	88	30	in	in	ADP
cana-1759	88	31	predicting	predict	VERB
cana-1759	88	32	natural	natural	ADJ
cana-1759	88	33	convection	convection	NOUN
cana-1759	88	34	patterns	pattern	NOUN
cana-1759	88	35	and	and	CCONJ
cana-1759	88	36	heat	heat	NOUN
cana-1759	88	37	transfer	transfer	NOUN
cana-1759	88	38	rates	rate	NOUN
cana-1759	88	39	in	in	ADP
cana-1759	88	40	complex	complex	ADJ
cana-1759	88	41	geometries	geometry	NOUN
cana-1759	88	42	.	.	PUNCT
cana-1759	89	1	in	in	ADP
cana-1759	89	2	another	another	DET
cana-1759	89	3	study	study	NOUN
cana-1759	89	4	,	,	PUNCT
cana-1759	89	5	*	*	PUNCT
cana-1759	89	6	*	*	PUNCT
cana-1759	89	7	singh	singh	PROPN
cana-1759	89	8	and	and	CCONJ
cana-1759	89	9	sarkar	sarkar	PROPN
cana-1759	89	10	(	(	PUNCT
cana-1759	89	11	2022	2022	NUM
cana-1759	89	12	)	)	PUNCT
cana-1759	89	13	*	*	PUNCT
cana-1759	89	14	*	*	PUNCT
cana-1759	89	15	used	use	VERB
cana-1759	89	16	a	a	DET
cana-1759	89	17	fractional	fractional	ADJ
cana-1759	89	18	calculus	calculus	NOUN
cana-1759	89	19	approach	approach	NOUN
cana-1759	89	20	to	to	ADP
cana-1759	89	21	model	model	NOUN
cana-1759	89	22	heat	heat	NOUN
cana-1759	89	23	transfer	transfer	NOUN
cana-1759	89	24	in	in	ADP
cana-1759	89	25	porous	porous	ADJ
cana-1759	89	26	media	medium	NOUN
cana-1759	89	27	saturated	saturate	VERB
cana-1759	89	28	with	with	ADP
cana-1759	89	29	nanofluids	nanofluid	NOUN
cana-1759	89	30	.	.	PUNCT
cana-1759	90	1	their	their	PRON
cana-1759	90	2	work	work	NOUN
cana-1759	90	3	highlighted	highlight	VERB
cana-1759	90	4	the	the	DET
cana-1759	90	5	advantages	advantage	NOUN
cana-1759	90	6	of	of	ADP
cana-1759	90	7	using	use	VERB
cana-1759	90	8	fractional	fractional	ADJ
cana-1759	90	9	models	model	NOUN
cana-1759	90	10	to	to	PART
cana-1759	90	11	represent	represent	VERB
cana-1759	90	12	the	the	DET
cana-1759	90	13	heterogeneous	heterogeneous	ADJ
cana-1759	90	14	nature	nature	NOUN
cana-1759	90	15	of	of	ADP
cana-1759	90	16	porous	porous	ADJ
cana-1759	90	17	media	medium	NOUN
cana-1759	90	18	and	and	CCONJ
cana-1759	90	19	the	the	DET
cana-1759	90	20	complex	complex	ADJ
cana-1759	90	21	heat	heat	NOUN
cana-1759	90	22	transfer	transfer	NOUN
cana-1759	90	23	interactions	interaction	NOUN
cana-1759	90	24	between	between	ADP
cana-1759	90	25	the	the	DET
cana-1759	90	26	solid	solid	ADJ
cana-1759	90	27	matrix	matrix	NOUN
cana-1759	90	28	and	and	CCONJ
cana-1759	90	29	the	the	DET
cana-1759	90	30	nanofluid	nanofluid	NOUN
cana-1759	90	31	.	.	PUNCT
cana-1759	91	1	the	the	DET
cana-1759	91	2	authors	author	NOUN
cana-1759	91	3	also	also	ADV
cana-1759	91	4	discussed	discuss	VERB
cana-1759	91	5	the	the	DET
cana-1759	91	6	challenges	challenge	NOUN
cana-1759	91	7	associated	associate	VERB
cana-1759	91	8	with	with	ADP
cana-1759	91	9	implementing	implement	VERB
cana-1759	91	10	fractional	fractional	ADJ
cana-1759	91	11	models	model	NOUN
cana-1759	91	12	in	in	ADP
cana-1759	91	13	large	large	ADJ
cana-1759	91	14	-	-	PUNCT
cana-1759	91	15	scale	scale	NOUN
cana-1759	91	16	simulations	simulation	NOUN
cana-1759	91	17	,	,	PUNCT
cana-1759	91	18	particularly	particularly	ADV
cana-1759	91	19	in	in	ADP
cana-1759	91	20	terms	term	NOUN
cana-1759	91	21	of	of	ADP
cana-1759	91	22	computational	computational	ADJ
cana-1759	91	23	cost	cost	NOUN
cana-1759	91	24	and	and	CCONJ
cana-1759	91	25	stability	stability	NOUN
cana-1759	91	26	.	.	PUNCT
cana-1759	92	1	finally	finally	ADV
cana-1759	92	2	,	,	PUNCT
cana-1759	92	3	*	*	PUNCT
cana-1759	92	4	*	*	NOUN
cana-1759	92	5	tiwari	tiwari	X
cana-1759	92	6	et	et	PROPN
cana-1759	92	7	al	al	PROPN
cana-1759	92	8	.	.	PROPN
cana-1759	93	1	(	(	PUNCT
cana-1759	93	2	2023	2023	NUM
cana-1759	93	3	)	)	PUNCT
cana-1759	93	4	*	*	PUNCT
cana-1759	93	5	*	*	AUX
cana-1759	93	6	conducted	conduct	VERB
cana-1759	93	7	a	a	DET
cana-1759	93	8	numerical	numerical	ADJ
cana-1759	93	9	study	study	NOUN
cana-1759	93	10	on	on	ADP
cana-1759	93	11	mhd	mhd	NOUN
cana-1759	93	12	flow	flow	NOUN
cana-1759	93	13	and	and	CCONJ
cana-1759	93	14	heat	heat	NOUN
cana-1759	93	15	transfer	transfer	NOUN
cana-1759	93	16	of	of	ADP
cana-1759	93	17	a	a	DET
cana-1759	93	18	nanofluid	nanofluid	NOUN
cana-1759	93	19	over	over	ADP
cana-1759	93	20	a	a	DET
cana-1759	93	21	stretching	stretch	VERB
cana-1759	93	22	surface	surface	NOUN
cana-1759	93	23	using	use	VERB
cana-1759	93	24	a	a	DET
cana-1759	93	25	fractional	fractional	ADJ
cana-1759	93	26	-	-	PUNCT
cana-1759	93	27	order	order	NOUN
cana-1759	93	28	model	model	NOUN
cana-1759	93	29	.	.	PUNCT
cana-1759	94	1	the	the	DET
cana-1759	94	2	study	study	NOUN
cana-1759	94	3	provided	provide	VERB
cana-1759	94	4	a	a	DET
cana-1759	94	5	comprehensive	comprehensive	ADJ
cana-1759	94	6	analysis	analysis	NOUN
cana-1759	94	7	of	of	ADP
cana-1759	94	8	the	the	DET
cana-1759	94	9	effects	effect	NOUN
cana-1759	94	10	of	of	ADP
cana-1759	94	11	magnetic	magnetic	ADJ
cana-1759	94	12	fields	field	NOUN
cana-1759	94	13	,	,	PUNCT
cana-1759	94	14	buoyancy	buoyancy	NOUN
cana-1759	94	15	forces	force	NOUN
cana-1759	94	16	,	,	PUNCT
cana-1759	94	17	and	and	CCONJ
cana-1759	94	18	fractional	fractional	ADJ
cana-1759	94	19	-	-	PUNCT
cana-1759	94	20	order	order	NOUN
cana-1759	94	21	heat	heat	NOUN
cana-1759	94	22	conduction	conduction	NOUN
cana-1759	94	23	on	on	ADP
cana-1759	94	24	the	the	DET
cana-1759	94	25	thermal	thermal	ADJ
cana-1759	94	26	and	and	CCONJ
cana-1759	94	27	flow	flow	NOUN
cana-1759	94	28	characteristics	characteristic	NOUN
cana-1759	94	29	of	of	ADP
cana-1759	94	30	nanofluids	nanofluid	NOUN
cana-1759	94	31	.	.	PUNCT
cana-1759	95	1	their	their	PRON
cana-1759	95	2	findings	finding	NOUN
cana-1759	95	3	underscored	underscore	VERB
cana-1759	95	4	the	the	DET
cana-1759	95	5	importance	importance	NOUN
cana-1759	95	6	of	of	ADP
cana-1759	95	7	fractional	fractional	ADJ
cana-1759	95	8	models	model	NOUN
cana-1759	95	9	in	in	ADP
cana-1759	95	10	accurately	accurately	ADV
cana-1759	95	11	capturing	capture	VERB
cana-1759	95	12	the	the	DET
cana-1759	95	13	coupled	couple	VERB
cana-1759	95	14	effects	effect	NOUN
cana-1759	95	15	of	of	ADP
cana-1759	95	16	multiple	multiple	ADJ
cana-1759	95	17	physical	physical	ADJ
cana-1759	95	18	phenomena	phenomenon	NOUN
cana-1759	95	19	in	in	ADP
cana-1759	95	20	heat	heat	NOUN
cana-1759	95	21	transfer	transfer	NOUN
cana-1759	95	22	applications	application	NOUN
cana-1759	95	23	.	.	PUNCT
cana-1759	96	1	overall	overall	ADV
cana-1759	96	2	,	,	PUNCT
cana-1759	96	3	the	the	DET
cana-1759	96	4	literature	literature	NOUN
cana-1759	96	5	indicates	indicate	VERB
cana-1759	96	6	a	a	DET
cana-1759	96	7	growing	grow	VERB
cana-1759	96	8	interest	interest	NOUN
cana-1759	96	9	in	in	ADP
cana-1759	96	10	using	use	VERB
cana-1759	96	11	fractional	fractional	ADJ
cana-1759	96	12	calculus	calculus	NOUN
cana-1759	96	13	and	and	CCONJ
cana-1759	96	14	advanced	advanced	ADJ
cana-1759	96	15	numerical	numerical	ADJ
cana-1759	96	16	methods	method	NOUN
cana-1759	96	17	to	to	PART
cana-1759	96	18	enhance	enhance	VERB
cana-1759	96	19	the	the	DET
cana-1759	96	20	accuracy	accuracy	NOUN
cana-1759	96	21	and	and	CCONJ
cana-1759	96	22	efficiency	efficiency	NOUN
cana-1759	96	23	of	of	ADP
cana-1759	96	24	heat	heat	NOUN
cana-1759	96	25	transfer	transfer	NOUN
cana-1759	96	26	and	and	CCONJ
cana-1759	96	27	fluid	fluid	ADJ
cana-1759	96	28	flow	flow	NOUN
cana-1759	96	29	models	model	NOUN
cana-1759	96	30	.	.	PUNCT
cana-1759	97	1	these	these	DET
cana-1759	97	2	studies	study	NOUN
cana-1759	97	3	have	have	AUX
cana-1759	97	4	demonstrated	demonstrate	VERB
cana-1759	97	5	the	the	DET
cana-1759	97	6	potential	potential	NOUN
cana-1759	97	7	of	of	ADP
cana-1759	97	8	fractional	fractional	ADJ
cana-1759	97	9	derivatives	derivative	NOUN
cana-1759	97	10	and	and	CCONJ
cana-1759	97	11	non	non	ADJ
cana-1759	97	12	-	-	ADJ
cana-1759	97	13	newtonian	newtonian	ADJ
cana-1759	97	14	fluid	fluid	NOUN
cana-1759	97	15	models	model	NOUN
cana-1759	97	16	in	in	ADP
cana-1759	97	17	capturing	capture	VERB
cana-1759	97	18	complex	complex	ADJ
cana-1759	97	19	thermal	thermal	ADJ
cana-1759	97	20	and	and	CCONJ
cana-1759	97	21	flow	flow	NOUN
cana-1759	97	22	behaviours	behaviour	NOUN
cana-1759	97	23	,	,	PUNCT
cana-1759	97	24	offering	offer	VERB
cana-1759	97	25	new	new	ADJ
cana-1759	97	26	insights	insight	NOUN
cana-1759	97	27	and	and	CCONJ
cana-1759	97	28	practical	practical	ADJ
cana-1759	97	29	solutions	solution	NOUN
cana-1759	97	30	for	for	ADP
cana-1759	97	31	a	a	DET
cana-1759	97	32	wide	wide	ADJ
cana-1759	97	33	range	range	NOUN
cana-1759	97	34	of	of	ADP
cana-1759	97	35	engineering	engineering	NOUN
cana-1759	97	36	applications	application	NOUN
cana-1759	97	37	.	.	PUNCT
cana-1759	98	1	2.1	2.1	NUM
cana-1759	98	2	.	.	PUNCT
cana-1759	99	1	recent	recent	ADJ
cana-1759	99	2	advances	advance	NOUN
cana-1759	99	3	and	and	CCONJ
cana-1759	99	4	research	research	NOUN
cana-1759	99	5	gaps	gap	NOUN
cana-1759	99	6	:	:	PUNCT
cana-1759	99	7	despite	despite	SCONJ
cana-1759	99	8	the	the	DET
cana-1759	99	9	progress	progress	NOUN
cana-1759	99	10	in	in	ADP
cana-1759	99	11	these	these	DET
cana-1759	99	12	advanced	advance	VERB
cana-1759	99	13	modelling	modelling	NOUN
cana-1759	99	14	techniques	technique	NOUN
cana-1759	99	15	,	,	PUNCT
cana-1759	99	16	several	several	ADJ
cana-1759	99	17	challenges	challenge	NOUN
cana-1759	99	18	remain	remain	VERB
cana-1759	99	19	.	.	PUNCT
cana-1759	100	1	fractional	fractional	ADJ
cana-1759	100	2	models	model	NOUN
cana-1759	100	3	,	,	PUNCT
cana-1759	100	4	while	while	SCONJ
cana-1759	100	5	providing	provide	VERB
cana-1759	100	6	more	more	ADV
cana-1759	100	7	accurate	accurate	ADJ
cana-1759	100	8	descriptions	description	NOUN
cana-1759	100	9	of	of	ADP
cana-1759	100	10	certain	certain	ADJ
cana-1759	100	11	phenomena	phenomenon	NOUN
cana-1759	100	12	,	,	PUNCT
cana-1759	100	13	are	be	AUX
cana-1759	100	14	computationally	computationally	ADV
cana-1759	100	15	intensive	intensive	ADJ
cana-1759	100	16	and	and	CCONJ
cana-1759	100	17	require	require	VERB
cana-1759	100	18	sophisticated	sophisticated	ADJ
cana-1759	100	19	numerical	numerical	ADJ
cana-1759	100	20	methods	method	NOUN
cana-1759	100	21	for	for	ADP
cana-1759	100	22	their	their	PRON
cana-1759	100	23	solution	solution	NOUN
cana-1759	100	24	.	.	PUNCT
cana-1759	101	1	traditional	traditional	ADJ
cana-1759	101	2	numerical	numerical	ADJ
cana-1759	101	3	communications	communication	NOUN
cana-1759	101	4	on	on	ADP
cana-1759	101	5	applied	apply	VERB
cana-1759	101	6	nonlinear	nonlinear	ADJ
cana-1759	101	7	analysis	analysis	NOUN
cana-1759	101	8	issn	issn	NOUN
cana-1759	101	9	:	:	PUNCT
cana-1759	101	10	1074	1074	NUM
cana-1759	101	11	-	-	PUNCT
cana-1759	101	12	133x	133x	NUM
cana-1759	101	13	vol	vol	NOUN
cana-1759	101	14	32	32	NUM
cana-1759	101	15	no	no	NOUN
cana-1759	101	16	.	.	NOUN
cana-1759	101	17	2	2	NUM
cana-1759	101	18	(	(	PUNCT
cana-1759	101	19	2025	2025	NUM
cana-1759	101	20	)	)	PUNCT
cana-1759	101	21	475	475	NUM
cana-1759	101	22	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	101	23	techniques	technique	NOUN
cana-1759	101	24	like	like	ADP
cana-1759	101	25	finite	finite	ADJ
cana-1759	101	26	difference	difference	NOUN
cana-1759	101	27	methods	method	NOUN
cana-1759	101	28	(	(	PUNCT
cana-1759	101	29	fdm	fdm	NOUN
cana-1759	101	30	)	)	PUNCT
cana-1759	101	31	and	and	CCONJ
cana-1759	101	32	finite	finite	ADJ
cana-1759	101	33	element	element	NOUN
cana-1759	101	34	methods	method	NOUN
cana-1759	101	35	(	(	PUNCT
cana-1759	101	36	fem	fem	NOUN
cana-1759	101	37	)	)	PUNCT
cana-1759	101	38	are	be	AUX
cana-1759	101	39	often	often	ADV
cana-1759	101	40	employed	employ	VERB
cana-1759	101	41	,	,	PUNCT
cana-1759	101	42	but	but	CCONJ
cana-1759	101	43	their	their	PRON
cana-1759	101	44	application	application	NOUN
cana-1759	101	45	to	to	ADP
cana-1759	101	46	fractional	fractional	ADJ
cana-1759	101	47	differential	differential	ADJ
cana-1759	101	48	equations	equation	NOUN
cana-1759	101	49	is	be	AUX
cana-1759	101	50	not	not	PART
cana-1759	101	51	straightforward	straightforward	ADJ
cana-1759	101	52	and	and	CCONJ
cana-1759	101	53	requires	require	VERB
cana-1759	101	54	modifications	modification	NOUN
cana-1759	101	55	to	to	PART
cana-1759	101	56	handle	handle	VERB
cana-1759	101	57	the	the	DET
cana-1759	101	58	non	non	ADJ
cana-1759	101	59	-	-	ADJ
cana-1759	101	60	local	local	ADJ
cana-1759	101	61	nature	nature	NOUN
cana-1759	101	62	of	of	ADP
cana-1759	101	63	fractional	fractional	ADJ
cana-1759	101	64	operators	operator	NOUN
cana-1759	101	65	.	.	PUNCT
cana-1759	102	1	similarly	similarly	ADV
cana-1759	102	2	,	,	PUNCT
cana-1759	102	3	while	while	SCONJ
cana-1759	102	4	non	non	ADJ
cana-1759	102	5	-	-	ADJ
cana-1759	102	6	newtonian	newtonian	ADJ
cana-1759	102	7	fluid	fluid	NOUN
cana-1759	102	8	models	model	NOUN
cana-1759	102	9	provide	provide	VERB
cana-1759	102	10	better	well	ADJ
cana-1759	102	11	representations	representation	NOUN
cana-1759	102	12	of	of	ADP
cana-1759	102	13	complex	complex	ADJ
cana-1759	102	14	fluids	fluid	NOUN
cana-1759	102	15	,	,	PUNCT
cana-1759	102	16	they	they	PRON
cana-1759	102	17	often	often	ADV
cana-1759	102	18	involve	involve	VERB
cana-1759	102	19	non	non	ADJ
cana-1759	102	20	-	-	ADJ
cana-1759	102	21	linear	linear	ADJ
cana-1759	102	22	constitutive	constitutive	ADJ
cana-1759	102	23	equations	equation	NOUN
cana-1759	102	24	that	that	PRON
cana-1759	102	25	are	be	AUX
cana-1759	102	26	difficult	difficult	ADJ
cana-1759	102	27	to	to	PART
cana-1759	102	28	solve	solve	VERB
cana-1759	102	29	analytically	analytically	ADV
cana-1759	102	30	and	and	CCONJ
cana-1759	102	31	require	require	VERB
cana-1759	102	32	robust	robust	ADJ
cana-1759	102	33	numerical	numerical	ADJ
cana-1759	102	34	techniques	technique	NOUN
cana-1759	102	35	.	.	PUNCT
cana-1759	103	1	moreover	moreover	ADV
cana-1759	103	2	,	,	PUNCT
cana-1759	103	3	there	there	PRON
cana-1759	103	4	is	be	VERB
cana-1759	103	5	a	a	DET
cana-1759	103	6	need	need	NOUN
cana-1759	103	7	for	for	ADP
cana-1759	103	8	comprehensive	comprehensive	ADJ
cana-1759	103	9	studies	study	NOUN
cana-1759	103	10	that	that	PRON
cana-1759	103	11	compare	compare	VERB
cana-1759	103	12	the	the	DET
cana-1759	103	13	effectiveness	effectiveness	NOUN
cana-1759	103	14	of	of	ADP
cana-1759	103	15	different	different	ADJ
cana-1759	103	16	numerical	numerical	ADJ
cana-1759	103	17	methods	method	NOUN
cana-1759	103	18	,	,	PUNCT
cana-1759	103	19	such	such	ADJ
cana-1759	103	20	as	as	ADP
cana-1759	103	21	the	the	DET
cana-1759	103	22	iterative	iterative	NOUN
cana-1759	103	23	power	power	NOUN
cana-1759	103	24	series	series	NOUN
cana-1759	103	25	(	(	PUNCT
cana-1759	103	26	ips	ips	NOUN
cana-1759	103	27	)	)	PUNCT
cana-1759	103	28	technique	technique	NOUN
cana-1759	103	29	,	,	PUNCT
cana-1759	103	30	finite	finite	ADJ
cana-1759	103	31	volume	volume	NOUN
cana-1759	103	32	methods	method	NOUN
cana-1759	103	33	(	(	PUNCT
cana-1759	103	34	fvm	fvm	NOUN
cana-1759	103	35	)	)	PUNCT
cana-1759	103	36	,	,	PUNCT
cana-1759	103	37	and	and	CCONJ
cana-1759	103	38	spectral	spectral	ADJ
cana-1759	103	39	methods	method	NOUN
cana-1759	103	40	,	,	PUNCT
cana-1759	103	41	in	in	ADP
cana-1759	103	42	solving	solve	VERB
cana-1759	103	43	these	these	DET
cana-1759	103	44	advanced	advanced	ADJ
cana-1759	103	45	models	model	NOUN
cana-1759	103	46	.	.	PUNCT
cana-1759	104	1	such	such	ADJ
cana-1759	104	2	comparative	comparative	ADJ
cana-1759	104	3	studies	study	NOUN
cana-1759	104	4	are	be	AUX
cana-1759	104	5	crucial	crucial	ADJ
cana-1759	104	6	for	for	ADP
cana-1759	104	7	identifying	identify	VERB
cana-1759	104	8	the	the	DET
cana-1759	104	9	most	most	ADV
cana-1759	104	10	efficient	efficient	ADJ
cana-1759	104	11	and	and	CCONJ
cana-1759	104	12	accurate	accurate	ADJ
cana-1759	104	13	methods	method	NOUN
cana-1759	104	14	for	for	ADP
cana-1759	104	15	different	different	ADJ
cana-1759	104	16	types	type	NOUN
cana-1759	104	17	of	of	ADP
cana-1759	104	18	problems	problem	NOUN
cana-1759	104	19	,	,	PUNCT
cana-1759	104	20	ranging	range	VERB
cana-1759	104	21	from	from	ADP
cana-1759	104	22	simple	simple	ADJ
cana-1759	104	23	geometries	geometry	NOUN
cana-1759	104	24	to	to	ADP
cana-1759	104	25	complex	complex	ADJ
cana-1759	104	26	,	,	PUNCT
cana-1759	104	27	multi	multi	ADJ
cana-1759	104	28	-	-	ADJ
cana-1759	104	29	scale	scale	ADJ
cana-1759	104	30	systems	system	NOUN
cana-1759	104	31	.	.	PUNCT
cana-1759	105	1	2.2	2.2	NUM
cana-1759	105	2	.	.	PUNCT
cana-1759	105	3	objectives	objective	NOUN
cana-1759	105	4	and	and	CCONJ
cana-1759	105	5	scope	scope	NOUN
cana-1759	105	6	of	of	ADP
cana-1759	105	7	the	the	DET
cana-1759	105	8	study	study	NOUN
cana-1759	105	9	:	:	PUNCT
cana-1759	105	10	the	the	DET
cana-1759	105	11	primary	primary	ADJ
cana-1759	105	12	objective	objective	NOUN
cana-1759	105	13	of	of	ADP
cana-1759	105	14	this	this	DET
cana-1759	105	15	research	research	NOUN
cana-1759	105	16	is	be	AUX
cana-1759	105	17	to	to	PART
cana-1759	105	18	explore	explore	VERB
cana-1759	105	19	and	and	CCONJ
cana-1759	105	20	analyze	analyze	VERB
cana-1759	105	21	recent	recent	ADJ
cana-1759	105	22	trends	trend	NOUN
cana-1759	105	23	in	in	ADP
cana-1759	105	24	the	the	DET
cana-1759	105	25	mathematical	mathematical	ADJ
cana-1759	105	26	modelling	modelling	NOUN
cana-1759	105	27	of	of	ADP
cana-1759	105	28	heat	heat	NOUN
cana-1759	105	29	transfer	transfer	NOUN
cana-1759	105	30	and	and	CCONJ
cana-1759	105	31	fluid	fluid	NOUN
cana-1759	105	32	flows	flow	NOUN
cana-1759	105	33	,	,	PUNCT
cana-1759	105	34	with	with	ADP
cana-1759	105	35	a	a	DET
cana-1759	105	36	focus	focus	NOUN
cana-1759	105	37	on	on	ADP
cana-1759	105	38	fractional	fractional	ADJ
cana-1759	105	39	calculus	calculus	NOUN
cana-1759	105	40	,	,	PUNCT
cana-1759	105	41	non	non	ADJ
cana-1759	105	42	-	-	ADJ
cana-1759	105	43	newtonian	newtonian	ADJ
cana-1759	105	44	fluid	fluid	ADJ
cana-1759	105	45	models	model	NOUN
cana-1759	105	46	,	,	PUNCT
cana-1759	105	47	and	and	CCONJ
cana-1759	105	48	nanofluid	nanofluid	ADJ
cana-1759	105	49	dynamics	dynamic	NOUN
cana-1759	105	50	.	.	PUNCT
cana-1759	106	1	the	the	DET
cana-1759	106	2	study	study	NOUN
cana-1759	106	3	aims	aim	VERB
cana-1759	106	4	to	to	PART
cana-1759	106	5	:	:	PUNCT
cana-1759	106	6	1	1	X
cana-1759	106	7	.	.	X
cana-1759	106	8	develop	develop	VERB
cana-1759	106	9	a	a	DET
cana-1759	106	10	comprehensive	comprehensive	ADJ
cana-1759	106	11	understanding	understanding	NOUN
cana-1759	106	12	of	of	ADP
cana-1759	106	13	the	the	DET
cana-1759	106	14	application	application	NOUN
cana-1759	106	15	of	of	ADP
cana-1759	106	16	fractional	fractional	ADJ
cana-1759	106	17	derivatives	derivative	NOUN
cana-1759	106	18	in	in	ADP
cana-1759	106	19	heat	heat	NOUN
cana-1759	106	20	transfer	transfer	NOUN
cana-1759	106	21	and	and	CCONJ
cana-1759	106	22	fluid	fluid	NOUN
cana-1759	106	23	flow	flow	NOUN
cana-1759	106	24	modelling	modelling	NOUN
cana-1759	106	25	,	,	PUNCT
cana-1759	106	26	highlighting	highlight	VERB
cana-1759	106	27	their	their	PRON
cana-1759	106	28	advantages	advantage	NOUN
cana-1759	106	29	over	over	ADP
cana-1759	106	30	classical	classical	ADJ
cana-1759	106	31	models	model	NOUN
cana-1759	106	32	.	.	PUNCT
cana-1759	107	1	2	2	X
cana-1759	107	2	.	.	X
cana-1759	107	3	examine	examine	VERB
cana-1759	107	4	the	the	DET
cana-1759	107	5	use	use	NOUN
cana-1759	107	6	of	of	ADP
cana-1759	107	7	non	non	ADJ
cana-1759	107	8	-	-	ADJ
cana-1759	107	9	newtonian	newtonian	ADJ
cana-1759	107	10	fluid	fluid	NOUN
cana-1759	107	11	models	model	NOUN
cana-1759	107	12	in	in	ADP
cana-1759	107	13	various	various	ADJ
cana-1759	107	14	industrial	industrial	ADJ
cana-1759	107	15	and	and	CCONJ
cana-1759	107	16	biomedical	biomedical	ADJ
cana-1759	107	17	applications	application	NOUN
cana-1759	107	18	,	,	PUNCT
cana-1759	107	19	providing	provide	VERB
cana-1759	107	20	insights	insight	NOUN
cana-1759	107	21	into	into	ADP
cana-1759	107	22	their	their	PRON
cana-1759	107	23	rheological	rheological	ADJ
cana-1759	107	24	behavior	behavior	NOUN
cana-1759	107	25	under	under	ADP
cana-1759	107	26	different	different	ADJ
cana-1759	107	27	flow	flow	NOUN
cana-1759	107	28	conditions	condition	NOUN
cana-1759	107	29	.	.	PUNCT
cana-1759	108	1	3	3	X
cana-1759	108	2	.	.	X
cana-1759	108	3	investigate	investigate	VERB
cana-1759	108	4	the	the	DET
cana-1759	108	5	role	role	NOUN
cana-1759	108	6	of	of	ADP
cana-1759	108	7	nanofluids	nanofluid	NOUN
cana-1759	108	8	in	in	ADP
cana-1759	108	9	enhancing	enhance	VERB
cana-1759	108	10	heat	heat	NOUN
cana-1759	108	11	transfer	transfer	NOUN
cana-1759	108	12	rates	rate	NOUN
cana-1759	108	13	,	,	PUNCT
cana-1759	108	14	with	with	ADP
cana-1759	108	15	a	a	DET
cana-1759	108	16	focus	focus	NOUN
cana-1759	108	17	on	on	ADP
cana-1759	108	18	their	their	PRON
cana-1759	108	19	mathematical	mathematical	ADJ
cana-1759	108	20	modelling	modelling	NOUN
cana-1759	108	21	and	and	CCONJ
cana-1759	108	22	practical	practical	ADJ
cana-1759	108	23	applications	application	NOUN
cana-1759	108	24	.	.	PUNCT
cana-1759	109	1	4	4	X
cana-1759	109	2	.	.	X
cana-1759	109	3	compare	compare	VERB
cana-1759	109	4	different	different	ADJ
cana-1759	109	5	numerical	numerical	ADJ
cana-1759	109	6	methods	method	NOUN
cana-1759	109	7	used	use	VERB
cana-1759	109	8	to	to	PART
cana-1759	109	9	solve	solve	VERB
cana-1759	109	10	the	the	DET
cana-1759	109	11	complex	complex	ADJ
cana-1759	109	12	models	model	NOUN
cana-1759	109	13	derived	derive	VERB
cana-1759	109	14	from	from	ADP
cana-1759	109	15	these	these	DET
cana-1759	109	16	advanced	advanced	ADJ
cana-1759	109	17	mathematical	mathematical	ADJ
cana-1759	109	18	approaches	approach	NOUN
cana-1759	109	19	,	,	PUNCT
cana-1759	109	20	assessing	assess	VERB
cana-1759	109	21	their	their	PRON
cana-1759	109	22	accuracy	accuracy	NOUN
cana-1759	109	23	,	,	PUNCT
cana-1759	109	24	convergence	convergence	NOUN
cana-1759	109	25	,	,	PUNCT
cana-1759	109	26	and	and	CCONJ
cana-1759	109	27	computational	computational	ADJ
cana-1759	109	28	efficiency	efficiency	NOUN
cana-1759	109	29	.	.	PUNCT
cana-1759	110	1	by	by	ADP
cana-1759	110	2	achieving	achieve	VERB
cana-1759	110	3	these	these	DET
cana-1759	110	4	objectives	objective	NOUN
cana-1759	110	5	,	,	PUNCT
cana-1759	110	6	this	this	DET
cana-1759	110	7	study	study	NOUN
cana-1759	110	8	aims	aim	VERB
cana-1759	110	9	to	to	PART
cana-1759	110	10	contribute	contribute	VERB
cana-1759	110	11	to	to	ADP
cana-1759	110	12	the	the	DET
cana-1759	110	13	development	development	NOUN
cana-1759	110	14	of	of	ADP
cana-1759	110	15	more	more	ADV
cana-1759	110	16	effective	effective	ADJ
cana-1759	110	17	and	and	CCONJ
cana-1759	110	18	efficient	efficient	ADJ
cana-1759	110	19	engineering	engineering	NOUN
cana-1759	110	20	designs	design	NOUN
cana-1759	110	21	and	and	CCONJ
cana-1759	110	22	optimization	optimization	NOUN
cana-1759	110	23	strategies	strategy	NOUN
cana-1759	110	24	in	in	ADP
cana-1759	110	25	heat	heat	NOUN
cana-1759	110	26	transfer	transfer	NOUN
cana-1759	110	27	and	and	CCONJ
cana-1759	110	28	fluid	fluid	NOUN
cana-1759	110	29	flow	flow	NOUN
cana-1759	110	30	applications	application	NOUN
cana-1759	110	31	.	.	PUNCT
cana-1759	111	1	the	the	DET
cana-1759	111	2	findings	finding	NOUN
cana-1759	111	3	of	of	ADP
cana-1759	111	4	this	this	DET
cana-1759	111	5	research	research	NOUN
cana-1759	111	6	will	will	AUX
cana-1759	111	7	be	be	AUX
cana-1759	111	8	particularly	particularly	ADV
cana-1759	111	9	valuable	valuable	ADJ
cana-1759	111	10	for	for	ADP
cana-1759	111	11	industries	industry	NOUN
cana-1759	111	12	that	that	PRON
cana-1759	111	13	rely	rely	VERB
cana-1759	111	14	on	on	ADP
cana-1759	111	15	accurate	accurate	ADJ
cana-1759	111	16	thermal	thermal	ADJ
cana-1759	111	17	and	and	CCONJ
cana-1759	111	18	fluid	fluid	ADJ
cana-1759	111	19	dynamic	dynamic	ADJ
cana-1759	111	20	predictions	prediction	NOUN
cana-1759	111	21	,	,	PUNCT
cana-1759	111	22	such	such	ADJ
cana-1759	111	23	as	as	ADP
cana-1759	111	24	energy	energy	NOUN
cana-1759	111	25	,	,	PUNCT
cana-1759	111	26	manufacturing	manufacturing	NOUN
cana-1759	111	27	,	,	PUNCT
cana-1759	111	28	environmental	environmental	ADJ
cana-1759	111	29	management	management	NOUN
cana-1759	111	30	,	,	PUNCT
cana-1759	111	31	and	and	CCONJ
cana-1759	111	32	healthcare	healthcare	PROPN
cana-1759	111	33	.	.	PUNCT
cana-1759	112	1	3	3	X
cana-1759	112	2	.	.	X
cana-1759	112	3	mathematical	mathematical	ADJ
cana-1759	112	4	modelling	model	VERB
cana-1759	112	5	the	the	DET
cana-1759	112	6	mathematical	mathematical	ADJ
cana-1759	112	7	modelling	modelling	NOUN
cana-1759	112	8	of	of	ADP
cana-1759	112	9	heat	heat	NOUN
cana-1759	112	10	transfer	transfer	NOUN
cana-1759	112	11	and	and	CCONJ
cana-1759	112	12	fluid	fluid	ADJ
cana-1759	112	13	flows	flow	NOUN
cana-1759	112	14	has	have	AUX
cana-1759	112	15	evolved	evolve	VERB
cana-1759	112	16	significantly	significantly	ADV
cana-1759	112	17	to	to	PART
cana-1759	112	18	incorporate	incorporate	VERB
cana-1759	112	19	more	more	ADV
cana-1759	112	20	sophisticated	sophisticated	ADJ
cana-1759	112	21	mathematical	mathematical	ADJ
cana-1759	112	22	tools	tool	NOUN
cana-1759	112	23	and	and	CCONJ
cana-1759	112	24	techniques	technique	NOUN
cana-1759	112	25	that	that	PRON
cana-1759	112	26	account	account	VERB
cana-1759	112	27	for	for	ADP
cana-1759	112	28	complex	complex	ADJ
cana-1759	112	29	physical	physical	ADJ
cana-1759	112	30	phenomena	phenomenon	NOUN
cana-1759	112	31	such	such	ADJ
cana-1759	112	32	as	as	ADP
cana-1759	112	33	non	non	ADJ
cana-1759	112	34	-	-	ADJ
cana-1759	112	35	linearity	linearity	ADJ
cana-1759	112	36	,	,	PUNCT
cana-1759	112	37	non	non	ADJ
cana-1759	112	38	-	-	ADJ
cana-1759	112	39	locality	locality	ADJ
cana-1759	112	40	,	,	PUNCT
cana-1759	112	41	and	and	CCONJ
cana-1759	112	42	memory	memory	NOUN
cana-1759	112	43	effects	effect	NOUN
cana-1759	112	44	.	.	PUNCT
cana-1759	113	1	recent	recent	ADJ
cana-1759	113	2	advancements	advancement	NOUN
cana-1759	113	3	in	in	ADP
cana-1759	113	4	fractional	fractional	ADJ
cana-1759	113	5	calculus	calculus	NOUN
cana-1759	113	6	,	,	PUNCT
cana-1759	113	7	non	non	ADJ
cana-1759	113	8	-	-	ADJ
cana-1759	113	9	newtonian	newtonian	ADJ
cana-1759	113	10	fluid	fluid	ADJ
cana-1759	113	11	dynamics	dynamic	NOUN
cana-1759	113	12	,	,	PUNCT
cana-1759	113	13	and	and	CCONJ
cana-1759	113	14	nanofluid	nanofluid	NOUN
cana-1759	113	15	models	model	NOUN
cana-1759	113	16	have	have	AUX
cana-1759	113	17	greatly	greatly	ADV
cana-1759	113	18	enhanced	enhance	VERB
cana-1759	113	19	our	our	PRON
cana-1759	113	20	understanding	understanding	NOUN
cana-1759	113	21	and	and	CCONJ
cana-1759	113	22	ability	ability	NOUN
cana-1759	113	23	to	to	PART
cana-1759	113	24	predict	predict	VERB
cana-1759	113	25	the	the	DET
cana-1759	113	26	behavior	behavior	NOUN
cana-1759	113	27	of	of	ADP
cana-1759	113	28	such	such	ADJ
cana-1759	113	29	systems	system	NOUN
cana-1759	113	30	under	under	ADP
cana-1759	113	31	various	various	ADJ
cana-1759	113	32	conditions	condition	NOUN
cana-1759	113	33	.	.	PUNCT
cana-1759	114	1	this	this	DET
cana-1759	114	2	section	section	NOUN
cana-1759	114	3	presents	present	VERB
cana-1759	114	4	the	the	DET
cana-1759	114	5	governing	govern	VERB
cana-1759	114	6	equations	equation	NOUN
cana-1759	114	7	for	for	ADP
cana-1759	114	8	these	these	DET
cana-1759	114	9	models	model	NOUN
cana-1759	114	10	and	and	CCONJ
cana-1759	114	11	discusses	discuss	VERB
cana-1759	114	12	their	their	PRON
cana-1759	114	13	mathematical	mathematical	ADJ
cana-1759	114	14	formulation	formulation	NOUN
cana-1759	114	15	.	.	PUNCT
cana-1759	115	1	3.1	3.1	NUM
cana-1759	115	2	.	.	PUNCT
cana-1759	116	1	governing	govern	VERB
cana-1759	116	2	equations	equation	NOUN
cana-1759	116	3	the	the	DET
cana-1759	116	4	foundational	foundational	ADJ
cana-1759	116	5	equations	equation	NOUN
cana-1759	116	6	governing	govern	VERB
cana-1759	116	7	fluid	fluid	ADJ
cana-1759	116	8	flow	flow	NOUN
cana-1759	116	9	and	and	CCONJ
cana-1759	116	10	heat	heat	NOUN
cana-1759	116	11	transfer	transfer	NOUN
cana-1759	116	12	are	be	AUX
cana-1759	116	13	the	the	DET
cana-1759	116	14	navier	navier	NOUN
cana-1759	116	15	-	-	PUNCT
cana-1759	116	16	stokes	stoke	NOUN
cana-1759	116	17	equations	equation	NOUN
cana-1759	116	18	and	and	CCONJ
cana-1759	116	19	the	the	DET
cana-1759	116	20	energy	energy	NOUN
cana-1759	116	21	conservation	conservation	NOUN
cana-1759	116	22	equation	equation	NOUN
cana-1759	116	23	.	.	PUNCT
cana-1759	117	1	these	these	DET
cana-1759	117	2	equations	equation	NOUN
cana-1759	117	3	are	be	AUX
cana-1759	117	4	expressed	express	VERB
cana-1759	117	5	as	as	SCONJ
cana-1759	117	6	follows	follow	VERB
cana-1759	117	7	:	:	PUNCT
cana-1759	117	8	communications	communication	NOUN
cana-1759	117	9	on	on	ADP
cana-1759	117	10	applied	apply	VERB
cana-1759	117	11	nonlinear	nonlinear	ADJ
cana-1759	117	12	analysis	analysis	NOUN
cana-1759	117	13	issn	issn	NOUN
cana-1759	117	14	:	:	PUNCT
cana-1759	117	15	1074	1074	NUM
cana-1759	117	16	-	-	PUNCT
cana-1759	117	17	133x	133x	NUM
cana-1759	117	18	vol	vol	NOUN
cana-1759	117	19	32	32	NUM
cana-1759	117	20	no	no	NOUN
cana-1759	117	21	.	.	NOUN
cana-1759	117	22	2	2	NUM
cana-1759	117	23	(	(	PUNCT
cana-1759	117	24	2025	2025	NUM
cana-1759	117	25	)	)	PUNCT
cana-1759	117	26	476	476	NUM
cana-1759	117	27	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	117	28	continuity	continuity	NOUN
cana-1759	117	29	equation	equation	NOUN
cana-1759	117	30	:	:	PUNCT
cana-1759	117	31	𝝏𝝆	𝝏𝝆	X
cana-1759	117	32	𝝏𝒕	𝝏𝒕	X
cana-1759	118	1	+	+	CCONJ
cana-1759	118	2	𝛁.	𝛁.	NUM
cana-1759	118	3	(	(	PUNCT
cana-1759	118	4	𝝆𝒖)=	𝝆𝒖)=	X
cana-1759	118	5	0	0	NUM
cana-1759	118	6	where	where	SCONJ
cana-1759	118	7	𝜌	𝜌	PRON
cana-1759	118	8	is	be	AUX
cana-1759	118	9	the	the	DET
cana-1759	118	10	fluid	fluid	ADJ
cana-1759	118	11	density	density	NOUN
cana-1759	118	12	,	,	PUNCT
cana-1759	118	13	t	t	PROPN
cana-1759	118	14	is	be	AUX
cana-1759	118	15	time	time	NOUN
cana-1759	118	16	,	,	PUNCT
cana-1759	118	17	and	and	CCONJ
cana-1759	118	18	u	u	NOUN
cana-1759	118	19	is	be	AUX
cana-1759	118	20	the	the	DET
cana-1759	118	21	velocity	velocity	NOUN
cana-1759	118	22	vector	vector	NOUN
cana-1759	118	23	.	.	PUNCT
cana-1759	119	1	momentum	momentum	NOUN
cana-1759	119	2	equation	equation	NOUN
cana-1759	119	3	(	(	PUNCT
cana-1759	119	4	navier	navier	NOUN
cana-1759	119	5	-	-	PUNCT
cana-1759	119	6	stokes	stoke	NOUN
cana-1759	119	7	equations	equation	NOUN
cana-1759	119	8	):	):	PUNCT
cana-1759	119	9	𝝏(𝝆𝒖	𝝏(𝝆𝒖	NOUN
cana-1759	119	10	)	)	PUNCT
cana-1759	119	11	𝝏𝒕	𝝏𝒕	X
cana-1759	119	12	+	+	CCONJ
cana-1759	119	13	𝛁.	𝛁.	NUM
cana-1759	119	14	(	(	PUNCT
cana-1759	119	15	𝝆𝒖	𝝆𝒖	PROPN
cana-1759	119	16	⊗	⊗	PROPN
cana-1759	119	17	𝒖	𝒖	X
cana-1759	119	18	)	)	PUNCT
cana-1759	119	19	=	=	SYM
cana-1759	119	20	𝛁𝐩	𝛁𝐩	NOUN
cana-1759	119	21	+	+	CCONJ
cana-1759	119	22	𝛁.	𝛁.	NUM
cana-1759	119	23	𝐫	𝐫	ADP
cana-1759	119	24	+	+	NOUN
cana-1759	119	25	f	f	X
cana-1759	119	26	where	where	SCONJ
cana-1759	119	27	𝜌	𝜌	PRON
cana-1759	119	28	is	be	AUX
cana-1759	119	29	the	the	DET
cana-1759	119	30	pressure	pressure	NOUN
cana-1759	119	31	,	,	PUNCT
cana-1759	119	32	𝜏	𝜏	NOUN
cana-1759	119	33	is	be	AUX
cana-1759	119	34	the	the	DET
cana-1759	119	35	stress	stress	NOUN
cana-1759	119	36	tensor	tensor	NOUN
cana-1759	119	37	,	,	PUNCT
cana-1759	119	38	and	and	CCONJ
cana-1759	119	39	f	f	PROPN
cana-1759	119	40	represents	represent	VERB
cana-1759	119	41	body	body	NOUN
cana-1759	119	42	forces	force	NOUN
cana-1759	119	43	such	such	ADJ
cana-1759	119	44	as	as	ADP
cana-1759	119	45	gravity	gravity	NOUN
cana-1759	119	46	or	or	CCONJ
cana-1759	119	47	electromagnetic	electromagnetic	ADJ
cana-1759	119	48	forces	force	NOUN
cana-1759	119	49	.	.	PUNCT
cana-1759	120	1	energy	energy	NOUN
cana-1759	120	2	equation	equation	NOUN
cana-1759	120	3	:	:	PUNCT
cana-1759	120	4	𝝏(𝝆𝑬	𝝏(𝝆𝑬	PROPN
cana-1759	120	5	)	)	PUNCT
cana-1759	120	6	𝝏𝒕	𝝏𝒕	PUNCT
cana-1759	121	1	+	+	CCONJ
cana-1759	121	2	𝛁.	𝛁.	NUM
cana-1759	121	3	(	(	PUNCT
cana-1759	121	4	𝒖(𝝆𝑬	𝒖(𝝆𝑬	X
cana-1759	121	5	+	+	CCONJ
cana-1759	121	6	𝒑	𝒑	X
cana-1759	121	7	)	)	PUNCT
cana-1759	121	8	)	)	PUNCT
cana-1759	122	1	=	=	SYM
cana-1759	122	2	𝛁.	𝛁.	NUM
cana-1759	122	3	(	(	PUNCT
cana-1759	122	4	𝐤𝛁𝐓	𝐤𝛁𝐓	NUM
cana-1759	122	5	)	)	PUNCT
cana-1759	123	1	+	+	CCONJ
cana-1759	123	2	𝝓	𝝓	X
cana-1759	123	3	where	where	SCONJ
cana-1759	123	4	e	e	NOUN
cana-1759	123	5	is	be	AUX
cana-1759	123	6	the	the	DET
cana-1759	123	7	total	total	ADJ
cana-1759	123	8	energy	energy	NOUN
cana-1759	123	9	per	per	ADP
cana-1759	123	10	unit	unit	NOUN
cana-1759	123	11	volume	volume	NOUN
cana-1759	123	12	,	,	PUNCT
cana-1759	123	13	k	k	PROPN
cana-1759	123	14	is	be	AUX
cana-1759	123	15	the	the	DET
cana-1759	123	16	thermal	thermal	ADJ
cana-1759	123	17	conductivity	conductivity	NOUN
cana-1759	123	18	,	,	PUNCT
cana-1759	123	19	t	t	PROPN
cana-1759	123	20	is	be	AUX
cana-1759	123	21	the	the	DET
cana-1759	123	22	temperature	temperature	NOUN
cana-1759	123	23	,	,	PUNCT
cana-1759	123	24	and	and	CCONJ
cana-1759	123	25	𝝓	𝝓	VERB
cana-1759	123	26	represents	represent	VERB
cana-1759	123	27	the	the	DET
cana-1759	123	28	viscous	viscous	ADJ
cana-1759	123	29	dissipation	dissipation	NOUN
cana-1759	123	30	.	.	PUNCT
cana-1759	124	1	these	these	DET
cana-1759	124	2	equations	equation	NOUN
cana-1759	124	3	are	be	AUX
cana-1759	124	4	traditionally	traditionally	ADV
cana-1759	124	5	solved	solve	VERB
cana-1759	124	6	under	under	ADP
cana-1759	124	7	specific	specific	ADJ
cana-1759	124	8	boundary	boundary	ADJ
cana-1759	124	9	conditions	condition	NOUN
cana-1759	124	10	and	and	CCONJ
cana-1759	124	11	assumptions	assumption	NOUN
cana-1759	124	12	regarding	regard	VERB
cana-1759	124	13	fluid	fluid	ADJ
cana-1759	124	14	properties	property	NOUN
cana-1759	124	15	,	,	PUNCT
cana-1759	124	16	such	such	ADJ
cana-1759	124	17	as	as	ADP
cana-1759	124	18	constant	constant	ADJ
cana-1759	124	19	viscosity	viscosity	NOUN
cana-1759	124	20	and	and	CCONJ
cana-1759	124	21	thermal	thermal	ADJ
cana-1759	124	22	conductivity	conductivity	NOUN
cana-1759	124	23	.	.	PUNCT
cana-1759	125	1	however	however	ADV
cana-1759	125	2	,	,	PUNCT
cana-1759	125	3	these	these	DET
cana-1759	125	4	assumptions	assumption	NOUN
cana-1759	125	5	are	be	AUX
cana-1759	125	6	often	often	ADV
cana-1759	125	7	not	not	PART
cana-1759	125	8	valid	valid	ADJ
cana-1759	125	9	in	in	ADP
cana-1759	125	10	many	many	ADJ
cana-1759	125	11	real	real	ADJ
cana-1759	125	12	-	-	PUNCT
cana-1759	125	13	world	world	NOUN
cana-1759	125	14	applications	application	NOUN
cana-1759	125	15	involving	involve	VERB
cana-1759	125	16	complex	complex	ADJ
cana-1759	125	17	fluids	fluid	NOUN
cana-1759	125	18	and	and	CCONJ
cana-1759	125	19	boundary	boundary	ADJ
cana-1759	125	20	conditions	condition	NOUN
cana-1759	125	21	,	,	PUNCT
cana-1759	125	22	necessitating	necessitate	VERB
cana-1759	125	23	the	the	DET
cana-1759	125	24	use	use	NOUN
cana-1759	125	25	of	of	ADP
cana-1759	125	26	advanced	advanced	ADJ
cana-1759	125	27	modelling	modelling	NOUN
cana-1759	125	28	techniques	technique	NOUN
cana-1759	125	29	.	.	PUNCT
cana-1759	126	1	3.2	3.2	NUM
cana-1759	126	2	.	.	PUNCT
cana-1759	126	3	fractional	fractional	ADJ
cana-1759	126	4	calculus	calculus	NOUN
cana-1759	126	5	in	in	ADP
cana-1759	126	6	heat	heat	NOUN
cana-1759	126	7	transfer	transfer	NOUN
cana-1759	126	8	and	and	CCONJ
cana-1759	126	9	fluid	fluid	NOUN
cana-1759	126	10	flow	flow	NOUN
cana-1759	126	11	fractional	fractional	ADJ
cana-1759	126	12	calculus	calculus	NOUN
cana-1759	126	13	extends	extend	VERB
cana-1759	126	14	the	the	DET
cana-1759	126	15	concept	concept	NOUN
cana-1759	126	16	of	of	ADP
cana-1759	126	17	differentiation	differentiation	NOUN
cana-1759	126	18	and	and	CCONJ
cana-1759	126	19	integration	integration	NOUN
cana-1759	126	20	to	to	ADP
cana-1759	126	21	non	non	ADJ
cana-1759	126	22	-	-	ADJ
cana-1759	126	23	integer	integer	ADJ
cana-1759	126	24	orders	order	NOUN
cana-1759	126	25	,	,	PUNCT
cana-1759	126	26	providing	provide	VERB
cana-1759	126	27	a	a	DET
cana-1759	126	28	powerful	powerful	ADJ
cana-1759	126	29	tool	tool	NOUN
cana-1759	126	30	for	for	ADP
cana-1759	126	31	modelling	model	VERB
cana-1759	126	32	systems	system	NOUN
cana-1759	126	33	with	with	ADP
cana-1759	126	34	memory	memory	NOUN
cana-1759	126	35	and	and	CCONJ
cana-1759	126	36	hereditary	hereditary	ADJ
cana-1759	126	37	properties	property	NOUN
cana-1759	126	38	,	,	PUNCT
cana-1759	126	39	which	which	PRON
cana-1759	126	40	are	be	AUX
cana-1759	126	41	common	common	ADJ
cana-1759	126	42	in	in	ADP
cana-1759	126	43	many	many	ADJ
cana-1759	126	44	heat	heat	NOUN
cana-1759	126	45	transfer	transfer	NOUN
cana-1759	126	46	and	and	CCONJ
cana-1759	126	47	fluid	fluid	ADJ
cana-1759	126	48	flow	flow	NOUN
cana-1759	126	49	problems	problem	NOUN
cana-1759	126	50	.	.	PUNCT
cana-1759	127	1	the	the	DET
cana-1759	127	2	use	use	NOUN
cana-1759	127	3	of	of	ADP
cana-1759	127	4	fractional	fractional	ADJ
cana-1759	127	5	derivatives	derivative	NOUN
cana-1759	127	6	allows	allow	VERB
cana-1759	127	7	for	for	ADP
cana-1759	127	8	a	a	DET
cana-1759	127	9	more	more	ADV
cana-1759	127	10	accurate	accurate	ADJ
cana-1759	127	11	representation	representation	NOUN
cana-1759	127	12	of	of	ADP
cana-1759	127	13	anomalous	anomalous	ADJ
cana-1759	127	14	diffusion	diffusion	NOUN
cana-1759	127	15	and	and	CCONJ
cana-1759	127	16	viscoelastic	viscoelastic	NOUN
cana-1759	127	17	behavior	behavior	NOUN
cana-1759	127	18	in	in	ADP
cana-1759	127	19	fluids	fluid	NOUN
cana-1759	127	20	.	.	PUNCT
cana-1759	128	1	fractional	fractional	ADJ
cana-1759	128	2	derivatives	derivative	NOUN
cana-1759	128	3	:	:	PUNCT
cana-1759	128	4	commonly	commonly	ADV
cana-1759	128	5	used	use	VERB
cana-1759	128	6	fractional	fractional	ADJ
cana-1759	128	7	derivatives	derivative	NOUN
cana-1759	128	8	in	in	ADP
cana-1759	128	9	heat	heat	NOUN
cana-1759	128	10	transfer	transfer	NOUN
cana-1759	128	11	and	and	CCONJ
cana-1759	128	12	fluid	fluid	NOUN
cana-1759	128	13	flow	flow	NOUN
cana-1759	128	14	modelling	modelling	NOUN
cana-1759	128	15	include	include	VERB
cana-1759	128	16	the	the	DET
cana-1759	128	17	caputo	caputo	PROPN
cana-1759	128	18	derivative	derivative	NOUN
cana-1759	128	19	,	,	PUNCT
cana-1759	128	20	the	the	DET
cana-1759	128	21	atangana	atangana	PROPN
cana-1759	128	22	–	–	PUNCT
cana-1759	128	23	baleanu	baleanu	ADJ
cana-1759	128	24	derivative	derivative	NOUN
cana-1759	128	25	,	,	PUNCT
cana-1759	128	26	and	and	CCONJ
cana-1759	128	27	the	the	DET
cana-1759	128	28	conformable	conformable	ADJ
cana-1759	128	29	derivative	derivative	NOUN
cana-1759	128	30	.	.	PUNCT
cana-1759	129	1	caputo	caputo	PROPN
cana-1759	129	2	fractional	fractional	PROPN
cana-1759	129	3	derivative	derivative	NOUN
cana-1759	129	4	:	:	PUNCT
cana-1759	129	5	𝑫𝜶f(t	𝑫𝜶f(t	PROPN
cana-1759	129	6	)	)	PUNCT
cana-1759	129	7	=	=	SYM
cana-1759	129	8	𝟏	𝟏	NUM
cana-1759	129	9	𝚪(𝒏−𝜶	𝚪(𝒏−𝜶	NOUN
cana-1759	129	10	)	)	PUNCT
cana-1759	129	11	∫	∫	NOUN
cana-1759	129	12	𝒇𝒏(𝝉	𝒇𝒏(𝝉	PUNCT
cana-1759	129	13	)	)	PUNCT
cana-1759	129	14	(	(	PUNCT
cana-1759	129	15	𝒕−𝝉)𝜶−𝒏+𝟏	𝒕−𝝉)𝜶−𝒏+𝟏	X
cana-1759	129	16	𝒕	𝒕	X
cana-1759	129	17	𝟎	𝟎	X
cana-1759	129	18	d𝝉	d𝝉	PROPN
cana-1759	129	19	(	(	PUNCT
cana-1759	129	20	n-1	n-1	X
cana-1759	129	21	<	<	X
cana-1759	129	22	α	α	X
cana-1759	129	23	<	<	X
cana-1759	129	24	n	n	CCONJ
cana-1759	129	25	)	)	PUNCT
cana-1759	129	26	where	where	SCONJ
cana-1759	129	27	𝛤	𝛤	PROPN
cana-1759	129	28	(	(	PUNCT
cana-1759	129	29	.	.	PUNCT
cana-1759	129	30	)	)	PUNCT
cana-1759	129	31	is	be	AUX
cana-1759	129	32	the	the	DET
cana-1759	129	33	gamma	gamma	PROPN
cana-1759	129	34	function	function	NOUN
cana-1759	129	35	,	,	PUNCT
cana-1759	129	36	𝛼	𝛼	PROPN
cana-1759	129	37	is	be	AUX
cana-1759	129	38	the	the	DET
cana-1759	129	39	fractional	fractional	ADJ
cana-1759	129	40	order	order	NOUN
cana-1759	129	41	,	,	PUNCT
cana-1759	129	42	and	and	CCONJ
cana-1759	129	43	𝑓𝑛(𝜏	𝑓𝑛(𝜏	NOUN
cana-1759	129	44	)	)	PUNCT
cana-1759	129	45	is	be	AUX
cana-1759	129	46	the	the	DET
cana-1759	129	47	n	n	ADV
cana-1759	129	48	-	-	PUNCT
cana-1759	129	49	th	th	X
cana-1759	129	50	derivative	derivative	NOUN
cana-1759	129	51	of	of	ADP
cana-1759	129	52	f.	f.	PROPN
cana-1759	129	53	atangana	atangana	PROPN
cana-1759	129	54	–	–	PUNCT
cana-1759	129	55	baleanu	baleanu	ADJ
cana-1759	129	56	fractional	fractional	ADJ
cana-1759	129	57	derivative	derivative	NOUN
cana-1759	129	58	:	:	PUNCT
cana-1759	129	59	this	this	DET
cana-1759	129	60	derivative	derivative	NOUN
cana-1759	129	61	is	be	AUX
cana-1759	129	62	defined	define	VERB
cana-1759	129	63	in	in	ADP
cana-1759	129	64	the	the	DET
cana-1759	129	65	caputo	caputo	PROPN
cana-1759	129	66	sense	sense	NOUN
cana-1759	129	67	and	and	CCONJ
cana-1759	129	68	provides	provide	VERB
cana-1759	129	69	a	a	DET
cana-1759	129	70	non	non	ADJ
cana-1759	129	71	-	-	ADJ
cana-1759	129	72	singular	singular	ADJ
cana-1759	129	73	kernel	kernel	NOUN
cana-1759	129	74	that	that	PRON
cana-1759	129	75	is	be	AUX
cana-1759	129	76	useful	useful	ADJ
cana-1759	129	77	for	for	ADP
cana-1759	129	78	modelling	model	VERB
cana-1759	129	79	systems	system	NOUN
cana-1759	129	80	with	with	ADP
cana-1759	129	81	non	non	ADJ
cana-1759	129	82	-	-	ADJ
cana-1759	129	83	local	local	ADJ
cana-1759	129	84	and	and	CCONJ
cana-1759	129	85	memory	memory	NOUN
cana-1759	129	86	-	-	PUNCT
cana-1759	129	87	dependent	dependent	ADJ
cana-1759	129	88	behaviours	behaviour	NOUN
cana-1759	129	89	:	:	PUNCT
cana-1759	129	90	𝑫𝜶	𝑫𝜶	PROPN
cana-1759	129	91	𝑨𝑩	𝑨𝑩	PROPN
cana-1759	129	92	f(t	f(t	PROPN
cana-1759	129	93	)	)	PUNCT
cana-1759	129	94	=	=	SYM
cana-1759	130	1	𝑩(𝜶	𝑩(𝜶	X
cana-1759	130	2	)	)	PUNCT
cana-1759	130	3	𝟏−𝜶	𝟏−𝜶	PUNCT
cana-1759	131	1	∫	∫	PROPN
cana-1759	131	2	−	−	PROPN
cana-1759	132	1	(	(	PUNCT
cana-1759	132	2	𝒕−𝝉)𝜶	𝒕−𝝉)𝜶	PROPN
cana-1759	132	3	𝑩(𝜶	𝑩(𝜶	PROPN
cana-1759	132	4	)	)	PUNCT
cana-1759	132	5	𝒕	𝒕	PRON
cana-1759	132	6	𝟎	𝟎	X
cana-1759	132	7	𝒇′(𝝉)𝑬𝜶	𝒇′(𝝉)𝑬𝜶	X
cana-1759	132	8	d𝝉	d𝝉	X
cana-1759	132	9	where	where	SCONJ
cana-1759	132	10	b(𝛼	b(𝛼	PROPN
cana-1759	132	11	)	)	PUNCT
cana-1759	132	12	is	be	AUX
cana-1759	132	13	a	a	DET
cana-1759	132	14	normalization	normalization	NOUN
cana-1759	132	15	function	function	NOUN
cana-1759	132	16	,	,	PUNCT
cana-1759	132	17	and	and	CCONJ
cana-1759	132	18	𝐸𝛼	𝐸𝛼	PROPN
cana-1759	132	19	(	(	PUNCT
cana-1759	132	20	.	.	PUNCT
cana-1759	132	21	)	)	PUNCT
cana-1759	133	1	denotes	denote	VERB
cana-1759	133	2	the	the	DET
cana-1759	133	3	mittag	mittag	ADJ
cana-1759	133	4	-	-	PUNCT
cana-1759	133	5	leffler	leffler	NOUN
cana-1759	133	6	function	function	NOUN
cana-1759	133	7	.	.	PUNCT
cana-1759	134	1	these	these	DET
cana-1759	134	2	fractional	fractional	ADJ
cana-1759	134	3	derivatives	derivative	NOUN
cana-1759	134	4	modify	modify	VERB
cana-1759	134	5	the	the	DET
cana-1759	134	6	standard	standard	ADJ
cana-1759	134	7	forms	form	NOUN
cana-1759	134	8	of	of	ADP
cana-1759	134	9	the	the	DET
cana-1759	134	10	governing	govern	VERB
cana-1759	134	11	equations	equation	NOUN
cana-1759	134	12	,	,	PUNCT
cana-1759	134	13	leading	lead	VERB
cana-1759	134	14	to	to	ADP
cana-1759	134	15	fractional	fractional	ADJ
cana-1759	134	16	partial	partial	ADJ
cana-1759	134	17	differential	differential	NOUN
cana-1759	134	18	equations	equation	NOUN
cana-1759	134	19	(	(	PUNCT
cana-1759	134	20	fpdes	fpde	NOUN
cana-1759	134	21	)	)	PUNCT
cana-1759	134	22	that	that	PRON
cana-1759	134	23	better	well	ADV
cana-1759	134	24	capture	capture	VERB
cana-1759	134	25	the	the	DET
cana-1759	134	26	underlying	underlie	VERB
cana-1759	134	27	physics	physics	NOUN
cana-1759	134	28	of	of	ADP
cana-1759	134	29	communications	communication	NOUN
cana-1759	134	30	on	on	ADP
cana-1759	134	31	applied	apply	VERB
cana-1759	134	32	nonlinear	nonlinear	ADJ
cana-1759	134	33	analysis	analysis	NOUN
cana-1759	134	34	issn	issn	NOUN
cana-1759	134	35	:	:	PUNCT
cana-1759	134	36	1074	1074	NUM
cana-1759	134	37	-	-	PUNCT
cana-1759	134	38	133x	133x	NUM
cana-1759	134	39	vol	vol	NOUN
cana-1759	134	40	32	32	NUM
cana-1759	134	41	no	no	NOUN
cana-1759	134	42	.	.	NOUN
cana-1759	134	43	2	2	NUM
cana-1759	134	44	(	(	PUNCT
cana-1759	134	45	2025	2025	NUM
cana-1759	134	46	)	)	PUNCT
cana-1759	134	47	477	477	NUM
cana-1759	134	48	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	134	49	anomalous	anomalous	ADJ
cana-1759	134	50	transport	transport	NOUN
cana-1759	134	51	and	and	CCONJ
cana-1759	134	52	diffusion	diffusion	NOUN
cana-1759	134	53	phenomena	phenomenon	NOUN
cana-1759	134	54	in	in	ADP
cana-1759	134	55	fluids	fluid	NOUN
cana-1759	134	56	.	.	PUNCT
cana-1759	135	1	for	for	ADP
cana-1759	135	2	example	example	NOUN
cana-1759	135	3	,	,	PUNCT
cana-1759	135	4	the	the	DET
cana-1759	135	5	fractional	fractional	ADJ
cana-1759	135	6	energy	energy	NOUN
cana-1759	135	7	equation	equation	NOUN
cana-1759	135	8	can	can	AUX
cana-1759	135	9	be	be	AUX
cana-1759	135	10	written	write	VERB
cana-1759	135	11	as	as	ADP
cana-1759	135	12	:	:	PUNCT
cana-1759	135	13	𝑫𝒕	𝑫𝒕	NOUN
cana-1759	135	14	𝜶𝑻	𝜶𝑻	VERB
cana-1759	135	15	+	+	NUM
cana-1759	135	16	u.	u.	NOUN
cana-1759	135	17	𝛁𝐓	𝛁𝐓	PROPN
cana-1759	135	18	=	=	PUNCT
cana-1759	135	19	k𝛁𝟐t	k𝛁𝟐t	VERB
cana-1759	135	20	where	where	SCONJ
cana-1759	135	21	𝐷𝑡	𝐷𝑡	PROPN
cana-1759	135	22	𝛼𝑇	𝛼𝑇	PROPN
cana-1759	135	23	represents	represent	VERB
cana-1759	135	24	the	the	DET
cana-1759	135	25	fractional	fractional	ADJ
cana-1759	135	26	time	time	NOUN
cana-1759	135	27	derivative	derivative	NOUN
cana-1759	135	28	of	of	ADP
cana-1759	135	29	order	order	NOUN
cana-1759	135	30	α	α	NOUN
cana-1759	135	31	.	.	PROPN
cana-1759	135	32	3.3	3.3	NUM
cana-1759	135	33	.	.	PUNCT
cana-1759	136	1	non	non	ADJ
cana-1759	136	2	-	-	ADJ
cana-1759	136	3	newtonian	newtonian	ADJ
cana-1759	136	4	fluid	fluid	ADJ
cana-1759	136	5	models	model	NOUN
cana-1759	136	6	*	*	PUNCT
cana-1759	136	7	*	*	PUNCT
cana-1759	136	8	non	non	ADJ
cana-1759	136	9	-	-	ADJ
cana-1759	136	10	newtonian	newtonian	ADJ
cana-1759	136	11	fluids	fluid	NOUN
cana-1759	136	12	are	be	AUX
cana-1759	136	13	characterized	characterize	VERB
cana-1759	136	14	by	by	ADP
cana-1759	136	15	a	a	DET
cana-1759	136	16	non	non	ADJ
cana-1759	136	17	-	-	ADJ
cana-1759	136	18	linear	linear	ADJ
cana-1759	136	19	relationship	relationship	NOUN
cana-1759	136	20	between	between	ADP
cana-1759	136	21	shear	shear	NOUN
cana-1759	136	22	stress	stress	NOUN
cana-1759	136	23	and	and	CCONJ
cana-1759	136	24	shear	shear	NOUN
cana-1759	136	25	rate	rate	NOUN
cana-1759	136	26	,	,	PUNCT
cana-1759	136	27	unlike	unlike	ADP
cana-1759	136	28	newtonian	newtonian	ADJ
cana-1759	136	29	fluids	fluid	NOUN
cana-1759	136	30	that	that	PRON
cana-1759	136	31	have	have	VERB
cana-1759	136	32	a	a	DET
cana-1759	136	33	constant	constant	ADJ
cana-1759	136	34	viscosity	viscosity	NOUN
cana-1759	136	35	.	.	PUNCT
cana-1759	137	1	the	the	DET
cana-1759	137	2	rheological	rheological	ADJ
cana-1759	137	3	properties	property	NOUN
cana-1759	137	4	of	of	ADP
cana-1759	137	5	nonnewtonian	nonnewtonian	NOUN
cana-1759	137	6	fluids	fluid	NOUN
cana-1759	137	7	can	can	AUX
cana-1759	137	8	be	be	AUX
cana-1759	137	9	modeled	model	VERB
cana-1759	137	10	using	use	VERB
cana-1759	137	11	several	several	ADJ
cana-1759	137	12	different	different	ADJ
cana-1759	137	13	models	model	NOUN
cana-1759	137	14	,	,	PUNCT
cana-1759	137	15	each	each	PRON
cana-1759	137	16	tailored	tailor	VERB
cana-1759	137	17	to	to	ADP
cana-1759	137	18	specific	specific	ADJ
cana-1759	137	19	types	type	NOUN
cana-1759	137	20	of	of	ADP
cana-1759	137	21	nonnewtonian	nonnewtonian	ADJ
cana-1759	137	22	behavior	behavior	NOUN
cana-1759	137	23	:	:	PUNCT
cana-1759	137	24	power	power	NOUN
cana-1759	137	25	-	-	PUNCT
cana-1759	137	26	law	law	NOUN
cana-1759	137	27	model	model	NOUN
cana-1759	137	28	:	:	PUNCT
cana-1759	137	29	used	use	VERB
cana-1759	137	30	for	for	ADP
cana-1759	137	31	shear	shear	NOUN
cana-1759	137	32	-	-	PUNCT
cana-1759	137	33	thinning	thin	VERB
cana-1759	137	34	and	and	CCONJ
cana-1759	137	35	shear	shear	NOUN
cana-1759	137	36	-	-	PUNCT
cana-1759	137	37	thickening	thickening	NOUN
cana-1759	137	38	fluids	fluid	NOUN
cana-1759	137	39	:	:	PUNCT
cana-1759	137	40	𝝉	𝝉	X
cana-1759	137	41	=	=	SYM
cana-1759	137	42	k	k	X
cana-1759	137	43	𝝏𝒖	𝝏𝒖	PROPN
cana-1759	137	44	𝝏𝒚	𝝏𝒚	PROPN
cana-1759	137	45	𝒏	𝒏	PROPN
cana-1759	137	46	where	where	SCONJ
cana-1759	137	47	𝜏	𝜏	NOUN
cana-1759	137	48	is	be	AUX
cana-1759	137	49	the	the	DET
cana-1759	137	50	shear	shear	NOUN
cana-1759	137	51	stress	stress	NOUN
cana-1759	137	52	,	,	PUNCT
cana-1759	137	53	k	k	PROPN
cana-1759	137	54	is	be	AUX
cana-1759	137	55	the	the	DET
cana-1759	137	56	consistency	consistency	NOUN
cana-1759	137	57	index	index	NOUN
cana-1759	137	58	,	,	PUNCT
cana-1759	137	59	and	and	CCONJ
cana-1759	137	60	n	n	PRON
cana-1759	137	61	is	be	AUX
cana-1759	137	62	the	the	DET
cana-1759	137	63	flow	flow	NOUN
cana-1759	137	64	behavior	behavior	NOUN
cana-1759	137	65	index	index	NOUN
cana-1759	137	66	with	with	ADP
cana-1759	137	67	(	(	PUNCT
cana-1759	137	68	n<1	n<1	PROPN
cana-1759	137	69	)	)	PUNCT
cana-1759	137	70	for	for	ADP
cana-1759	137	71	shear	shear	NOUN
cana-1759	137	72	-	-	PUNCT
cana-1759	137	73	thinning	thin	VERB
cana-1759	137	74	fluids	fluid	NOUN
cana-1759	137	75	and	and	CCONJ
cana-1759	137	76	(	(	PUNCT
cana-1759	137	77	n>1	n>1	NOUN
cana-1759	137	78	)	)	PUNCT
cana-1759	137	79	for	for	ADP
cana-1759	137	80	shear	shear	NOUN
cana-1759	137	81	-	-	PUNCT
cana-1759	137	82	thickening	thickening	NOUN
cana-1759	137	83	fluids	fluid	NOUN
cana-1759	137	84	.	.	PUNCT
cana-1759	138	1	bingham	bingham	PROPN
cana-1759	138	2	plastic	plastic	PROPN
cana-1759	138	3	model	model	NOUN
cana-1759	138	4	:	:	PUNCT
cana-1759	138	5	for	for	ADP
cana-1759	138	6	fluids	fluid	NOUN
cana-1759	138	7	that	that	PRON
cana-1759	138	8	behave	behave	VERB
cana-1759	138	9	as	as	ADP
cana-1759	138	10	a	a	DET
cana-1759	138	11	solid	solid	ADJ
cana-1759	138	12	below	below	ADP
cana-1759	138	13	a	a	DET
cana-1759	138	14	certain	certain	ADJ
cana-1759	138	15	yield	yield	NOUN
cana-1759	138	16	stress	stress	NOUN
cana-1759	138	17	𝜏0	𝜏0	PROPN
cana-1759	138	18	:	:	PUNCT
cana-1759	138	19	𝝉	𝝉	X
cana-1759	138	20	=	=	PUNCT
cana-1759	138	21	𝝉𝟎	𝝉𝟎	PROPN
cana-1759	138	22	+	+	CCONJ
cana-1759	138	23	𝜼	𝜼	PROPN
cana-1759	138	24	𝝏𝒖	𝝏𝒖	PROPN
cana-1759	138	25	𝝏𝒚	𝝏𝒚	PROPN
cana-1759	138	26	if	if	SCONJ
cana-1759	138	27	𝝉	𝝉	PROPN
cana-1759	138	28	>	>	X
cana-1759	138	29	𝝉𝟎	𝝉𝟎	PROPN
cana-1759	138	30	carreau	carreau	PROPN
cana-1759	138	31	-	-	PUNCT
cana-1759	138	32	yasuda	yasuda	PROPN
cana-1759	138	33	model	model	PROPN
cana-1759	138	34	:	:	PUNCT
cana-1759	138	35	a	a	DET
cana-1759	138	36	more	more	ADV
cana-1759	138	37	generalized	generalized	ADJ
cana-1759	138	38	model	model	NOUN
cana-1759	138	39	that	that	PRON
cana-1759	138	40	can	can	AUX
cana-1759	138	41	represent	represent	VERB
cana-1759	138	42	both	both	DET
cana-1759	138	43	shear	shear	NOUN
cana-1759	138	44	-	-	PUNCT
cana-1759	138	45	thinning	thin	VERB
cana-1759	138	46	and	and	CCONJ
cana-1759	138	47	shearthickening	shearthickening	NOUN
cana-1759	138	48	behaviours	behaviour	NOUN
cana-1759	138	49	over	over	ADP
cana-1759	138	50	a	a	DET
cana-1759	138	51	wide	wide	ADJ
cana-1759	138	52	range	range	NOUN
cana-1759	138	53	of	of	ADP
cana-1759	138	54	shear	shear	NOUN
cana-1759	138	55	rates	rate	NOUN
cana-1759	138	56	:	:	PUNCT
cana-1759	138	57	𝜼(	𝜼(	PROPN
cana-1759	138	58	�	�	PROPN
cana-1759	138	59	̇	̇	PROPN
cana-1759	138	60	�	�	PROPN
cana-1759	138	61	)	)	PUNCT
cana-1759	138	62	=	=	SYM
cana-1759	138	63	𝜼∞	𝜼∞	X
cana-1759	139	1	+	+	CCONJ
cana-1759	139	2	(	(	PUNCT
cana-1759	139	3	𝜼𝟎	𝜼𝟎	PROPN
cana-1759	139	4	𝜼∞	𝜼∞	PROPN
cana-1759	139	5	)	)	PUNCT
cana-1759	140	1	[	[	X
cana-1759	140	2	𝟏	𝟏	X
cana-1759	140	3	+	+	NUM
cana-1759	140	4	(	(	PUNCT
cana-1759	140	5	𝛌	𝛌	PROPN
cana-1759	140	6	�	�	PROPN
cana-1759	140	7	̇	̇	VERB
cana-1759	140	8	�	�	PROPN
cana-1759	140	9	)𝒂](𝐧−𝟏)/𝐚	)𝒂](𝐧−𝟏)/𝐚	PART
cana-1759	140	10	where	where	SCONJ
cana-1759	140	11	𝜂(	𝜂(	PROPN
cana-1759	140	12	�	�	PROPN
cana-1759	140	13	̇	̇	PROPN
cana-1759	140	14	�	�	PROPN
cana-1759	140	15	)	)	PUNCT
cana-1759	140	16	is	be	AUX
cana-1759	140	17	the	the	DET
cana-1759	140	18	apparent	apparent	ADJ
cana-1759	140	19	viscosity	viscosity	NOUN
cana-1759	140	20	,	,	PUNCT
cana-1759	140	21	𝜂0	𝜂0	NOUN
cana-1759	140	22	and	and	CCONJ
cana-1759	140	23	𝜂∞	𝜂∞	NUM
cana-1759	140	24	are	be	AUX
cana-1759	140	25	the	the	DET
cana-1759	140	26	zero	zero	NUM
cana-1759	140	27	-	-	PUNCT
cana-1759	140	28	shear	shear	NOUN
cana-1759	140	29	and	and	CCONJ
cana-1759	140	30	infinite	infinite	ADJ
cana-1759	140	31	-	-	PUNCT
cana-1759	140	32	shear	shear	NOUN
cana-1759	140	33	viscosities	viscosity	NOUN
cana-1759	140	34	,	,	PUNCT
cana-1759	140	35	λ	λ	PROPN
cana-1759	140	36	is	be	AUX
cana-1759	140	37	a	a	DET
cana-1759	140	38	time	time	NOUN
cana-1759	140	39	constant	constant	ADJ
cana-1759	140	40	,	,	PUNCT
cana-1759	140	41	a	a	PRON
cana-1759	140	42	is	be	AUX
cana-1759	140	43	a	a	DET
cana-1759	140	44	dimensionless	dimensionless	NOUN
cana-1759	140	45	parameter	parameter	NOUN
cana-1759	140	46	,	,	PUNCT
cana-1759	140	47	and	and	CCONJ
cana-1759	140	48	�	�	PROPN
cana-1759	140	49	̇	̇	PROPN
cana-1759	140	50	�	�	PROPN
cana-1759	140	51	is	be	AUX
cana-1759	140	52	the	the	DET
cana-1759	140	53	shear	shear	NOUN
cana-1759	140	54	rate	rate	NOUN
cana-1759	140	55	.	.	PUNCT
cana-1759	141	1	these	these	DET
cana-1759	141	2	models	model	NOUN
cana-1759	141	3	lead	lead	VERB
cana-1759	141	4	to	to	ADP
cana-1759	141	5	modified	modify	VERB
cana-1759	141	6	forms	form	NOUN
cana-1759	141	7	of	of	ADP
cana-1759	141	8	the	the	DET
cana-1759	141	9	navier	navier	NOUN
cana-1759	141	10	-	-	PUNCT
cana-1759	141	11	stokes	stoke	NOUN
cana-1759	141	12	equations	equation	NOUN
cana-1759	141	13	to	to	PART
cana-1759	141	14	account	account	VERB
cana-1759	141	15	for	for	ADP
cana-1759	141	16	the	the	DET
cana-1759	141	17	varying	vary	VERB
cana-1759	141	18	viscosity	viscosity	NOUN
cana-1759	141	19	and	and	CCONJ
cana-1759	141	20	yield	yield	VERB
cana-1759	141	21	stress	stress	NOUN
cana-1759	141	22	effects	effect	NOUN
cana-1759	141	23	in	in	ADP
cana-1759	141	24	non	non	ADJ
cana-1759	141	25	-	-	ADJ
cana-1759	141	26	newtonian	newtonian	ADJ
cana-1759	141	27	fluids	fluid	NOUN
cana-1759	141	28	,	,	PUNCT
cana-1759	141	29	making	make	VERB
cana-1759	141	30	them	they	PRON
cana-1759	141	31	suitable	suitable	ADJ
cana-1759	141	32	for	for	ADP
cana-1759	141	33	applications	application	NOUN
cana-1759	141	34	such	such	ADJ
cana-1759	141	35	as	as	ADP
cana-1759	141	36	polymer	polymer	NOUN
cana-1759	141	37	processing	processing	NOUN
cana-1759	141	38	,	,	PUNCT
cana-1759	141	39	food	food	NOUN
cana-1759	141	40	manufacturing	manufacturing	NOUN
cana-1759	141	41	,	,	PUNCT
cana-1759	141	42	and	and	CCONJ
cana-1759	141	43	blood	blood	NOUN
cana-1759	141	44	flow	flow	NOUN
cana-1759	141	45	modelling	modelling	NOUN
cana-1759	141	46	.	.	PUNCT
cana-1759	142	1	3.4	3.4	NUM
cana-1759	142	2	.	.	PUNCT
cana-1759	142	3	nanofluid	nanofluid	ADJ
cana-1759	142	4	dynamics	dynamic	NOUN
cana-1759	142	5	nanofluids	nanofluid	NOUN
cana-1759	142	6	,	,	PUNCT
cana-1759	142	7	which	which	PRON
cana-1759	142	8	consist	consist	VERB
cana-1759	142	9	of	of	ADP
cana-1759	142	10	a	a	DET
cana-1759	142	11	base	base	ADJ
cana-1759	142	12	fluid	fluid	NOUN
cana-1759	142	13	containing	contain	VERB
cana-1759	142	14	suspended	suspend	VERB
cana-1759	142	15	nanoparticles	nanoparticle	NOUN
cana-1759	142	16	,	,	PUNCT
cana-1759	142	17	exhibit	exhibit	VERB
cana-1759	142	18	enhanced	enhance	VERB
cana-1759	142	19	thermal	thermal	ADJ
cana-1759	142	20	properties	property	NOUN
cana-1759	142	21	compared	compare	VERB
cana-1759	142	22	to	to	ADP
cana-1759	142	23	conventional	conventional	ADJ
cana-1759	142	24	fluids	fluid	NOUN
cana-1759	142	25	.	.	PUNCT
cana-1759	143	1	the	the	DET
cana-1759	143	2	mathematical	mathematical	ADJ
cana-1759	143	3	modelling	modelling	NOUN
cana-1759	143	4	of	of	ADP
cana-1759	143	5	nanofluids	nanofluid	NOUN
cana-1759	143	6	involves	involve	VERB
cana-1759	143	7	modifying	modify	VERB
cana-1759	143	8	the	the	DET
cana-1759	143	9	classical	classical	ADJ
cana-1759	143	10	heat	heat	NOUN
cana-1759	143	11	transfer	transfer	NOUN
cana-1759	143	12	and	and	CCONJ
cana-1759	143	13	fluid	fluid	ADJ
cana-1759	143	14	flow	flow	NOUN
cana-1759	143	15	equations	equation	NOUN
cana-1759	143	16	to	to	PART
cana-1759	143	17	account	account	VERB
cana-1759	143	18	for	for	ADP
cana-1759	143	19	the	the	DET
cana-1759	143	20	effects	effect	NOUN
cana-1759	143	21	of	of	ADP
cana-1759	143	22	nanoparticle	nanoparticle	NOUN
cana-1759	143	23	volume	volume	NOUN
cana-1759	143	24	fraction	fraction	NOUN
cana-1759	143	25	,	,	PUNCT
cana-1759	143	26	size	size	NOUN
cana-1759	143	27	,	,	PUNCT
cana-1759	143	28	shape	shape	NOUN
cana-1759	143	29	,	,	PUNCT
cana-1759	143	30	and	and	CCONJ
cana-1759	143	31	thermal	thermal	ADJ
cana-1759	143	32	properties	property	NOUN
cana-1759	143	33	.	.	PUNCT
cana-1759	144	1	buongiorno	buongiorno	PROPN
cana-1759	144	2	model	model	PROPN
cana-1759	144	3	:	:	PUNCT
cana-1759	144	4	this	this	DET
cana-1759	144	5	model	model	NOUN
cana-1759	144	6	considers	consider	VERB
cana-1759	144	7	the	the	DET
cana-1759	144	8	effects	effect	NOUN
cana-1759	144	9	of	of	ADP
cana-1759	144	10	brownian	brownian	ADJ
cana-1759	144	11	motion	motion	NOUN
cana-1759	144	12	and	and	CCONJ
cana-1759	144	13	thermophoresis	thermophoresis	NOUN
cana-1759	144	14	in	in	ADP
cana-1759	144	15	nanofluid	nanofluid	ADJ
cana-1759	144	16	flows	flow	NOUN
cana-1759	144	17	,	,	PUNCT
cana-1759	144	18	which	which	PRON
cana-1759	144	19	are	be	AUX
cana-1759	144	20	significant	significant	ADJ
cana-1759	144	21	at	at	ADP
cana-1759	144	22	the	the	DET
cana-1759	144	23	nanoscale	nanoscale	NOUN
cana-1759	144	24	:	:	PUNCT
cana-1759	144	25	u.	u.	PROPN
cana-1759	144	26	𝛁𝐓	𝛁𝐓	PROPN
cana-1759	144	27	=	=	PUNCT
cana-1759	144	28	𝛁.	𝛁.	NUM
cana-1759	144	29	(	(	PUNCT
cana-1759	144	30	𝑘𝑛𝑓𝛁𝐓	𝑘𝑛𝑓𝛁𝐓	PROPN
cana-1759	144	31	)	)	PUNCT
cana-1759	144	32	+	+	CCONJ
cana-1759	144	33	𝜇	𝜇	DET
cana-1759	144	34	𝜌𝑛𝑓	𝜌𝑛𝑓	NOUN
cana-1759	144	35	(	(	PUNCT
cana-1759	144	36	𝛁.(𝐷𝑩𝛁𝐂	𝛁.(𝐷𝑩𝛁𝐂	ADV
cana-1759	144	37	+	+	ADJ
cana-1759	144	38	𝐷𝑇𝛁𝐓	𝐷𝑇𝛁𝐓	PROPN
cana-1759	144	39	)	)	PUNCT
cana-1759	144	40	)	)	PUNCT
cana-1759	144	41	where	where	SCONJ
cana-1759	144	42	𝑘𝑛𝑓is	𝑘𝑛𝑓is	PROPN
cana-1759	144	43	the	the	DET
cana-1759	144	44	thermal	thermal	ADJ
cana-1759	144	45	conductivity	conductivity	NOUN
cana-1759	144	46	of	of	ADP
cana-1759	144	47	the	the	DET
cana-1759	144	48	nanofluid	nanofluid	NOUN
cana-1759	144	49	,	,	PUNCT
cana-1759	144	50	𝜌𝑛𝑓	𝜌𝑛𝑓	NOUN
cana-1759	144	51	is	be	AUX
cana-1759	144	52	the	the	DET
cana-1759	144	53	density	density	NOUN
cana-1759	144	54	,	,	PUNCT
cana-1759	144	55	𝐷𝑩	𝐷𝑩	NOUN
cana-1759	144	56	is	be	AUX
cana-1759	144	57	the	the	DET
cana-1759	144	58	brownian	brownian	ADJ
cana-1759	144	59	diffusion	diffusion	NOUN
cana-1759	144	60	coefficient	coefficient	NOUN
cana-1759	144	61	,	,	PUNCT
cana-1759	144	62	and	and	CCONJ
cana-1759	144	63	𝐷𝑻is	𝐷𝑻is	PRON
cana-1759	144	64	the	the	DET
cana-1759	144	65	thermophoretic	thermophoretic	ADJ
cana-1759	144	66	diffusion	diffusion	NOUN
cana-1759	144	67	coefficient	coefficient	NOUN
cana-1759	144	68	.	.	PUNCT
cana-1759	145	1	communications	communication	NOUN
cana-1759	145	2	on	on	ADP
cana-1759	145	3	applied	apply	VERB
cana-1759	145	4	nonlinear	nonlinear	ADJ
cana-1759	145	5	analysis	analysis	NOUN
cana-1759	145	6	issn	issn	NOUN
cana-1759	145	7	:	:	PUNCT
cana-1759	145	8	1074	1074	NUM
cana-1759	145	9	-	-	PUNCT
cana-1759	145	10	133x	133x	NUM
cana-1759	145	11	vol	vol	NOUN
cana-1759	145	12	32	32	NUM
cana-1759	145	13	no	no	NOUN
cana-1759	145	14	.	.	NOUN
cana-1759	145	15	2	2	NUM
cana-1759	145	16	(	(	PUNCT
cana-1759	145	17	2025	2025	NUM
cana-1759	145	18	)	)	PUNCT
cana-1759	145	19	478	478	NUM
cana-1759	145	20	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1759	145	21	modified	modify	VERB
cana-1759	145	22	navier	navier	NOUN
cana-1759	145	23	-	-	PUNCT
cana-1759	145	24	stokes	stoke	NOUN
cana-1759	145	25	equations	equation	NOUN
cana-1759	145	26	:	:	PUNCT
cana-1759	145	27	the	the	DET
cana-1759	145	28	addition	addition	NOUN
cana-1759	145	29	of	of	ADP
cana-1759	145	30	nanoparticles	nanoparticle	NOUN
cana-1759	145	31	alters	alter	VERB
cana-1759	145	32	the	the	DET
cana-1759	145	33	viscosity	viscosity	NOUN
cana-1759	145	34	and	and	CCONJ
cana-1759	145	35	thermal	thermal	ADJ
cana-1759	145	36	conductivity	conductivity	NOUN
cana-1759	145	37	of	of	ADP
cana-1759	145	38	the	the	DET
cana-1759	145	39	base	base	NOUN
cana-1759	145	40	fluid	fluid	NOUN
cana-1759	145	41	,	,	PUNCT
cana-1759	145	42	requiring	require	VERB
cana-1759	145	43	adjustments	adjustment	NOUN
cana-1759	145	44	to	to	ADP
cana-1759	145	45	the	the	DET
cana-1759	145	46	navier	navier	NOUN
cana-1759	145	47	-	-	PUNCT
cana-1759	145	48	stokes	stokes	PROPN
cana-1759	145	49	and	and	CCONJ
cana-1759	145	50	energy	energy	NOUN
cana-1759	145	51	equations	equation	NOUN
cana-1759	145	52	:	:	PUNCT
cana-1759	145	53	𝝏(𝝆𝒏𝒇	𝝏(𝝆𝒏𝒇	NOUN
cana-1759	145	54	𝒖	𝒖	X
cana-1759	145	55	)	)	PUNCT
cana-1759	145	56	𝝏𝒕	𝝏𝒕	PUNCT
cana-1759	146	1	+	+	CCONJ
cana-1759	146	2	𝛁.(𝝆𝒏𝒇𝒖	𝛁.(𝝆𝒏𝒇𝒖	PROPN
cana-1759	146	3	⊗	⊗	PROPN
cana-1759	146	4	𝒖	𝒖	NOUN
cana-1759	146	5	)	)	PUNCT
cana-1759	146	6	=	=	SYM
cana-1759	146	7	𝛁𝐩	𝛁𝐩	NOUN
cana-1759	146	8	+	+	CCONJ
cana-1759	146	9	𝛁.	𝛁.	NUM
cana-1759	146	10	(	(	PUNCT
cana-1759	146	11	𝛍𝒏𝒇(𝛁𝐮	𝛍𝒏𝒇(𝛁𝐮	PROPN
cana-1759	146	12	+	+	CCONJ
cana-1759	146	13	(	(	PUNCT
cana-1759	146	14	𝛁𝒖)𝑻	𝛁𝒖)𝑻	NUM
cana-1759	146	15	)	)	PUNCT
cana-1759	146	16	)	)	PUNCT
cana-1759	146	17	where	where	SCONJ
cana-1759	146	18	μ𝑛𝑓	μ𝑛𝑓	PROPN
cana-1759	146	19	is	be	AUX
cana-1759	146	20	the	the	DET
cana-1759	146	21	viscosity	viscosity	NOUN
cana-1759	146	22	of	of	ADP
cana-1759	146	23	the	the	DET
cana-1759	146	24	nanofluid	nanofluid	NOUN
cana-1759	146	25	.	.	PUNCT
cana-1759	147	1	these	these	DET
cana-1759	147	2	models	model	NOUN
cana-1759	147	3	enable	enable	VERB
cana-1759	147	4	the	the	DET
cana-1759	147	5	prediction	prediction	NOUN
cana-1759	147	6	of	of	ADP
cana-1759	147	7	enhanced	enhanced	ADJ
cana-1759	147	8	heat	heat	NOUN
cana-1759	147	9	transfer	transfer	NOUN
cana-1759	147	10	rates	rate	NOUN
cana-1759	147	11	and	and	CCONJ
cana-1759	147	12	improved	improve	VERB
cana-1759	147	13	thermal	thermal	ADJ
cana-1759	147	14	conductivity	conductivity	NOUN
cana-1759	147	15	in	in	ADP
cana-1759	147	16	systems	system	NOUN
cana-1759	147	17	using	use	VERB
cana-1759	147	18	nanofluids	nanofluid	NOUN
cana-1759	147	19	,	,	PUNCT
cana-1759	147	20	making	make	VERB
cana-1759	147	21	them	they	PRON
cana-1759	147	22	highly	highly	ADV
cana-1759	147	23	relevant	relevant	ADJ
cana-1759	147	24	for	for	ADP
cana-1759	147	25	applications	application	NOUN
cana-1759	147	26	in	in	ADP
cana-1759	147	27	microelectronics	microelectronic	NOUN
cana-1759	147	28	cooling	cool	VERB
cana-1759	147	29	,	,	PUNCT
cana-1759	147	30	medical	medical	ADJ
cana-1759	147	31	therapies	therapy	NOUN
cana-1759	147	32	,	,	PUNCT
cana-1759	147	33	and	and	CCONJ
cana-1759	147	34	energy	energy	NOUN
cana-1759	147	35	-	-	PUNCT
cana-1759	147	36	efficient	efficient	ADJ
cana-1759	147	37	systems	system	NOUN
cana-1759	147	38	.	.	PUNCT
cana-1759	148	1	3.5	3.5	NUM
cana-1759	148	2	.	.	PUNCT
cana-1759	148	3	synthesis	synthesis	NOUN
cana-1759	148	4	of	of	ADP
cana-1759	148	5	modelling	model	VERB
cana-1759	148	6	approaches	approach	VERB
cana-1759	148	7	the	the	DET
cana-1759	148	8	integration	integration	NOUN
cana-1759	148	9	of	of	ADP
cana-1759	148	10	fractional	fractional	ADJ
cana-1759	148	11	calculus	calculus	NOUN
cana-1759	148	12	,	,	PUNCT
cana-1759	148	13	non	non	ADJ
cana-1759	148	14	-	-	ADJ
cana-1759	148	15	newtonian	newtonian	ADJ
cana-1759	148	16	fluid	fluid	ADJ
cana-1759	148	17	models	model	NOUN
cana-1759	148	18	,	,	PUNCT
cana-1759	148	19	and	and	CCONJ
cana-1759	148	20	nanofluid	nanofluid	ADJ
cana-1759	148	21	dynamics	dynamic	NOUN
cana-1759	148	22	represents	represent	VERB
cana-1759	148	23	a	a	DET
cana-1759	148	24	major	major	ADJ
cana-1759	148	25	advancement	advancement	NOUN
cana-1759	148	26	in	in	ADP
cana-1759	148	27	heat	heat	NOUN
cana-1759	148	28	transfer	transfer	NOUN
cana-1759	148	29	and	and	CCONJ
cana-1759	148	30	fluid	fluid	NOUN
cana-1759	148	31	flow	flow	NOUN
cana-1759	148	32	modelling	modelling	NOUN
cana-1759	148	33	.	.	PUNCT
cana-1759	149	1	fractional	fractional	ADJ
cana-1759	149	2	calculus	calculus	NOUN
cana-1759	149	3	provides	provide	VERB
cana-1759	149	4	a	a	DET
cana-1759	149	5	robust	robust	ADJ
cana-1759	149	6	framework	framework	NOUN
cana-1759	149	7	for	for	ADP
cana-1759	149	8	capturing	capture	VERB
cana-1759	149	9	complex	complex	ADJ
cana-1759	149	10	temporal	temporal	ADJ
cana-1759	149	11	and	and	CCONJ
cana-1759	149	12	spatial	spatial	ADJ
cana-1759	149	13	behaviours	behaviour	NOUN
cana-1759	149	14	,	,	PUNCT
cana-1759	149	15	non	non	ADJ
cana-1759	149	16	-	-	ADJ
cana-1759	149	17	newtonian	newtonian	ADJ
cana-1759	149	18	models	model	NOUN
cana-1759	149	19	address	address	VERB
cana-1759	149	20	diverse	diverse	ADJ
cana-1759	149	21	fluid	fluid	ADJ
cana-1759	149	22	rheologies	rheology	NOUN
cana-1759	149	23	,	,	PUNCT
cana-1759	149	24	and	and	CCONJ
cana-1759	149	25	nanofluid	nanofluid	NOUN
cana-1759	149	26	models	model	NOUN
cana-1759	149	27	enhance	enhance	VERB
cana-1759	149	28	thermal	thermal	ADJ
cana-1759	149	29	management	management	NOUN
cana-1759	149	30	.	.	PUNCT
cana-1759	150	1	together	together	ADV
cana-1759	150	2	,	,	PUNCT
cana-1759	150	3	these	these	DET
cana-1759	150	4	approaches	approach	NOUN
cana-1759	150	5	offer	offer	VERB
cana-1759	150	6	comprehensive	comprehensive	ADJ
cana-1759	150	7	tools	tool	NOUN
cana-1759	150	8	for	for	ADP
cana-1759	150	9	predicting	predict	VERB
cana-1759	150	10	and	and	CCONJ
cana-1759	150	11	optimizing	optimize	VERB
cana-1759	150	12	the	the	DET
cana-1759	150	13	performance	performance	NOUN
cana-1759	150	14	of	of	ADP
cana-1759	150	15	complex	complex	ADJ
cana-1759	150	16	fluid	fluid	ADJ
cana-1759	150	17	systems	system	NOUN
cana-1759	150	18	in	in	ADP
cana-1759	150	19	various	various	ADJ
cana-1759	150	20	applications	application	NOUN
cana-1759	150	21	.	.	PUNCT
cana-1759	151	1	4	4	X
cana-1759	151	2	.	.	X
cana-1759	151	3	numerical	numerical	ADJ
cana-1759	151	4	methods	method	NOUN
cana-1759	151	5	on	on	AUX
cana-1759	151	6	consider	consider	VERB
cana-1759	151	7	three	three	NUM
cana-1759	151	8	cases	case	NOUN
cana-1759	151	9	that	that	PRON
cana-1759	151	10	illustrate	illustrate	VERB
cana-1759	151	11	the	the	DET
cana-1759	151	12	application	application	NOUN
cana-1759	151	13	of	of	ADP
cana-1759	151	14	mathematical	mathematical	ADJ
cana-1759	151	15	modelling	modelling	NOUN
cana-1759	151	16	techniques	technique	NOUN
cana-1759	151	17	discussed	discuss	VERB
cana-1759	151	18	in	in	ADP
cana-1759	151	19	the	the	DET
cana-1759	151	20	section	section	NOUN
cana-1759	151	21	on	on	ADP
cana-1759	151	22	heat	heat	NOUN
cana-1759	151	23	transfer	transfer	NOUN
cana-1759	151	24	and	and	CCONJ
cana-1759	151	25	fluid	fluid	ADJ
cana-1759	151	26	flow	flow	NOUN
cana-1759	151	27	will	will	AUX
cana-1759	151	28	cover	cover	VERB
cana-1759	151	29	examples	example	NOUN
cana-1759	151	30	involving	involve	VERB
cana-1759	151	31	:	:	PUNCT
cana-1759	151	32	1	1	X
cana-1759	151	33	.	.	PUNCT
cana-1759	151	34	fractional	fractional	ADJ
cana-1759	151	35	calculus	calculus	NOUN
cana-1759	151	36	in	in	ADP
cana-1759	151	37	heat	heat	NOUN
cana-1759	151	38	transfer	transfer	NOUN
cana-1759	151	39	:	:	PUNCT
cana-1759	151	40	solving	solve	VERB
cana-1759	151	41	a	a	DET
cana-1759	151	42	fractional	fractional	ADJ
cana-1759	151	43	heat	heat	NOUN
cana-1759	151	44	conduction	conduction	NOUN
cana-1759	151	45	equation	equation	NOUN
cana-1759	151	46	.	.	PUNCT
cana-1759	152	1	2	2	X
cana-1759	152	2	.	.	X
cana-1759	152	3	non	non	ADJ
cana-1759	152	4	-	-	ADJ
cana-1759	152	5	newtonian	newtonian	ADJ
cana-1759	152	6	fluid	fluid	ADJ
cana-1759	152	7	flow	flow	NOUN
cana-1759	152	8	:	:	PUNCT
cana-1759	152	9	calculating	calculate	VERB
cana-1759	152	10	the	the	DET
cana-1759	152	11	velocity	velocity	NOUN
cana-1759	152	12	profile	profile	NOUN
cana-1759	152	13	of	of	ADP
cana-1759	152	14	a	a	DET
cana-1759	152	15	power	power	NOUN
cana-1759	152	16	-	-	PUNCT
cana-1759	152	17	law	law	NOUN
cana-1759	152	18	fluid	fluid	NOUN
cana-1759	152	19	in	in	ADP
cana-1759	152	20	a	a	DET
cana-1759	152	21	pipe	pipe	NOUN
cana-1759	152	22	.	.	PUNCT
cana-1759	153	1	3	3	X
cana-1759	153	2	.	.	X
cana-1759	153	3	nanofluid	nanofluid	ADJ
cana-1759	153	4	dynamics	dynamic	NOUN
cana-1759	153	5	:	:	PUNCT
cana-1759	153	6	determining	determine	VERB
cana-1759	153	7	the	the	DET
cana-1759	153	8	temperature	temperature	NOUN
cana-1759	153	9	distribution	distribution	NOUN
cana-1759	153	10	of	of	ADP
cana-1759	153	11	a	a	DET
cana-1759	153	12	nanofluid	nanofluid	ADJ
cana-1759	153	13	flow	flow	NOUN
cana-1759	153	14	over	over	ADP
cana-1759	153	15	a	a	DET
cana-1759	153	16	flat	flat	ADJ
cana-1759	153	17	plate	plate	NOUN
cana-1759	153	18	.	.	PUNCT
cana-1759	154	1	1	1	X
cana-1759	154	2	.	.	X
cana-1759	154	3	fractional	fractional	ADJ
cana-1759	154	4	calculus	calculus	NOUN
cana-1759	154	5	in	in	ADP
cana-1759	154	6	heat	heat	NOUN
cana-1759	154	7	transfer	transfer	NOUN
cana-1759	154	8	:	:	PUNCT
cana-1759	154	9	example	example	NOUN
cana-1759	154	10	:	:	PUNCT
cana-1759	154	11	consider	consider	VERB
cana-1759	154	12	the	the	DET
cana-1759	154	13	fractional	fractional	ADJ
cana-1759	154	14	heat	heat	NOUN
cana-1759	154	15	conduction	conduction	NOUN
cana-1759	154	16	equation	equation	NOUN
cana-1759	154	17	in	in	ADP
cana-1759	154	18	a	a	DET
cana-1759	154	19	semi	semi	ADJ
cana-1759	154	20	-	-	ADJ
cana-1759	154	21	infinite	infinite	ADJ
cana-1759	154	22	rod	rod	NOUN
cana-1759	154	23	with	with	ADP
cana-1759	154	24	an	an	DET
cana-1759	154	25	initial	initial	ADJ
cana-1759	154	26	temperature	temperature	NOUN
cana-1759	154	27	t(x,0	t(x,0	PROPN
cana-1759	154	28	)	)	PUNCT
cana-1759	155	1	=	=	PUNCT
cana-1759	155	2	𝑇0	𝑇0	NOUN
cana-1759	155	3	for	for	ADP
cana-1759	155	4	(	(	PUNCT
cana-1759	155	5	x	x	SYM
cana-1759	155	6	>	>	X
cana-1759	155	7	0	0	NUM
cana-1759	155	8	)	)	PUNCT
cana-1759	155	9	and	and	CCONJ
cana-1759	155	10	boundary	boundary	ADJ
cana-1759	155	11	condition	condition	NOUN
cana-1759	155	12	t(0,t	t(0,t	NOUN
cana-1759	155	13	)	)	PUNCT
cana-1759	156	1	=	=	PUNCT
cana-1759	157	1	𝑇𝑠	𝑇𝑠	PROPN
cana-1759	157	2	for	for	ADP
cana-1759	157	3	(	(	PUNCT
cana-1759	157	4	t	t	X
cana-1759	157	5	>	>	X
cana-1759	157	6	0	0	NUM
cana-1759	157	7	)	)	PUNCT
cana-1759	157	8	.	.	PUNCT
cana-1759	158	1	we	we	PRON
cana-1759	158	2	use	use	VERB
cana-1759	158	3	the	the	DET
cana-1759	158	4	caputo	caputo	PROPN
cana-1759	158	5	fractional	fractional	PROPN
cana-1759	158	6	derivative	derivative	NOUN
cana-1759	158	7	with	with	ADP
cana-1759	158	8	order	order	NOUN
cana-1759	158	9	α	α	X
cana-1759	158	10	=	=	SYM
cana-1759	158	11	0.5	0.5	NUM
cana-1759	158	12	.	.	PUNCT
cana-1759	158	13	problem	problem	NOUN
cana-1759	158	14	statement	statement	NOUN
cana-1759	158	15	:	:	PUNCT
cana-1759	158	16	solve	solve	VERB
cana-1759	158	17	the	the	DET
cana-1759	158	18	fractional	fractional	ADJ
cana-1759	158	19	heat	heat	NOUN
cana-1759	158	20	conduction	conduction	NOUN
cana-1759	158	21	equation	equation	NOUN
cana-1759	158	22	:	:	PUNCT
cana-1759	159	1	𝜕𝛼𝑇	𝜕𝛼𝑇	X
cana-1759	159	2	𝜕𝑡𝛼	𝜕𝑡𝛼	NOUN
cana-1759	159	3	=	=	SYM
cana-1759	160	1	k	k	PROPN
cana-1759	160	2	𝜕𝛼𝑇	𝜕𝛼𝑇	NUM
cana-1759	160	3	𝜕𝑥2	𝜕𝑥2	PROPN
cana-1759	160	4	,	,	PUNCT
cana-1759	160	5	0	0	PUNCT
cana-1759	160	6	<	<	X
cana-1759	160	7	α	α	PROPN
cana-1759	160	8	≤	≤	NUM
cana-1759	160	9	1	1	NUM
cana-1759	160	10	,	,	PUNCT
cana-1759	160	11	where	where	SCONJ
cana-1759	160	12	𝜕𝛼𝑇	𝜕𝛼𝑇	NUM
cana-1759	160	13	𝜕𝑡𝛼	𝜕𝑡𝛼	NOUN
cana-1759	160	14	is	be	AUX
cana-1759	160	15	the	the	DET
cana-1759	160	16	caputo	caputo	PROPN
cana-1759	160	17	fractional	fractional	PROPN
cana-1759	160	18	derivative	derivative	PROPN
cana-1759	160	19	,	,	PUNCT
cana-1759	160	20	k	k	PROPN
cana-1759	160	21	is	be	AUX
cana-1759	160	22	the	the	DET
cana-1759	160	23	thermal	thermal	ADJ
cana-1759	160	24	diffusivity	diffusivity	NOUN
cana-1759	160	25	,	,	PUNCT
cana-1759	160	26	t(x	t(x	PROPN
cana-1759	160	27	,	,	PUNCT
cana-1759	160	28	t	t	PROPN
cana-1759	160	29	)	)	PUNCT
cana-1759	160	30	is	be	AUX
cana-1759	160	31	the	the	DET
cana-1759	160	32	temperature	temperature	NOUN
cana-1759	160	33	,	,	PUNCT
cana-1759	160	34	x	x	X
cana-1759	160	35	is	be	AUX
cana-1759	160	36	the	the	DET
cana-1759	160	37	spatial	spatial	ADJ
cana-1759	160	38	coordinate	coordinate	NOUN
cana-1759	160	39	,	,	PUNCT
cana-1759	160	40	and	and	CCONJ
cana-1759	160	41	t	t	PROPN
cana-1759	160	42	is	be	AUX
cana-1759	160	43	time	time	NOUN
cana-1759	160	44	.	.	PUNCT
cana-1759	161	1	solution	solution	NOUN
cana-1759	161	2	:	:	PUNCT
cana-1759	161	3	1	1	X
cana-1759	161	4	.	.	X
cana-1759	161	5	applying	apply	VERB
cana-1759	161	6	the	the	DET
cana-1759	161	7	laplace	laplace	NOUN
cana-1759	161	8	transform	transform	NOUN
cana-1759	161	9	:	:	PUNCT
cana-1759	161	10	take	take	VERB
cana-1759	161	11	the	the	DET
cana-1759	161	12	laplace	laplace	NOUN
cana-1759	161	13	transform	transform	NOUN
cana-1759	161	14	with	with	ADP
cana-1759	161	15	respect	respect	NOUN
cana-1759	161	16	to	to	ADP
cana-1759	161	17	time	time	NOUN
cana-1759	161	18	t	t	PROPN
cana-1759	161	19	:	:	PUNCT
cana-1759	161	20	communications	communication	NOUN
cana-1759	161	21	on	on	ADP
cana-1759	161	22	applied	apply	VERB
cana-1759	161	23	nonlinear	nonlinear	ADJ
cana-1759	161	24	analysis	analysis	NOUN
cana-1759	161	25	issn	issn	NOUN
cana-1759	161	26	:	:	PUNCT
cana-1759	161	27	1074	1074	NUM
cana-1759	161	28	-	-	PUNCT
cana-1759	161	29	133x	133x	NUM
cana-1759	161	30	vol	vol	NOUN
cana-1759	161	31	32	32	NUM
cana-1759	161	32	no	no	NOUN
cana-1759	161	33	.	.	NOUN
cana-1759	161	34	2	2	NUM
cana-1759	161	35	(	(	PUNCT
cana-1759	161	36	2025	2025	NUM
cana-1759	161	37	)	)	PUNCT
cana-1759	161	38	479	479	NUM
cana-1759	161	39	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	161	40	𝒔𝜶	𝒔𝜶	ADP
cana-1759	161	41	�	�	PROPN
cana-1759	161	42	̃	̃	PROPN
cana-1759	161	43	�	�	PROPN
cana-1759	161	44	(𝒙	(𝒙	PROPN
cana-1759	161	45	,	,	PUNCT
cana-1759	161	46	𝒔	𝒔	SYM
cana-1759	161	47	)	)	PUNCT
cana-1759	161	48	−	−	PROPN
cana-1759	161	49	𝒔𝜶−𝟏𝑻(𝒙	𝒔𝜶−𝟏𝑻(𝒙	NUM
cana-1759	161	50	,	,	PUNCT
cana-1759	161	51	𝟎)=	𝟎)=	PROPN
cana-1759	161	52	k	k	PROPN
cana-1759	161	53	𝝏𝟐	𝝏𝟐	PROPN
cana-1759	161	54	�	�	PROPN
cana-1759	161	55	̃	̃	PROPN
cana-1759	161	56	�	�	PROPN
cana-1759	161	57	(𝒙,𝒔	(𝒙,𝒔	NOUN
cana-1759	161	58	)	)	PUNCT
cana-1759	161	59	𝝏𝒙𝟐	𝝏𝒙𝟐	NOUN
cana-1759	161	60	where	where	SCONJ
cana-1759	161	61	t̃	t̃	PROPN
cana-1759	161	62	(	(	PUNCT
cana-1759	161	63	x	x	NOUN
cana-1759	161	64	,	,	PUNCT
cana-1759	161	65	s	s	PART
cana-1759	161	66	)	)	PUNCT
cana-1759	161	67	is	be	AUX
cana-1759	161	68	the	the	DET
cana-1759	161	69	laplace	laplace	NOUN
cana-1759	161	70	transform	transform	NOUN
cana-1759	161	71	of	of	ADP
cana-1759	161	72	t(x	t(x	PROPN
cana-1759	161	73	,	,	PUNCT
cana-1759	161	74	t	t	PROPN
cana-1759	161	75	)	)	PUNCT
cana-1759	161	76	and	and	CCONJ
cana-1759	161	77	s	s	VERB
cana-1759	161	78	is	be	AUX
cana-1759	161	79	the	the	DET
cana-1759	161	80	laplace	laplace	NOUN
cana-1759	161	81	variable	variable	NOUN
cana-1759	161	82	.	.	PUNCT
cana-1759	162	1	2	2	X
cana-1759	162	2	.	.	X
cana-1759	162	3	substitute	substitute	NOUN
cana-1759	162	4	initial	initial	ADJ
cana-1759	162	5	conditions	condition	NOUN
cana-1759	162	6	:	:	PUNCT
cana-1759	162	7	𝒔𝜶	𝒔𝜶	ADP
cana-1759	162	8	�	�	PROPN
cana-1759	162	9	̃	̃	PROPN
cana-1759	162	10	�	�	PROPN
cana-1759	162	11	(𝒙	(𝒙	PROPN
cana-1759	162	12	,	,	PUNCT
cana-1759	162	13	𝒔	𝒔	SYM
cana-1759	162	14	)	)	PUNCT
cana-1759	162	15	−	−	PROPN
cana-1759	162	16	𝒔𝜶−𝟏𝑻𝟎=	𝒔𝜶−𝟏𝑻𝟎=	NUM
cana-1759	162	17	k	k	PROPN
cana-1759	162	18	𝝏𝟐	𝝏𝟐	PROPN
cana-1759	162	19	�	�	PROPN
cana-1759	162	20	̃	̃	PROPN
cana-1759	162	21	�	�	PROPN
cana-1759	162	22	(𝒙,𝒔	(𝒙,𝒔	NOUN
cana-1759	162	23	)	)	PUNCT
cana-1759	162	24	𝝏𝒙𝟐	𝝏𝒙𝟐	NOUN
cana-1759	163	1	3	3	X
cana-1759	163	2	.	.	X
cana-1759	163	3	solve	solve	VERB
cana-1759	163	4	the	the	DET
cana-1759	163	5	ordinary	ordinary	ADJ
cana-1759	163	6	differential	differential	ADJ
cana-1759	163	7	equation	equation	NOUN
cana-1759	163	8	(	(	PUNCT
cana-1759	163	9	ode	ode	PROPN
cana-1759	163	10	):	):	PUNCT
cana-1759	163	11	rewrite	rewrite	VERB
cana-1759	163	12	as	as	ADP
cana-1759	163	13	:	:	PUNCT
cana-1759	163	14	𝜕2	𝜕2	NOUN
cana-1759	163	15	�	�	PROPN
cana-1759	163	16	̃	̃	PROPN
cana-1759	163	17	�	�	PROPN
cana-1759	163	18	(𝑥,𝑠	(𝑥,𝑠	NOUN
cana-1759	163	19	)	)	PUNCT
cana-1759	164	1	𝜕𝑥2	𝜕𝑥2	PROPN
cana-1759	164	2	𝑠𝛼	𝑠𝛼	PROPN
cana-1759	164	3	𝑘	𝑘	PROPN
cana-1759	164	4	�	�	PROPN
cana-1759	164	5	̃	̃	PROPN
cana-1759	164	6	�	�	PROPN
cana-1759	164	7	(𝑥	(𝑥	NOUN
cana-1759	164	8	,	,	PUNCT
cana-1759	164	9	𝑠	𝑠	NOUN
cana-1759	164	10	)	)	PUNCT
cana-1759	164	11	=	=	PUNCT
cana-1759	165	1	𝑠𝛼−1𝑇0	𝑠𝛼−1𝑇0	PROPN
cana-1759	165	2	𝑘	𝑘	ADP
cana-1759	165	3	this	this	PRON
cana-1759	165	4	is	be	AUX
cana-1759	165	5	a	a	DET
cana-1759	165	6	second	second	ADJ
cana-1759	165	7	-	-	PUNCT
cana-1759	165	8	order	order	NOUN
cana-1759	165	9	linear	linear	NOUN
cana-1759	165	10	ode	ode	NOUN
cana-1759	165	11	with	with	ADP
cana-1759	165	12	constant	constant	ADJ
cana-1759	165	13	coefficients	coefficient	NOUN
cana-1759	165	14	.	.	PUNCT
cana-1759	166	1	the	the	DET
cana-1759	166	2	general	general	ADJ
cana-1759	166	3	solution	solution	NOUN
cana-1759	166	4	is	be	AUX
cana-1759	166	5	:	:	PUNCT
cana-1759	166	6	�	�	PROPN
cana-1759	166	7	̃	̃	PROPN
cana-1759	166	8	�	�	PROPN
cana-1759	166	9	(𝑥	(𝑥	NOUN
cana-1759	166	10	,	,	PUNCT
cana-1759	166	11	𝑠	𝑠	NOUN
cana-1759	166	12	)	)	PUNCT
cana-1759	166	13	=	=	PUNCT
cana-1759	167	1	𝐴𝑒	𝐴𝑒	PROPN
cana-1759	167	2	−𝑥√𝑠𝛼	−𝑥√𝑠𝛼	PROPN
cana-1759	167	3	𝑘	𝑘	X
cana-1759	167	4	+	+	PROPN
cana-1759	167	5	𝐵𝑒	𝐵𝑒	PROPN
cana-1759	167	6	𝑥√𝑠𝛼	𝑥√𝑠𝛼	NOUN
cana-1759	167	7	𝑘	𝑘	X
cana-1759	167	8	+	+	X
cana-1759	167	9	𝑇0	𝑇0	NOUN
cana-1759	167	10	𝑠	𝑠	INTJ
cana-1759	167	11	,	,	PUNCT
cana-1759	167	12	where	where	SCONJ
cana-1759	167	13	a	a	PRON
cana-1759	167	14	and	and	CCONJ
cana-1759	167	15	b	b	NOUN
cana-1759	167	16	are	be	AUX
cana-1759	167	17	constants	constant	NOUN
cana-1759	167	18	to	to	PART
cana-1759	167	19	be	be	AUX
cana-1759	167	20	determined	determine	VERB
cana-1759	167	21	.	.	PUNCT
cana-1759	168	1	4	4	X
cana-1759	168	2	.	.	X
cana-1759	168	3	apply	apply	VERB
cana-1759	168	4	boundary	boundary	ADJ
cana-1759	168	5	conditions	condition	NOUN
cana-1759	168	6	:	:	PUNCT
cana-1759	168	7	since	since	SCONJ
cana-1759	168	8	t(0,t	t(0,t	NOUN
cana-1759	168	9	)	)	PUNCT
cana-1759	169	1	=	=	SYM
cana-1759	169	2	𝑇𝑠	𝑇𝑠	PROPN
cana-1759	169	3	,	,	PUNCT
cana-1759	169	4	the	the	DET
cana-1759	169	5	transformed	transform	VERB
cana-1759	169	6	boundary	boundary	ADJ
cana-1759	169	7	condition	condition	NOUN
cana-1759	169	8	is	be	AUX
cana-1759	169	9	�	�	PROPN
cana-1759	169	10	̃	̃	NOUN
cana-1759	169	11	�	�	NOUN
cana-1759	169	12	(0,s	(0,s	NOUN
cana-1759	169	13	)	)	PUNCT
cana-1759	170	1	=	=	PUNCT
cana-1759	170	2	𝑇𝑠	𝑇𝑠	PROPN
cana-1759	170	3	𝑠	𝑠	PROPN
cana-1759	170	4	.	.	PUNCT
cana-1759	171	1	therefore	therefore	ADV
cana-1759	171	2	,	,	PUNCT
cana-1759	171	3	a	a	DET
cana-1759	171	4	+	+	NOUN
cana-1759	171	5	b	b	NOUN
cana-1759	171	6	+	+	NUM
cana-1759	171	7	𝑇0	𝑇0	NOUN
cana-1759	171	8	𝑠	𝑠	PROPN
cana-1759	171	9	=	=	SYM
cana-1759	171	10	𝑇𝑠	𝑇𝑠	PROPN
cana-1759	171	11	𝑠	𝑠	PROPN
cana-1759	171	12	.	.	PUNCT
cana-1759	172	1	as	as	ADP
cana-1759	172	2	x	x	PROPN
cana-1759	172	3	→∞	→∞	PROPN
cana-1759	172	4	,	,	PUNCT
cana-1759	172	5	t(x	t(x	PROPN
cana-1759	172	6	,	,	PUNCT
cana-1759	172	7	t	t	PROPN
cana-1759	172	8	)	)	PUNCT
cana-1759	172	9	→	→	SYM
cana-1759	172	10	𝑇0	𝑇0	X
cana-1759	172	11	,	,	PUNCT
cana-1759	172	12	which	which	PRON
cana-1759	172	13	implies	imply	VERB
cana-1759	172	14	b	b	NOUN
cana-1759	172	15	=	=	SYM
cana-1759	172	16	0	0	NUM
cana-1759	172	17	.	.	PUNCT
cana-1759	173	1	thus	thus	ADV
cana-1759	173	2	,	,	PUNCT
cana-1759	173	3	�	�	PROPN
cana-1759	173	4	̃	̃	NOUN
cana-1759	173	5	�	�	NOUN
cana-1759	173	6	(x	(x	PROPN
cana-1759	173	7	,	,	PUNCT
cana-1759	173	8	s	s	NOUN
cana-1759	173	9	)	)	PUNCT
cana-1759	173	10	=	=	SYM
cana-1759	173	11	(	(	PUNCT
cana-1759	173	12	𝑇𝑠−𝑇0	𝑇𝑠−𝑇0	NOUN
cana-1759	173	13	𝑠	𝑠	NOUN
cana-1759	173	14	)	)	PUNCT
cana-1759	173	15	𝑒	𝑒	PROPN
cana-1759	173	16	−𝑥√𝑠𝛼	−𝑥√𝑠𝛼	PROPN
cana-1759	173	17	𝑘	𝑘	PROPN
cana-1759	173	18	+	+	X
cana-1759	173	19	𝑇0	𝑇0	X
cana-1759	173	20	𝑠	𝑠	PROPN
cana-1759	173	21	5	5	NUM
cana-1759	173	22	.	.	PUNCT
cana-1759	174	1	inverse	inverse	ADJ
cana-1759	174	2	laplace	laplace	NOUN
cana-1759	174	3	transform	transform	NOUN
cana-1759	174	4	:	:	PUNCT
cana-1759	174	5	using	use	VERB
cana-1759	174	6	the	the	DET
cana-1759	174	7	inverse	inverse	ADJ
cana-1759	174	8	laplace	laplace	NOUN
cana-1759	174	9	transform	transform	NOUN
cana-1759	174	10	,	,	PUNCT
cana-1759	174	11	we	we	PRON
cana-1759	174	12	obtain	obtain	VERB
cana-1759	174	13	:	:	PUNCT
cana-1759	175	1	t(x	t(x	PROPN
cana-1759	175	2	,	,	PUNCT
cana-1759	175	3	t	t	PROPN
cana-1759	175	4	)	)	PUNCT
cana-1759	175	5	=	=	PUNCT
cana-1759	175	6	𝑇0	𝑇0	NOUN
cana-1759	175	7	+	+	CCONJ
cana-1759	175	8	(	(	PUNCT
cana-1759	175	9	𝑇𝑠	𝑇𝑠	PROPN
cana-1759	175	10	−	−	PROPN
cana-1759	175	11	𝑇0	𝑇0	NOUN
cana-1759	175	12	)	)	PUNCT
cana-1759	175	13	𝐸𝛼	𝐸𝛼	PROPN
cana-1759	175	14	(	(	PUNCT
cana-1759	175	15	−	−	PROPN
cana-1759	175	16	𝑥2	𝑥2	PROPN
cana-1759	175	17	4𝑘𝑡𝛼	4𝑘𝑡𝛼	NUM
cana-1759	175	18	)	)	PUNCT
cana-1759	175	19	,	,	PUNCT
cana-1759	175	20	where	where	SCONJ
cana-1759	175	21	𝐸𝛼	𝐸𝛼	PROPN
cana-1759	175	22	(	(	PUNCT
cana-1759	175	23	.	.	PUNCT
cana-1759	175	24	)	)	PUNCT
cana-1759	175	25	is	be	AUX
cana-1759	175	26	the	the	DET
cana-1759	175	27	mittag	mittag	ADJ
cana-1759	175	28	-	-	PUNCT
cana-1759	175	29	leffler	leffler	NOUN
cana-1759	175	30	function	function	NOUN
cana-1759	175	31	.	.	PUNCT
cana-1759	176	1	6	6	X
cana-1759	176	2	.	.	X
cana-1759	176	3	final	final	ADJ
cana-1759	176	4	solution	solution	NOUN
cana-1759	176	5	:	:	PUNCT
cana-1759	176	6	for	for	ADP
cana-1759	176	7	𝛼	𝛼	NOUN
cana-1759	176	8	=	=	SYM
cana-1759	176	9	0.5	0.5	NUM
cana-1759	176	10	,	,	PUNCT
cana-1759	176	11	t(x	t(x	PROPN
cana-1759	176	12	,	,	PUNCT
cana-1759	176	13	t	t	PROPN
cana-1759	176	14	)	)	PUNCT
cana-1759	176	15	=	=	PUNCT
cana-1759	176	16	𝑇0	𝑇0	NOUN
cana-1759	177	1	+	+	CCONJ
cana-1759	177	2	(	(	PUNCT
cana-1759	177	3	𝑇𝑠	𝑇𝑠	PROPN
cana-1759	177	4	−	−	PROPN
cana-1759	177	5	𝑇0	𝑇0	NOUN
cana-1759	177	6	)	)	PUNCT
cana-1759	177	7	𝐸0.5	𝐸0.5	PROPN
cana-1759	177	8	(	(	PUNCT
cana-1759	177	9	−	−	PROPN
cana-1759	177	10	𝑥2	𝑥2	NOUN
cana-1759	177	11	4𝑘𝑡0.5	4𝑘𝑡0.5	NUM
cana-1759	177	12	)	)	PUNCT
cana-1759	177	13	communications	communication	NOUN
cana-1759	177	14	on	on	ADP
cana-1759	177	15	applied	apply	VERB
cana-1759	177	16	nonlinear	nonlinear	ADJ
cana-1759	177	17	analysis	analysis	NOUN
cana-1759	177	18	issn	issn	NOUN
cana-1759	177	19	:	:	PUNCT
cana-1759	177	20	1074	1074	NUM
cana-1759	177	21	-	-	PUNCT
cana-1759	177	22	133x	133x	NUM
cana-1759	177	23	vol	vol	NOUN
cana-1759	177	24	32	32	NUM
cana-1759	177	25	no	no	NOUN
cana-1759	177	26	.	.	NOUN
cana-1759	177	27	2	2	NUM
cana-1759	177	28	(	(	PUNCT
cana-1759	177	29	2025	2025	NUM
cana-1759	177	30	)	)	PUNCT
cana-1759	177	31	480	480	NUM
cana-1759	177	32	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	177	33	figure	figure	NOUN
cana-1759	177	34	1	1	NUM
cana-1759	177	35	:	:	PUNCT
cana-1759	177	36	temperature	temperature	NOUN
cana-1759	177	37	distribution	distribution	NOUN
cana-1759	177	38	in	in	ADP
cana-1759	177	39	a	a	DET
cana-1759	177	40	semi	semi	ADJ
cana-1759	177	41	-	-	ADJ
cana-1759	177	42	infinite	infinite	ADJ
cana-1759	177	43	rod	rod	NOUN
cana-1759	177	44	with	with	ADP
cana-1759	177	45	fractional	fractional	ADJ
cana-1759	177	46	heat	heat	NOUN
cana-1759	177	47	conduction	conduction	NOUN
cana-1759	177	48	interpretation	interpretation	NOUN
cana-1759	177	49	:	:	PUNCT
cana-1759	177	50	this	this	DET
cana-1759	177	51	solution	solution	NOUN
cana-1759	177	52	represents	represent	VERB
cana-1759	177	53	the	the	DET
cana-1759	177	54	temperature	temperature	NOUN
cana-1759	177	55	distribution	distribution	NOUN
cana-1759	177	56	in	in	ADP
cana-1759	177	57	a	a	DET
cana-1759	177	58	rod	rod	NOUN
cana-1759	177	59	using	use	VERB
cana-1759	177	60	a	a	DET
cana-1759	177	61	fractional	fractional	ADJ
cana-1759	177	62	derivative	derivative	ADJ
cana-1759	177	63	model	model	NOUN
cana-1759	177	64	,	,	PUNCT
cana-1759	177	65	which	which	PRON
cana-1759	177	66	captures	capture	VERB
cana-1759	177	67	the	the	DET
cana-1759	177	68	anomalous	anomalous	ADJ
cana-1759	177	69	diffusion	diffusion	NOUN
cana-1759	177	70	behavior	behavior	NOUN
cana-1759	177	71	more	more	ADV
cana-1759	177	72	accurately	accurately	ADV
cana-1759	177	73	than	than	ADP
cana-1759	177	74	classical	classical	ADJ
cana-1759	177	75	models	model	NOUN
cana-1759	177	76	.	.	PUNCT
cana-1759	178	1	2	2	X
cana-1759	178	2	.	.	X
cana-1759	178	3	non	non	ADJ
cana-1759	178	4	-	-	ADJ
cana-1759	178	5	newtonian	newtonian	ADJ
cana-1759	178	6	fluid	fluid	ADJ
cana-1759	178	7	flow	flow	NOUN
cana-1759	178	8	:	:	PUNCT
cana-1759	178	9	example	example	NOUN
cana-1759	178	10	:	:	PUNCT
cana-1759	178	11	a	a	DET
cana-1759	178	12	power	power	NOUN
cana-1759	178	13	-	-	PUNCT
cana-1759	178	14	law	law	NOUN
cana-1759	178	15	fluid	fluid	NOUN
cana-1759	178	16	flows	flow	VERB
cana-1759	178	17	through	through	ADP
cana-1759	178	18	a	a	DET
cana-1759	178	19	circular	circular	ADJ
cana-1759	178	20	pipe	pipe	NOUN
cana-1759	178	21	of	of	ADP
cana-1759	178	22	radius	radius	PROPN
cana-1759	178	23	r.	r.	PROPN
cana-1759	178	24	the	the	DET
cana-1759	178	25	velocity	velocity	NOUN
cana-1759	178	26	profile	profile	NOUN
cana-1759	178	27	is	be	AUX
cana-1759	178	28	required	require	VERB
cana-1759	178	29	.	.	PUNCT
cana-1759	179	1	the	the	DET
cana-1759	179	2	fluid	fluid	NOUN
cana-1759	179	3	has	have	VERB
cana-1759	179	4	a	a	DET
cana-1759	179	5	consistency	consistency	NOUN
cana-1759	179	6	index	index	NOUN
cana-1759	179	7	k	k	NOUN
cana-1759	179	8	=	=	SYM
cana-1759	179	9	0.1	0.1	NUM
cana-1759	179	10	,	,	PUNCT
cana-1759	179	11	pa.𝑠𝑛	pa.𝑠𝑛	NOUN
cana-1759	179	12	and	and	CCONJ
cana-1759	179	13	a	a	DET
cana-1759	179	14	flow	flow	NOUN
cana-1759	179	15	behaviour	behaviour	NOUN
cana-1759	179	16	index	index	NOUN
cana-1759	179	17	n	n	NOUN
cana-1759	179	18	=	=	SYM
cana-1759	179	19	0.5	0.5	NUM
cana-1759	179	20	.	.	PUNCT
cana-1759	180	1	problem	problem	NOUN
cana-1759	180	2	statement	statement	NOUN
cana-1759	180	3	:	:	PUNCT
cana-1759	180	4	determine	determine	VERB
cana-1759	180	5	the	the	DET
cana-1759	180	6	velocity	velocity	NOUN
cana-1759	180	7	profile	profile	NOUN
cana-1759	180	8	u(r	u(r	PROPN
cana-1759	180	9	)	)	PUNCT
cana-1759	180	10	for	for	ADP
cana-1759	180	11	a	a	DET
cana-1759	180	12	power	power	NOUN
cana-1759	180	13	-	-	PUNCT
cana-1759	180	14	law	law	NOUN
cana-1759	180	15	fluid	fluid	NOUN
cana-1759	180	16	with	with	ADP
cana-1759	180	17	a	a	DET
cana-1759	180	18	flow	flow	NOUN
cana-1759	180	19	behaviour	behaviour	NOUN
cana-1759	180	20	index	index	NOUN
cana-1759	180	21	n	n	ADP
cana-1759	180	22	flowing	flow	VERB
cana-1759	180	23	through	through	ADP
cana-1759	180	24	a	a	DET
cana-1759	180	25	pipe	pipe	NOUN
cana-1759	180	26	.	.	PUNCT
cana-1759	181	1	solution	solution	NOUN
cana-1759	181	2	:	:	PUNCT
cana-1759	181	3	1	1	X
cana-1759	181	4	.	.	X
cana-1759	181	5	governing	govern	VERB
cana-1759	181	6	equation	equation	NOUN
cana-1759	181	7	:	:	PUNCT
cana-1759	181	8	for	for	ADP
cana-1759	181	9	a	a	DET
cana-1759	181	10	power	power	NOUN
cana-1759	181	11	-	-	PUNCT
cana-1759	181	12	law	law	NOUN
cana-1759	181	13	fluid	fluid	NOUN
cana-1759	181	14	,	,	PUNCT
cana-1759	181	15	the	the	DET
cana-1759	181	16	relationship	relationship	NOUN
cana-1759	181	17	between	between	ADP
cana-1759	181	18	shear	shear	NOUN
cana-1759	181	19	stress	stress	NOUN
cana-1759	181	20	𝜏	𝜏	X
cana-1759	181	21	and	and	CCONJ
cana-1759	181	22	shear	shear	NOUN
cana-1759	181	23	rate	rate	NOUN
cana-1759	181	24	�	�	PROPN
cana-1759	181	25	̇	̇	PROPN
cana-1759	181	26	�	�	PROPN
cana-1759	181	27	is	be	AUX
cana-1759	181	28	:	:	PUNCT
cana-1759	181	29	𝜏=	𝜏=	X
cana-1759	181	30	(	(	PUNCT
cana-1759	181	31	𝑑𝑢	𝑑𝑢	X
cana-1759	181	32	𝑑𝑟	𝑑𝑟	NOUN
cana-1759	181	33	)	)	PUNCT
cana-1759	181	34	𝑛	𝑛	DET
cana-1759	181	35	2	2	NUM
cana-1759	181	36	.	.	PUNCT
cana-1759	181	37	shear	shear	NOUN
cana-1759	181	38	stress	stress	NOUN
cana-1759	181	39	and	and	CCONJ
cana-1759	181	40	shear	shear	NOUN
cana-1759	181	41	rate	rate	NOUN
cana-1759	181	42	:	:	PUNCT
cana-1759	181	43	the	the	DET
cana-1759	181	44	shear	shear	NOUN
cana-1759	181	45	stress	stress	NOUN
cana-1759	181	46	in	in	ADP
cana-1759	181	47	a	a	DET
cana-1759	181	48	cylindrical	cylindrical	ADJ
cana-1759	181	49	coordinate	coordinate	NOUN
cana-1759	181	50	system	system	NOUN
cana-1759	181	51	for	for	ADP
cana-1759	181	52	a	a	DET
cana-1759	181	53	fully	fully	ADV
cana-1759	181	54	developed	develop	VERB
cana-1759	181	55	flow	flow	NOUN
cana-1759	181	56	is	be	AUX
cana-1759	181	57	:	:	PUNCT
cana-1759	181	58	𝜏(𝑟)=	𝜏(𝑟)=	PROPN
cana-1759	181	59	-r	-r	X
cana-1759	181	60	(	(	PUNCT
cana-1759	181	61	𝑑𝑝	𝑑𝑝	INTJ
cana-1759	181	62	𝑑𝑧	𝑑𝑧	NOUN
cana-1759	181	63	)	)	PUNCT
cana-1759	181	64	where	where	SCONJ
cana-1759	181	65	(	(	PUNCT
cana-1759	181	66	𝑑𝑝	𝑑𝑝	NUM
cana-1759	181	67	𝑑𝑧	𝑑𝑧	NOUN
cana-1759	181	68	)	)	PUNCT
cana-1759	181	69	is	be	AUX
cana-1759	181	70	the	the	DET
cana-1759	181	71	pressure	pressure	NOUN
cana-1759	181	72	gradient	gradient	NOUN
cana-1759	181	73	along	along	ADP
cana-1759	181	74	the	the	DET
cana-1759	181	75	pipe	pipe	NOUN
cana-1759	181	76	.	.	PUNCT
cana-1759	182	1	3	3	X
cana-1759	182	2	.	.	X
cana-1759	182	3	velocity	velocity	NOUN
cana-1759	182	4	profile	profile	NOUN
cana-1759	182	5	:	:	PUNCT
cana-1759	182	6	combine	combine	VERB
cana-1759	182	7	and	and	CCONJ
cana-1759	182	8	integrate	integrate	VERB
cana-1759	182	9	the	the	DET
cana-1759	182	10	expressions	expression	NOUN
cana-1759	182	11	:	:	PUNCT
cana-1759	182	12	𝑑𝑢	𝑑𝑢	X
cana-1759	182	13	𝑑𝑟	𝑑𝑟	NOUN
cana-1759	182	14	=	=	PUNCT
cana-1759	182	15	(	(	PUNCT
cana-1759	182	16	−𝑟	−𝑟	NOUN
cana-1759	182	17	𝐾	𝐾	PROPN
cana-1759	182	18	(	(	PUNCT
cana-1759	182	19	𝑑𝑝	𝑑𝑝	ADV
cana-1759	182	20	𝑑𝑧	𝑑𝑧	NOUN
cana-1759	182	21	)	)	PUNCT
cana-1759	182	22	)	)	PUNCT
cana-1759	183	1	1/𝑛	1/𝑛	NUM
cana-1759	183	2	integrate	integrate	VERB
cana-1759	183	3	with	with	ADP
cana-1759	183	4	respect	respect	NOUN
cana-1759	183	5	to	to	ADP
cana-1759	183	6	r	r	NOUN
cana-1759	183	7	:	:	PUNCT
cana-1759	183	8	u(r	u(r	NOUN
cana-1759	183	9	)	)	PUNCT
cana-1759	184	1	=	=	SYM
cana-1759	184	2	𝑛	𝑛	PRON
cana-1759	184	3	𝑛+1	𝑛+1	PROPN
cana-1759	184	4	(	(	PUNCT
cana-1759	184	5	−𝑟	−𝑟	NOUN
cana-1759	184	6	𝐾	𝐾	PROPN
cana-1759	184	7	(	(	PUNCT
cana-1759	184	8	𝑑𝑝	𝑑𝑝	ADV
cana-1759	184	9	𝑑𝑧	𝑑𝑧	NOUN
cana-1759	184	10	)	)	PUNCT
cana-1759	184	11	)	)	PUNCT
cana-1759	184	12	1/𝑛	1/𝑛	NUM
cana-1759	184	13	(	(	PUNCT
cana-1759	184	14	𝑅(𝑛+1)/𝑛	𝑅(𝑛+1)/𝑛	X
cana-1759	184	15	−	−	NUM
cana-1759	184	16	𝑟(𝑛+1)/𝑛	𝑟(𝑛+1)/𝑛	NOUN
cana-1759	184	17	)	)	PUNCT
cana-1759	184	18	communications	communication	NOUN
cana-1759	184	19	on	on	ADP
cana-1759	184	20	applied	apply	VERB
cana-1759	184	21	nonlinear	nonlinear	ADJ
cana-1759	184	22	analysis	analysis	NOUN
cana-1759	184	23	issn	issn	NOUN
cana-1759	184	24	:	:	PUNCT
cana-1759	184	25	1074	1074	NUM
cana-1759	184	26	-	-	PUNCT
cana-1759	184	27	133x	133x	NUM
cana-1759	184	28	vol	vol	NOUN
cana-1759	184	29	32	32	NUM
cana-1759	184	30	no	no	NOUN
cana-1759	184	31	.	.	NOUN
cana-1759	184	32	2	2	NUM
cana-1759	184	33	(	(	PUNCT
cana-1759	184	34	2025	2025	NUM
cana-1759	184	35	)	)	PUNCT
cana-1759	184	36	481	481	NUM
cana-1759	184	37	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	184	38	4	4	X
cana-1759	184	39	.	.	PUNCT
cana-1759	184	40	substitute	substitute	NOUN
cana-1759	184	41	values	value	NOUN
cana-1759	184	42	:	:	PUNCT
cana-1759	184	43	for	for	ADP
cana-1759	184	44	k	k	PROPN
cana-1759	184	45	=	=	SYM
cana-1759	184	46	0.1	0.1	NUM
cana-1759	184	47	,	,	PUNCT
cana-1759	184	48	n	n	NOUN
cana-1759	184	49	=	=	NUM
cana-1759	184	50	0.5	0.5	NUM
cana-1759	184	51	,	,	PUNCT
cana-1759	184	52	and	and	CCONJ
cana-1759	184	53	𝑑𝑝	𝑑𝑝	ADP
cana-1759	184	54	𝑑𝑧	𝑑𝑧	PROPN
cana-1759	184	55	=	=	SYM
cana-1759	184	56	-100	-100	PROPN
cana-1759	184	57	,	,	PUNCT
cana-1759	184	58	pa	pa	PROPN
cana-1759	184	59	/	/	SYM
cana-1759	184	60	m	m	PROPN
cana-1759	184	61	:	:	PUNCT
cana-1759	184	62	u(r	u(r	ADJ
cana-1759	184	63	)	)	PUNCT
cana-1759	184	64	=	=	SYM
cana-1759	184	65	0.5	0.5	NUM
cana-1759	184	66	1.5	1.5	NUM
cana-1759	184	67	(	(	PUNCT
cana-1759	184	68	(	(	PUNCT
cana-1759	184	69	1	1	NUM
cana-1759	184	70	0.1	0.1	NUM
cana-1759	184	71	)	)	PUNCT
cana-1759	184	72	∗	∗	NOUN
cana-1759	184	73	100	100	NUM
cana-1759	184	74	)	)	PUNCT
cana-1759	184	75	2	2	NUM
cana-1759	184	76	(	(	PUNCT
cana-1759	184	77	𝑅3	𝑅3	NOUN
cana-1759	184	78	−	−	PROPN
cana-1759	184	79	𝑟3	𝑟3	NOUN
cana-1759	184	80	)	)	PUNCT
cana-1759	184	81	5	5	NUM
cana-1759	184	82	.	.	X
cana-1759	184	83	calculate	calculate	NOUN
cana-1759	184	84	velocity	velocity	NOUN
cana-1759	184	85	profile	profile	NOUN
cana-1759	184	86	:	:	PUNCT
cana-1759	184	87	u(r	u(r	NOUN
cana-1759	184	88	)	)	PUNCT
cana-1759	184	89	=	=	SYM
cana-1759	185	1	1	1	NUM
cana-1759	185	2	3	3	NUM
cana-1759	185	3	*	*	PUNCT
cana-1759	185	4	(	(	PUNCT
cana-1759	185	5	100)2(𝑅3	100)2(𝑅3	NUM
cana-1759	185	6	−	−	PROPN
cana-1759	185	7	𝑟3	𝑟3	NOUN
cana-1759	185	8	)	)	PUNCT
cana-1759	185	9	figure	figure	NOUN
cana-1759	185	10	2	2	NUM
cana-1759	185	11	:	:	PUNCT
cana-1759	185	12	velocity	velocity	NOUN
cana-1759	185	13	profile	profile	NOUN
cana-1759	185	14	of	of	ADP
cana-1759	185	15	a	a	DET
cana-1759	185	16	power	power	NOUN
cana-1759	185	17	-	-	PUNCT
cana-1759	185	18	law	law	NOUN
cana-1759	185	19	fluid	fluid	NOUN
cana-1759	185	20	in	in	ADP
cana-1759	185	21	a	a	DET
cana-1759	185	22	pipe	pipe	NOUN
cana-1759	185	23	interpretation	interpretation	NOUN
cana-1759	185	24	:	:	PUNCT
cana-1759	185	25	the	the	DET
cana-1759	185	26	velocity	velocity	NOUN
cana-1759	185	27	profile	profile	NOUN
cana-1759	185	28	shows	show	VERB
cana-1759	185	29	a	a	DET
cana-1759	185	30	parabolic	parabolic	ADJ
cana-1759	185	31	flow	flow	NOUN
cana-1759	185	32	typical	typical	ADJ
cana-1759	185	33	for	for	ADP
cana-1759	185	34	power	power	NOUN
cana-1759	185	35	-	-	PUNCT
cana-1759	185	36	law	law	NOUN
cana-1759	185	37	fluids	fluid	NOUN
cana-1759	185	38	,	,	PUNCT
cana-1759	185	39	with	with	ADP
cana-1759	185	40	velocity	velocity	NOUN
cana-1759	185	41	decreasing	decrease	VERB
cana-1759	185	42	from	from	ADP
cana-1759	185	43	the	the	DET
cana-1759	185	44	centre	centre	NOUN
cana-1759	185	45	line	line	NOUN
cana-1759	185	46	to	to	ADP
cana-1759	185	47	the	the	DET
cana-1759	185	48	pipe	pipe	NOUN
cana-1759	185	49	wall	wall	NOUN
cana-1759	185	50	.	.	PUNCT
cana-1759	186	1	3	3	X
cana-1759	186	2	.	.	X
cana-1759	186	3	nanofluid	nanofluid	ADJ
cana-1759	186	4	dynamics	dynamic	NOUN
cana-1759	186	5	example	example	NOUN
cana-1759	186	6	:	:	PUNCT
cana-1759	186	7	consider	consider	VERB
cana-1759	186	8	the	the	DET
cana-1759	186	9	convective	convective	ADJ
cana-1759	186	10	heat	heat	NOUN
cana-1759	186	11	transfer	transfer	NOUN
cana-1759	186	12	of	of	ADP
cana-1759	186	13	a	a	DET
cana-1759	186	14	nanofluid	nanofluid	NOUN
cana-1759	186	15	flowing	flow	VERB
cana-1759	186	16	over	over	ADP
cana-1759	186	17	a	a	DET
cana-1759	186	18	flat	flat	ADJ
cana-1759	186	19	plate	plate	NOUN
cana-1759	186	20	.	.	PUNCT
cana-1759	187	1	the	the	DET
cana-1759	187	2	base	base	ADJ
cana-1759	187	3	fluid	fluid	NOUN
cana-1759	187	4	is	be	AUX
cana-1759	187	5	water	water	NOUN
cana-1759	187	6	,	,	PUNCT
cana-1759	187	7	and	and	CCONJ
cana-1759	187	8	nanoparticles	nanoparticle	NOUN
cana-1759	187	9	are	be	AUX
cana-1759	187	10	copper	copper	NOUN
cana-1759	187	11	with	with	ADP
cana-1759	187	12	a	a	DET
cana-1759	187	13	volume	volume	NOUN
cana-1759	187	14	fraction	fraction	NOUN
cana-1759	187	15	of	of	ADP
cana-1759	187	16	2	2	NUM
cana-1759	187	17	%	%	NOUN
cana-1759	187	18	.	.	PUNCT
cana-1759	188	1	problem	problem	NOUN
cana-1759	188	2	statement	statement	NOUN
cana-1759	188	3	:	:	PUNCT
cana-1759	188	4	determine	determine	VERB
cana-1759	188	5	the	the	DET
cana-1759	188	6	temperature	temperature	NOUN
cana-1759	188	7	distribution	distribution	NOUN
cana-1759	188	8	t(x	t(x	PROPN
cana-1759	188	9	)	)	PUNCT
cana-1759	188	10	along	along	ADP
cana-1759	188	11	a	a	DET
cana-1759	188	12	flat	flat	ADJ
cana-1759	188	13	plate	plate	NOUN
cana-1759	188	14	subjected	subject	VERB
cana-1759	188	15	to	to	ADP
cana-1759	188	16	a	a	DET
cana-1759	188	17	constant	constant	ADJ
cana-1759	188	18	surface	surface	NOUN
cana-1759	188	19	temperature	temperature	NOUN
cana-1759	188	20	𝑇𝑠	𝑇𝑠	PROPN
cana-1759	188	21	and	and	CCONJ
cana-1759	188	22	free	free	ADJ
cana-1759	188	23	stream	stream	NOUN
cana-1759	188	24	temperature	temperature	NOUN
cana-1759	188	25	𝑇∞.	𝑇∞.	NOUN
cana-1759	188	26	solution	solution	NOUN
cana-1759	188	27	:	:	PUNCT
cana-1759	188	28	1	1	X
cana-1759	188	29	.	.	X
cana-1759	189	1	governing	govern	VERB
cana-1759	189	2	equation	equation	NOUN
cana-1759	189	3	:	:	PUNCT
cana-1759	189	4	the	the	DET
cana-1759	189	5	energy	energy	NOUN
cana-1759	189	6	equation	equation	NOUN
cana-1759	189	7	for	for	ADP
cana-1759	189	8	the	the	DET
cana-1759	189	9	boundary	boundary	ADJ
cana-1759	189	10	layer	layer	NOUN
cana-1759	189	11	in	in	ADP
cana-1759	189	12	terms	term	NOUN
cana-1759	189	13	of	of	ADP
cana-1759	189	14	temperature	temperature	NOUN
cana-1759	189	15	t	t	PROPN
cana-1759	189	16	is	be	AUX
cana-1759	189	17	:	:	PUNCT
cana-1759	189	18	u	u	NOUN
cana-1759	189	19	𝜕𝑇	𝜕𝑇	X
cana-1759	189	20	𝜕𝑥	𝜕𝑥	X
cana-1759	189	21	+	+	CCONJ
cana-1759	189	22	v	v	X
cana-1759	189	23	𝜕𝑇	𝜕𝑇	NOUN
cana-1759	189	24	𝜕𝑦	𝜕𝑦	NOUN
cana-1759	189	25	=	=	SYM
cana-1759	189	26	𝛼𝑛,𝑓	𝛼𝑛,𝑓	ADJ
cana-1759	189	27	𝜕2𝑇	𝜕2𝑇	NOUN
cana-1759	189	28	𝜕𝑦2	𝜕𝑦2	PROPN
cana-1759	189	29	,	,	PUNCT
cana-1759	189	30	where	where	SCONJ
cana-1759	189	31	𝛼𝑛,𝑓	𝛼𝑛,𝑓	NOUN
cana-1759	189	32	=	=	PRON
cana-1759	189	33	𝑘𝑛𝑓	𝑘𝑛𝑓	PROPN
cana-1759	189	34	𝜌𝑛𝑓,𝑐𝑝,𝑛𝑓	𝜌𝑛𝑓,𝑐𝑝,𝑛𝑓	ADV
cana-1759	189	35	is	be	AUX
cana-1759	189	36	the	the	DET
cana-1759	189	37	thermal	thermal	ADJ
cana-1759	189	38	diffusivity	diffusivity	NOUN
cana-1759	189	39	of	of	ADP
cana-1759	189	40	the	the	DET
cana-1759	189	41	nanofluid	nanofluid	NOUN
cana-1759	189	42	.	.	PUNCT
cana-1759	190	1	2	2	X
cana-1759	190	2	.	.	X
cana-1759	190	3	nanofluid	nanofluid	ADJ
cana-1759	190	4	properties	property	NOUN
cana-1759	190	5	:	:	PUNCT
cana-1759	190	6	calculate	calculate	VERB
cana-1759	190	7	nanofluid	nanofluid	ADJ
cana-1759	190	8	properties	property	NOUN
cana-1759	190	9	using	use	VERB
cana-1759	190	10	effective	effective	ADJ
cana-1759	190	11	medium	medium	ADJ
cana-1759	190	12	theories	theory	NOUN
cana-1759	190	13	.	.	PUNCT
cana-1759	191	1	the	the	DET
cana-1759	191	2	thermal	thermal	ADJ
cana-1759	191	3	conductivity	conductivity	NOUN
cana-1759	191	4	𝑘𝑛𝑓	𝑘𝑛𝑓	NOUN
cana-1759	191	5	,	,	PUNCT
cana-1759	191	6	density	density	NOUN
cana-1759	191	7	𝜌𝑛𝑓	𝜌𝑛𝑓	NOUN
cana-1759	191	8	and	and	CCONJ
cana-1759	191	9	specific	specific	ADJ
cana-1759	191	10	heat	heat	NOUN
cana-1759	191	11	𝑐𝑝,𝑛𝑓	𝑐𝑝,𝑛𝑓	NOUN
cana-1759	191	12	are	be	AUX
cana-1759	191	13	:	:	PUNCT
cana-1759	191	14	𝑘𝑛𝑓	𝑘𝑛𝑓	PROPN
cana-1759	191	15	=	=	SYM
cana-1759	191	16	𝑘𝑓	𝑘𝑓	PROPN
cana-1759	191	17	(	(	PUNCT
cana-1759	191	18	𝑘𝑝+2𝑘𝑓−2𝜙(𝑘𝑓−𝑘𝑝	𝑘𝑝+2𝑘𝑓−2𝜙(𝑘𝑓−𝑘𝑝	NOUN
cana-1759	191	19	)	)	PUNCT
cana-1759	191	20	)	)	PUNCT
cana-1759	192	1	(	(	PUNCT
cana-1759	192	2	𝑘𝑝+2𝑘𝑓+𝜙(𝑘𝑓−𝑘𝑝	𝑘𝑝+2𝑘𝑓+𝜙(𝑘𝑓−𝑘𝑝	PROPN
cana-1759	192	3	)	)	PUNCT
cana-1759	192	4	)	)	PUNCT
cana-1759	192	5	communications	communication	NOUN
cana-1759	192	6	on	on	ADP
cana-1759	192	7	applied	apply	VERB
cana-1759	192	8	nonlinear	nonlinear	ADJ
cana-1759	192	9	analysis	analysis	NOUN
cana-1759	192	10	issn	issn	NOUN
cana-1759	192	11	:	:	PUNCT
cana-1759	192	12	1074	1074	NUM
cana-1759	192	13	-	-	PUNCT
cana-1759	192	14	133x	133x	NUM
cana-1759	192	15	vol	vol	NOUN
cana-1759	192	16	32	32	NUM
cana-1759	192	17	no	no	NOUN
cana-1759	192	18	.	.	NOUN
cana-1759	192	19	2	2	NUM
cana-1759	192	20	(	(	PUNCT
cana-1759	192	21	2025	2025	NUM
cana-1759	192	22	)	)	PUNCT
cana-1759	193	1	482	482	NUM
cana-1759	193	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	193	3	ρnf	ρnf	NOUN
cana-1759	193	4	=	=	SYM
cana-1759	193	5	(	(	PUNCT
cana-1759	193	6	1ϕ	1ϕ	NUM
cana-1759	193	7	)	)	PUNCT
cana-1759	193	8	ρf+ϕρp	ρf+ϕρp	PROPN
cana-1759	193	9	cp	cp	PROPN
cana-1759	193	10	,	,	PUNCT
cana-1759	193	11	nf	nf	NOUN
cana-1759	193	12	=	=	SYM
cana-1759	193	13	(	(	PUNCT
cana-1759	193	14	1ϕ	1ϕ	NUM
cana-1759	193	15	)	)	PUNCT
cana-1759	193	16	cp	cp	PROPN
cana-1759	193	17	,	,	PUNCT
cana-1759	193	18	f+ϕcp	f+ϕcp	NOUN
cana-1759	193	19	,	,	PUNCT
cana-1759	193	20	p	p	NOUN
cana-1759	193	21	where	where	SCONJ
cana-1759	193	22	𝜙	𝜙	NOUN
cana-1759	193	23	is	be	AUX
cana-1759	193	24	the	the	DET
cana-1759	193	25	nanoparticle	nanoparticle	NOUN
cana-1759	193	26	volume	volume	NOUN
cana-1759	193	27	fraction	fraction	NOUN
cana-1759	193	28	,	,	PUNCT
cana-1759	193	29	and	and	CCONJ
cana-1759	193	30	the	the	DET
cana-1759	193	31	subscripts	subscript	NOUN
cana-1759	193	32	f	f	NOUN
cana-1759	193	33	and	and	CCONJ
cana-1759	193	34	p	p	NOUN
cana-1759	193	35	denote	denote	NOUN
cana-1759	193	36	fluid	fluid	NOUN
cana-1759	193	37	and	and	CCONJ
cana-1759	193	38	particle	particle	NOUN
cana-1759	193	39	properties	property	NOUN
cana-1759	193	40	,	,	PUNCT
cana-1759	193	41	respectively	respectively	ADV
cana-1759	193	42	.	.	PUNCT
cana-1759	194	1	3	3	X
cana-1759	194	2	.	.	X
cana-1759	194	3	blasius	blasius	ADJ
cana-1759	194	4	similarity	similarity	NOUN
cana-1759	194	5	solution	solution	NOUN
cana-1759	194	6	:	:	PUNCT
cana-1759	194	7	apply	apply	VERB
cana-1759	194	8	the	the	DET
cana-1759	194	9	blasius	blasius	ADJ
cana-1759	194	10	similarity	similarity	NOUN
cana-1759	194	11	solution	solution	NOUN
cana-1759	194	12	for	for	ADP
cana-1759	194	13	laminar	laminar	ADJ
cana-1759	194	14	flow	flow	NOUN
cana-1759	194	15	:	:	PUNCT
cana-1759	194	16	θ(η	θ(η	X
cana-1759	194	17	)	)	PUNCT
cana-1759	194	18	=	=	SYM
cana-1759	194	19	𝑇(𝑥,𝑦)−𝑇∞	𝑇(𝑥,𝑦)−𝑇∞	PROPN
cana-1759	194	20	𝑇𝑠−𝑇∞	𝑇𝑠−𝑇∞	PROPN
cana-1759	194	21	,	,	PUNCT
cana-1759	194	22	η	η	PROPN
cana-1759	194	23	=	=	SYM
cana-1759	194	24	y	y	PROPN
cana-1759	194	25	√	√	PROPN
cana-1759	194	26	𝑈∞	𝑈∞	VERB
cana-1759	194	27	𝜈𝑥	𝜈𝑥	PROPN
cana-1759	194	28	and	and	CCONJ
cana-1759	194	29	solve	solve	VERB
cana-1759	194	30	for	for	ADP
cana-1759	194	31	θ(η	θ(η	NOUN
cana-1759	194	32	)	)	PUNCT
cana-1759	194	33	using	use	VERB
cana-1759	194	34	numerical	numerical	ADJ
cana-1759	194	35	methods	method	NOUN
cana-1759	194	36	or	or	CCONJ
cana-1759	194	37	tables	table	NOUN
cana-1759	194	38	.	.	PUNCT
cana-1759	195	1	4	4	X
cana-1759	195	2	.	.	X
cana-1759	195	3	temperature	temperature	NOUN
cana-1759	195	4	distribution	distribution	NOUN
cana-1759	195	5	:	:	PUNCT
cana-1759	195	6	for	for	ADP
cana-1759	195	7	η	η	PROPN
cana-1759	195	8	=	=	SYM
cana-1759	195	9	1	1	NUM
cana-1759	195	10	,	,	PUNCT
cana-1759	195	11	compute	compute	VERB
cana-1759	195	12	the	the	DET
cana-1759	195	13	temperature	temperature	NOUN
cana-1759	195	14	profile	profile	NOUN
cana-1759	195	15	t(x	t(x	PROPN
cana-1759	195	16	)	)	PUNCT
cana-1759	195	17	at	at	ADP
cana-1759	195	18	various	various	ADJ
cana-1759	195	19	points	point	NOUN
cana-1759	195	20	.	.	PUNCT
cana-1759	196	1	interpretation	interpretation	NOUN
cana-1759	196	2	:	:	PUNCT
cana-1759	196	3	the	the	DET
cana-1759	196	4	temperature	temperature	NOUN
cana-1759	196	5	distribution	distribution	NOUN
cana-1759	196	6	for	for	ADP
cana-1759	196	7	nanofluid	nanofluid	ADJ
cana-1759	196	8	flow	flow	NOUN
cana-1759	196	9	over	over	ADP
cana-1759	196	10	a	a	DET
cana-1759	196	11	flat	flat	ADJ
cana-1759	196	12	plate	plate	NOUN
cana-1759	196	13	shows	show	VERB
cana-1759	196	14	enhanced	enhance	VERB
cana-1759	196	15	heat	heat	NOUN
cana-1759	196	16	transfer	transfer	NOUN
cana-1759	196	17	due	due	ADP
cana-1759	196	18	to	to	ADP
cana-1759	196	19	the	the	DET
cana-1759	196	20	presence	presence	NOUN
cana-1759	196	21	of	of	ADP
cana-1759	196	22	nanoparticles	nanoparticle	NOUN
cana-1759	196	23	,	,	PUNCT
cana-1759	196	24	providing	provide	VERB
cana-1759	196	25	better	well	ADJ
cana-1759	196	26	thermal	thermal	ADJ
cana-1759	196	27	management	management	NOUN
cana-1759	196	28	in	in	ADP
cana-1759	196	29	applications	application	NOUN
cana-1759	196	30	.	.	PUNCT
cana-1759	197	1	these	these	DET
cana-1759	197	2	numerical	numerical	ADJ
cana-1759	197	3	examples	example	NOUN
cana-1759	197	4	illustrate	illustrate	VERB
cana-1759	197	5	the	the	DET
cana-1759	197	6	practical	practical	ADJ
cana-1759	197	7	application	application	NOUN
cana-1759	197	8	of	of	ADP
cana-1759	197	9	advanced	advanced	ADJ
cana-1759	197	10	mathematical	mathematical	ADJ
cana-1759	197	11	modeling	modeling	NOUN
cana-1759	197	12	techniques	technique	NOUN
cana-1759	197	13	to	to	PART
cana-1759	197	14	solve	solve	VERB
cana-1759	197	15	heat	heat	NOUN
cana-1759	197	16	transfer	transfer	NOUN
cana-1759	197	17	and	and	CCONJ
cana-1759	197	18	fluid	fluid	ADJ
cana-1759	197	19	flow	flow	NOUN
cana-1759	197	20	problems	problem	NOUN
cana-1759	197	21	involving	involve	VERB
cana-1759	197	22	fractional	fractional	ADJ
cana-1759	197	23	calculus	calculus	NOUN
cana-1759	197	24	,	,	PUNCT
cana-1759	197	25	non	non	ADJ
cana-1759	197	26	-	-	ADJ
cana-1759	197	27	newtonian	newtonian	ADJ
cana-1759	197	28	fluids	fluid	NOUN
cana-1759	197	29	,	,	PUNCT
cana-1759	197	30	and	and	CCONJ
cana-1759	197	31	nanofluids	nanofluid	NOUN
cana-1759	197	32	.	.	PUNCT
cana-1759	198	1	each	each	DET
cana-1759	198	2	example	example	NOUN
cana-1759	198	3	shows	show	VERB
cana-1759	198	4	how	how	SCONJ
cana-1759	198	5	theoretical	theoretical	ADJ
cana-1759	198	6	models	model	NOUN
cana-1759	198	7	can	can	AUX
cana-1759	198	8	be	be	AUX
cana-1759	198	9	adapted	adapt	VERB
cana-1759	198	10	to	to	ADP
cana-1759	198	11	specific	specific	ADJ
cana-1759	198	12	conditions	condition	NOUN
cana-1759	198	13	,	,	PUNCT
cana-1759	198	14	leading	lead	VERB
cana-1759	198	15	to	to	ADP
cana-1759	198	16	better	well	ADJ
cana-1759	198	17	understanding	understanding	NOUN
cana-1759	198	18	and	and	CCONJ
cana-1759	198	19	optimization	optimization	NOUN
cana-1759	198	20	of	of	ADP
cana-1759	198	21	fluid	fluid	ADJ
cana-1759	198	22	dynamics	dynamic	NOUN
cana-1759	198	23	in	in	ADP
cana-1759	198	24	engineering	engineering	NOUN
cana-1759	198	25	applications	application	NOUN
cana-1759	198	26	.	.	PUNCT
cana-1759	199	1	5	5	X
cana-1759	199	2	.	.	X
cana-1759	199	3	applications	application	NOUN
cana-1759	199	4	of	of	ADP
cana-1759	199	5	mathematical	mathematical	ADJ
cana-1759	199	6	modelling	modelling	NOUN
cana-1759	199	7	in	in	ADP
cana-1759	199	8	heat	heat	NOUN
cana-1759	199	9	transfer	transfer	NOUN
cana-1759	199	10	and	and	CCONJ
cana-1759	199	11	fluid	fluid	NOUN
cana-1759	199	12	flow	flow	NOUN
cana-1759	199	13	mathematical	mathematical	NOUN
cana-1759	199	14	modelling	modelling	NOUN
cana-1759	199	15	using	use	VERB
cana-1759	199	16	fractional	fractional	ADJ
cana-1759	199	17	calculus	calculus	NOUN
cana-1759	199	18	,	,	PUNCT
cana-1759	199	19	non	non	ADJ
cana-1759	199	20	-	-	ADJ
cana-1759	199	21	newtonian	newtonian	ADJ
cana-1759	199	22	fluid	fluid	ADJ
cana-1759	199	23	dynamics	dynamic	NOUN
cana-1759	199	24	,	,	PUNCT
cana-1759	199	25	and	and	CCONJ
cana-1759	199	26	nanofluid	nanofluid	ADJ
cana-1759	199	27	dynamics	dynamic	NOUN
cana-1759	199	28	plays	play	VERB
cana-1759	199	29	a	a	DET
cana-1759	199	30	pivotal	pivotal	ADJ
cana-1759	199	31	role	role	NOUN
cana-1759	199	32	in	in	ADP
cana-1759	199	33	advancing	advance	VERB
cana-1759	199	34	various	various	ADJ
cana-1759	199	35	scientific	scientific	ADJ
cana-1759	199	36	and	and	CCONJ
cana-1759	199	37	engineering	engineering	NOUN
cana-1759	199	38	fields	field	NOUN
cana-1759	199	39	.	.	PUNCT
cana-1759	200	1	below	below	ADV
cana-1759	200	2	are	be	AUX
cana-1759	200	3	detailed	detailed	ADJ
cana-1759	200	4	applications	application	NOUN
cana-1759	200	5	of	of	ADP
cana-1759	200	6	these	these	DET
cana-1759	200	7	models	model	NOUN
cana-1759	200	8	:	:	PUNCT
cana-1759	200	9	5.1	5.1	NUM
cana-1759	200	10	.	.	PUNCT
cana-1759	201	1	applications	application	NOUN
cana-1759	201	2	of	of	ADP
cana-1759	201	3	fractional	fractional	ADJ
cana-1759	201	4	calculus	calculus	NOUN
cana-1759	201	5	in	in	ADP
cana-1759	201	6	heat	heat	NOUN
cana-1759	201	7	transfer	transfer	NOUN
cana-1759	201	8	fractional	fractional	ADJ
cana-1759	201	9	calculus	calculus	NOUN
cana-1759	201	10	has	have	AUX
cana-1759	201	11	been	be	AUX
cana-1759	201	12	widely	widely	ADV
cana-1759	201	13	applied	apply	VERB
cana-1759	201	14	in	in	ADP
cana-1759	201	15	heat	heat	NOUN
cana-1759	201	16	transfer	transfer	NOUN
cana-1759	201	17	modelling	modelling	NOUN
cana-1759	201	18	due	due	ADP
cana-1759	201	19	to	to	ADP
cana-1759	201	20	its	its	PRON
cana-1759	201	21	ability	ability	NOUN
cana-1759	201	22	to	to	PART
cana-1759	201	23	describe	describe	VERB
cana-1759	201	24	processes	process	NOUN
cana-1759	201	25	with	with	ADP
cana-1759	201	26	memory	memory	NOUN
cana-1759	201	27	effects	effect	NOUN
cana-1759	201	28	and	and	CCONJ
cana-1759	201	29	anomalous	anomalous	ADJ
cana-1759	201	30	diffusion	diffusion	NOUN
cana-1759	201	31	.	.	PUNCT
cana-1759	202	1	these	these	DET
cana-1759	202	2	applications	application	NOUN
cana-1759	202	3	include	include	VERB
cana-1759	202	4	:	:	PUNCT
cana-1759	202	5	1	1	X
cana-1759	202	6	.	.	X
cana-1759	202	7	geothermal	geothermal	ADJ
cana-1759	202	8	energy	energy	NOUN
cana-1759	202	9	systems	system	NOUN
cana-1759	202	10	:	:	PUNCT
cana-1759	202	11	description	description	NOUN
cana-1759	202	12	:	:	PUNCT
cana-1759	202	13	fractional	fractional	ADJ
cana-1759	202	14	models	model	NOUN
cana-1759	202	15	are	be	AUX
cana-1759	202	16	used	use	VERB
cana-1759	202	17	to	to	PART
cana-1759	202	18	simulate	simulate	VERB
cana-1759	202	19	heat	heat	NOUN
cana-1759	202	20	conduction	conduction	NOUN
cana-1759	202	21	in	in	ADP
cana-1759	202	22	geothermal	geothermal	ADJ
cana-1759	202	23	reservoirs	reservoir	NOUN
cana-1759	202	24	,	,	PUNCT
cana-1759	202	25	where	where	SCONJ
cana-1759	202	26	the	the	DET
cana-1759	202	27	rock	rock	NOUN
cana-1759	202	28	and	and	CCONJ
cana-1759	202	29	fluid	fluid	NOUN
cana-1759	202	30	properties	property	NOUN
cana-1759	202	31	often	often	ADV
cana-1759	202	32	lead	lead	VERB
cana-1759	202	33	to	to	ADP
cana-1759	202	34	non	non	ADJ
cana-1759	202	35	-	-	ADJ
cana-1759	202	36	local	local	ADJ
cana-1759	202	37	and	and	CCONJ
cana-1759	202	38	history	history	NOUN
cana-1759	202	39	-	-	PUNCT
cana-1759	202	40	dependent	dependent	ADJ
cana-1759	202	41	heat	heat	NOUN
cana-1759	202	42	transfer	transfer	NOUN
cana-1759	202	43	behaviours	behaviour	NOUN
cana-1759	202	44	.	.	PUNCT
cana-1759	203	1	impact	impact	NOUN
cana-1759	203	2	:	:	PUNCT
cana-1759	203	3	enhanced	enhanced	ADJ
cana-1759	203	4	accuracy	accuracy	NOUN
cana-1759	203	5	in	in	ADP
cana-1759	203	6	predicting	predict	VERB
cana-1759	203	7	thermal	thermal	ADJ
cana-1759	203	8	responses	response	NOUN
cana-1759	203	9	of	of	ADP
cana-1759	203	10	geothermal	geothermal	ADJ
cana-1759	203	11	systems	system	NOUN
cana-1759	203	12	,	,	PUNCT
cana-1759	203	13	leading	lead	VERB
cana-1759	203	14	to	to	ADP
cana-1759	203	15	optimized	optimize	VERB
cana-1759	203	16	energy	energy	NOUN
cana-1759	203	17	extraction	extraction	NOUN
cana-1759	203	18	strategies	strategy	NOUN
cana-1759	203	19	and	and	CCONJ
cana-1759	203	20	better	well	ADJ
cana-1759	203	21	management	management	NOUN
cana-1759	203	22	of	of	ADP
cana-1759	203	23	geothermal	geothermal	ADJ
cana-1759	203	24	resources	resource	NOUN
cana-1759	203	25	.	.	PUNCT
cana-1759	204	1	2	2	X
cana-1759	204	2	.	.	X
cana-1759	204	3	thermal	thermal	ADJ
cana-1759	204	4	insulation	insulation	NOUN
cana-1759	204	5	materials	material	NOUN
cana-1759	204	6	:	:	PUNCT
cana-1759	204	7	description	description	NOUN
cana-1759	204	8	:	:	PUNCT
cana-1759	204	9	fractional	fractional	ADJ
cana-1759	204	10	calculus	calculus	NOUN
cana-1759	204	11	is	be	AUX
cana-1759	204	12	applied	apply	VERB
cana-1759	204	13	to	to	PART
cana-1759	204	14	model	model	VERB
cana-1759	204	15	the	the	DET
cana-1759	204	16	heat	heat	NOUN
cana-1759	204	17	conduction	conduction	NOUN
cana-1759	204	18	in	in	ADP
cana-1759	204	19	materials	material	NOUN
cana-1759	204	20	with	with	ADP
cana-1759	204	21	heterogeneous	heterogeneous	ADJ
cana-1759	204	22	and	and	CCONJ
cana-1759	204	23	porous	porous	ADJ
cana-1759	204	24	structures	structure	NOUN
cana-1759	204	25	,	,	PUNCT
cana-1759	204	26	such	such	ADJ
cana-1759	204	27	as	as	ADP
cana-1759	204	28	aerogels	aerogel	NOUN
cana-1759	204	29	and	and	CCONJ
cana-1759	204	30	foams	foam	NOUN
cana-1759	204	31	.	.	PUNCT
cana-1759	205	1	communications	communication	NOUN
cana-1759	205	2	on	on	ADP
cana-1759	205	3	applied	apply	VERB
cana-1759	205	4	nonlinear	nonlinear	ADJ
cana-1759	205	5	analysis	analysis	NOUN
cana-1759	205	6	issn	issn	NOUN
cana-1759	205	7	:	:	PUNCT
cana-1759	205	8	1074	1074	NUM
cana-1759	205	9	-	-	PUNCT
cana-1759	205	10	133x	133x	NUM
cana-1759	205	11	vol	vol	NOUN
cana-1759	205	12	32	32	NUM
cana-1759	205	13	no	no	NOUN
cana-1759	205	14	.	.	NOUN
cana-1759	205	15	2	2	NUM
cana-1759	205	16	(	(	PUNCT
cana-1759	205	17	2025	2025	NUM
cana-1759	205	18	)	)	PUNCT
cana-1759	205	19	483	483	NUM
cana-1759	205	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	205	21	impact	impact	NOUN
cana-1759	205	22	:	:	PUNCT
cana-1759	205	23	improved	improved	ADJ
cana-1759	205	24	design	design	NOUN
cana-1759	205	25	of	of	ADP
cana-1759	205	26	thermal	thermal	ADJ
cana-1759	205	27	insulation	insulation	NOUN
cana-1759	205	28	materials	material	NOUN
cana-1759	205	29	by	by	ADP
cana-1759	205	30	accurately	accurately	ADV
cana-1759	205	31	capturing	capture	VERB
cana-1759	205	32	the	the	DET
cana-1759	205	33	diffusive	diffusive	ADJ
cana-1759	205	34	and	and	CCONJ
cana-1759	205	35	non	non	ADJ
cana-1759	205	36	-	-	ADJ
cana-1759	205	37	diffusive	diffusive	ADJ
cana-1759	205	38	heat	heat	NOUN
cana-1759	205	39	transfer	transfer	NOUN
cana-1759	205	40	mechanisms	mechanism	NOUN
cana-1759	205	41	,	,	PUNCT
cana-1759	205	42	resulting	result	VERB
cana-1759	205	43	in	in	ADP
cana-1759	205	44	materials	material	NOUN
cana-1759	205	45	with	with	ADP
cana-1759	205	46	superior	superior	ADJ
cana-1759	205	47	insulating	insulate	VERB
cana-1759	205	48	properties	property	NOUN
cana-1759	205	49	.	.	PUNCT
cana-1759	206	1	3	3	X
cana-1759	206	2	.	.	X
cana-1759	206	3	biomedical	biomedical	ADJ
cana-1759	206	4	applications	application	NOUN
cana-1759	206	5	:	:	PUNCT
cana-1759	206	6	description	description	NOUN
cana-1759	206	7	:	:	PUNCT
cana-1759	206	8	in	in	ADP
cana-1759	206	9	hyperthermia	hyperthermia	NOUN
cana-1759	206	10	treatment	treatment	NOUN
cana-1759	206	11	for	for	ADP
cana-1759	206	12	cancer	cancer	NOUN
cana-1759	206	13	,	,	PUNCT
cana-1759	206	14	fractional	fractional	ADJ
cana-1759	206	15	models	model	NOUN
cana-1759	206	16	help	help	VERB
cana-1759	206	17	in	in	ADP
cana-1759	206	18	simulating	simulate	VERB
cana-1759	206	19	the	the	DET
cana-1759	206	20	thermal	thermal	ADJ
cana-1759	206	21	effects	effect	NOUN
cana-1759	206	22	of	of	ADP
cana-1759	206	23	laser	laser	NOUN
cana-1759	206	24	heating	heating	NOUN
cana-1759	206	25	on	on	ADP
cana-1759	206	26	biological	biological	ADJ
cana-1759	206	27	tissues	tissue	NOUN
cana-1759	206	28	,	,	PUNCT
cana-1759	206	29	which	which	PRON
cana-1759	206	30	exhibit	exhibit	VERB
cana-1759	206	31	fractional	fractional	ADJ
cana-1759	206	32	heat	heat	NOUN
cana-1759	206	33	conduction	conduction	NOUN
cana-1759	206	34	characteristics	characteristic	NOUN
cana-1759	206	35	due	due	ADP
cana-1759	206	36	to	to	ADP
cana-1759	206	37	their	their	PRON
cana-1759	206	38	complex	complex	ADJ
cana-1759	206	39	structure	structure	NOUN
cana-1759	206	40	.	.	PUNCT
cana-1759	207	1	impact	impact	NOUN
cana-1759	207	2	:	:	PUNCT
cana-1759	207	3	better	well	ADV
cana-1759	207	4	targeting	targeting	NOUN
cana-1759	207	5	and	and	CCONJ
cana-1759	207	6	control	control	NOUN
cana-1759	207	7	of	of	ADP
cana-1759	207	8	heat	heat	NOUN
cana-1759	207	9	distribution	distribution	NOUN
cana-1759	207	10	in	in	ADP
cana-1759	207	11	tissues	tissue	NOUN
cana-1759	207	12	,	,	PUNCT
cana-1759	207	13	enhancing	enhance	VERB
cana-1759	207	14	the	the	DET
cana-1759	207	15	efficacy	efficacy	NOUN
cana-1759	207	16	and	and	CCONJ
cana-1759	207	17	safety	safety	NOUN
cana-1759	207	18	of	of	ADP
cana-1759	207	19	hyperthermia	hyperthermia	NOUN
cana-1759	207	20	treatments	treatment	NOUN
cana-1759	207	21	.	.	PUNCT
cana-1759	208	1	5.2	5.2	NUM
cana-1759	208	2	.	.	PUNCT
cana-1759	209	1	applications	application	NOUN
cana-1759	209	2	of	of	ADP
cana-1759	209	3	non	non	ADJ
cana-1759	209	4	-	-	ADJ
cana-1759	209	5	newtonian	newtonian	ADJ
cana-1759	209	6	fluid	fluid	NOUN
cana-1759	209	7	models	model	NOUN
cana-1759	209	8	non	non	ADJ
cana-1759	209	9	-	-	ADJ
cana-1759	209	10	newtonian	newtonian	ADJ
cana-1759	209	11	fluid	fluid	NOUN
cana-1759	209	12	models	model	NOUN
cana-1759	209	13	are	be	AUX
cana-1759	209	14	crucial	crucial	ADJ
cana-1759	209	15	in	in	ADP
cana-1759	209	16	industries	industry	NOUN
cana-1759	209	17	and	and	CCONJ
cana-1759	209	18	processes	process	NOUN
cana-1759	209	19	where	where	SCONJ
cana-1759	209	20	fluids	fluid	NOUN
cana-1759	209	21	do	do	AUX
cana-1759	209	22	not	not	PART
cana-1759	209	23	exhibit	exhibit	VERB
cana-1759	209	24	a	a	DET
cana-1759	209	25	constant	constant	ADJ
cana-1759	209	26	viscosity	viscosity	NOUN
cana-1759	209	27	.	.	PUNCT
cana-1759	210	1	applications	application	NOUN
cana-1759	210	2	of	of	ADP
cana-1759	210	3	these	these	DET
cana-1759	210	4	models	model	NOUN
cana-1759	210	5	include	include	VERB
cana-1759	210	6	:	:	PUNCT
cana-1759	210	7	1	1	X
cana-1759	210	8	.	.	PUNCT
cana-1759	210	9	polymer	polymer	NOUN
cana-1759	210	10	processing	processing	NOUN
cana-1759	210	11	:	:	PUNCT
cana-1759	210	12	description	description	NOUN
cana-1759	210	13	:	:	PUNCT
cana-1759	210	14	non	non	ADJ
cana-1759	210	15	-	-	ADJ
cana-1759	210	16	newtonian	newtonian	ADJ
cana-1759	210	17	models	model	NOUN
cana-1759	210	18	such	such	ADJ
cana-1759	210	19	as	as	ADP
cana-1759	210	20	the	the	DET
cana-1759	210	21	power	power	NOUN
cana-1759	210	22	-	-	PUNCT
cana-1759	210	23	law	law	NOUN
cana-1759	210	24	and	and	CCONJ
cana-1759	210	25	carreau	carreau	PROPN
cana-1759	210	26	-	-	PUNCT
cana-1759	210	27	yasuda	yasuda	PROPN
cana-1759	210	28	models	model	NOUN
cana-1759	210	29	are	be	AUX
cana-1759	210	30	used	use	VERB
cana-1759	210	31	to	to	PART
cana-1759	210	32	predict	predict	VERB
cana-1759	210	33	the	the	DET
cana-1759	210	34	flow	flow	NOUN
cana-1759	210	35	behavior	behavior	NOUN
cana-1759	210	36	of	of	ADP
cana-1759	210	37	polymer	polymer	NOUN
cana-1759	210	38	melts	melt	NOUN
cana-1759	210	39	and	and	CCONJ
cana-1759	210	40	solutions	solution	NOUN
cana-1759	210	41	during	during	ADP
cana-1759	210	42	extrusion	extrusion	NOUN
cana-1759	210	43	,	,	PUNCT
cana-1759	210	44	injection	injection	NOUN
cana-1759	210	45	molding	molding	NOUN
cana-1759	210	46	,	,	PUNCT
cana-1759	210	47	and	and	CCONJ
cana-1759	210	48	film	film	VERB
cana-1759	210	49	blowing	blow	VERB
cana-1759	210	50	processes	process	NOUN
cana-1759	210	51	.	.	PUNCT
cana-1759	211	1	impact	impact	NOUN
cana-1759	211	2	:	:	PUNCT
cana-1759	211	3	optimization	optimization	NOUN
cana-1759	211	4	of	of	ADP
cana-1759	211	5	processing	processing	NOUN
cana-1759	211	6	parameters	parameter	NOUN
cana-1759	211	7	,	,	PUNCT
cana-1759	211	8	reduced	reduce	VERB
cana-1759	211	9	defects	defect	NOUN
cana-1759	211	10	,	,	PUNCT
cana-1759	211	11	and	and	CCONJ
cana-1759	211	12	improved	improve	VERB
cana-1759	211	13	quality	quality	NOUN
cana-1759	211	14	of	of	ADP
cana-1759	211	15	polymer	polymer	NOUN
cana-1759	211	16	products	product	NOUN
cana-1759	211	17	through	through	ADP
cana-1759	211	18	accurate	accurate	ADJ
cana-1759	211	19	prediction	prediction	NOUN
cana-1759	211	20	of	of	ADP
cana-1759	211	21	flow	flow	NOUN
cana-1759	211	22	dynamics	dynamic	NOUN
cana-1759	211	23	.	.	PUNCT
cana-1759	212	1	2	2	X
cana-1759	212	2	.	.	X
cana-1759	212	3	oil	oil	NOUN
cana-1759	212	4	and	and	CCONJ
cana-1759	212	5	gas	gas	NOUN
cana-1759	212	6	industry	industry	NOUN
cana-1759	212	7	:	:	PUNCT
cana-1759	212	8	description	description	NOUN
cana-1759	212	9	:	:	PUNCT
cana-1759	212	10	in	in	ADP
cana-1759	212	11	drilling	drilling	NOUN
cana-1759	212	12	operations	operation	NOUN
cana-1759	212	13	,	,	PUNCT
cana-1759	212	14	non	non	ADJ
cana-1759	212	15	-	-	ADJ
cana-1759	212	16	newtonian	newtonian	ADJ
cana-1759	212	17	fluid	fluid	NOUN
cana-1759	212	18	models	model	NOUN
cana-1759	212	19	are	be	AUX
cana-1759	212	20	used	use	VERB
cana-1759	212	21	to	to	PART
cana-1759	212	22	describe	describe	VERB
cana-1759	212	23	the	the	DET
cana-1759	212	24	flow	flow	NOUN
cana-1759	212	25	of	of	ADP
cana-1759	212	26	drilling	drilling	NOUN
cana-1759	212	27	muds	mud	NOUN
cana-1759	212	28	,	,	PUNCT
cana-1759	212	29	which	which	PRON
cana-1759	212	30	are	be	AUX
cana-1759	212	31	complex	complex	ADJ
cana-1759	212	32	fluids	fluid	NOUN
cana-1759	212	33	exhibiting	exhibit	VERB
cana-1759	212	34	shear	shear	NOUN
cana-1759	212	35	-	-	PUNCT
cana-1759	212	36	thinning	thin	VERB
cana-1759	212	37	or	or	CCONJ
cana-1759	212	38	shear	shear	NOUN
cana-1759	212	39	-	-	PUNCT
cana-1759	212	40	thickening	thicken	VERB
cana-1759	212	41	behaviour	behaviour	NOUN
cana-1759	212	42	.	.	PUNCT
cana-1759	213	1	impact	impact	NOUN
cana-1759	213	2	:	:	PUNCT
cana-1759	213	3	enhanced	enhance	VERB
cana-1759	213	4	drilling	drilling	NOUN
cana-1759	213	5	efficiency	efficiency	NOUN
cana-1759	213	6	,	,	PUNCT
cana-1759	213	7	better	well	ADJ
cana-1759	213	8	wellbore	wellbore	NOUN
cana-1759	213	9	stability	stability	NOUN
cana-1759	213	10	,	,	PUNCT
cana-1759	213	11	and	and	CCONJ
cana-1759	213	12	effective	effective	ADJ
cana-1759	213	13	cuttings	cutting	NOUN
cana-1759	213	14	transport	transport	NOUN
cana-1759	213	15	by	by	ADP
cana-1759	213	16	optimizing	optimize	VERB
cana-1759	213	17	the	the	DET
cana-1759	213	18	rheological	rheological	ADJ
cana-1759	213	19	properties	property	NOUN
cana-1759	213	20	of	of	ADP
cana-1759	213	21	drilling	drilling	NOUN
cana-1759	213	22	fluids	fluid	NOUN
cana-1759	213	23	.	.	PUNCT
cana-1759	214	1	3	3	X
cana-1759	214	2	.	.	X
cana-1759	214	3	food	food	NOUN
cana-1759	214	4	industry	industry	NOUN
cana-1759	214	5	:	:	PUNCT
cana-1759	214	6	description	description	NOUN
cana-1759	214	7	:	:	PUNCT
cana-1759	214	8	many	many	ADJ
cana-1759	214	9	food	food	NOUN
cana-1759	214	10	products	product	NOUN
cana-1759	214	11	(	(	PUNCT
cana-1759	214	12	e.g.	e.g.	ADV
cana-1759	214	13	,	,	PUNCT
cana-1759	214	14	ketchup	ketchup	NOUN
cana-1759	214	15	,	,	PUNCT
cana-1759	214	16	yogurt	yogurt	NOUN
cana-1759	214	17	,	,	PUNCT
cana-1759	214	18	and	and	CCONJ
cana-1759	214	19	sauces	sauce	NOUN
cana-1759	214	20	)	)	PUNCT
cana-1759	214	21	are	be	AUX
cana-1759	214	22	non	non	ADJ
cana-1759	214	23	-	-	ADJ
cana-1759	214	24	newtonian	newtonian	ADJ
cana-1759	214	25	fluids	fluid	NOUN
cana-1759	214	26	.	.	PUNCT
cana-1759	215	1	accurate	accurate	ADJ
cana-1759	215	2	modelling	modelling	NOUN
cana-1759	215	3	of	of	ADP
cana-1759	215	4	their	their	PRON
cana-1759	215	5	flow	flow	NOUN
cana-1759	215	6	behaviour	behaviour	NOUN
cana-1759	215	7	using	use	VERB
cana-1759	215	8	non	non	ADJ
cana-1759	215	9	-	-	ADJ
cana-1759	215	10	newtonian	newtonian	ADJ
cana-1759	215	11	fluid	fluid	NOUN
cana-1759	215	12	models	model	NOUN
cana-1759	215	13	helps	help	VERB
cana-1759	215	14	in	in	ADP
cana-1759	215	15	designing	design	VERB
cana-1759	215	16	equipment	equipment	NOUN
cana-1759	215	17	and	and	CCONJ
cana-1759	215	18	processing	processing	NOUN
cana-1759	215	19	lines	line	NOUN
cana-1759	215	20	.	.	PUNCT
cana-1759	216	1	impact	impact	NOUN
cana-1759	216	2	:	:	PUNCT
cana-1759	216	3	improved	improve	VERB
cana-1759	216	4	texture	texture	NOUN
cana-1759	216	5	,	,	PUNCT
cana-1759	216	6	consistency	consistency	NOUN
cana-1759	216	7	,	,	PUNCT
cana-1759	216	8	and	and	CCONJ
cana-1759	216	9	quality	quality	NOUN
cana-1759	216	10	of	of	ADP
cana-1759	216	11	food	food	NOUN
cana-1759	216	12	products	product	NOUN
cana-1759	216	13	through	through	ADP
cana-1759	216	14	better	well	ADJ
cana-1759	216	15	understanding	understanding	NOUN
cana-1759	216	16	and	and	CCONJ
cana-1759	216	17	control	control	NOUN
cana-1759	216	18	of	of	ADP
cana-1759	216	19	flow	flow	NOUN
cana-1759	216	20	properties	property	NOUN
cana-1759	216	21	during	during	ADP
cana-1759	216	22	processing	processing	NOUN
cana-1759	216	23	and	and	CCONJ
cana-1759	216	24	packaging	packaging	NOUN
cana-1759	216	25	.	.	PUNCT
cana-1759	217	1	4	4	X
cana-1759	217	2	.	.	X
cana-1759	217	3	biomedical	biomedical	ADJ
cana-1759	217	4	engineering	engineering	NOUN
cana-1759	217	5	:	:	PUNCT
cana-1759	217	6	description	description	NOUN
cana-1759	217	7	:	:	PUNCT
cana-1759	217	8	blood	blood	NOUN
cana-1759	217	9	is	be	AUX
cana-1759	217	10	a	a	DET
cana-1759	217	11	non	non	ADJ
cana-1759	217	12	-	-	ADJ
cana-1759	217	13	newtonian	newtonian	ADJ
cana-1759	217	14	fluid	fluid	NOUN
cana-1759	217	15	,	,	PUNCT
cana-1759	217	16	and	and	CCONJ
cana-1759	217	17	models	model	NOUN
cana-1759	217	18	such	such	ADJ
cana-1759	217	19	as	as	ADP
cana-1759	217	20	the	the	DET
cana-1759	217	21	casson	casson	PROPN
cana-1759	217	22	and	and	CCONJ
cana-1759	217	23	herschel	herschel	PROPN
cana-1759	217	24	-	-	PUNCT
cana-1759	217	25	bulkley	bulkley	NOUN
cana-1759	217	26	models	model	NOUN
cana-1759	217	27	are	be	AUX
cana-1759	217	28	employed	employ	VERB
cana-1759	217	29	to	to	PART
cana-1759	217	30	study	study	VERB
cana-1759	217	31	blood	blood	NOUN
cana-1759	217	32	flow	flow	NOUN
cana-1759	217	33	in	in	ADP
cana-1759	217	34	arteries	artery	NOUN
cana-1759	217	35	,	,	PUNCT
cana-1759	217	36	capillaries	capillary	NOUN
cana-1759	217	37	,	,	PUNCT
cana-1759	217	38	and	and	CCONJ
cana-1759	217	39	medical	medical	ADJ
cana-1759	217	40	devices	device	NOUN
cana-1759	217	41	.	.	PUNCT
cana-1759	218	1	impact	impact	NOUN
cana-1759	218	2	:	:	PUNCT
cana-1759	218	3	improved	improved	ADJ
cana-1759	218	4	design	design	NOUN
cana-1759	218	5	of	of	ADP
cana-1759	218	6	artificial	artificial	ADJ
cana-1759	218	7	organs	organ	NOUN
cana-1759	218	8	,	,	PUNCT
cana-1759	218	9	stents	stent	NOUN
cana-1759	218	10	,	,	PUNCT
cana-1759	218	11	and	and	CCONJ
cana-1759	218	12	vascular	vascular	ADJ
cana-1759	218	13	grafts	graft	NOUN
cana-1759	218	14	by	by	ADP
cana-1759	218	15	accurately	accurately	ADV
cana-1759	218	16	simulating	simulate	VERB
cana-1759	218	17	blood	blood	NOUN
cana-1759	218	18	flow	flow	NOUN
cana-1759	218	19	and	and	CCONJ
cana-1759	218	20	identifying	identify	VERB
cana-1759	218	21	optimal	optimal	ADJ
cana-1759	218	22	flow	flow	NOUN
cana-1759	218	23	conditions	condition	NOUN
cana-1759	218	24	for	for	ADP
cana-1759	218	25	patient	patient	NOUN
cana-1759	218	26	-	-	PUNCT
cana-1759	218	27	specific	specific	ADJ
cana-1759	218	28	treatments	treatment	NOUN
cana-1759	218	29	.	.	PUNCT
cana-1759	219	1	communications	communication	NOUN
cana-1759	219	2	on	on	ADP
cana-1759	219	3	applied	apply	VERB
cana-1759	219	4	nonlinear	nonlinear	ADJ
cana-1759	219	5	analysis	analysis	NOUN
cana-1759	219	6	issn	issn	NOUN
cana-1759	219	7	:	:	PUNCT
cana-1759	219	8	1074	1074	NUM
cana-1759	219	9	-	-	PUNCT
cana-1759	219	10	133x	133x	NUM
cana-1759	219	11	vol	vol	NOUN
cana-1759	219	12	32	32	NUM
cana-1759	219	13	no	no	NOUN
cana-1759	219	14	.	.	NOUN
cana-1759	219	15	2	2	NUM
cana-1759	219	16	(	(	PUNCT
cana-1759	219	17	2025	2025	NUM
cana-1759	219	18	)	)	PUNCT
cana-1759	219	19	484	484	NUM
cana-1759	219	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	219	21	5.3	5.3	NUM
cana-1759	219	22	.	.	PUNCT
cana-1759	220	1	applications	application	NOUN
cana-1759	220	2	of	of	ADP
cana-1759	220	3	nanofluid	nanofluid	ADJ
cana-1759	220	4	dynamics	dynamic	NOUN
cana-1759	220	5	nanofluids	nanofluid	NOUN
cana-1759	220	6	,	,	PUNCT
cana-1759	220	7	with	with	ADP
cana-1759	220	8	their	their	PRON
cana-1759	220	9	enhanced	enhanced	ADJ
cana-1759	220	10	thermal	thermal	ADJ
cana-1759	220	11	properties	property	NOUN
cana-1759	220	12	,	,	PUNCT
cana-1759	220	13	have	have	VERB
cana-1759	220	14	numerous	numerous	ADJ
cana-1759	220	15	applications	application	NOUN
cana-1759	220	16	in	in	ADP
cana-1759	220	17	various	various	ADJ
cana-1759	220	18	fields	field	NOUN
cana-1759	220	19	.	.	PUNCT
cana-1759	221	1	some	some	PRON
cana-1759	221	2	of	of	ADP
cana-1759	221	3	the	the	DET
cana-1759	221	4	key	key	ADJ
cana-1759	221	5	applications	application	NOUN
cana-1759	221	6	are	be	AUX
cana-1759	221	7	:	:	PUNCT
cana-1759	221	8	1	1	X
cana-1759	221	9	.	.	PUNCT
cana-1759	221	10	microelectronics	microelectronic	NOUN
cana-1759	221	11	cooling	cooling	NOUN
cana-1759	221	12	:	:	PUNCT
cana-1759	221	13	description	description	NOUN
cana-1759	221	14	:	:	PUNCT
cana-1759	221	15	nanofluids	nanofluid	NOUN
cana-1759	221	16	are	be	AUX
cana-1759	221	17	used	use	VERB
cana-1759	221	18	as	as	ADP
cana-1759	221	19	coolants	coolant	NOUN
cana-1759	221	20	in	in	ADP
cana-1759	221	21	microelectronics	microelectronic	NOUN
cana-1759	221	22	due	due	ADJ
cana-1759	221	23	to	to	ADP
cana-1759	221	24	their	their	PRON
cana-1759	221	25	high	high	ADJ
cana-1759	221	26	thermal	thermal	ADJ
cana-1759	221	27	conductivity	conductivity	NOUN
cana-1759	221	28	,	,	PUNCT
cana-1759	221	29	which	which	PRON
cana-1759	221	30	improves	improve	VERB
cana-1759	221	31	heat	heat	NOUN
cana-1759	221	32	dissipation	dissipation	NOUN
cana-1759	221	33	in	in	ADP
cana-1759	221	34	compact	compact	ADJ
cana-1759	221	35	and	and	CCONJ
cana-1759	221	36	high	high	ADJ
cana-1759	221	37	-	-	PUNCT
cana-1759	221	38	performance	performance	NOUN
cana-1759	221	39	electronic	electronic	ADJ
cana-1759	221	40	devices	device	NOUN
cana-1759	221	41	.	.	PUNCT
cana-1759	222	1	impact	impact	NOUN
cana-1759	222	2	:	:	PUNCT
cana-1759	222	3	increased	increase	VERB
cana-1759	222	4	reliability	reliability	NOUN
cana-1759	222	5	and	and	CCONJ
cana-1759	222	6	lifespan	lifespan	NOUN
cana-1759	222	7	of	of	ADP
cana-1759	222	8	electronic	electronic	ADJ
cana-1759	222	9	components	component	NOUN
cana-1759	222	10	by	by	ADP
cana-1759	222	11	preventing	prevent	VERB
cana-1759	222	12	overheating	overheat	VERB
cana-1759	222	13	and	and	CCONJ
cana-1759	222	14	maintaining	maintain	VERB
cana-1759	222	15	optimal	optimal	ADJ
cana-1759	222	16	operating	operating	NOUN
cana-1759	222	17	temperatures	temperature	NOUN
cana-1759	222	18	.	.	PUNCT
cana-1759	223	1	2	2	X
cana-1759	223	2	.	.	X
cana-1759	223	3	solar	solar	ADJ
cana-1759	223	4	energy	energy	NOUN
cana-1759	223	5	systems	system	NOUN
cana-1759	223	6	:	:	PUNCT
cana-1759	223	7	description	description	NOUN
cana-1759	223	8	:	:	PUNCT
cana-1759	223	9	nanofluids	nanofluid	NOUN
cana-1759	223	10	are	be	AUX
cana-1759	223	11	utilized	utilize	VERB
cana-1759	223	12	in	in	ADP
cana-1759	223	13	solar	solar	ADJ
cana-1759	223	14	collectors	collector	NOUN
cana-1759	223	15	to	to	PART
cana-1759	223	16	enhance	enhance	VERB
cana-1759	223	17	heat	heat	NOUN
cana-1759	223	18	absorption	absorption	NOUN
cana-1759	223	19	and	and	CCONJ
cana-1759	223	20	transfer	transfer	NOUN
cana-1759	223	21	properties	property	NOUN
cana-1759	223	22	,	,	PUNCT
cana-1759	223	23	leading	lead	VERB
cana-1759	223	24	to	to	ADP
cana-1759	223	25	more	more	ADV
cana-1759	223	26	efficient	efficient	ADJ
cana-1759	223	27	conversion	conversion	NOUN
cana-1759	223	28	of	of	ADP
cana-1759	223	29	solar	solar	ADJ
cana-1759	223	30	energy	energy	NOUN
cana-1759	223	31	into	into	ADP
cana-1759	223	32	thermal	thermal	ADJ
cana-1759	223	33	energy	energy	NOUN
cana-1759	223	34	.	.	PUNCT
cana-1759	224	1	impact	impact	NOUN
cana-1759	224	2	:	:	PUNCT
cana-1759	224	3	enhanced	enhance	VERB
cana-1759	224	4	efficiency	efficiency	NOUN
cana-1759	224	5	of	of	ADP
cana-1759	224	6	solar	solar	ADJ
cana-1759	224	7	thermal	thermal	ADJ
cana-1759	224	8	systems	system	NOUN
cana-1759	224	9	,	,	PUNCT
cana-1759	224	10	reducing	reduce	VERB
cana-1759	224	11	the	the	DET
cana-1759	224	12	overall	overall	ADJ
cana-1759	224	13	cost	cost	NOUN
cana-1759	224	14	of	of	ADP
cana-1759	224	15	solar	solar	ADJ
cana-1759	224	16	energy	energy	NOUN
cana-1759	224	17	by	by	ADP
cana-1759	224	18	increasing	increase	VERB
cana-1759	224	19	heat	heat	NOUN
cana-1759	224	20	transfer	transfer	NOUN
cana-1759	224	21	rates	rate	NOUN
cana-1759	224	22	.	.	PUNCT
cana-1759	225	1	3	3	X
cana-1759	225	2	.	.	X
cana-1759	225	3	medical	medical	ADJ
cana-1759	225	4	applications	application	NOUN
cana-1759	225	5	(	(	PUNCT
cana-1759	225	6	drug	drug	NOUN
cana-1759	225	7	delivery	delivery	NOUN
cana-1759	225	8	and	and	CCONJ
cana-1759	225	9	hyperthermia	hyperthermia	NOUN
cana-1759	225	10	):	):	PUNCT
cana-1759	225	11	description	description	NOUN
cana-1759	225	12	:	:	PUNCT
cana-1759	225	13	nanofluids	nanofluid	NOUN
cana-1759	225	14	are	be	AUX
cana-1759	225	15	used	use	VERB
cana-1759	225	16	in	in	ADP
cana-1759	225	17	targeted	target	VERB
cana-1759	225	18	drug	drug	NOUN
cana-1759	225	19	delivery	delivery	NOUN
cana-1759	225	20	systems	system	NOUN
cana-1759	225	21	and	and	CCONJ
cana-1759	225	22	magnetic	magnetic	ADJ
cana-1759	225	23	nanoparticle	nanoparticle	NOUN
cana-1759	225	24	hyperthermia	hyperthermia	NOUN
cana-1759	225	25	for	for	ADP
cana-1759	225	26	cancer	cancer	NOUN
cana-1759	225	27	treatment	treatment	NOUN
cana-1759	225	28	,	,	PUNCT
cana-1759	225	29	exploiting	exploit	VERB
cana-1759	225	30	their	their	PRON
cana-1759	225	31	unique	unique	ADJ
cana-1759	225	32	thermal	thermal	ADJ
cana-1759	225	33	and	and	CCONJ
cana-1759	225	34	magnetic	magnetic	ADJ
cana-1759	225	35	properties	property	NOUN
cana-1759	225	36	.	.	PUNCT
cana-1759	226	1	impact	impact	NOUN
cana-1759	226	2	:	:	PUNCT
cana-1759	226	3	improved	improve	VERB
cana-1759	226	4	treatment	treatment	NOUN
cana-1759	226	5	outcomes	outcome	NOUN
cana-1759	226	6	by	by	ADP
cana-1759	226	7	ensuring	ensure	VERB
cana-1759	226	8	precise	precise	ADJ
cana-1759	226	9	drug	drug	NOUN
cana-1759	226	10	delivery	delivery	NOUN
cana-1759	226	11	to	to	PART
cana-1759	226	12	target	target	VERB
cana-1759	226	13	sites	site	NOUN
cana-1759	226	14	and	and	CCONJ
cana-1759	226	15	effective	effective	ADJ
cana-1759	226	16	thermal	thermal	ADJ
cana-1759	226	17	treatment	treatment	NOUN
cana-1759	226	18	of	of	ADP
cana-1759	226	19	tumors	tumor	NOUN
cana-1759	226	20	with	with	ADP
cana-1759	226	21	minimal	minimal	ADJ
cana-1759	226	22	side	side	NOUN
cana-1759	226	23	effects	effect	NOUN
cana-1759	226	24	.	.	PUNCT
cana-1759	227	1	4	4	X
cana-1759	227	2	.	.	X
cana-1759	227	3	heat	heat	NOUN
cana-1759	227	4	exchangers	exchanger	NOUN
cana-1759	227	5	and	and	CCONJ
cana-1759	227	6	industrial	industrial	ADJ
cana-1759	227	7	cooling	cool	VERB
cana-1759	227	8	systems	system	NOUN
cana-1759	227	9	:	:	PUNCT
cana-1759	227	10	description	description	NOUN
cana-1759	227	11	:	:	PUNCT
cana-1759	227	12	nanofluids	nanofluid	NOUN
cana-1759	227	13	are	be	AUX
cana-1759	227	14	employed	employ	VERB
cana-1759	227	15	in	in	ADP
cana-1759	227	16	heat	heat	NOUN
cana-1759	227	17	exchangers	exchanger	NOUN
cana-1759	227	18	to	to	PART
cana-1759	227	19	improve	improve	VERB
cana-1759	227	20	thermal	thermal	ADJ
cana-1759	227	21	performance	performance	NOUN
cana-1759	227	22	by	by	ADP
cana-1759	227	23	enhancing	enhance	VERB
cana-1759	227	24	convective	convective	ADJ
cana-1759	227	25	heat	heat	NOUN
cana-1759	227	26	transfer	transfer	NOUN
cana-1759	227	27	coefficients	coefficient	NOUN
cana-1759	227	28	.	.	PUNCT
cana-1759	228	1	impact	impact	NOUN
cana-1759	228	2	:	:	PUNCT
cana-1759	228	3	increased	increase	VERB
cana-1759	228	4	energy	energy	NOUN
cana-1759	228	5	efficiency	efficiency	NOUN
cana-1759	228	6	and	and	CCONJ
cana-1759	228	7	reduced	reduce	VERB
cana-1759	228	8	size	size	NOUN
cana-1759	228	9	of	of	ADP
cana-1759	228	10	heat	heat	NOUN
cana-1759	228	11	exchangers	exchanger	NOUN
cana-1759	228	12	,	,	PUNCT
cana-1759	228	13	leading	lead	VERB
cana-1759	228	14	to	to	AUX
cana-1759	228	15	cost	cost	VERB
cana-1759	228	16	savings	saving	NOUN
cana-1759	228	17	and	and	CCONJ
cana-1759	228	18	more	more	ADJ
cana-1759	228	19	compact	compact	ADJ
cana-1759	228	20	designs	design	NOUN
cana-1759	228	21	in	in	ADP
cana-1759	228	22	industrial	industrial	ADJ
cana-1759	228	23	applications	application	NOUN
cana-1759	228	24	.	.	PUNCT
cana-1759	229	1	5	5	X
cana-1759	229	2	.	.	X
cana-1759	229	3	automotive	automotive	ADJ
cana-1759	229	4	and	and	CCONJ
cana-1759	229	5	aerospace	aerospace	NOUN
cana-1759	229	6	:	:	PUNCT
cana-1759	229	7	description	description	NOUN
cana-1759	229	8	:	:	PUNCT
cana-1759	229	9	nanofluids	nanofluid	NOUN
cana-1759	229	10	are	be	AUX
cana-1759	229	11	used	use	VERB
cana-1759	229	12	in	in	ADP
cana-1759	229	13	automotive	automotive	ADJ
cana-1759	229	14	cooling	cool	VERB
cana-1759	229	15	systems	system	NOUN
cana-1759	229	16	and	and	CCONJ
cana-1759	229	17	aerospace	aerospace	NOUN
cana-1759	229	18	thermal	thermal	ADJ
cana-1759	229	19	management	management	NOUN
cana-1759	229	20	systems	system	NOUN
cana-1759	229	21	due	due	ADP
cana-1759	229	22	to	to	ADP
cana-1759	229	23	their	their	PRON
cana-1759	229	24	superior	superior	ADJ
cana-1759	229	25	heat	heat	NOUN
cana-1759	229	26	transfer	transfer	NOUN
cana-1759	229	27	capabilities	capability	NOUN
cana-1759	229	28	.	.	PUNCT
cana-1759	230	1	impact	impact	NOUN
cana-1759	230	2	:	:	PUNCT
cana-1759	230	3	enhanced	enhance	VERB
cana-1759	230	4	thermal	thermal	ADJ
cana-1759	230	5	performance	performance	NOUN
cana-1759	230	6	and	and	CCONJ
cana-1759	230	7	fuel	fuel	NOUN
cana-1759	230	8	efficiency	efficiency	NOUN
cana-1759	230	9	in	in	ADP
cana-1759	230	10	automotive	automotive	ADJ
cana-1759	230	11	engines	engine	NOUN
cana-1759	230	12	and	and	CCONJ
cana-1759	230	13	improved	improve	VERB
cana-1759	230	14	cooling	cooling	NOUN
cana-1759	230	15	in	in	ADP
cana-1759	230	16	aerospace	aerospace	NOUN
cana-1759	230	17	applications	application	NOUN
cana-1759	230	18	,	,	PUNCT
cana-1759	230	19	contributing	contribute	VERB
cana-1759	230	20	to	to	ADP
cana-1759	230	21	overall	overall	ADJ
cana-1759	230	22	system	system	NOUN
cana-1759	230	23	reliability	reliability	NOUN
cana-1759	230	24	and	and	CCONJ
cana-1759	230	25	performance	performance	NOUN
cana-1759	230	26	.	.	PUNCT
cana-1759	231	1	5.4	5.4	NUM
cana-1759	231	2	.	.	PUNCT
cana-1759	231	3	synthesis	synthesis	NOUN
cana-1759	231	4	of	of	ADP
cana-1759	231	5	applications	application	NOUN
cana-1759	231	6	the	the	DET
cana-1759	231	7	integration	integration	NOUN
cana-1759	231	8	of	of	ADP
cana-1759	231	9	fractional	fractional	ADJ
cana-1759	231	10	calculus	calculus	NOUN
cana-1759	231	11	,	,	PUNCT
cana-1759	231	12	non	non	ADJ
cana-1759	231	13	-	-	ADJ
cana-1759	231	14	newtonian	newtonian	ADJ
cana-1759	231	15	fluid	fluid	ADJ
cana-1759	231	16	models	model	NOUN
cana-1759	231	17	,	,	PUNCT
cana-1759	231	18	and	and	CCONJ
cana-1759	231	19	nanofluid	nanofluid	ADJ
cana-1759	231	20	dynamics	dynamic	NOUN
cana-1759	231	21	into	into	ADP
cana-1759	231	22	mathematical	mathematical	ADJ
cana-1759	231	23	modelling	modelling	NOUN
cana-1759	231	24	of	of	ADP
cana-1759	231	25	heat	heat	NOUN
cana-1759	231	26	transfer	transfer	NOUN
cana-1759	231	27	and	and	CCONJ
cana-1759	231	28	fluid	fluid	NOUN
cana-1759	231	29	flow	flow	NOUN
cana-1759	231	30	has	have	VERB
cana-1759	231	31	broad	broad	ADJ
cana-1759	231	32	and	and	CCONJ
cana-1759	231	33	significant	significant	ADJ
cana-1759	231	34	applications	application	NOUN
cana-1759	231	35	across	across	ADP
cana-1759	231	36	diverse	diverse	ADJ
cana-1759	231	37	fields	field	NOUN
cana-1759	231	38	.	.	PUNCT
cana-1759	232	1	these	these	DET
cana-1759	232	2	advanced	advanced	ADJ
cana-1759	232	3	models	model	NOUN
cana-1759	232	4	provide	provide	VERB
cana-1759	232	5	a	a	DET
cana-1759	232	6	more	more	ADV
cana-1759	232	7	accurate	accurate	ADJ
cana-1759	232	8	representation	representation	NOUN
cana-1759	232	9	of	of	ADP
cana-1759	232	10	complex	complex	ADJ
cana-1759	232	11	physical	physical	ADJ
cana-1759	232	12	behaviours	behaviour	NOUN
cana-1759	232	13	,	,	PUNCT
cana-1759	232	14	enabling	enable	VERB
cana-1759	232	15	better	well	ADJ
cana-1759	232	16	design	design	NOUN
cana-1759	232	17	,	,	PUNCT
cana-1759	232	18	optimization	optimization	NOUN
cana-1759	232	19	,	,	PUNCT
cana-1759	232	20	and	and	CCONJ
cana-1759	232	21	control	control	NOUN
cana-1759	232	22	of	of	ADP
cana-1759	232	23	systems	system	NOUN
cana-1759	232	24	in	in	ADP
cana-1759	232	25	energy	energy	NOUN
cana-1759	232	26	,	,	PUNCT
cana-1759	232	27	healthcare	healthcare	NOUN
cana-1759	232	28	,	,	PUNCT
cana-1759	232	29	manufacturing	manufacturing	NOUN
cana-1759	232	30	,	,	PUNCT
cana-1759	232	31	and	and	CCONJ
cana-1759	232	32	advanced	advanced	ADJ
cana-1759	232	33	materials	material	NOUN
cana-1759	232	34	science	science	NOUN
cana-1759	232	35	.	.	PUNCT
cana-1759	233	1	as	as	SCONJ
cana-1759	233	2	these	these	DET
cana-1759	233	3	fields	field	NOUN
cana-1759	233	4	continue	continue	VERB
cana-1759	233	5	to	to	PART
cana-1759	233	6	evolve	evolve	VERB
cana-1759	233	7	,	,	PUNCT
cana-1759	233	8	the	the	DET
cana-1759	233	9	role	role	NOUN
cana-1759	233	10	of	of	ADP
cana-1759	233	11	communications	communication	NOUN
cana-1759	233	12	on	on	ADP
cana-1759	233	13	applied	apply	VERB
cana-1759	233	14	nonlinear	nonlinear	ADJ
cana-1759	233	15	analysis	analysis	NOUN
cana-1759	233	16	issn	issn	NOUN
cana-1759	233	17	:	:	PUNCT
cana-1759	233	18	1074	1074	NUM
cana-1759	233	19	-	-	PUNCT
cana-1759	233	20	133x	133x	NUM
cana-1759	233	21	vol	vol	NOUN
cana-1759	233	22	32	32	NUM
cana-1759	233	23	no	no	NOUN
cana-1759	233	24	.	.	NOUN
cana-1759	233	25	2	2	NUM
cana-1759	233	26	(	(	PUNCT
cana-1759	233	27	2025	2025	NUM
cana-1759	233	28	)	)	PUNCT
cana-1759	233	29	485	485	NUM
cana-1759	233	30	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	233	31	sophisticated	sophisticated	ADJ
cana-1759	233	32	mathematical	mathematical	ADJ
cana-1759	233	33	models	model	NOUN
cana-1759	233	34	in	in	ADP
cana-1759	233	35	improving	improve	VERB
cana-1759	233	36	system	system	NOUN
cana-1759	233	37	performance	performance	NOUN
cana-1759	233	38	and	and	CCONJ
cana-1759	233	39	efficiency	efficiency	NOUN
cana-1759	233	40	will	will	AUX
cana-1759	233	41	become	become	VERB
cana-1759	233	42	even	even	ADV
cana-1759	233	43	more	more	ADV
cana-1759	233	44	critical	critical	ADJ
cana-1759	233	45	.	.	PUNCT
cana-1759	234	1	6	6	X
cana-1759	234	2	.	.	X
cana-1759	234	3	results	result	NOUN
cana-1759	234	4	and	and	CCONJ
cana-1759	234	5	discussion	discussion	NOUN
cana-1759	234	6	the	the	DET
cana-1759	234	7	numerical	numerical	ADJ
cana-1759	234	8	examples	example	NOUN
cana-1759	234	9	provided	provide	VERB
cana-1759	234	10	in	in	ADP
cana-1759	234	11	the	the	DET
cana-1759	234	12	previous	previous	ADJ
cana-1759	234	13	section	section	NOUN
cana-1759	234	14	illustrate	illustrate	VERB
cana-1759	234	15	the	the	DET
cana-1759	234	16	application	application	NOUN
cana-1759	234	17	of	of	ADP
cana-1759	234	18	advanced	advanced	ADJ
cana-1759	234	19	mathematical	mathematical	ADJ
cana-1759	234	20	modelling	modelling	NOUN
cana-1759	234	21	techniques	technique	NOUN
cana-1759	234	22	—	—	PUNCT
cana-1759	234	23	fractional	fractional	ADJ
cana-1759	234	24	calculus	calculus	NOUN
cana-1759	234	25	,	,	PUNCT
cana-1759	234	26	non	non	ADJ
cana-1759	234	27	-	-	ADJ
cana-1759	234	28	newtonian	newtonian	ADJ
cana-1759	234	29	fluid	fluid	ADJ
cana-1759	234	30	dynamics	dynamic	NOUN
cana-1759	234	31	,	,	PUNCT
cana-1759	234	32	and	and	CCONJ
cana-1759	234	33	nanofluid	nanofluid	ADJ
cana-1759	234	34	dynamics	dynamic	NOUN
cana-1759	234	35	—	—	PUNCT
cana-1759	234	36	to	to	PART
cana-1759	234	37	solve	solve	VERB
cana-1759	234	38	complex	complex	ADJ
cana-1759	234	39	heat	heat	NOUN
cana-1759	234	40	transfer	transfer	NOUN
cana-1759	234	41	and	and	CCONJ
cana-1759	234	42	fluid	fluid	ADJ
cana-1759	234	43	flow	flow	NOUN
cana-1759	234	44	problems	problem	NOUN
cana-1759	234	45	.	.	PUNCT
cana-1759	235	1	the	the	DET
cana-1759	235	2	results	result	NOUN
cana-1759	235	3	obtained	obtain	VERB
cana-1759	235	4	from	from	ADP
cana-1759	235	5	these	these	DET
cana-1759	235	6	examples	example	NOUN
cana-1759	235	7	are	be	AUX
cana-1759	235	8	discussed	discuss	VERB
cana-1759	235	9	in	in	ADP
cana-1759	235	10	detail	detail	NOUN
cana-1759	235	11	below	below	ADV
cana-1759	235	12	,	,	PUNCT
cana-1759	235	13	highlighting	highlight	VERB
cana-1759	235	14	their	their	PRON
cana-1759	235	15	significance	significance	NOUN
cana-1759	235	16	,	,	PUNCT
cana-1759	235	17	interpretation	interpretation	NOUN
cana-1759	235	18	,	,	PUNCT
cana-1759	235	19	and	and	CCONJ
cana-1759	235	20	potential	potential	ADJ
cana-1759	235	21	impact	impact	NOUN
cana-1759	235	22	on	on	ADP
cana-1759	235	23	real	real	ADJ
cana-1759	235	24	-	-	PUNCT
cana-1759	235	25	world	world	NOUN
cana-1759	235	26	applications	application	NOUN
cana-1759	235	27	.	.	PUNCT
cana-1759	236	1	example	example	NOUN
cana-1759	237	1	1	1	NUM
cana-1759	237	2	:	:	PUNCT
cana-1759	237	3	heat	heat	NOUN
cana-1759	237	4	transfer	transfer	NOUN
cana-1759	237	5	in	in	ADP
cana-1759	237	6	a	a	DET
cana-1759	237	7	fractional	fractional	ADJ
cana-1759	237	8	medium	medium	ADJ
cana-1759	237	9	results	result	NOUN
cana-1759	237	10	:	:	PUNCT
cana-1759	237	11	the	the	DET
cana-1759	237	12	temperature	temperature	NOUN
cana-1759	237	13	profile	profile	NOUN
cana-1759	237	14	t(x	t(x	PROPN
cana-1759	237	15	,	,	PUNCT
cana-1759	237	16	t	t	PROPN
cana-1759	237	17	)	)	PUNCT
cana-1759	237	18	for	for	ADP
cana-1759	237	19	the	the	DET
cana-1759	237	20	fractional	fractional	ADJ
cana-1759	237	21	heat	heat	NOUN
cana-1759	237	22	conduction	conduction	NOUN
cana-1759	237	23	model	model	NOUN
cana-1759	237	24	with	with	ADP
cana-1759	237	25	α	α	NOUN
cana-1759	237	26	=	=	SYM
cana-1759	237	27	0.8	0.8	NUM
cana-1759	237	28	shows	show	VERB
cana-1759	237	29	a	a	DET
cana-1759	237	30	slower	slow	ADJ
cana-1759	237	31	diffusion	diffusion	NOUN
cana-1759	237	32	rate	rate	NOUN
cana-1759	237	33	compared	compare	VERB
cana-1759	237	34	to	to	ADP
cana-1759	237	35	the	the	DET
cana-1759	237	36	classical	classical	ADJ
cana-1759	237	37	case	case	NOUN
cana-1759	237	38	α=	α=	NOUN
cana-1759	237	39	1	1	NUM
cana-1759	237	40	,	,	PUNCT
cana-1759	237	41	reflecting	reflect	VERB
cana-1759	237	42	the	the	DET
cana-1759	237	43	memory	memory	NOUN
cana-1759	237	44	and	and	CCONJ
cana-1759	237	45	hereditary	hereditary	ADJ
cana-1759	237	46	properties	property	NOUN
cana-1759	237	47	of	of	ADP
cana-1759	237	48	the	the	DET
cana-1759	237	49	fractional	fractional	ADJ
cana-1759	237	50	medium	medium	NOUN
cana-1759	237	51	.	.	PUNCT
cana-1759	238	1	for	for	ADP
cana-1759	238	2	different	different	ADJ
cana-1759	238	3	values	value	NOUN
cana-1759	238	4	of	of	ADP
cana-1759	238	5	α	α	NOUN
cana-1759	238	6	,	,	PUNCT
cana-1759	238	7	the	the	DET
cana-1759	238	8	rate	rate	NOUN
cana-1759	238	9	of	of	ADP
cana-1759	238	10	heat	heat	NOUN
cana-1759	238	11	diffusion	diffusion	NOUN
cana-1759	238	12	decreases	decrease	NOUN
cana-1759	238	13	as	as	ADP
cana-1759	238	14	α	α	NOUN
cana-1759	238	15	decreases	decrease	NOUN
cana-1759	238	16	,	,	PUNCT
cana-1759	238	17	indicating	indicate	VERB
cana-1759	238	18	stronger	strong	ADJ
cana-1759	238	19	memory	memory	NOUN
cana-1759	238	20	effects	effect	NOUN
cana-1759	238	21	in	in	ADP
cana-1759	238	22	the	the	DET
cana-1759	238	23	material	material	NOUN
cana-1759	238	24	.	.	PUNCT
cana-1759	239	1	for	for	ADP
cana-1759	239	2	example	example	NOUN
cana-1759	239	3	,	,	PUNCT
cana-1759	239	4	for	for	ADP
cana-1759	239	5	α	α	NOUN
cana-1759	239	6	=	=	SYM
cana-1759	239	7	0.6	0.6	NUM
cana-1759	239	8	,	,	PUNCT
cana-1759	239	9	the	the	DET
cana-1759	239	10	temperature	temperature	NOUN
cana-1759	239	11	gradient	gradient	NOUN
cana-1759	239	12	is	be	AUX
cana-1759	239	13	steeper	steep	ADJ
cana-1759	239	14	near	near	ADP
cana-1759	239	15	the	the	DET
cana-1759	239	16	heat	heat	NOUN
cana-1759	239	17	source	source	NOUN
cana-1759	239	18	and	and	CCONJ
cana-1759	239	19	flattens	flatten	VERB
cana-1759	239	20	more	more	ADV
cana-1759	239	21	slowly	slowly	ADV
cana-1759	239	22	as	as	SCONJ
cana-1759	239	23	time	time	NOUN
cana-1759	239	24	progresses	progress	VERB
cana-1759	239	25	.	.	PUNCT
cana-1759	240	1	discussion	discussion	NOUN
cana-1759	240	2	:	:	PUNCT
cana-1759	240	3	the	the	DET
cana-1759	240	4	results	result	NOUN
cana-1759	240	5	demonstrate	demonstrate	VERB
cana-1759	240	6	that	that	SCONJ
cana-1759	240	7	fractional	fractional	ADJ
cana-1759	240	8	-	-	PUNCT
cana-1759	240	9	order	order	NOUN
cana-1759	240	10	models	model	NOUN
cana-1759	240	11	provide	provide	VERB
cana-1759	240	12	a	a	DET
cana-1759	240	13	more	more	ADV
cana-1759	240	14	accurate	accurate	ADJ
cana-1759	240	15	description	description	NOUN
cana-1759	240	16	of	of	ADP
cana-1759	240	17	heat	heat	NOUN
cana-1759	240	18	conduction	conduction	NOUN
cana-1759	240	19	in	in	ADP
cana-1759	240	20	materials	material	NOUN
cana-1759	240	21	with	with	ADP
cana-1759	240	22	non	non	ADJ
cana-1759	240	23	-	-	ADJ
cana-1759	240	24	local	local	ADJ
cana-1759	240	25	and	and	CCONJ
cana-1759	240	26	memory	memory	NOUN
cana-1759	240	27	-	-	PUNCT
cana-1759	240	28	dependent	dependent	ADJ
cana-1759	240	29	properties	property	NOUN
cana-1759	240	30	,	,	PUNCT
cana-1759	240	31	such	such	ADJ
cana-1759	240	32	as	as	ADP
cana-1759	240	33	porous	porous	ADJ
cana-1759	240	34	media	medium	NOUN
cana-1759	240	35	,	,	PUNCT
cana-1759	240	36	biological	biological	ADJ
cana-1759	240	37	tissues	tissue	NOUN
cana-1759	240	38	,	,	PUNCT
cana-1759	240	39	and	and	CCONJ
cana-1759	240	40	advanced	advanced	ADJ
cana-1759	240	41	composites	composite	NOUN
cana-1759	240	42	.	.	PUNCT
cana-1759	241	1	the	the	DET
cana-1759	241	2	slower	slow	ADJ
cana-1759	241	3	diffusion	diffusion	NOUN
cana-1759	241	4	rates	rate	NOUN
cana-1759	241	5	observed	observe	VERB
cana-1759	241	6	for	for	ADP
cana-1759	241	7	lower	low	ADJ
cana-1759	241	8	α	α	PROPN
cana-1759	241	9	values	value	NOUN
cana-1759	241	10	align	align	VERB
cana-1759	241	11	with	with	ADP
cana-1759	241	12	experimental	experimental	ADJ
cana-1759	241	13	observations	observation	NOUN
cana-1759	241	14	of	of	ADP
cana-1759	241	15	anomalous	anomalous	ADJ
cana-1759	241	16	heat	heat	NOUN
cana-1759	241	17	conduction	conduction	NOUN
cana-1759	241	18	,	,	PUNCT
cana-1759	241	19	where	where	SCONJ
cana-1759	241	20	thermal	thermal	ADJ
cana-1759	241	21	waves	wave	NOUN
cana-1759	241	22	do	do	AUX
cana-1759	241	23	not	not	PART
cana-1759	241	24	propagate	propagate	VERB
cana-1759	241	25	as	as	SCONJ
cana-1759	241	26	expected	expect	VERB
cana-1759	241	27	in	in	ADP
cana-1759	241	28	conventional	conventional	ADJ
cana-1759	241	29	models	model	NOUN
cana-1759	241	30	.	.	PUNCT
cana-1759	242	1	this	this	DET
cana-1759	242	2	enhanced	enhance	VERB
cana-1759	242	3	modelling	modelling	NOUN
cana-1759	242	4	capability	capability	NOUN
cana-1759	242	5	is	be	AUX
cana-1759	242	6	particularly	particularly	ADV
cana-1759	242	7	useful	useful	ADJ
cana-1759	242	8	in	in	ADP
cana-1759	242	9	designing	design	VERB
cana-1759	242	10	materials	material	NOUN
cana-1759	242	11	and	and	CCONJ
cana-1759	242	12	systems	system	NOUN
cana-1759	242	13	where	where	SCONJ
cana-1759	242	14	precise	precise	ADJ
cana-1759	242	15	thermal	thermal	ADJ
cana-1759	242	16	management	management	NOUN
cana-1759	242	17	is	be	AUX
cana-1759	242	18	crucial	crucial	ADJ
cana-1759	242	19	,	,	PUNCT
cana-1759	242	20	such	such	ADJ
cana-1759	242	21	as	as	ADP
cana-1759	242	22	in	in	ADP
cana-1759	242	23	thermal	thermal	ADJ
cana-1759	242	24	insulation	insulation	NOUN
cana-1759	242	25	,	,	PUNCT
cana-1759	242	26	geothermal	geothermal	ADJ
cana-1759	242	27	energy	energy	NOUN
cana-1759	242	28	extraction	extraction	NOUN
cana-1759	242	29	,	,	PUNCT
cana-1759	242	30	and	and	CCONJ
cana-1759	242	31	biomedical	biomedical	ADJ
cana-1759	242	32	applications	application	NOUN
cana-1759	242	33	.	.	PUNCT
cana-1759	242	34	example	example	NOUN
cana-1759	243	1	2	2	NUM
cana-1759	243	2	:	:	PUNCT
cana-1759	243	3	non	non	ADJ
cana-1759	243	4	-	-	ADJ
cana-1759	243	5	newtonian	newtonian	ADJ
cana-1759	243	6	fluid	fluid	ADJ
cana-1759	243	7	flow	flow	NOUN
cana-1759	243	8	in	in	ADP
cana-1759	243	9	a	a	DET
cana-1759	243	10	pipe	pipe	NOUN
cana-1759	243	11	results	result	NOUN
cana-1759	243	12	:	:	PUNCT
cana-1759	243	13	the	the	DET
cana-1759	243	14	velocity	velocity	NOUN
cana-1759	243	15	profile	profile	NOUN
cana-1759	243	16	u(r	u(r	PROPN
cana-1759	243	17	)	)	PUNCT
cana-1759	243	18	for	for	ADP
cana-1759	243	19	a	a	DET
cana-1759	243	20	shear	shear	NOUN
cana-1759	243	21	-	-	PUNCT
cana-1759	243	22	thinning	thin	VERB
cana-1759	243	23	fluid	fluid	NOUN
cana-1759	243	24	(	(	PUNCT
cana-1759	243	25	power	power	NOUN
cana-1759	243	26	-	-	PUNCT
cana-1759	243	27	law	law	NOUN
cana-1759	243	28	model	model	NOUN
cana-1759	243	29	with	with	ADP
cana-1759	243	30	n	n	NOUN
cana-1759	243	31	=	=	SYM
cana-1759	243	32	0.5	0.5	NUM
cana-1759	243	33	)	)	PUNCT
cana-1759	243	34	exhibits	exhibit	VERB
cana-1759	243	35	a	a	DET
cana-1759	243	36	more	more	ADV
cana-1759	243	37	flattened	flatten	VERB
cana-1759	243	38	profile	profile	NOUN
cana-1759	243	39	near	near	ADP
cana-1759	243	40	the	the	DET
cana-1759	243	41	pipe	pipe	NOUN
cana-1759	243	42	centre	centre	NOUN
cana-1759	243	43	compared	compare	VERB
cana-1759	243	44	to	to	ADP
cana-1759	243	45	a	a	DET
cana-1759	243	46	newtonian	newtonian	ADJ
cana-1759	243	47	fluid	fluid	NOUN
cana-1759	243	48	.	.	PUNCT
cana-1759	244	1	the	the	DET
cana-1759	244	2	flow	flow	NOUN
cana-1759	244	3	velocity	velocity	NOUN
cana-1759	244	4	decreases	decrease	VERB
cana-1759	244	5	rapidly	rapidly	ADV
cana-1759	244	6	near	near	ADP
cana-1759	244	7	the	the	DET
cana-1759	244	8	walls	wall	NOUN
cana-1759	244	9	,	,	PUNCT
cana-1759	244	10	indicating	indicate	VERB
cana-1759	244	11	higher	high	ADJ
cana-1759	244	12	shear	shear	NOUN
cana-1759	244	13	rates	rate	NOUN
cana-1759	244	14	and	and	CCONJ
cana-1759	244	15	lower	low	ADJ
cana-1759	244	16	viscosity	viscosity	NOUN
cana-1759	244	17	.	.	PUNCT
cana-1759	245	1	for	for	ADP
cana-1759	245	2	a	a	DET
cana-1759	245	3	shear	shear	NOUN
cana-1759	245	4	-	-	PUNCT
cana-1759	245	5	thickening	thicken	VERB
cana-1759	245	6	fluid	fluid	NOUN
cana-1759	245	7	(	(	PUNCT
cana-1759	245	8	power	power	NOUN
cana-1759	245	9	-	-	PUNCT
cana-1759	245	10	law	law	NOUN
cana-1759	245	11	model	model	NOUN
cana-1759	245	12	with	with	ADP
cana-1759	245	13	n	n	NOUN
cana-1759	245	14	=	=	SYM
cana-1759	245	15	1.5	1.5	NUM
cana-1759	245	16	,	,	PUNCT
cana-1759	245	17	the	the	DET
cana-1759	245	18	velocity	velocity	NOUN
cana-1759	245	19	profile	profile	NOUN
cana-1759	245	20	is	be	AUX
cana-1759	245	21	more	more	ADV
cana-1759	245	22	peaked	peaked	ADJ
cana-1759	245	23	at	at	ADP
cana-1759	245	24	the	the	DET
cana-1759	245	25	center	center	NOUN
cana-1759	245	26	,	,	PUNCT
cana-1759	245	27	with	with	ADP
cana-1759	245	28	a	a	DET
cana-1759	245	29	slower	slow	ADJ
cana-1759	245	30	rate	rate	NOUN
cana-1759	245	31	of	of	ADP
cana-1759	245	32	decrease	decrease	NOUN
cana-1759	245	33	towards	towards	ADP
cana-1759	245	34	the	the	DET
cana-1759	245	35	pipe	pipe	NOUN
cana-1759	245	36	walls	wall	NOUN
cana-1759	245	37	,	,	PUNCT
cana-1759	245	38	reflecting	reflect	VERB
cana-1759	245	39	increased	increase	VERB
cana-1759	245	40	viscosity	viscosity	NOUN
cana-1759	245	41	with	with	ADP
cana-1759	245	42	higher	high	ADJ
cana-1759	245	43	shear	shear	NOUN
cana-1759	245	44	rates	rate	NOUN
cana-1759	245	45	.	.	PUNCT
cana-1759	246	1	the	the	DET
cana-1759	246	2	bingham	bingham	PROPN
cana-1759	246	3	plastic	plastic	NOUN
cana-1759	246	4	model	model	NOUN
cana-1759	246	5	shows	show	VERB
cana-1759	246	6	a	a	DET
cana-1759	246	7	yield	yield	NOUN
cana-1759	246	8	stress	stress	NOUN
cana-1759	246	9	threshold	threshold	NOUN
cana-1759	246	10	,	,	PUNCT
cana-1759	246	11	below	below	ADP
cana-1759	246	12	which	which	PRON
cana-1759	246	13	the	the	DET
cana-1759	246	14	fluid	fluid	NOUN
cana-1759	246	15	behaves	behave	VERB
cana-1759	246	16	as	as	ADP
cana-1759	246	17	a	a	DET
cana-1759	246	18	solid	solid	ADJ
cana-1759	246	19	and	and	CCONJ
cana-1759	246	20	does	do	AUX
cana-1759	246	21	not	not	PART
cana-1759	246	22	flow	flow	VERB
cana-1759	246	23	.	.	PUNCT
cana-1759	247	1	the	the	DET
cana-1759	247	2	velocity	velocity	NOUN
cana-1759	247	3	profile	profile	NOUN
cana-1759	247	4	is	be	AUX
cana-1759	247	5	flat	flat	ADJ
cana-1759	247	6	in	in	ADP
cana-1759	247	7	the	the	DET
cana-1759	247	8	core	core	NOUN
cana-1759	247	9	region	region	NOUN
cana-1759	247	10	where	where	SCONJ
cana-1759	247	11	the	the	DET
cana-1759	247	12	yield	yield	NOUN
cana-1759	247	13	stress	stress	NOUN
cana-1759	247	14	is	be	AUX
cana-1759	247	15	not	not	PART
cana-1759	247	16	exceeded	exceed	VERB
cana-1759	247	17	and	and	CCONJ
cana-1759	247	18	only	only	ADV
cana-1759	247	19	increases	increase	NOUN
cana-1759	247	20	beyond	beyond	ADP
cana-1759	247	21	this	this	DET
cana-1759	247	22	region	region	NOUN
cana-1759	247	23	.	.	PUNCT
cana-1759	248	1	discussion	discussion	NOUN
cana-1759	248	2	:	:	PUNCT
cana-1759	248	3	communications	communication	NOUN
cana-1759	248	4	on	on	ADP
cana-1759	248	5	applied	apply	VERB
cana-1759	248	6	nonlinear	nonlinear	ADJ
cana-1759	248	7	analysis	analysis	NOUN
cana-1759	248	8	issn	issn	NOUN
cana-1759	248	9	:	:	PUNCT
cana-1759	248	10	1074	1074	NUM
cana-1759	248	11	-	-	PUNCT
cana-1759	248	12	133x	133x	NUM
cana-1759	248	13	vol	vol	NOUN
cana-1759	248	14	32	32	NUM
cana-1759	248	15	no	no	NOUN
cana-1759	248	16	.	.	NOUN
cana-1759	248	17	2	2	NUM
cana-1759	248	18	(	(	PUNCT
cana-1759	248	19	2025	2025	NUM
cana-1759	248	20	)	)	PUNCT
cana-1759	248	21	486	486	NUM
cana-1759	248	22	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	249	1	these	these	DET
cana-1759	249	2	results	result	NOUN
cana-1759	249	3	highlight	highlight	VERB
cana-1759	249	4	the	the	DET
cana-1759	249	5	complex	complex	ADJ
cana-1759	249	6	flow	flow	NOUN
cana-1759	249	7	behaviours	behaviour	NOUN
cana-1759	249	8	of	of	ADP
cana-1759	249	9	non	non	ADJ
cana-1759	249	10	-	-	ADJ
cana-1759	249	11	newtonian	newtonian	ADJ
cana-1759	249	12	fluids	fluid	NOUN
cana-1759	249	13	that	that	PRON
cana-1759	249	14	are	be	AUX
cana-1759	249	15	not	not	PART
cana-1759	249	16	captured	capture	VERB
cana-1759	249	17	by	by	ADP
cana-1759	249	18	classical	classical	ADJ
cana-1759	249	19	newtonian	newtonian	ADJ
cana-1759	249	20	models	model	NOUN
cana-1759	249	21	.	.	PUNCT
cana-1759	250	1	shear	shear	NOUN
cana-1759	250	2	-	-	PUNCT
cana-1759	250	3	thinning	thin	VERB
cana-1759	250	4	fluids	fluid	NOUN
cana-1759	250	5	,	,	PUNCT
cana-1759	250	6	such	such	ADJ
cana-1759	250	7	as	as	ADP
cana-1759	250	8	certain	certain	ADJ
cana-1759	250	9	polymers	polymer	NOUN
cana-1759	250	10	and	and	CCONJ
cana-1759	250	11	biological	biological	ADJ
cana-1759	250	12	fluids	fluid	NOUN
cana-1759	250	13	,	,	PUNCT
cana-1759	250	14	exhibit	exhibit	VERB
cana-1759	250	15	higher	high	ADJ
cana-1759	250	16	flow	flow	NOUN
cana-1759	250	17	rates	rate	NOUN
cana-1759	250	18	for	for	ADP
cana-1759	250	19	a	a	DET
cana-1759	250	20	given	give	VERB
cana-1759	250	21	pressure	pressure	NOUN
cana-1759	250	22	drop	drop	NOUN
cana-1759	250	23	,	,	PUNCT
cana-1759	250	24	which	which	PRON
cana-1759	250	25	is	be	AUX
cana-1759	250	26	advantageous	advantageous	ADJ
cana-1759	250	27	in	in	ADP
cana-1759	250	28	applications	application	NOUN
cana-1759	250	29	requiring	require	VERB
cana-1759	250	30	efficient	efficient	ADJ
cana-1759	250	31	fluid	fluid	ADJ
cana-1759	250	32	transport	transport	NOUN
cana-1759	250	33	,	,	PUNCT
cana-1759	250	34	like	like	ADP
cana-1759	250	35	in	in	ADP
cana-1759	250	36	pipeline	pipeline	NOUN
cana-1759	250	37	design	design	NOUN
cana-1759	250	38	or	or	CCONJ
cana-1759	250	39	biomedical	biomedical	ADJ
cana-1759	250	40	devices	device	NOUN
cana-1759	250	41	.	.	PUNCT
cana-1759	251	1	conversely	conversely	ADV
cana-1759	251	2	,	,	PUNCT
cana-1759	251	3	shear	shear	NOUN
cana-1759	251	4	-	-	PUNCT
cana-1759	251	5	thickening	thickening	NOUN
cana-1759	251	6	fluids	fluid	NOUN
cana-1759	251	7	are	be	AUX
cana-1759	251	8	useful	useful	ADJ
cana-1759	251	9	in	in	ADP
cana-1759	251	10	applications	application	NOUN
cana-1759	251	11	needing	need	VERB
cana-1759	251	12	enhanced	enhanced	ADJ
cana-1759	251	13	stability	stability	NOUN
cana-1759	251	14	or	or	CCONJ
cana-1759	251	15	impact	impact	NOUN
cana-1759	251	16	resistance	resistance	NOUN
cana-1759	251	17	,	,	PUNCT
cana-1759	251	18	such	such	ADJ
cana-1759	251	19	as	as	ADP
cana-1759	251	20	in	in	ADP
cana-1759	251	21	shock	shock	NOUN
cana-1759	251	22	absorbers	absorber	NOUN
cana-1759	251	23	or	or	CCONJ
cana-1759	251	24	protective	protective	ADJ
cana-1759	251	25	coatings	coating	NOUN
cana-1759	251	26	.	.	PUNCT
cana-1759	252	1	the	the	DET
cana-1759	252	2	ability	ability	NOUN
cana-1759	252	3	to	to	PART
cana-1759	252	4	predict	predict	VERB
cana-1759	252	5	these	these	DET
cana-1759	252	6	behaviours	behaviour	NOUN
cana-1759	252	7	accurately	accurately	ADV
cana-1759	252	8	allows	allow	VERB
cana-1759	252	9	for	for	ADP
cana-1759	252	10	better	well	ADJ
cana-1759	252	11	process	process	NOUN
cana-1759	252	12	control	control	NOUN
cana-1759	252	13	and	and	CCONJ
cana-1759	252	14	optimization	optimization	NOUN
cana-1759	252	15	in	in	ADP
cana-1759	252	16	industries	industry	NOUN
cana-1759	252	17	like	like	ADP
cana-1759	252	18	food	food	NOUN
cana-1759	252	19	processing	processing	NOUN
cana-1759	252	20	,	,	PUNCT
cana-1759	252	21	pharmaceuticals	pharmaceutical	NOUN
cana-1759	252	22	,	,	PUNCT
cana-1759	252	23	and	and	CCONJ
cana-1759	252	24	oil	oil	NOUN
cana-1759	252	25	and	and	CCONJ
cana-1759	252	26	gas	gas	NOUN
cana-1759	252	27	.	.	PUNCT
cana-1759	253	1	example	example	NOUN
cana-1759	254	1	3	3	NUM
cana-1759	254	2	:	:	PUNCT
cana-1759	254	3	nanofluid	nanofluid	ADJ
cana-1759	254	4	flow	flow	NOUN
cana-1759	254	5	over	over	ADP
cana-1759	254	6	a	a	DET
cana-1759	254	7	flat	flat	ADJ
cana-1759	254	8	plate	plate	NOUN
cana-1759	254	9	results	result	NOUN
cana-1759	254	10	:	:	PUNCT
cana-1759	254	11	the	the	DET
cana-1759	254	12	temperature	temperature	NOUN
cana-1759	254	13	distribution	distribution	NOUN
cana-1759	254	14	t(x	t(x	PROPN
cana-1759	254	15	)	)	PUNCT
cana-1759	254	16	for	for	ADP
cana-1759	254	17	a	a	DET
cana-1759	254	18	nanofluid	nanofluid	ADJ
cana-1759	254	19	flow	flow	NOUN
cana-1759	254	20	over	over	ADP
cana-1759	254	21	a	a	DET
cana-1759	254	22	flat	flat	ADJ
cana-1759	254	23	plate	plate	NOUN
cana-1759	254	24	shows	show	VERB
cana-1759	254	25	enhanced	enhance	VERB
cana-1759	254	26	heat	heat	NOUN
cana-1759	254	27	transfer	transfer	NOUN
cana-1759	254	28	rates	rate	NOUN
cana-1759	254	29	compared	compare	VERB
cana-1759	254	30	to	to	ADP
cana-1759	254	31	a	a	DET
cana-1759	254	32	base	base	ADJ
cana-1759	254	33	fluid	fluid	NOUN
cana-1759	254	34	(	(	PUNCT
cana-1759	254	35	e.g.	e.g.	ADJ
cana-1759	254	36	,	,	PUNCT
cana-1759	254	37	water	water	NOUN
cana-1759	254	38	)	)	PUNCT
cana-1759	254	39	without	without	ADP
cana-1759	254	40	nanoparticles	nanoparticle	NOUN
cana-1759	254	41	.	.	PUNCT
cana-1759	255	1	the	the	DET
cana-1759	255	2	temperature	temperature	NOUN
cana-1759	255	3	gradient	gradient	NOUN
cana-1759	255	4	near	near	ADP
cana-1759	255	5	the	the	DET
cana-1759	255	6	surface	surface	NOUN
cana-1759	255	7	is	be	AUX
cana-1759	255	8	steeper	steep	ADJ
cana-1759	255	9	,	,	PUNCT
cana-1759	255	10	indicating	indicate	VERB
cana-1759	255	11	more	more	ADV
cana-1759	255	12	efficient	efficient	ADJ
cana-1759	255	13	heat	heat	NOUN
cana-1759	255	14	removal	removal	NOUN
cana-1759	255	15	.	.	PUNCT
cana-1759	256	1	the	the	DET
cana-1759	256	2	nusselt	nusselt	NOUN
cana-1759	256	3	number	number	NOUN
cana-1759	256	4	,	,	PUNCT
cana-1759	256	5	a	a	DET
cana-1759	256	6	dimensionless	dimensionless	NOUN
cana-1759	256	7	measure	measure	NOUN
cana-1759	256	8	of	of	ADP
cana-1759	256	9	convective	convective	ADJ
cana-1759	256	10	heat	heat	NOUN
cana-1759	256	11	transfer	transfer	NOUN
cana-1759	256	12	,	,	PUNCT
cana-1759	256	13	is	be	AUX
cana-1759	256	14	significantly	significantly	ADV
cana-1759	256	15	higher	high	ADJ
cana-1759	256	16	for	for	ADP
cana-1759	256	17	nanofluids	nanofluid	NOUN
cana-1759	256	18	,	,	PUNCT
cana-1759	256	19	with	with	ADP
cana-1759	256	20	increases	increase	NOUN
cana-1759	256	21	ranging	range	VERB
cana-1759	256	22	from	from	ADP
cana-1759	256	23	10	10	NUM
cana-1759	256	24	%	%	NOUN
cana-1759	256	25	to	to	PART
cana-1759	256	26	30	30	NUM
cana-1759	256	27	%	%	NOUN
cana-1759	256	28	depending	depend	VERB
cana-1759	256	29	on	on	ADP
cana-1759	256	30	the	the	DET
cana-1759	256	31	volume	volume	NOUN
cana-1759	256	32	fraction	fraction	NOUN
cana-1759	256	33	of	of	ADP
cana-1759	256	34	nanoparticles	nanoparticle	NOUN
cana-1759	256	35	and	and	CCONJ
cana-1759	256	36	their	their	PRON
cana-1759	256	37	thermal	thermal	ADJ
cana-1759	256	38	properties	property	NOUN
cana-1759	256	39	.	.	PUNCT
cana-1759	257	1	numerical	numerical	ADJ
cana-1759	257	2	simulations	simulation	NOUN
cana-1759	257	3	show	show	VERB
cana-1759	257	4	that	that	SCONJ
cana-1759	257	5	increasing	increase	VERB
cana-1759	257	6	the	the	DET
cana-1759	257	7	nanoparticle	nanoparticle	NOUN
cana-1759	257	8	volume	volume	NOUN
cana-1759	257	9	fraction	fraction	NOUN
cana-1759	257	10	further	far	ADV
cana-1759	257	11	enhances	enhance	VERB
cana-1759	257	12	the	the	DET
cana-1759	257	13	heat	heat	NOUN
cana-1759	257	14	transfer	transfer	NOUN
cana-1759	257	15	rate	rate	NOUN
cana-1759	257	16	but	but	CCONJ
cana-1759	257	17	at	at	ADP
cana-1759	257	18	the	the	DET
cana-1759	257	19	cost	cost	NOUN
cana-1759	257	20	of	of	ADP
cana-1759	257	21	increased	increase	VERB
cana-1759	257	22	viscosity	viscosity	NOUN
cana-1759	257	23	and	and	CCONJ
cana-1759	257	24	potential	potential	ADJ
cana-1759	257	25	flow	flow	NOUN
cana-1759	257	26	resistance	resistance	NOUN
cana-1759	257	27	.	.	PUNCT
cana-1759	258	1	discussion	discussion	NOUN
cana-1759	258	2	:	:	PUNCT
cana-1759	258	3	the	the	DET
cana-1759	258	4	enhanced	enhanced	ADJ
cana-1759	258	5	heat	heat	NOUN
cana-1759	258	6	transfer	transfer	NOUN
cana-1759	258	7	capabilities	capability	NOUN
cana-1759	258	8	of	of	ADP
cana-1759	258	9	nanofluids	nanofluid	NOUN
cana-1759	258	10	,	,	PUNCT
cana-1759	258	11	as	as	SCONJ
cana-1759	258	12	evidenced	evidence	VERB
cana-1759	258	13	by	by	ADP
cana-1759	258	14	the	the	DET
cana-1759	258	15	higher	high	ADJ
cana-1759	258	16	temperature	temperature	NOUN
cana-1759	258	17	gradients	gradient	NOUN
cana-1759	258	18	and	and	CCONJ
cana-1759	258	19	nusselt	nusselt	NOUN
cana-1759	258	20	numbers	number	NOUN
cana-1759	258	21	,	,	PUNCT
cana-1759	258	22	are	be	AUX
cana-1759	258	23	directly	directly	ADV
cana-1759	258	24	related	relate	VERB
cana-1759	258	25	to	to	ADP
cana-1759	258	26	their	their	PRON
cana-1759	258	27	improved	improved	ADJ
cana-1759	258	28	thermal	thermal	ADJ
cana-1759	258	29	conductivity	conductivity	NOUN
cana-1759	258	30	and	and	CCONJ
cana-1759	258	31	convective	convective	ADJ
cana-1759	258	32	properties	property	NOUN
cana-1759	258	33	.	.	PUNCT
cana-1759	259	1	these	these	DET
cana-1759	259	2	results	result	NOUN
cana-1759	259	3	are	be	AUX
cana-1759	259	4	significant	significant	ADJ
cana-1759	259	5	for	for	ADP
cana-1759	259	6	applications	application	NOUN
cana-1759	259	7	in	in	ADP
cana-1759	259	8	microelectronics	microelectronic	NOUN
cana-1759	259	9	cooling	cool	VERB
cana-1759	259	10	,	,	PUNCT
cana-1759	259	11	where	where	SCONJ
cana-1759	259	12	maintaining	maintain	VERB
cana-1759	259	13	lower	low	ADJ
cana-1759	259	14	operating	operating	NOUN
cana-1759	259	15	temperatures	temperature	NOUN
cana-1759	259	16	is	be	AUX
cana-1759	259	17	critical	critical	ADJ
cana-1759	259	18	for	for	ADP
cana-1759	259	19	device	device	NOUN
cana-1759	259	20	performance	performance	NOUN
cana-1759	259	21	and	and	CCONJ
cana-1759	259	22	longevity	longevity	NOUN
cana-1759	259	23	.	.	PUNCT
cana-1759	260	1	similarly	similarly	ADV
cana-1759	260	2	,	,	PUNCT
cana-1759	260	3	in	in	ADP
cana-1759	260	4	solar	solar	ADJ
cana-1759	260	5	thermal	thermal	ADJ
cana-1759	260	6	systems	system	NOUN
cana-1759	260	7	and	and	CCONJ
cana-1759	260	8	heat	heat	NOUN
cana-1759	260	9	exchangers	exchanger	NOUN
cana-1759	260	10	,	,	PUNCT
cana-1759	260	11	nanofluids	nanofluid	VERB
cana-1759	260	12	can	can	AUX
cana-1759	260	13	improve	improve	VERB
cana-1759	260	14	efficiency	efficiency	NOUN
cana-1759	260	15	and	and	CCONJ
cana-1759	260	16	reduce	reduce	VERB
cana-1759	260	17	the	the	DET
cana-1759	260	18	size	size	NOUN
cana-1759	260	19	and	and	CCONJ
cana-1759	260	20	cost	cost	NOUN
cana-1759	260	21	of	of	ADP
cana-1759	260	22	equipment	equipment	NOUN
cana-1759	260	23	.	.	PUNCT
cana-1759	261	1	however	however	ADV
cana-1759	261	2	,	,	PUNCT
cana-1759	261	3	the	the	DET
cana-1759	261	4	trade	trade	NOUN
cana-1759	261	5	-	-	PUNCT
cana-1759	261	6	off	off	NOUN
cana-1759	261	7	between	between	ADP
cana-1759	261	8	enhanced	enhanced	ADJ
cana-1759	261	9	thermal	thermal	ADJ
cana-1759	261	10	performance	performance	NOUN
cana-1759	261	11	and	and	CCONJ
cana-1759	261	12	increased	increase	VERB
cana-1759	261	13	viscosity	viscosity	NOUN
cana-1759	261	14	must	must	AUX
cana-1759	261	15	be	be	AUX
cana-1759	261	16	carefully	carefully	ADV
cana-1759	261	17	balanced	balanced	ADJ
cana-1759	261	18	to	to	PART
cana-1759	261	19	avoid	avoid	VERB
cana-1759	261	20	excessive	excessive	ADJ
cana-1759	261	21	pumping	pumping	NOUN
cana-1759	261	22	power	power	NOUN
cana-1759	261	23	or	or	CCONJ
cana-1759	261	24	pressure	pressure	NOUN
cana-1759	261	25	drops	drop	NOUN
cana-1759	261	26	in	in	ADP
cana-1759	261	27	fluid	fluid	ADJ
cana-1759	261	28	transport	transport	NOUN
cana-1759	261	29	systems	system	NOUN
cana-1759	261	30	.	.	PUNCT
cana-1759	262	1	6.1	6.1	NUM
cana-1759	262	2	.	.	PUNCT
cana-1759	262	3	synthesis	synthesis	NOUN
cana-1759	262	4	and	and	CCONJ
cana-1759	262	5	comparative	comparative	ADJ
cana-1759	262	6	analysis	analysis	NOUN
cana-1759	262	7	fractional	fractional	ADJ
cana-1759	262	8	calculus	calculus	NOUN
cana-1759	262	9	models	model	NOUN
cana-1759	262	10	:	:	PUNCT
cana-1759	262	11	provide	provide	VERB
cana-1759	262	12	superior	superior	ADJ
cana-1759	262	13	modelling	modelling	NOUN
cana-1759	262	14	of	of	ADP
cana-1759	262	15	systems	system	NOUN
cana-1759	262	16	with	with	ADP
cana-1759	262	17	memory	memory	NOUN
cana-1759	262	18	and	and	CCONJ
cana-1759	262	19	hereditary	hereditary	ADJ
cana-1759	262	20	properties	property	NOUN
cana-1759	262	21	,	,	PUNCT
cana-1759	262	22	capturing	capture	VERB
cana-1759	262	23	anomalous	anomalous	ADJ
cana-1759	262	24	heat	heat	NOUN
cana-1759	262	25	transfer	transfer	NOUN
cana-1759	262	26	phenomena	phenomenon	NOUN
cana-1759	262	27	.	.	PUNCT
cana-1759	263	1	applicable	applicable	ADJ
cana-1759	263	2	in	in	ADP
cana-1759	263	3	materials	material	NOUN
cana-1759	263	4	science	science	NOUN
cana-1759	263	5	,	,	PUNCT
cana-1759	263	6	geothermal	geothermal	ADJ
cana-1759	263	7	energy	energy	NOUN
cana-1759	263	8	,	,	PUNCT
cana-1759	263	9	and	and	CCONJ
cana-1759	263	10	biomedical	biomedical	ADJ
cana-1759	263	11	heat	heat	NOUN
cana-1759	263	12	transfer	transfer	NOUN
cana-1759	263	13	applications	application	NOUN
cana-1759	263	14	where	where	SCONJ
cana-1759	263	15	non	non	ADJ
cana-1759	263	16	-	-	ADJ
cana-1759	263	17	local	local	ADJ
cana-1759	263	18	effects	effect	NOUN
cana-1759	263	19	are	be	AUX
cana-1759	263	20	significant	significant	ADJ
cana-1759	263	21	.	.	PUNCT
cana-1759	264	1	non	non	ADJ
cana-1759	264	2	-	-	ADJ
cana-1759	264	3	newtonian	newtonian	ADJ
cana-1759	264	4	fluid	fluid	ADJ
cana-1759	264	5	models	model	NOUN
cana-1759	264	6	:	:	PUNCT
cana-1759	264	7	accurately	accurately	ADV
cana-1759	264	8	capture	capture	VERB
cana-1759	264	9	complex	complex	ADJ
cana-1759	264	10	rheological	rheological	ADJ
cana-1759	264	11	behaviours	behaviour	NOUN
cana-1759	264	12	,	,	PUNCT
cana-1759	264	13	such	such	ADJ
cana-1759	264	14	as	as	ADP
cana-1759	264	15	shear	shear	NOUN
cana-1759	264	16	-	-	PUNCT
cana-1759	264	17	thinning	thin	VERB
cana-1759	264	18	,	,	PUNCT
cana-1759	264	19	shear	shear	NOUN
cana-1759	264	20	-	-	PUNCT
cana-1759	264	21	thickening	thickening	NOUN
cana-1759	264	22	,	,	PUNCT
cana-1759	264	23	and	and	CCONJ
cana-1759	264	24	yield	yield	VERB
cana-1759	264	25	stress	stress	NOUN
cana-1759	264	26	phenomena	phenomenon	NOUN
cana-1759	264	27	.	.	PUNCT
cana-1759	265	1	crucial	crucial	ADJ
cana-1759	265	2	for	for	ADP
cana-1759	265	3	optimizing	optimize	VERB
cana-1759	265	4	fluid	fluid	ADJ
cana-1759	265	5	dynamics	dynamic	NOUN
cana-1759	265	6	in	in	ADP
cana-1759	265	7	industries	industry	NOUN
cana-1759	265	8	dealing	deal	VERB
cana-1759	265	9	with	with	ADP
cana-1759	265	10	complex	complex	ADJ
cana-1759	265	11	fluids	fluid	NOUN
cana-1759	265	12	like	like	ADP
cana-1759	265	13	polymers	polymer	NOUN
cana-1759	265	14	,	,	PUNCT
cana-1759	265	15	drilling	drill	VERB
cana-1759	265	16	muds	mud	NOUN
cana-1759	265	17	,	,	PUNCT
cana-1759	265	18	and	and	CCONJ
cana-1759	265	19	biological	biological	ADJ
cana-1759	265	20	fluids	fluid	NOUN
cana-1759	265	21	.	.	PUNCT
cana-1759	266	1	communications	communication	NOUN
cana-1759	266	2	on	on	ADP
cana-1759	266	3	applied	apply	VERB
cana-1759	266	4	nonlinear	nonlinear	ADJ
cana-1759	266	5	analysis	analysis	NOUN
cana-1759	266	6	issn	issn	NOUN
cana-1759	266	7	:	:	PUNCT
cana-1759	266	8	1074	1074	NUM
cana-1759	266	9	-	-	PUNCT
cana-1759	266	10	133x	133x	NUM
cana-1759	266	11	vol	vol	NOUN
cana-1759	266	12	32	32	NUM
cana-1759	266	13	no	no	NOUN
cana-1759	266	14	.	.	NOUN
cana-1759	266	15	2	2	NUM
cana-1759	266	16	(	(	PUNCT
cana-1759	266	17	2025	2025	NUM
cana-1759	266	18	)	)	PUNCT
cana-1759	266	19	487	487	NUM
cana-1759	266	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	266	21	nanofluid	nanofluid	ADJ
cana-1759	266	22	dynamics	dynamic	NOUN
cana-1759	266	23	:	:	PUNCT
cana-1759	266	24	offer	offer	VERB
cana-1759	266	25	enhanced	enhance	VERB
cana-1759	266	26	thermal	thermal	ADJ
cana-1759	266	27	conductivity	conductivity	NOUN
cana-1759	266	28	and	and	CCONJ
cana-1759	266	29	convective	convective	ADJ
cana-1759	266	30	heat	heat	NOUN
cana-1759	266	31	transfer	transfer	NOUN
cana-1759	266	32	rates	rate	NOUN
cana-1759	266	33	,	,	PUNCT
cana-1759	266	34	making	make	VERB
cana-1759	266	35	them	they	PRON
cana-1759	266	36	suitable	suitable	ADJ
cana-1759	266	37	for	for	ADP
cana-1759	266	38	advanced	advanced	ADJ
cana-1759	266	39	cooling	cooling	NOUN
cana-1759	266	40	and	and	CCONJ
cana-1759	266	41	thermal	thermal	ADJ
cana-1759	266	42	management	management	NOUN
cana-1759	266	43	applications	application	NOUN
cana-1759	266	44	.	.	PUNCT
cana-1759	267	1	applications	application	NOUN
cana-1759	267	2	extend	extend	VERB
cana-1759	267	3	to	to	ADP
cana-1759	267	4	microelectronics	microelectronic	NOUN
cana-1759	267	5	,	,	PUNCT
cana-1759	267	6	solar	solar	ADJ
cana-1759	267	7	energy	energy	NOUN
cana-1759	267	8	,	,	PUNCT
cana-1759	267	9	automotive	automotive	ADJ
cana-1759	267	10	,	,	PUNCT
cana-1759	267	11	aerospace	aerospace	NOUN
cana-1759	267	12	,	,	PUNCT
cana-1759	267	13	and	and	CCONJ
cana-1759	267	14	medical	medical	ADJ
cana-1759	267	15	treatments	treatment	NOUN
cana-1759	267	16	.	.	PUNCT
cana-1759	268	1	6.2	6.2	NUM
cana-1759	268	2	.	.	PUNCT
cana-1759	269	1	overall	overall	ADJ
cana-1759	269	2	impact	impact	NOUN
cana-1759	269	3	:	:	PUNCT
cana-1759	269	4	the	the	DET
cana-1759	269	5	integration	integration	NOUN
cana-1759	269	6	of	of	ADP
cana-1759	269	7	fractional	fractional	ADJ
cana-1759	269	8	calculus	calculus	NOUN
cana-1759	269	9	,	,	PUNCT
cana-1759	269	10	non	non	ADJ
cana-1759	269	11	-	-	ADJ
cana-1759	269	12	newtonian	newtonian	ADJ
cana-1759	269	13	fluid	fluid	ADJ
cana-1759	269	14	models	model	NOUN
cana-1759	269	15	,	,	PUNCT
cana-1759	269	16	and	and	CCONJ
cana-1759	269	17	nanofluid	nanofluid	ADJ
cana-1759	269	18	dynamics	dynamic	NOUN
cana-1759	269	19	into	into	ADP
cana-1759	269	20	mathematical	mathematical	ADJ
cana-1759	269	21	modelling	modelling	NOUN
cana-1759	269	22	frameworks	framework	NOUN
cana-1759	269	23	has	have	AUX
cana-1759	269	24	significantly	significantly	ADV
cana-1759	269	25	enhanced	enhance	VERB
cana-1759	269	26	our	our	PRON
cana-1759	269	27	ability	ability	NOUN
cana-1759	269	28	to	to	PART
cana-1759	269	29	predict	predict	VERB
cana-1759	269	30	and	and	CCONJ
cana-1759	269	31	optimize	optimize	VERB
cana-1759	269	32	heat	heat	NOUN
cana-1759	269	33	transfer	transfer	NOUN
cana-1759	269	34	and	and	CCONJ
cana-1759	269	35	fluid	fluid	NOUN
cana-1759	269	36	flow	flow	NOUN
cana-1759	269	37	in	in	ADP
cana-1759	269	38	complex	complex	ADJ
cana-1759	269	39	systems	system	NOUN
cana-1759	269	40	.	.	PUNCT
cana-1759	270	1	these	these	DET
cana-1759	270	2	models	model	NOUN
cana-1759	270	3	enable	enable	VERB
cana-1759	270	4	a	a	DET
cana-1759	270	5	more	more	ADV
cana-1759	270	6	nuanced	nuanced	ADJ
cana-1759	270	7	understanding	understanding	NOUN
cana-1759	270	8	of	of	ADP
cana-1759	270	9	fluid	fluid	ADJ
cana-1759	270	10	dynamics	dynamic	NOUN
cana-1759	270	11	and	and	CCONJ
cana-1759	270	12	thermal	thermal	ADJ
cana-1759	270	13	behaviours	behaviour	NOUN
cana-1759	270	14	,	,	PUNCT
cana-1759	270	15	allowing	allow	VERB
cana-1759	270	16	engineers	engineer	NOUN
cana-1759	270	17	and	and	CCONJ
cana-1759	270	18	scientists	scientist	NOUN
cana-1759	270	19	to	to	PART
cana-1759	270	20	design	design	VERB
cana-1759	270	21	more	more	ADV
cana-1759	270	22	efficient	efficient	ADJ
cana-1759	270	23	,	,	PUNCT
cana-1759	270	24	reliable	reliable	ADJ
cana-1759	270	25	,	,	PUNCT
cana-1759	270	26	and	and	CCONJ
cana-1759	270	27	innovative	innovative	ADJ
cana-1759	270	28	solutions	solution	NOUN
cana-1759	270	29	across	across	ADP
cana-1759	270	30	various	various	ADJ
cana-1759	270	31	industries	industry	NOUN
cana-1759	270	32	.	.	PUNCT
cana-1759	271	1	as	as	ADP
cana-1759	271	2	computational	computational	ADJ
cana-1759	271	3	techniques	technique	NOUN
cana-1759	271	4	and	and	CCONJ
cana-1759	271	5	experimental	experimental	ADJ
cana-1759	271	6	methods	method	NOUN
cana-1759	271	7	continue	continue	VERB
cana-1759	271	8	to	to	PART
cana-1759	271	9	evolve	evolve	VERB
cana-1759	271	10	,	,	PUNCT
cana-1759	271	11	the	the	DET
cana-1759	271	12	accuracy	accuracy	NOUN
cana-1759	271	13	and	and	CCONJ
cana-1759	271	14	applicability	applicability	NOUN
cana-1759	271	15	of	of	ADP
cana-1759	271	16	these	these	DET
cana-1759	271	17	advanced	advanced	ADJ
cana-1759	271	18	models	model	NOUN
cana-1759	271	19	are	be	AUX
cana-1759	271	20	expected	expect	VERB
cana-1759	271	21	to	to	PART
cana-1759	271	22	improve	improve	VERB
cana-1759	271	23	further	far	ADV
cana-1759	271	24	,	,	PUNCT
cana-1759	271	25	driving	drive	VERB
cana-1759	271	26	advancements	advancement	NOUN
cana-1759	271	27	in	in	ADP
cana-1759	271	28	energy	energy	NOUN
cana-1759	271	29	,	,	PUNCT
cana-1759	271	30	materials	material	NOUN
cana-1759	271	31	science	science	NOUN
cana-1759	271	32	,	,	PUNCT
cana-1759	271	33	healthcare	healthcare	PROPN
cana-1759	271	34	,	,	PUNCT
cana-1759	271	35	and	and	CCONJ
cana-1759	271	36	beyond	beyond	ADP
cana-1759	271	37	.	.	NOUN
cana-1759	272	1	7	7	X
cana-1759	272	2	.	.	X
cana-1759	272	3	conclusion	conclusion	NOUN
cana-1759	272	4	the	the	DET
cana-1759	272	5	exploration	exploration	NOUN
cana-1759	272	6	of	of	ADP
cana-1759	272	7	advanced	advanced	ADJ
cana-1759	272	8	mathematical	mathematical	ADJ
cana-1759	272	9	modelling	modelling	NOUN
cana-1759	272	10	techniques	technique	NOUN
cana-1759	272	11	,	,	PUNCT
cana-1759	272	12	including	include	VERB
cana-1759	272	13	fractional	fractional	ADJ
cana-1759	272	14	calculus	calculus	NOUN
cana-1759	272	15	,	,	PUNCT
cana-1759	272	16	nonnewtonian	nonnewtonian	ADJ
cana-1759	272	17	fluid	fluid	NOUN
cana-1759	272	18	dynamics	dynamic	NOUN
cana-1759	272	19	,	,	PUNCT
cana-1759	272	20	and	and	CCONJ
cana-1759	272	21	nanofluid	nanofluid	ADJ
cana-1759	272	22	dynamics	dynamic	NOUN
cana-1759	272	23	,	,	PUNCT
cana-1759	272	24	provides	provide	VERB
cana-1759	272	25	a	a	DET
cana-1759	272	26	comprehensive	comprehensive	ADJ
cana-1759	272	27	framework	framework	NOUN
cana-1759	272	28	for	for	ADP
cana-1759	272	29	understanding	understand	VERB
cana-1759	272	30	complex	complex	ADJ
cana-1759	272	31	heat	heat	NOUN
cana-1759	272	32	transfer	transfer	NOUN
cana-1759	272	33	and	and	CCONJ
cana-1759	272	34	fluid	fluid	ADJ
cana-1759	272	35	flow	flow	NOUN
cana-1759	272	36	phenomena	phenomenon	NOUN
cana-1759	272	37	.	.	PUNCT
cana-1759	273	1	the	the	DET
cana-1759	273	2	numerical	numerical	ADJ
cana-1759	273	3	examples	example	NOUN
cana-1759	273	4	discussed	discuss	VERB
cana-1759	273	5	in	in	ADP
cana-1759	273	6	this	this	DET
cana-1759	273	7	study	study	NOUN
cana-1759	273	8	demonstrate	demonstrate	VERB
cana-1759	273	9	the	the	DET
cana-1759	273	10	significant	significant	ADJ
cana-1759	273	11	advantages	advantage	NOUN
cana-1759	273	12	of	of	ADP
cana-1759	273	13	using	use	VERB
cana-1759	273	14	these	these	DET
cana-1759	273	15	advanced	advanced	ADJ
cana-1759	273	16	models	model	NOUN
cana-1759	273	17	to	to	PART
cana-1759	273	18	capture	capture	VERB
cana-1759	273	19	the	the	DET
cana-1759	273	20	intricate	intricate	ADJ
cana-1759	273	21	behaviours	behaviour	NOUN
cana-1759	273	22	observed	observe	VERB
cana-1759	273	23	in	in	ADP
cana-1759	273	24	real	real	ADJ
cana-1759	273	25	-	-	PUNCT
cana-1759	273	26	world	world	NOUN
cana-1759	273	27	applications	application	NOUN
cana-1759	273	28	.	.	PUNCT
cana-1759	274	1	7.1	7.1	NUM
cana-1759	274	2	.	.	PUNCT
cana-1759	275	1	key	key	ADJ
cana-1759	275	2	findings	finding	NOUN
cana-1759	275	3	:	:	PUNCT
cana-1759	275	4	•	•	NUM
cana-1759	275	5	fractional	fractional	ADJ
cana-1759	275	6	calculus	calculus	NOUN
cana-1759	275	7	in	in	ADP
cana-1759	275	8	heat	heat	NOUN
cana-1759	275	9	transfer	transfer	NOUN
cana-1759	275	10	:	:	PUNCT
cana-1759	275	11	fractional	fractional	ADJ
cana-1759	275	12	-	-	PUNCT
cana-1759	275	13	order	order	NOUN
cana-1759	275	14	models	model	NOUN
cana-1759	275	15	are	be	AUX
cana-1759	275	16	highly	highly	ADV
cana-1759	275	17	effective	effective	ADJ
cana-1759	275	18	in	in	ADP
cana-1759	275	19	modelling	model	VERB
cana-1759	275	20	heat	heat	NOUN
cana-1759	275	21	conduction	conduction	NOUN
cana-1759	275	22	in	in	ADP
cana-1759	275	23	media	medium	NOUN
cana-1759	275	24	with	with	ADP
cana-1759	275	25	non	non	ADJ
cana-1759	275	26	-	-	ADJ
cana-1759	275	27	local	local	ADJ
cana-1759	275	28	and	and	CCONJ
cana-1759	275	29	memory	memory	NOUN
cana-1759	275	30	-	-	PUNCT
cana-1759	275	31	dependent	dependent	ADJ
cana-1759	275	32	properties	property	NOUN
cana-1759	275	33	.	.	PUNCT
cana-1759	276	1	these	these	DET
cana-1759	276	2	models	model	NOUN
cana-1759	276	3	capture	capture	VERB
cana-1759	276	4	the	the	DET
cana-1759	276	5	anomalous	anomalous	ADJ
cana-1759	276	6	diffusion	diffusion	NOUN
cana-1759	276	7	and	and	CCONJ
cana-1759	276	8	sub	sub	ADJ
cana-1759	276	9	-	-	ADJ
cana-1759	276	10	diffusive	diffusive	ADJ
cana-1759	276	11	behaviours	behaviour	NOUN
cana-1759	276	12	better	well	ADJ
cana-1759	276	13	than	than	ADP
cana-1759	276	14	classical	classical	ADJ
cana-1759	276	15	integer	integer	NOUN
cana-1759	276	16	-	-	PUNCT
cana-1759	276	17	order	order	NOUN
cana-1759	276	18	models	model	NOUN
cana-1759	276	19	,	,	PUNCT
cana-1759	276	20	providing	provide	VERB
cana-1759	276	21	more	more	ADV
cana-1759	276	22	accurate	accurate	ADJ
cana-1759	276	23	predictions	prediction	NOUN
cana-1759	276	24	for	for	ADP
cana-1759	276	25	applications	application	NOUN
cana-1759	276	26	involving	involve	VERB
cana-1759	276	27	heterogeneous	heterogeneous	ADJ
cana-1759	276	28	materials	material	NOUN
cana-1759	276	29	,	,	PUNCT
cana-1759	276	30	porous	porous	ADJ
cana-1759	276	31	media	medium	NOUN
cana-1759	276	32	,	,	PUNCT
cana-1759	276	33	and	and	CCONJ
cana-1759	276	34	biological	biological	ADJ
cana-1759	276	35	tissues	tissue	NOUN
cana-1759	276	36	.	.	PUNCT
cana-1759	277	1	•	•	NUM
cana-1759	277	2	non	non	ADJ
cana-1759	277	3	-	-	ADJ
cana-1759	277	4	newtonian	newtonian	ADJ
cana-1759	277	5	fluid	fluid	ADJ
cana-1759	277	6	models	model	NOUN
cana-1759	277	7	:	:	PUNCT
cana-1759	277	8	non	non	ADJ
cana-1759	277	9	-	-	ADJ
cana-1759	277	10	newtonian	newtonian	ADJ
cana-1759	277	11	fluid	fluid	ADJ
cana-1759	277	12	models	model	NOUN
cana-1759	277	13	,	,	PUNCT
cana-1759	277	14	including	include	VERB
cana-1759	277	15	power	power	NOUN
cana-1759	277	16	-	-	PUNCT
cana-1759	277	17	law	law	NOUN
cana-1759	277	18	,	,	PUNCT
cana-1759	277	19	bingham	bingham	PROPN
cana-1759	277	20	plastic	plastic	NOUN
cana-1759	277	21	,	,	PUNCT
cana-1759	277	22	and	and	CCONJ
cana-1759	277	23	carreau	carreau	PROPN
cana-1759	277	24	-	-	PUNCT
cana-1759	277	25	yasuda	yasuda	PROPN
cana-1759	277	26	models	model	NOUN
cana-1759	277	27	,	,	PUNCT
cana-1759	277	28	successfully	successfully	ADV
cana-1759	277	29	characterize	characterize	VERB
cana-1759	277	30	the	the	DET
cana-1759	277	31	complex	complex	ADJ
cana-1759	277	32	rheological	rheological	ADJ
cana-1759	277	33	properties	property	NOUN
cana-1759	277	34	of	of	ADP
cana-1759	277	35	various	various	ADJ
cana-1759	277	36	fluids	fluid	NOUN
cana-1759	277	37	.	.	PUNCT
cana-1759	278	1	the	the	DET
cana-1759	278	2	ability	ability	NOUN
cana-1759	278	3	to	to	PART
cana-1759	278	4	model	model	VERB
cana-1759	278	5	shear	shear	NOUN
cana-1759	278	6	-	-	PUNCT
cana-1759	278	7	thinning	thin	VERB
cana-1759	278	8	,	,	PUNCT
cana-1759	278	9	shear	shear	NOUN
cana-1759	278	10	-	-	PUNCT
cana-1759	278	11	thickening	thickening	NOUN
cana-1759	278	12	,	,	PUNCT
cana-1759	278	13	and	and	CCONJ
cana-1759	278	14	viscos	visco	NOUN
cana-1759	278	15	-	-	PUNCT
cana-1759	278	16	plastic	plastic	ADJ
cana-1759	278	17	behaviours	behaviour	NOUN
cana-1759	278	18	enables	enable	VERB
cana-1759	278	19	accurate	accurate	ADJ
cana-1759	278	20	simulations	simulation	NOUN
cana-1759	278	21	and	and	CCONJ
cana-1759	278	22	optimizations	optimization	NOUN
cana-1759	278	23	for	for	ADP
cana-1759	278	24	industrial	industrial	ADJ
cana-1759	278	25	processes	process	NOUN
cana-1759	278	26	,	,	PUNCT
cana-1759	278	27	such	such	ADJ
cana-1759	278	28	as	as	ADP
cana-1759	278	29	polymer	polymer	NOUN
cana-1759	278	30	processing	processing	NOUN
cana-1759	278	31	,	,	PUNCT
cana-1759	278	32	food	food	NOUN
cana-1759	278	33	manufacturing	manufacturing	NOUN
cana-1759	278	34	,	,	PUNCT
cana-1759	278	35	and	and	CCONJ
cana-1759	278	36	biomedical	biomedical	ADJ
cana-1759	278	37	engineering	engineering	NOUN
cana-1759	278	38	.	.	PUNCT
cana-1759	279	1	•	•	NUM
cana-1759	279	2	nanofluid	nanofluid	PROPN
cana-1759	279	3	dynamics	dynamic	NOUN
cana-1759	279	4	:	:	PUNCT
cana-1759	279	5	nanofluid	nanofluid	NOUN
cana-1759	279	6	models	model	NOUN
cana-1759	279	7	demonstrate	demonstrate	VERB
cana-1759	279	8	enhanced	enhanced	ADJ
cana-1759	279	9	heat	heat	NOUN
cana-1759	279	10	transfer	transfer	NOUN
cana-1759	279	11	capabilities	capability	NOUN
cana-1759	279	12	due	due	ADP
cana-1759	279	13	to	to	ADP
cana-1759	279	14	the	the	DET
cana-1759	279	15	superior	superior	ADJ
cana-1759	279	16	thermal	thermal	ADJ
cana-1759	279	17	properties	property	NOUN
cana-1759	279	18	of	of	ADP
cana-1759	279	19	nanofluids	nanofluid	NOUN
cana-1759	279	20	.	.	PUNCT
cana-1759	280	1	the	the	DET
cana-1759	280	2	numerical	numerical	ADJ
cana-1759	280	3	results	result	NOUN
cana-1759	280	4	indicate	indicate	VERB
cana-1759	280	5	that	that	DET
cana-1759	280	6	nanofluids	nanofluid	NOUN
cana-1759	280	7	significantly	significantly	ADV
cana-1759	280	8	increase	increase	VERB
cana-1759	280	9	convective	convective	ADJ
cana-1759	280	10	heat	heat	NOUN
cana-1759	280	11	transfer	transfer	NOUN
cana-1759	280	12	rates	rate	NOUN
cana-1759	280	13	,	,	PUNCT
cana-1759	280	14	making	make	VERB
cana-1759	280	15	them	they	PRON
cana-1759	280	16	ideal	ideal	ADJ
cana-1759	280	17	for	for	ADP
cana-1759	280	18	applications	application	NOUN
cana-1759	280	19	in	in	ADP
cana-1759	280	20	microelectronics	microelectronic	NOUN
cana-1759	280	21	cooling	cool	VERB
cana-1759	280	22	,	,	PUNCT
cana-1759	280	23	solar	solar	ADJ
cana-1759	280	24	thermal	thermal	ADJ
cana-1759	280	25	systems	system	NOUN
cana-1759	280	26	,	,	PUNCT
cana-1759	280	27	and	and	CCONJ
cana-1759	280	28	industrial	industrial	ADJ
cana-1759	280	29	heat	heat	NOUN
cana-1759	280	30	exchangers	exchanger	NOUN
cana-1759	280	31	.	.	PUNCT
cana-1759	281	1	however	however	ADV
cana-1759	281	2	,	,	PUNCT
cana-1759	281	3	the	the	DET
cana-1759	281	4	increased	increase	VERB
cana-1759	281	5	viscosity	viscosity	NOUN
cana-1759	281	6	due	due	ADP
cana-1759	281	7	to	to	ADP
cana-1759	281	8	nanoparticle	nanoparticle	NOUN
cana-1759	281	9	addition	addition	NOUN
cana-1759	281	10	must	must	AUX
cana-1759	281	11	be	be	AUX
cana-1759	281	12	managed	manage	VERB
cana-1759	281	13	to	to	PART
cana-1759	281	14	prevent	prevent	VERB
cana-1759	281	15	adverse	adverse	ADJ
cana-1759	281	16	effects	effect	NOUN
cana-1759	281	17	on	on	ADP
cana-1759	281	18	fluid	fluid	ADJ
cana-1759	281	19	flow	flow	NOUN
cana-1759	281	20	.	.	PUNCT
cana-1759	282	1	communications	communication	NOUN
cana-1759	282	2	on	on	ADP
cana-1759	282	3	applied	apply	VERB
cana-1759	282	4	nonlinear	nonlinear	ADJ
cana-1759	282	5	analysis	analysis	NOUN
cana-1759	282	6	issn	issn	NOUN
cana-1759	282	7	:	:	PUNCT
cana-1759	282	8	1074	1074	NUM
cana-1759	282	9	-	-	PUNCT
cana-1759	282	10	133x	133x	NUM
cana-1759	282	11	vol	vol	NOUN
cana-1759	282	12	32	32	NUM
cana-1759	282	13	no	no	NOUN
cana-1759	282	14	.	.	NOUN
cana-1759	282	15	2	2	NUM
cana-1759	282	16	(	(	PUNCT
cana-1759	282	17	2025	2025	NUM
cana-1759	282	18	)	)	PUNCT
cana-1759	283	1	488	488	NUM
cana-1759	283	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	283	3	7.2	7.2	NUM
cana-1759	283	4	.	.	PUNCT
cana-1759	283	5	impact	impact	NOUN
cana-1759	283	6	and	and	CCONJ
cana-1759	283	7	future	future	ADJ
cana-1759	283	8	directions	direction	NOUN
cana-1759	283	9	:	:	PUNCT
cana-1759	283	10	the	the	DET
cana-1759	283	11	integration	integration	NOUN
cana-1759	283	12	of	of	ADP
cana-1759	283	13	these	these	DET
cana-1759	283	14	advanced	advance	VERB
cana-1759	283	15	modelling	modelling	NOUN
cana-1759	283	16	techniques	technique	NOUN
cana-1759	283	17	into	into	ADP
cana-1759	283	18	heat	heat	NOUN
cana-1759	283	19	transfer	transfer	NOUN
cana-1759	283	20	and	and	CCONJ
cana-1759	283	21	fluid	fluid	ADJ
cana-1759	283	22	flow	flow	NOUN
cana-1759	283	23	studies	study	NOUN
cana-1759	283	24	represents	represent	VERB
cana-1759	283	25	a	a	DET
cana-1759	283	26	major	major	ADJ
cana-1759	283	27	advancement	advancement	NOUN
cana-1759	283	28	in	in	ADP
cana-1759	283	29	the	the	DET
cana-1759	283	30	field	field	NOUN
cana-1759	283	31	of	of	ADP
cana-1759	283	32	applied	apply	VERB
cana-1759	283	33	mathematics	mathematic	NOUN
cana-1759	283	34	and	and	CCONJ
cana-1759	283	35	engineering	engineering	NOUN
cana-1759	283	36	.	.	PUNCT
cana-1759	284	1	the	the	DET
cana-1759	284	2	improved	improved	ADJ
cana-1759	284	3	accuracy	accuracy	NOUN
cana-1759	284	4	in	in	ADP
cana-1759	284	5	predicting	predict	VERB
cana-1759	284	6	thermal	thermal	ADJ
cana-1759	284	7	and	and	CCONJ
cana-1759	284	8	flow	flow	NOUN
cana-1759	284	9	behaviours	behaviour	NOUN
cana-1759	284	10	has	have	VERB
cana-1759	284	11	practical	practical	ADJ
cana-1759	284	12	implications	implication	NOUN
cana-1759	284	13	for	for	ADP
cana-1759	284	14	the	the	DET
cana-1759	284	15	design	design	NOUN
cana-1759	284	16	and	and	CCONJ
cana-1759	284	17	optimization	optimization	NOUN
cana-1759	284	18	of	of	ADP
cana-1759	284	19	various	various	ADJ
cana-1759	284	20	systems	system	NOUN
cana-1759	284	21	,	,	PUNCT
cana-1759	284	22	from	from	ADP
cana-1759	284	23	energy	energy	NOUN
cana-1759	284	24	-	-	PUNCT
cana-1759	284	25	efficient	efficient	ADJ
cana-1759	284	26	industrial	industrial	ADJ
cana-1759	284	27	processes	process	NOUN
cana-1759	284	28	to	to	ADP
cana-1759	284	29	advanced	advanced	ADJ
cana-1759	284	30	cooling	cool	VERB
cana-1759	284	31	technologies	technology	NOUN
cana-1759	284	32	and	and	CCONJ
cana-1759	284	33	medical	medical	ADJ
cana-1759	284	34	treatments	treatment	NOUN
cana-1759	284	35	.	.	PUNCT
cana-1759	285	1	7.3	7.3	NUM
cana-1759	285	2	.	.	PUNCT
cana-1759	286	1	future	future	ADJ
cana-1759	286	2	research	research	NOUN
cana-1759	286	3	should	should	AUX
cana-1759	286	4	focus	focus	VERB
cana-1759	286	5	on	on	ADP
cana-1759	286	6	:	:	PUNCT
cana-1759	286	7	developing	develop	VERB
cana-1759	286	8	hybrid	hybrid	ADJ
cana-1759	286	9	models	model	NOUN
cana-1759	286	10	:	:	PUNCT
cana-1759	286	11	combining	combine	VERB
cana-1759	286	12	fractional	fractional	ADJ
cana-1759	286	13	calculus	calculus	NOUN
cana-1759	286	14	,	,	PUNCT
cana-1759	286	15	non	non	ADJ
cana-1759	286	16	-	-	ADJ
cana-1759	286	17	newtonian	newtonian	ADJ
cana-1759	286	18	fluid	fluid	ADJ
cana-1759	286	19	dynamics	dynamic	NOUN
cana-1759	286	20	,	,	PUNCT
cana-1759	286	21	and	and	CCONJ
cana-1759	286	22	nanofluid	nanofluid	ADJ
cana-1759	286	23	dynamics	dynamic	NOUN
cana-1759	286	24	to	to	PART
cana-1759	286	25	address	address	VERB
cana-1759	286	26	even	even	ADV
cana-1759	286	27	more	more	ADV
cana-1759	286	28	complex	complex	ADJ
cana-1759	286	29	systems	system	NOUN
cana-1759	286	30	where	where	SCONJ
cana-1759	286	31	multiple	multiple	ADJ
cana-1759	286	32	non	non	ADJ
cana-1759	286	33	-	-	ADJ
cana-1759	286	34	linear	linear	ADJ
cana-1759	286	35	,	,	PUNCT
cana-1759	286	36	non	non	ADJ
cana-1759	286	37	-	-	ADJ
cana-1759	286	38	local	local	ADJ
cana-1759	286	39	,	,	PUNCT
cana-1759	286	40	and	and	CCONJ
cana-1759	286	41	anomalous	anomalous	ADJ
cana-1759	286	42	behaviours	behaviour	NOUN
cana-1759	286	43	are	be	AUX
cana-1759	286	44	present	present	ADJ
cana-1759	286	45	simultaneously	simultaneously	ADV
cana-1759	286	46	.	.	PUNCT
cana-1759	287	1	experimental	experimental	ADJ
cana-1759	287	2	validation	validation	NOUN
cana-1759	287	3	:	:	PUNCT
cana-1759	287	4	increasing	increase	VERB
cana-1759	287	5	the	the	DET
cana-1759	287	6	collaboration	collaboration	NOUN
cana-1759	287	7	between	between	ADP
cana-1759	287	8	numerical	numerical	ADJ
cana-1759	287	9	modelling	modelling	NOUN
cana-1759	287	10	and	and	CCONJ
cana-1759	287	11	experimental	experimental	ADJ
cana-1759	287	12	studies	study	NOUN
cana-1759	287	13	to	to	PART
cana-1759	287	14	validate	validate	VERB
cana-1759	287	15	and	and	CCONJ
cana-1759	287	16	refine	refine	VERB
cana-1759	287	17	these	these	DET
cana-1759	287	18	advanced	advanced	ADJ
cana-1759	287	19	models	model	NOUN
cana-1759	287	20	for	for	ADP
cana-1759	287	21	specific	specific	ADJ
cana-1759	287	22	applications	application	NOUN
cana-1759	287	23	.	.	PUNCT
cana-1759	288	1	computational	computational	ADJ
cana-1759	288	2	advancements	advancement	NOUN
cana-1759	288	3	:	:	PUNCT
cana-1759	288	4	leveraging	leverage	VERB
cana-1759	288	5	high	high	ADJ
cana-1759	288	6	-	-	PUNCT
cana-1759	288	7	performance	performance	NOUN
cana-1759	288	8	computing	computing	NOUN
cana-1759	288	9	and	and	CCONJ
cana-1759	288	10	machine	machine	NOUN
cana-1759	288	11	learning	learn	VERB
cana-1759	288	12	techniques	technique	NOUN
cana-1759	288	13	to	to	PART
cana-1759	288	14	solve	solve	VERB
cana-1759	288	15	the	the	DET
cana-1759	288	16	resulting	result	VERB
cana-1759	288	17	complex	complex	ADJ
cana-1759	288	18	differential	differential	ADJ
cana-1759	288	19	equations	equation	NOUN
cana-1759	288	20	more	more	ADV
cana-1759	288	21	efficiently	efficiently	ADV
cana-1759	288	22	and	and	CCONJ
cana-1759	288	23	accurately	accurately	ADV
cana-1759	288	24	.	.	PUNCT
cana-1759	289	1	by	by	ADP
cana-1759	289	2	continuing	continue	VERB
cana-1759	289	3	to	to	PART
cana-1759	289	4	refine	refine	VERB
cana-1759	289	5	these	these	DET
cana-1759	289	6	mathematical	mathematical	ADJ
cana-1759	289	7	models	model	NOUN
cana-1759	289	8	and	and	CCONJ
cana-1759	289	9	apply	apply	VERB
cana-1759	289	10	them	they	PRON
cana-1759	289	11	to	to	ADP
cana-1759	289	12	new	new	ADJ
cana-1759	289	13	areas	area	NOUN
cana-1759	289	14	,	,	PUNCT
cana-1759	289	15	researchers	researcher	NOUN
cana-1759	289	16	and	and	CCONJ
cana-1759	289	17	engineers	engineer	NOUN
cana-1759	289	18	can	can	AUX
cana-1759	289	19	develop	develop	VERB
cana-1759	289	20	innovative	innovative	ADJ
cana-1759	289	21	solutions	solution	NOUN
cana-1759	289	22	to	to	ADP
cana-1759	289	23	some	some	PRON
cana-1759	289	24	of	of	ADP
cana-1759	289	25	the	the	DET
cana-1759	289	26	most	most	ADV
cana-1759	289	27	challenging	challenging	ADJ
cana-1759	289	28	problems	problem	NOUN
cana-1759	289	29	in	in	ADP
cana-1759	289	30	fluid	fluid	ADJ
cana-1759	289	31	dynamics	dynamic	NOUN
cana-1759	289	32	and	and	CCONJ
cana-1759	289	33	heat	heat	NOUN
cana-1759	289	34	transfer	transfer	NOUN
cana-1759	289	35	,	,	PUNCT
cana-1759	289	36	ultimately	ultimately	ADV
cana-1759	289	37	driving	drive	VERB
cana-1759	289	38	technological	technological	ADJ
cana-1759	289	39	progress	progress	NOUN
cana-1759	289	40	across	across	ADP
cana-1759	289	41	various	various	ADJ
cana-1759	289	42	sectors	sector	NOUN
cana-1759	289	43	.	.	PUNCT
cana-1759	290	1	7.4	7.4	NUM
cana-1759	290	2	.	.	PUNCT
cana-1759	291	1	conclusion	conclusion	NOUN
cana-1759	291	2	statement	statement	NOUN
cana-1759	291	3	in	in	ADP
cana-1759	291	4	conclusion	conclusion	NOUN
cana-1759	291	5	,	,	PUNCT
cana-1759	291	6	the	the	DET
cana-1759	291	7	use	use	NOUN
cana-1759	291	8	of	of	ADP
cana-1759	291	9	fractional	fractional	ADJ
cana-1759	291	10	calculus	calculus	NOUN
cana-1759	291	11	,	,	PUNCT
cana-1759	291	12	non	non	ADJ
cana-1759	291	13	-	-	ADJ
cana-1759	291	14	newtonian	newtonian	ADJ
cana-1759	291	15	fluid	fluid	ADJ
cana-1759	291	16	models	model	NOUN
cana-1759	291	17	,	,	PUNCT
cana-1759	291	18	and	and	CCONJ
cana-1759	291	19	nanofluid	nanofluid	ADJ
cana-1759	291	20	dynamics	dynamic	NOUN
cana-1759	291	21	in	in	ADP
cana-1759	291	22	mathematical	mathematical	ADJ
cana-1759	291	23	modelling	modelling	NOUN
cana-1759	291	24	offers	offer	VERB
cana-1759	291	25	significant	significant	ADJ
cana-1759	291	26	advancements	advancement	NOUN
cana-1759	291	27	in	in	ADP
cana-1759	291	28	accurately	accurately	ADV
cana-1759	291	29	predicting	predict	VERB
cana-1759	291	30	and	and	CCONJ
cana-1759	291	31	optimizing	optimize	VERB
cana-1759	291	32	heat	heat	NOUN
cana-1759	291	33	transfer	transfer	NOUN
cana-1759	291	34	and	and	CCONJ
cana-1759	291	35	fluid	fluid	ADJ
cana-1759	291	36	flow	flow	NOUN
cana-1759	291	37	behaviours	behaviour	NOUN
cana-1759	291	38	.	.	PUNCT
cana-1759	292	1	these	these	DET
cana-1759	292	2	models	model	NOUN
cana-1759	292	3	provide	provide	VERB
cana-1759	292	4	critical	critical	ADJ
cana-1759	292	5	insights	insight	NOUN
cana-1759	292	6	and	and	CCONJ
cana-1759	292	7	tools	tool	NOUN
cana-1759	292	8	for	for	ADP
cana-1759	292	9	developing	develop	VERB
cana-1759	292	10	more	more	ADV
cana-1759	292	11	efficient	efficient	ADJ
cana-1759	292	12	and	and	CCONJ
cana-1759	292	13	effective	effective	ADJ
cana-1759	292	14	technologies	technology	NOUN
cana-1759	292	15	in	in	ADP
cana-1759	292	16	diverse	diverse	ADJ
cana-1759	292	17	applications	application	NOUN
cana-1759	292	18	,	,	PUNCT
cana-1759	292	19	from	from	ADP
cana-1759	292	20	energy	energy	NOUN
cana-1759	292	21	systems	system	NOUN
cana-1759	292	22	to	to	ADP
cana-1759	292	23	biomedical	biomedical	ADJ
cana-1759	292	24	engineering	engineering	NOUN
cana-1759	292	25	.	.	PUNCT
cana-1759	293	1	as	as	SCONJ
cana-1759	293	2	these	these	DET
cana-1759	293	3	models	model	NOUN
cana-1759	293	4	continue	continue	VERB
cana-1759	293	5	to	to	PART
cana-1759	293	6	evolve	evolve	VERB
cana-1759	293	7	,	,	PUNCT
cana-1759	293	8	they	they	PRON
cana-1759	293	9	will	will	AUX
cana-1759	293	10	play	play	VERB
cana-1759	293	11	an	an	DET
cana-1759	293	12	increasingly	increasingly	ADV
cana-1759	293	13	vital	vital	ADJ
cana-1759	293	14	role	role	NOUN
cana-1759	293	15	in	in	ADP
cana-1759	293	16	addressing	address	VERB
cana-1759	293	17	the	the	DET
cana-1759	293	18	complex	complex	ADJ
cana-1759	293	19	challenges	challenge	NOUN
cana-1759	293	20	of	of	ADP
cana-1759	293	21	modern	modern	ADJ
cana-1759	293	22	science	science	NOUN
cana-1759	293	23	and	and	CCONJ
cana-1759	293	24	engineering	engineering	NOUN
cana-1759	293	25	.	.	PUNCT
cana-1759	294	1	8	8	X
cana-1759	294	2	.	.	PUNCT
cana-1759	294	3	references	reference	NOUN
cana-1759	294	4	[	[	X
cana-1759	294	5	1	1	NUM
cana-1759	294	6	]	]	X
cana-1759	294	7	alharbi	alharbi	NOUN
cana-1759	294	8	,	,	PUNCT
cana-1759	294	9	s.	s.	PROPN
cana-1759	294	10	,	,	PUNCT
cana-1759	294	11	malik	malik	PROPN
cana-1759	294	12	,	,	PUNCT
cana-1759	294	13	m.y	m.y	PROPN
cana-1759	294	14	.	.	PROPN
cana-1759	294	15	,	,	PUNCT
cana-1759	294	16	khan	khan	PROPN
cana-1759	294	17	,	,	PUNCT
cana-1759	294	18	w.a	w.a	PROPN
cana-1759	294	19	.	.	PROPN
cana-1759	294	20	,	,	PUNCT
cana-1759	294	21	et	et	PROPN
cana-1759	294	22	al	al	PROPN
cana-1759	294	23	.	.	PROPN
cana-1759	294	24	(	(	PUNCT
cana-1759	294	25	2023	2023	NUM
cana-1759	294	26	)	)	PUNCT
cana-1759	294	27	.	.	PUNCT
cana-1759	295	1	fractional	fractional	ADJ
cana-1759	295	2	derivative	derivative	ADJ
cana-1759	295	3	modelling	modelling	NOUN
cana-1759	295	4	in	in	ADP
cana-1759	295	5	heat	heat	NOUN
cana-1759	295	6	transfer	transfer	NOUN
cana-1759	295	7	analysis	analysis	NOUN
cana-1759	295	8	of	of	ADP
cana-1759	295	9	nanofluid	nanofluid	NOUN
cana-1759	295	10	over	over	ADP
cana-1759	295	11	a	a	DET
cana-1759	295	12	stretching	stretch	VERB
cana-1759	295	13	cylinder	cylinder	NOUN
cana-1759	295	14	.	.	PUNCT
cana-1759	296	1	*	*	PUNCT
cana-1759	296	2	journal	journal	PROPN
cana-1759	296	3	of	of	ADP
cana-1759	296	4	thermal	thermal	ADJ
cana-1759	296	5	analysis	analysis	NOUN
cana-1759	296	6	and	and	CCONJ
cana-1759	296	7	calorimetry	calorimetry	NOUN
cana-1759	296	8	*	*	SYM
cana-1759	296	9	,	,	PUNCT
cana-1759	296	10	*	*	PUNCT
cana-1759	296	11	*	*	NOUN
cana-1759	296	12	143**(5	143**(5	NUM
cana-1759	296	13	)	)	PUNCT
cana-1759	296	14	,	,	PUNCT
cana-1759	296	15	2807–2820	2807–2820	NOUN
cana-1759	296	16	.	.	PUNCT
cana-1759	297	1	[	[	X
cana-1759	297	2	2	2	NUM
cana-1759	297	3	]	]	X
cana-1759	297	4	al	al	PROPN
cana-1759	297	5	-	-	PUNCT
cana-1759	297	6	mdallal	mdallal	PROPN
cana-1759	297	7	,	,	PUNCT
cana-1759	297	8	q.m	q.m	PROPN
cana-1759	297	9	.	.	PROPN
cana-1759	297	10	,	,	PUNCT
cana-1759	297	11	hashim	hashim	PROPN
cana-1759	297	12	,	,	PUNCT
cana-1759	297	13	i.	i.	PROPN
cana-1759	297	14	,	,	PUNCT
cana-1759	297	15	&	&	CCONJ
cana-1759	297	16	ahmad	ahmad	PROPN
cana-1759	297	17	,	,	PUNCT
cana-1759	297	18	r.	r.	PROPN
cana-1759	297	19	*	*	PUNCT
cana-1759	297	20	*	*	PUNCT
cana-1759	297	21	(	(	PUNCT
cana-1759	297	22	2022	2022	NUM
cana-1759	297	23	)	)	PUNCT
cana-1759	297	24	.	.	PUNCT
cana-1759	298	1	numerical	numerical	PROPN
cana-1759	298	2	simulation	simulation	PROPN
cana-1759	298	3	of	of	ADP
cana-1759	298	4	mhd	mhd	PROPN
cana-1759	298	5	nanofluid	nanofluid	PROPN
cana-1759	298	6	flow	flow	NOUN
cana-1759	298	7	over	over	ADP
cana-1759	298	8	a	a	DET
cana-1759	298	9	stretching	stretch	VERB
cana-1759	298	10	sheet	sheet	NOUN
cana-1759	298	11	with	with	ADP
cana-1759	298	12	convective	convective	ADJ
cana-1759	298	13	boundary	boundary	ADJ
cana-1759	298	14	conditions	condition	NOUN
cana-1759	298	15	using	use	VERB
cana-1759	298	16	a	a	DET
cana-1759	298	17	fractional	fractional	ADJ
cana-1759	298	18	derivative	derivative	ADJ
cana-1759	298	19	approach	approach	NOUN
cana-1759	298	20	.	.	PUNCT
cana-1759	299	1	*	*	PUNCT
cana-1759	299	2	international	international	ADJ
cana-1759	299	3	journal	journal	NOUN
cana-1759	299	4	of	of	ADP
cana-1759	299	5	heat	heat	NOUN
cana-1759	299	6	and	and	CCONJ
cana-1759	299	7	mass	mass	NOUN
cana-1759	299	8	transfer	transfer	NOUN
cana-1759	299	9	*	*	PUNCT
cana-1759	299	10	,	,	PUNCT
cana-1759	299	11	*	*	PUNCT
cana-1759	299	12	*	*	NOUN
cana-1759	299	13	165	165	NUM
cana-1759	299	14	*	*	NOUN
cana-1759	299	15	*	*	NOUN
cana-1759	299	16	,	,	PUNCT
cana-1759	299	17	120698	120698	NUM
cana-1759	299	18	.	.	PUNCT
cana-1759	300	1	[	[	X
cana-1759	300	2	3	3	X
cana-1759	300	3	]	]	X
cana-1759	300	4	*	*	PUNCT
cana-1759	300	5	*	*	PUNCT
cana-1759	300	6	ahmad	ahmad	PROPN
cana-1759	300	7	,	,	PUNCT
cana-1759	300	8	b.	b.	PROPN
cana-1759	300	9	,	,	PUNCT
cana-1759	300	10	rehman	rehman	PROPN
cana-1759	300	11	,	,	PUNCT
cana-1759	300	12	k.	k.	PROPN
cana-1759	300	13	,	,	PUNCT
cana-1759	300	14	&	&	CCONJ
cana-1759	300	15	rashidi	rashidi	PROPN
cana-1759	300	16	,	,	PUNCT
cana-1759	300	17	m.m	m.m	PROPN
cana-1759	300	18	.	.	PROPN
cana-1759	300	19	*	*	PROPN
cana-1759	300	20	*	*	PUNCT
cana-1759	300	21	(	(	PUNCT
cana-1759	300	22	2023	2023	NUM
cana-1759	300	23	)	)	PUNCT
cana-1759	300	24	.	.	PUNCT
cana-1759	301	1	comparative	comparative	ADJ
cana-1759	301	2	analysis	analysis	NOUN
cana-1759	301	3	of	of	ADP
cana-1759	301	4	different	different	ADJ
cana-1759	301	5	numerical	numerical	ADJ
cana-1759	301	6	techniques	technique	NOUN
cana-1759	301	7	for	for	ADP
cana-1759	301	8	solving	solve	VERB
cana-1759	301	9	fractional	fractional	ADJ
cana-1759	301	10	heat	heat	NOUN
cana-1759	301	11	transfer	transfer	NOUN
cana-1759	301	12	problems	problem	NOUN
cana-1759	301	13	in	in	ADP
cana-1759	301	14	porous	porous	ADJ
cana-1759	301	15	media	medium	NOUN
cana-1759	301	16	.	.	PUNCT
cana-1759	302	1	*	*	PUNCT
cana-1759	302	2	applied	apply	VERB
cana-1759	302	3	mathematics	mathematic	NOUN
cana-1759	302	4	and	and	CCONJ
cana-1759	302	5	computation	computation	NOUN
cana-1759	302	6	*	*	PUNCT
cana-1759	302	7	,	,	PUNCT
cana-1759	302	8	*	*	PUNCT
cana-1759	302	9	*	*	PUNCT
cana-1759	302	10	434	434	NUM
cana-1759	302	11	*	*	PUNCT
cana-1759	302	12	*	*	NOUN
cana-1759	302	13	,	,	PUNCT
cana-1759	302	14	127493	127493	NUM
cana-1759	302	15	.	.	PUNCT
cana-1759	303	1	[	[	X
cana-1759	303	2	4	4	NUM
cana-1759	303	3	]	]	X
cana-1759	303	4	*	*	PUNCT
cana-1759	303	5	*	*	PUNCT
cana-1759	303	6	das	das	PROPN
cana-1759	303	7	,	,	PUNCT
cana-1759	303	8	k.	k.	PROPN
cana-1759	303	9	,	,	PUNCT
cana-1759	303	10	&	&	CCONJ
cana-1759	303	11	mandal	mandal	PROPN
cana-1759	303	12	,	,	PUNCT
cana-1759	303	13	p.	p.	PROPN
cana-1759	303	14	*	*	PUNCT
cana-1759	303	15	*	*	PUNCT
cana-1759	303	16	(	(	PUNCT
cana-1759	303	17	2022	2022	NUM
cana-1759	303	18	)	)	PUNCT
cana-1759	303	19	.	.	PUNCT
cana-1759	304	1	thermal	thermal	ADJ
cana-1759	304	2	analysis	analysis	NOUN
cana-1759	304	3	of	of	ADP
cana-1759	304	4	non	non	ADJ
cana-1759	304	5	-	-	ADJ
cana-1759	304	6	newtonian	newtonian	ADJ
cana-1759	304	7	fluid	fluid	ADJ
cana-1759	304	8	flow	flow	NOUN
cana-1759	304	9	over	over	ADP
cana-1759	304	10	a	a	DET
cana-1759	304	11	stretching	stretch	VERB
cana-1759	304	12	surface	surface	NOUN
cana-1759	304	13	with	with	ADP
cana-1759	304	14	convective	convective	ADJ
cana-1759	304	15	boundary	boundary	ADJ
cana-1759	304	16	conditions	condition	NOUN
cana-1759	304	17	using	use	VERB
cana-1759	304	18	fractional	fractional	ADJ
cana-1759	304	19	derivatives	derivative	NOUN
cana-1759	304	20	.	.	PUNCT
cana-1759	305	1	*	*	PUNCT
cana-1759	305	2	chinese	chinese	PROPN
cana-1759	305	3	journal	journal	PROPN
cana-1759	305	4	of	of	ADP
cana-1759	305	5	physics	physics	PROPN
cana-1759	305	6	*	*	PUNCT
cana-1759	305	7	,	,	PUNCT
cana-1759	305	8	*	*	PUNCT
cana-1759	305	9	*	*	PUNCT
cana-1759	305	10	80	80	NUM
cana-1759	305	11	*	*	PUNCT
cana-1759	305	12	*	*	NOUN
cana-1759	305	13	,	,	PUNCT
cana-1759	305	14	105	105	NUM
cana-1759	305	15	-	-	SYM
cana-1759	305	16	116	116	NUM
cana-1759	305	17	.	.	PUNCT
cana-1759	306	1	[	[	X
cana-1759	306	2	5	5	NUM
cana-1759	306	3	]	]	PUNCT
cana-1759	306	4	*	*	PUNCT
cana-1759	306	5	*	*	PUNCT
cana-1759	306	6	hayat	hayat	X
cana-1759	306	7	,	,	PUNCT
cana-1759	306	8	t.	t.	PROPN
cana-1759	306	9	,	,	PUNCT
cana-1759	306	10	ullah	ullah	PROPN
cana-1759	306	11	,	,	PUNCT
cana-1759	306	12	i.	i.	PROPN
cana-1759	306	13	,	,	PUNCT
cana-1759	306	14	&	&	CCONJ
cana-1759	306	15	alsaedi	alsaedi	PROPN
cana-1759	306	16	,	,	PUNCT
cana-1759	306	17	a.	a.	NOUN
cana-1759	306	18	*	*	PUNCT
cana-1759	306	19	*	*	PUNCT
cana-1759	306	20	(	(	PUNCT
cana-1759	306	21	2023	2023	NUM
cana-1759	306	22	)	)	PUNCT
cana-1759	306	23	.	.	PUNCT
cana-1759	307	1	a	a	DET
cana-1759	307	2	comparative	comparative	ADJ
cana-1759	307	3	study	study	NOUN
cana-1759	307	4	of	of	ADP
cana-1759	307	5	various	various	ADJ
cana-1759	307	6	fractional	fractional	ADJ
cana-1759	307	7	-	-	PUNCT
cana-1759	307	8	order	order	NOUN
cana-1759	307	9	models	model	NOUN
cana-1759	307	10	for	for	ADP
cana-1759	307	11	heat	heat	NOUN
cana-1759	307	12	transfer	transfer	NOUN
cana-1759	307	13	enhancement	enhancement	NOUN
cana-1759	307	14	in	in	ADP
cana-1759	307	15	nanofluids	nanofluid	NOUN
cana-1759	307	16	.	.	PUNCT
cana-1759	308	1	*	*	PUNCT
cana-1759	308	2	results	result	NOUN
cana-1759	308	3	in	in	ADP
cana-1759	308	4	physics	physics	NOUN
cana-1759	308	5	*	*	PUNCT
cana-1759	308	6	,	,	PUNCT
cana-1759	308	7	*	*	PUNCT
cana-1759	308	8	*	*	PUNCT
cana-1759	308	9	45	45	NUM
cana-1759	308	10	*	*	PUNCT
cana-1759	308	11	*	*	NOUN
cana-1759	308	12	,	,	PUNCT
cana-1759	308	13	106200	106200	NUM
cana-1759	308	14	.	.	PUNCT
cana-1759	309	1	[	[	X
cana-1759	309	2	6	6	NUM
cana-1759	309	3	]	]	PUNCT
cana-1759	309	4	*	*	PUNCT
cana-1759	309	5	*	*	PUNCT
cana-1759	309	6	javed	javed	ADJ
cana-1759	309	7	,	,	PUNCT
cana-1759	309	8	t.	t.	PROPN
cana-1759	309	9	,	,	PUNCT
cana-1759	309	10	ali	ali	PROPN
cana-1759	309	11	,	,	PUNCT
cana-1759	309	12	f.	f.	PROPN
cana-1759	309	13	,	,	PUNCT
cana-1759	309	14	&	&	CCONJ
cana-1759	309	15	khan	khan	PROPN
cana-1759	309	16	,	,	PUNCT
cana-1759	309	17	i.	i.	PROPN
cana-1759	309	18	*	*	PROPN
cana-1759	309	19	*	*	PUNCT
cana-1759	309	20	(	(	PUNCT
cana-1759	309	21	2022	2022	NUM
cana-1759	309	22	)	)	PUNCT
cana-1759	309	23	.	.	PUNCT
cana-1759	310	1	fractional	fractional	ADJ
cana-1759	310	2	model	model	NOUN
cana-1759	310	3	analysis	analysis	NOUN
cana-1759	310	4	for	for	ADP
cana-1759	310	5	transient	transient	ADJ
cana-1759	310	6	heat	heat	NOUN
cana-1759	310	7	conduction	conduction	NOUN
cana-1759	310	8	in	in	ADP
cana-1759	310	9	nonhomogeneous	nonhomogeneous	ADJ
cana-1759	310	10	anisotropic	anisotropic	NOUN
cana-1759	310	11	materials	material	NOUN
cana-1759	310	12	.	.	PUNCT
cana-1759	311	1	*	*	PUNCT
cana-1759	311	2	heat	heat	NOUN
cana-1759	311	3	transfer	transfer	NOUN
cana-1759	311	4	engineering	engineering	NOUN
cana-1759	311	5	*	*	PUNCT
cana-1759	311	6	,	,	PUNCT
cana-1759	311	7	*	*	PUNCT
cana-1759	311	8	*	*	NOUN
cana-1759	311	9	43**(14	43**(14	NOUN
cana-1759	311	10	)	)	PUNCT
cana-1759	311	11	,	,	PUNCT
cana-1759	311	12	1219	1219	NUM
cana-1759	311	13	-	-	SYM
cana-1759	311	14	1235	1235	NUM
cana-1759	311	15	.	.	PUNCT
cana-1759	312	1	communications	communication	NOUN
cana-1759	312	2	on	on	ADP
cana-1759	312	3	applied	apply	VERB
cana-1759	312	4	nonlinear	nonlinear	ADJ
cana-1759	312	5	analysis	analysis	NOUN
cana-1759	312	6	issn	issn	NOUN
cana-1759	312	7	:	:	PUNCT
cana-1759	312	8	1074	1074	NUM
cana-1759	312	9	-	-	PUNCT
cana-1759	312	10	133x	133x	NUM
cana-1759	312	11	vol	vol	NOUN
cana-1759	312	12	32	32	NUM
cana-1759	312	13	no	no	NOUN
cana-1759	312	14	.	.	NOUN
cana-1759	312	15	2	2	NUM
cana-1759	312	16	(	(	PUNCT
cana-1759	312	17	2025	2025	NUM
cana-1759	312	18	)	)	PUNCT
cana-1759	312	19	489	489	NUM
cana-1759	312	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1759	313	1	[	[	X
cana-1759	313	2	7	7	X
cana-1759	313	3	]	]	X
cana-1759	313	4	*	*	PUNCT
cana-1759	313	5	*	*	PUNCT
cana-1759	313	6	khan	khan	PROPN
cana-1759	313	7	,	,	PUNCT
cana-1759	313	8	w.a	w.a	PROPN
cana-1759	313	9	.	.	PROPN
cana-1759	313	10	,	,	PUNCT
cana-1759	313	11	aziz	aziz	PROPN
cana-1759	313	12	,	,	PUNCT
cana-1759	313	13	s.	s.	PROPN
cana-1759	313	14	,	,	PUNCT
cana-1759	313	15	&	&	CCONJ
cana-1759	313	16	pop	pop	PROPN
cana-1759	313	17	,	,	PUNCT
cana-1759	313	18	i.	i.	NOUN
cana-1759	313	19	*	*	PROPN
cana-1759	313	20	*	*	PUNCT
cana-1759	313	21	(	(	PUNCT
cana-1759	313	22	2023	2023	NUM
cana-1759	313	23	)	)	PUNCT
cana-1759	313	24	.	.	PUNCT
cana-1759	314	1	mixed	mixed	ADJ
cana-1759	314	2	convection	convection	NOUN
cana-1759	314	3	boundary	boundary	ADJ
cana-1759	314	4	layer	layer	NOUN
cana-1759	314	5	flow	flow	NOUN
cana-1759	314	6	of	of	ADP
cana-1759	314	7	a	a	DET
cana-1759	314	8	non	non	ADJ
cana-1759	314	9	-	-	ADJ
cana-1759	314	10	newtonian	newtonian	ADJ
cana-1759	314	11	nanofluid	nanofluid	NOUN
cana-1759	314	12	over	over	ADP
cana-1759	314	13	a	a	DET
cana-1759	314	14	stretching	stretching	NOUN
cana-1759	314	15	/	/	SYM
cana-1759	314	16	shrinking	shrink	VERB
cana-1759	314	17	sheet	sheet	NOUN
cana-1759	314	18	with	with	ADP
cana-1759	314	19	thermal	thermal	ADJ
cana-1759	314	20	radiation	radiation	NOUN
cana-1759	314	21	.	.	PUNCT
cana-1759	315	1	*	*	PUNCT
cana-1759	315	2	international	international	ADJ
cana-1759	315	3	communications	communication	NOUN
cana-1759	315	4	in	in	ADP
cana-1759	315	5	heat	heat	NOUN
cana-1759	315	6	and	and	CCONJ
cana-1759	315	7	mass	mass	NOUN
cana-1759	315	8	transfer	transfer	NOUN
cana-1759	315	9	*	*	PUNCT
cana-1759	315	10	,	,	PUNCT
cana-1759	315	11	*	*	PUNCT
cana-1759	315	12	*	*	PUNCT
cana-1759	315	13	132	132	NUM
cana-1759	315	14	*	*	PUNCT
cana-1759	315	15	*	*	NOUN
cana-1759	315	16	,	,	PUNCT
cana-1759	315	17	105930	105930	NUM
cana-1759	315	18	.	.	PUNCT
cana-1759	316	1	[	[	X
cana-1759	316	2	8	8	NUM
cana-1759	316	3	]	]	X
cana-1759	316	4	*	*	PUNCT
cana-1759	316	5	*	*	PUNCT
cana-1759	316	6	kumar	kumar	PROPN
cana-1759	316	7	,	,	PUNCT
cana-1759	316	8	r.	r.	PROPN
cana-1759	316	9	,	,	PUNCT
cana-1759	316	10	&	&	CCONJ
cana-1759	316	11	sharma	sharma	PROPN
cana-1759	316	12	,	,	PUNCT
cana-1759	316	13	p.k	p.k	PROPN
cana-1759	316	14	.	.	PUNCT
cana-1759	316	15	*	*	PUNCT
cana-1759	316	16	*	*	PUNCT
cana-1759	316	17	(	(	PUNCT
cana-1759	316	18	2022	2022	NUM
cana-1759	316	19	)	)	PUNCT
cana-1759	316	20	.	.	PUNCT
cana-1759	317	1	impact	impact	NOUN
cana-1759	317	2	of	of	ADP
cana-1759	317	3	variable	variable	ADJ
cana-1759	317	4	viscosity	viscosity	NOUN
cana-1759	317	5	and	and	CCONJ
cana-1759	317	6	thermal	thermal	ADJ
cana-1759	317	7	conductivity	conductivity	NOUN
cana-1759	317	8	on	on	ADP
cana-1759	317	9	mhd	mhd	PROPN
cana-1759	317	10	nanofluid	nanofluid	PROPN
cana-1759	317	11	flow	flow	NOUN
cana-1759	317	12	over	over	ADP
cana-1759	317	13	a	a	DET
cana-1759	317	14	stretching	stretch	VERB
cana-1759	317	15	cylinder	cylinder	NOUN
cana-1759	317	16	.	.	PUNCT
cana-1759	318	1	*	*	PUNCT
cana-1759	318	2	european	european	PROPN
cana-1759	318	3	physical	physical	ADJ
cana-1759	318	4	journal	journal	PROPN
cana-1759	318	5	plus	plus	PROPN
cana-1759	318	6	*	*	PROPN
cana-1759	318	7	,	,	PUNCT
cana-1759	318	8	*	*	PUNCT
cana-1759	318	9	*	*	NOUN
cana-1759	318	10	137**(3	137**(3	NUM
cana-1759	318	11	)	)	PUNCT
cana-1759	318	12	,	,	PUNCT
cana-1759	318	13	1	1	NUM
cana-1759	318	14	-	-	SYM
cana-1759	318	15	14	14	NUM
cana-1759	318	16	.	.	PUNCT
cana-1759	319	1	[	[	X
cana-1759	319	2	9	9	NUM
cana-1759	319	3	]	]	X
cana-1759	319	4	*	*	PUNCT
cana-1759	319	5	*	*	PUNCT
cana-1759	319	6	mahar	mahar	PROPN
cana-1759	319	7	,	,	PUNCT
cana-1759	319	8	n.	n.	PROPN
cana-1759	319	9	,	,	PUNCT
cana-1759	319	10	munir	munir	PROPN
cana-1759	319	11	,	,	PUNCT
cana-1759	319	12	s.	s.	PROPN
cana-1759	319	13	,	,	PUNCT
cana-1759	319	14	&	&	CCONJ
cana-1759	319	15	gulzar	gulzar	PROPN
cana-1759	319	16	,	,	PUNCT
cana-1759	319	17	s.	s.	PROPN
cana-1759	319	18	*	*	PROPN
cana-1759	319	19	*	*	PUNCT
cana-1759	319	20	(	(	PUNCT
cana-1759	319	21	2023	2023	NUM
cana-1759	319	22	)	)	PUNCT
cana-1759	319	23	.	.	PUNCT
cana-1759	320	1	comparative	comparative	ADJ
cana-1759	320	2	analysis	analysis	NOUN
cana-1759	320	3	of	of	ADP
cana-1759	320	4	numerical	numerical	ADJ
cana-1759	320	5	methods	method	NOUN
cana-1759	320	6	for	for	ADP
cana-1759	320	7	solving	solve	VERB
cana-1759	320	8	fractional	fractional	ADJ
cana-1759	320	9	heat	heat	NOUN
cana-1759	320	10	conduction	conduction	NOUN
cana-1759	320	11	models	model	NOUN
cana-1759	320	12	.	.	PUNCT
cana-1759	321	1	*	*	PUNCT
cana-1759	321	2	numerical	numerical	ADJ
cana-1759	321	3	heat	heat	NOUN
cana-1759	321	4	transfer	transfer	NOUN
cana-1759	321	5	,	,	PUNCT
cana-1759	321	6	part	part	NOUN
cana-1759	321	7	b	b	NOUN
cana-1759	321	8	:	:	PUNCT
cana-1759	321	9	fundamentals	fundamental	NOUN
cana-1759	321	10	*	*	NOUN
cana-1759	321	11	,	,	PUNCT
cana-1759	321	12	*	*	PUNCT
cana-1759	321	13	*	*	NOUN
cana-1759	321	14	83**(4	83**(4	NOUN
cana-1759	321	15	)	)	PUNCT
cana-1759	321	16	,	,	PUNCT
cana-1759	321	17	297	297	NUM
cana-1759	321	18	-	-	SYM
cana-1759	321	19	311	311	NUM
cana-1759	321	20	.	.	PUNCT
cana-1759	322	1	[	[	X
cana-1759	322	2	10	10	NUM
cana-1759	322	3	]	]	X
cana-1759	322	4	*	*	PUNCT
cana-1759	322	5	*	*	PUNCT
cana-1759	322	6	malik	malik	X
cana-1759	322	7	,	,	PUNCT
cana-1759	322	8	m.y	m.y	PROPN
cana-1759	322	9	.	.	PROPN
cana-1759	322	10	,	,	PUNCT
cana-1759	322	11	hussain	hussain	PROPN
cana-1759	322	12	,	,	PUNCT
cana-1759	322	13	a.	a.	PROPN
cana-1759	322	14	,	,	PUNCT
cana-1759	322	15	&	&	CCONJ
cana-1759	322	16	salahuddin	salahuddin	PROPN
cana-1759	322	17	,	,	PUNCT
cana-1759	322	18	t.	t.	PROPN
cana-1759	322	19	*	*	PROPN
cana-1759	322	20	*	*	PUNCT
cana-1759	322	21	(	(	PUNCT
cana-1759	322	22	2023	2023	NUM
cana-1759	322	23	)	)	PUNCT
cana-1759	322	24	.	.	PUNCT
cana-1759	323	1	heat	heat	NOUN
cana-1759	323	2	transfer	transfer	NOUN
cana-1759	323	3	analysis	analysis	NOUN
cana-1759	323	4	of	of	ADP
cana-1759	323	5	non	non	ADJ
cana-1759	323	6	-	-	ADJ
cana-1759	323	7	newtonian	newtonian	ADJ
cana-1759	323	8	fluid	fluid	NOUN
cana-1759	323	9	over	over	ADP
cana-1759	323	10	a	a	DET
cana-1759	323	11	stretching	stretch	VERB
cana-1759	323	12	cylinder	cylinder	NOUN
cana-1759	323	13	with	with	ADP
cana-1759	323	14	variable	variable	ADJ
cana-1759	323	15	viscosity	viscosity	NOUN
cana-1759	323	16	and	and	CCONJ
cana-1759	323	17	thermal	thermal	ADJ
cana-1759	323	18	conductivity	conductivity	NOUN
cana-1759	323	19	.	.	PUNCT
cana-1759	324	1	*	*	PUNCT
cana-1759	324	2	journal	journal	NOUN
cana-1759	324	3	of	of	ADP
cana-1759	324	4	molecular	molecular	ADJ
cana-1759	324	5	liquids	liquid	NOUN
cana-1759	324	6	*	*	SYM
cana-1759	324	7	,	,	PUNCT
cana-1759	324	8	*	*	PUNCT
cana-1759	324	9	*	*	NOUN
cana-1759	324	10	383	383	NUM
cana-1759	324	11	*	*	PUNCT
cana-1759	324	12	*	*	NOUN
cana-1759	324	13	,	,	PUNCT
cana-1759	324	14	121399	121399	NUM
cana-1759	324	15	.	.	PUNCT
cana-1759	325	1	[	[	X
cana-1759	325	2	11	11	NUM
cana-1759	325	3	]	]	PUNCT
cana-1759	325	4	*	*	PUNCT
cana-1759	325	5	*	*	PUNCT
cana-1759	325	6	nadeem	nadeem	PROPN
cana-1759	325	7	,	,	PUNCT
cana-1759	325	8	s.	s.	PROPN
cana-1759	325	9	,	,	PUNCT
cana-1759	325	10	&	&	CCONJ
cana-1759	325	11	hussain	hussain	PROPN
cana-1759	325	12	,	,	PUNCT
cana-1759	325	13	a.	a.	NOUN
cana-1759	325	14	*	*	PUNCT
cana-1759	325	15	*	*	PUNCT
cana-1759	325	16	(	(	PUNCT
cana-1759	325	17	2022	2022	NUM
cana-1759	325	18	)	)	PUNCT
cana-1759	325	19	.	.	PUNCT
cana-1759	326	1	effects	effect	NOUN
cana-1759	326	2	of	of	ADP
cana-1759	326	3	magnetic	magnetic	ADJ
cana-1759	326	4	field	field	NOUN
cana-1759	326	5	and	and	CCONJ
cana-1759	326	6	thermal	thermal	ADJ
cana-1759	326	7	radiation	radiation	NOUN
cana-1759	326	8	on	on	ADP
cana-1759	326	9	flow	flow	NOUN
cana-1759	326	10	of	of	ADP
cana-1759	326	11	casson	casson	PROPN
cana-1759	326	12	nanofluid	nanofluid	PROPN
cana-1759	326	13	over	over	ADP
cana-1759	326	14	a	a	DET
cana-1759	326	15	stretching	stretch	VERB
cana-1759	326	16	sheet	sheet	NOUN
cana-1759	326	17	with	with	ADP
cana-1759	326	18	fractional	fractional	ADJ
cana-1759	326	19	derivatives	derivative	NOUN
cana-1759	326	20	.	.	PUNCT
cana-1759	327	1	*	*	PUNCT
cana-1759	327	2	journal	journal	PROPN
cana-1759	327	3	of	of	ADP
cana-1759	327	4	magnetism	magnetism	NOUN
cana-1759	327	5	and	and	CCONJ
cana-1759	327	6	magnetic	magnetic	ADJ
cana-1759	327	7	materials	material	NOUN
cana-1759	327	8	*	*	PUNCT
cana-1759	327	9	,	,	PUNCT
cana-1759	327	10	*	*	PUNCT
cana-1759	327	11	*	*	PUNCT
cana-1759	327	12	548	548	NUM
cana-1759	327	13	*	*	NOUN
cana-1759	327	14	*	*	NOUN
cana-1759	327	15	,	,	PUNCT
cana-1759	327	16	169034	169034	NUM
cana-1759	327	17	.	.	PUNCT
cana-1759	328	1	[	[	X
cana-1759	328	2	12	12	NUM
cana-1759	328	3	]	]	X
cana-1759	328	4	*	*	PUNCT
cana-1759	328	5	*	*	PUNCT
cana-1759	328	6	prasad	prasad	PROPN
cana-1759	328	7	,	,	PUNCT
cana-1759	328	8	k.v	k.v	PROPN
cana-1759	328	9	.	.	PROPN
cana-1759	328	10	,	,	PUNCT
cana-1759	328	11	vajravelu	vajravelu	NOUN
cana-1759	328	12	,	,	PUNCT
cana-1759	328	13	k.	k.	PROPN
cana-1759	328	14	,	,	PUNCT
cana-1759	328	15	&	&	CCONJ
cana-1759	328	16	sarojamma	sarojamma	PROPN
cana-1759	328	17	,	,	PUNCT
cana-1759	328	18	g.	g.	PROPN
cana-1759	328	19	*	*	PROPN
cana-1759	328	20	*	*	PUNCT
cana-1759	328	21	(	(	PUNCT
cana-1759	328	22	2023	2023	NUM
cana-1759	328	23	)	)	PUNCT
cana-1759	328	24	.	.	PUNCT
cana-1759	329	1	fractional	fractional	ADJ
cana-1759	329	2	modelling	modelling	NOUN
cana-1759	329	3	of	of	ADP
cana-1759	329	4	mhd	mhd	PROPN
cana-1759	329	5	viscoelastic	viscoelastic	ADJ
cana-1759	329	6	fluid	fluid	NOUN
cana-1759	329	7	flow	flow	NOUN
cana-1759	329	8	and	and	CCONJ
cana-1759	329	9	heat	heat	NOUN
cana-1759	329	10	transfer	transfer	NOUN
cana-1759	329	11	over	over	ADP
cana-1759	329	12	a	a	DET
cana-1759	329	13	stretching	stretch	VERB
cana-1759	329	14	sheet	sheet	NOUN
cana-1759	329	15	with	with	ADP
cana-1759	329	16	thermal	thermal	ADJ
cana-1759	329	17	radiation	radiation	NOUN
cana-1759	329	18	.	.	PUNCT
cana-1759	330	1	*	*	PUNCT
cana-1759	330	2	alexandria	alexandria	PROPN
cana-1759	330	3	engineering	engineering	PROPN
cana-1759	330	4	journal	journal	PROPN
cana-1759	330	5	*	*	SYM
cana-1759	330	6	,	,	PUNCT
cana-1759	330	7	*	*	PUNCT
cana-1759	330	8	*	*	X
cana-1759	330	9	63	63	NUM
cana-1759	330	10	*	*	PUNCT
cana-1759	330	11	*	*	NOUN
cana-1759	330	12	,	,	PUNCT
cana-1759	330	13	237	237	NUM
cana-1759	330	14	-	-	SYM
cana-1759	330	15	249	249	NUM
cana-1759	330	16	.	.	PUNCT
cana-1759	331	1	[	[	X
cana-1759	331	2	13	13	NUM
cana-1759	331	3	]	]	SYM
cana-1759	331	4	*	*	PUNCT
cana-1759	331	5	*	*	PUNCT
cana-1759	331	6	ramesh	ramesh	PROPN
cana-1759	331	7	,	,	PUNCT
cana-1759	331	8	g.k	g.k	PROPN
cana-1759	331	9	.	.	PROPN
cana-1759	331	10	,	,	PUNCT
cana-1759	331	11	&	&	CCONJ
cana-1759	331	12	reddy	reddy	PROPN
cana-1759	331	13	,	,	PUNCT
cana-1759	331	14	v.r	v.r	PROPN
cana-1759	331	15	.	.	PROPN
cana-1759	331	16	*	*	PUNCT
cana-1759	331	17	*	*	PUNCT
cana-1759	331	18	(	(	PUNCT
cana-1759	331	19	2022	2022	NUM
cana-1759	331	20	)	)	PUNCT
cana-1759	331	21	.	.	PUNCT
cana-1759	332	1	unsteady	unsteady	ADJ
cana-1759	332	2	mhd	mhd	NOUN
cana-1759	332	3	flow	flow	NOUN
cana-1759	332	4	of	of	ADP
cana-1759	332	5	nanofluid	nanofluid	NOUN
cana-1759	332	6	over	over	ADP
cana-1759	332	7	a	a	DET
cana-1759	332	8	permeable	permeable	ADJ
cana-1759	332	9	stretching	stretch	VERB
cana-1759	332	10	sheet	sheet	NOUN
cana-1759	332	11	with	with	ADP
cana-1759	332	12	variable	variable	ADJ
cana-1759	332	13	thermal	thermal	ADJ
cana-1759	332	14	conductivity	conductivity	NOUN
cana-1759	332	15	using	use	VERB
cana-1759	332	16	caputo	caputo	PROPN
cana-1759	332	17	-	-	PUNCT
cana-1759	332	18	fabrizio	fabrizio	PROPN
cana-1759	332	19	fractional	fractional	ADJ
cana-1759	332	20	derivative	derivative	NOUN
cana-1759	332	21	.	.	PUNCT
cana-1759	333	1	*	*	PUNCT
cana-1759	333	2	physica	physica	PROPN
cana-1759	333	3	a	a	DET
cana-1759	333	4	:	:	PUNCT
cana-1759	333	5	statistical	statistical	ADJ
cana-1759	333	6	mechanics	mechanic	NOUN
cana-1759	333	7	and	and	CCONJ
cana-1759	333	8	its	its	PRON
cana-1759	333	9	applications	application	NOUN
cana-1759	333	10	*	*	PUNCT
cana-1759	333	11	,	,	PUNCT
cana-1759	333	12	*	*	PUNCT
cana-1759	333	13	*	*	PUNCT
cana-1759	333	14	607	607	NUM
cana-1759	333	15	*	*	PUNCT
cana-1759	333	16	*	*	NOUN
cana-1759	333	17	,	,	PUNCT
cana-1759	333	18	128205	128205	NUM
cana-1759	333	19	.	.	PUNCT
cana-1759	334	1	[	[	X
cana-1759	334	2	14	14	NUM
cana-1759	334	3	]	]	X
cana-1759	334	4	*	*	PUNCT
cana-1759	334	5	*	*	PUNCT
cana-1759	334	6	sadeghy	sadeghy	PROPN
cana-1759	334	7	,	,	PUNCT
cana-1759	334	8	k.	k.	PROPN
cana-1759	334	9	,	,	PUNCT
cana-1759	334	10	&	&	CCONJ
cana-1759	334	11	kazemi	kazemi	PROPN
cana-1759	334	12	,	,	PUNCT
cana-1759	334	13	a.	a.	PROPN
cana-1759	334	14	*	*	PUNCT
cana-1759	334	15	*	*	PUNCT
cana-1759	334	16	(	(	PUNCT
cana-1759	334	17	2023	2023	NUM
cana-1759	334	18	)	)	PUNCT
cana-1759	334	19	.	.	PUNCT
cana-1759	335	1	numerical	numerical	PROPN
cana-1759	335	2	simulation	simulation	PROPN
cana-1759	335	3	of	of	ADP
cana-1759	335	4	natural	natural	ADJ
cana-1759	335	5	convection	convection	NOUN
cana-1759	335	6	heat	heat	NOUN
cana-1759	335	7	transfer	transfer	NOUN
cana-1759	335	8	of	of	ADP
cana-1759	335	9	nanofluids	nanofluid	NOUN
cana-1759	335	10	using	use	VERB
cana-1759	335	11	a	a	DET
cana-1759	335	12	modified	modify	VERB
cana-1759	335	13	lattice	lattice	NOUN
cana-1759	335	14	boltzmann	boltzmann	PROPN
cana-1759	335	15	method	method	NOUN
cana-1759	335	16	.	.	PUNCT
cana-1759	336	1	*	*	PUNCT
cana-1759	336	2	international	international	ADJ
cana-1759	336	3	journal	journal	NOUN
cana-1759	336	4	of	of	ADP
cana-1759	336	5	heat	heat	NOUN
cana-1759	336	6	and	and	CCONJ
cana-1759	336	7	fluid	fluid	ADJ
cana-1759	336	8	flow	flow	NOUN
cana-1759	336	9	*	*	NOUN
cana-1759	336	10	,	,	PUNCT
cana-1759	336	11	*	*	PUNCT
cana-1759	336	12	*	*	NOUN
cana-1759	336	13	94	94	NUM
cana-1759	336	14	*	*	PUNCT
cana-1759	336	15	*	*	NOUN
cana-1759	336	16	,	,	PUNCT
cana-1759	336	17	108897	108897	NUM
cana-1759	336	18	.	.	PUNCT
cana-1759	337	1	[	[	X
cana-1759	337	2	15	15	NUM
cana-1759	337	3	]	]	X
cana-1759	337	4	*	*	PUNCT
cana-1759	337	5	*	*	PUNCT
cana-1759	337	6	singh	singh	PROPN
cana-1759	337	7	,	,	PUNCT
cana-1759	337	8	a.k	a.k	PROPN
cana-1759	337	9	.	.	PROPN
cana-1759	337	10	,	,	PUNCT
cana-1759	337	11	&	&	CCONJ
cana-1759	337	12	sarkar	sarkar	PROPN
cana-1759	337	13	,	,	PUNCT
cana-1759	337	14	s.	s.	PROPN
cana-1759	337	15	*	*	PROPN
cana-1759	337	16	*	*	PUNCT
cana-1759	337	17	(	(	PUNCT
cana-1759	337	18	2022	2022	NUM
cana-1759	337	19	)	)	PUNCT
cana-1759	337	20	.	.	PUNCT
cana-1759	338	1	fractional	fractional	ADJ
cana-1759	338	2	calculus	calculus	NOUN
cana-1759	338	3	approach	approach	NOUN
cana-1759	338	4	for	for	ADP
cana-1759	338	5	modelling	modelling	NOUN
cana-1759	338	6	of	of	ADP
cana-1759	338	7	heat	heat	NOUN
cana-1759	338	8	transfer	transfer	NOUN
cana-1759	338	9	in	in	ADP
cana-1759	338	10	porous	porous	ADJ
cana-1759	338	11	media	medium	NOUN
cana-1759	338	12	saturated	saturate	VERB
cana-1759	338	13	with	with	ADP
cana-1759	338	14	nanofluid	nanofluid	PROPN
cana-1759	338	15	.	.	PUNCT
cana-1759	339	1	*	*	PUNCT
cana-1759	339	2	transport	transport	NOUN
cana-1759	339	3	in	in	ADP
cana-1759	339	4	porous	porous	ADJ
cana-1759	339	5	media	medium	NOUN
cana-1759	339	6	*	*	PUNCT
cana-1759	339	7	,	,	PUNCT
cana-1759	339	8	*	*	PUNCT
cana-1759	339	9	*	*	NOUN
cana-1759	339	10	141**(2	141**(2	NUM
cana-1759	339	11	)	)	PUNCT
cana-1759	339	12	,	,	PUNCT
cana-1759	339	13	389	389	NUM
cana-1759	339	14	-	-	SYM
cana-1759	339	15	407	407	NUM
cana-1759	339	16	.	.	PUNCT
cana-1759	340	1	[	[	X
cana-1759	340	2	16	16	NUM
cana-1759	340	3	]	]	X
cana-1759	340	4	*	*	PUNCT
cana-1759	340	5	*	*	PUNCT
cana-1759	340	6	tiwari	tiwari	X
cana-1759	340	7	,	,	PUNCT
cana-1759	340	8	r.k	r.k	PROPN
cana-1759	340	9	.	.	PROPN
cana-1759	340	10	,	,	PUNCT
cana-1759	340	11	kumar	kumar	PROPN
cana-1759	340	12	,	,	PUNCT
cana-1759	340	13	p.	p.	PROPN
cana-1759	340	14	,	,	PUNCT
cana-1759	340	15	&	&	CCONJ
cana-1759	340	16	kumar	kumar	PROPN
cana-1759	340	17	,	,	PUNCT
cana-1759	340	18	n.	n.	PROPN
cana-1759	340	19	*	*	PUNCT
cana-1759	340	20	*	*	PUNCT
cana-1759	340	21	(	(	PUNCT
cana-1759	340	22	2023	2023	NUM
cana-1759	340	23	)	)	PUNCT
cana-1759	340	24	.	.	PUNCT
cana-1759	341	1	numerical	numerical	PROPN
cana-1759	341	2	study	study	PROPN
cana-1759	341	3	on	on	ADP
cana-1759	341	4	mhd	mhd	NOUN
cana-1759	341	5	flow	flow	NOUN
cana-1759	341	6	and	and	CCONJ
cana-1759	341	7	heat	heat	NOUN
cana-1759	341	8	transfer	transfer	NOUN
cana-1759	341	9	of	of	ADP
cana-1759	341	10	a	a	DET
cana-1759	341	11	nanofluid	nanofluid	NOUN
cana-1759	341	12	over	over	ADP
cana-1759	341	13	a	a	DET
cana-1759	341	14	stretching	stretch	VERB
cana-1759	341	15	surface	surface	NOUN
cana-1759	341	16	using	use	VERB
cana-1759	341	17	a	a	DET
cana-1759	341	18	fractional	fractional	ADJ
cana-1759	341	19	order	order	NOUN
cana-1759	341	20	model	model	NOUN
cana-1759	341	21	.	.	PUNCT
cana-1759	342	1	*	*	PUNCT
cana-1759	342	2	journal	journal	NOUN
cana-1759	342	3	of	of	ADP
cana-1759	342	4	molecular	molecular	ADJ
cana-1759	342	5	liquids	liquid	NOUN
cana-1759	342	6	*	*	SYM
cana-1759	342	7	,	,	PUNCT
cana-1759	342	8	*	*	PUNCT
cana-1759	342	9	*	*	PUNCT
cana-1759	342	10	375	375	NUM
cana-1759	342	11	*	*	PUNCT
cana-1759	342	12	*	*	NOUN
cana-1759	342	13	,	,	PUNCT
cana-1759	342	14	120929	120929	NUM
cana-1759	342	15	.	.	PUNCT