id sid tid token lemma pos cana-333 1 1 communications communication NOUN cana-333 1 2 on on ADP cana-333 1 3 applied apply VERB cana-333 1 4 nonlinear nonlinear ADJ cana-333 1 5 analysis analysis NOUN cana-333 1 6 issn issn NOUN cana-333 1 7 : : PUNCT cana-333 1 8 1074 1074 NUM cana-333 1 9 - - PUNCT cana-333 1 10 133x 133x NUM cana-333 1 11 vol vol NOUN cana-333 1 12 31 31 NUM cana-333 1 13 no no NOUN cana-333 1 14 . . NOUN cana-333 1 15 1 1 NUM cana-333 1 16 ( ( PUNCT cana-333 1 17 2024 2024 NUM cana-333 1 18 ) ) PUNCT cana-333 1 19 104 104 NUM cana-333 1 20 https://internationalpubls.com https://internationalpubls.com X cana-333 1 21 effect effect NOUN cana-333 1 22 of of ADP cana-333 1 23 heat heat NOUN cana-333 1 24 source source NOUN cana-333 1 25 on on ADP cana-333 1 26 mhd mhd NOUN cana-333 1 27 convective convective ADJ cana-333 1 28 flow flow NOUN cana-333 1 29 of of ADP cana-333 1 30 nonnewtonian nonnewtonian ADJ cana-333 1 31 fluid fluid NOUN cana-333 1 32 past past ADP cana-333 1 33 an an DET cana-333 1 34 oscillating oscillate VERB cana-333 1 35 porous porous ADJ cana-333 1 36 plate plate NOUN cana-333 1 37 in in ADP cana-333 1 38 porous porous ADJ cana-333 1 39 medium medium ADJ cana-333 1 40 rajni1 rajni1 NOUN cana-333 1 41 , , PUNCT cana-333 1 42 monika monika PROPN cana-333 1 43 kalra2 kalra2 PROPN cana-333 1 44 1research 1research NUM cana-333 1 45 scholar scholar NOUN cana-333 1 46 , , PUNCT cana-333 1 47 department department NOUN cana-333 1 48 of of ADP cana-333 1 49 mathematics mathematics PROPN cana-333 1 50 , , PUNCT cana-333 1 51 chandigarh chandigarh PROPN cana-333 1 52 university university NOUN cana-333 1 53 , , PUNCT cana-333 1 54 gharuan gharuan PROPN cana-333 1 55 , , PUNCT cana-333 1 56 mohali mohali VERB cana-333 1 57 ssssrjs@gmail.com ssssrjs@gmail.com PROPN cana-333 1 58 . . PUNCT cana-333 2 1 2associate 2associate NUM cana-333 2 2 professor professor NOUN cana-333 2 3 , , PUNCT cana-333 2 4 department department NOUN cana-333 2 5 of of ADP cana-333 2 6 mathematics mathematics PROPN cana-333 2 7 , , PUNCT cana-333 2 8 chandigarh chandigarh PROPN cana-333 2 9 university university NOUN cana-333 2 10 , , PUNCT cana-333 2 11 gharuan gharuan PROPN cana-333 2 12 , , PUNCT cana-333 2 13 mohali mohali PROPN cana-333 2 14 kalra.01@gmail.com kalra.01@gmail.com PROPN cana-333 2 15 article article PROPN cana-333 2 16 history history NOUN cana-333 2 17 : : PUNCT cana-333 2 18 received receive VERB cana-333 2 19 : : PUNCT cana-333 2 20 20 20 NUM cana-333 2 21 - - SYM cana-333 2 22 09 09 NUM cana-333 2 23 - - PUNCT cana-333 2 24 2023 2023 NUM cana-333 2 25 revised revise VERB cana-333 2 26 : : PUNCT cana-333 2 27 30 30 NUM cana-333 2 28 - - SYM cana-333 2 29 10 10 NUM cana-333 2 30 - - PUNCT cana-333 2 31 2023 2023 NUM cana-333 2 32 accepted accept VERB cana-333 2 33 : : PUNCT cana-333 2 34 25 25 NUM cana-333 2 35 - - SYM cana-333 2 36 11 11 NUM cana-333 2 37 - - SYM cana-333 2 38 2023 2023 NUM cana-333 2 39 abstract abstract NOUN cana-333 2 40 : : PUNCT cana-333 2 41 introduction introduction NOUN cana-333 2 42 : : PUNCT cana-333 2 43 an an DET cana-333 2 44 investigation investigation NOUN cana-333 2 45 was be AUX cana-333 2 46 conducted conduct VERB cana-333 2 47 to to PART cana-333 2 48 analyse analyse VERB cana-333 2 49 the the DET cana-333 2 50 impact impact NOUN cana-333 2 51 of of ADP cana-333 2 52 unsteady unsteady ADJ cana-333 2 53 flow flow NOUN cana-333 2 54 caused cause VERB cana-333 2 55 by by ADP cana-333 2 56 nonnewtonian nonnewtonian ADJ cana-333 2 57 fluid fluid NOUN cana-333 2 58 with with ADP cana-333 2 59 magneto magneto ADJ cana-333 2 60 hydrodynamic hydrodynamic ADJ cana-333 2 61 properties property NOUN cana-333 2 62 on on ADP cana-333 2 63 an an DET cana-333 2 64 oscillating oscillate VERB cana-333 2 65 plate plate NOUN cana-333 2 66 made make VERB cana-333 2 67 of of ADP cana-333 2 68 porous porous ADJ cana-333 2 69 material material NOUN cana-333 2 70 in in ADP cana-333 2 71 a a DET cana-333 2 72 porous porous ADJ cana-333 2 73 medium medium NOUN cana-333 2 74 . . PUNCT cana-333 3 1 the the DET cana-333 3 2 analysis analysis NOUN cana-333 3 3 of of ADP cana-333 3 4 convective convective ADJ cana-333 3 5 heat heat NOUN cana-333 3 6 transfer transfer NOUN cana-333 3 7 included include VERB cana-333 3 8 additional additional ADJ cana-333 3 9 parameters parameter NOUN cana-333 3 10 such such ADJ cana-333 3 11 as as ADP cana-333 3 12 electrically electrically ADV cana-333 3 13 conducting conduct VERB cana-333 3 14 unsteady unsteady ADJ cana-333 3 15 flow flow NOUN cana-333 3 16 - - PUNCT cana-333 3 17 facing face VERB cana-333 3 18 applied apply VERB cana-333 3 19 magnetic magnetic ADJ cana-333 3 20 force force NOUN cana-333 3 21 . . PUNCT cana-333 4 1 the the DET cana-333 4 2 perturbation perturbation NOUN cana-333 4 3 method method NOUN cana-333 4 4 was be AUX cana-333 4 5 used use VERB cana-333 4 6 to to PART cana-333 4 7 transform transform VERB cana-333 4 8 the the DET cana-333 4 9 governing govern VERB cana-333 4 10 equations equation NOUN cana-333 4 11 into into ADP cana-333 4 12 non non ADJ cana-333 4 13 - - ADJ cana-333 4 14 linear linear ADJ cana-333 4 15 differential differential ADJ cana-333 4 16 equations equation NOUN cana-333 4 17 with with ADP cana-333 4 18 utmost utmost ADJ cana-333 4 19 precision precision NOUN cana-333 4 20 . . PUNCT cana-333 5 1 moreover moreover ADV cana-333 5 2 , , PUNCT cana-333 5 3 matlab matlab PROPN cana-333 5 4 was be AUX cana-333 5 5 used use VERB cana-333 5 6 to to PART cana-333 5 7 precisely precisely ADV cana-333 5 8 evolve evolve VERB cana-333 5 9 temperature temperature NOUN cana-333 5 10 and and CCONJ cana-333 5 11 velocity velocity NOUN cana-333 5 12 profiles profile NOUN cana-333 5 13 for for ADP cana-333 5 14 different different ADJ cana-333 5 15 parameters parameter NOUN cana-333 5 16 such such ADJ cana-333 5 17 as as ADP cana-333 5 18 grashof grashof ADJ cana-333 5 19 number number NOUN cana-333 5 20 , , PUNCT cana-333 5 21 prandtl prandtl NOUN cana-333 5 22 number number NOUN cana-333 5 23 , , PUNCT cana-333 5 24 skin skin NOUN cana-333 5 25 friction friction NOUN cana-333 5 26 , , PUNCT cana-333 5 27 magnetic magnetic ADJ cana-333 5 28 parameter parameter NOUN cana-333 5 29 , , PUNCT cana-333 5 30 and and CCONJ cana-333 5 31 source source NOUN cana-333 5 32 / / SYM cana-333 5 33 sink sink NOUN cana-333 5 34 . . PUNCT cana-333 6 1 the the DET cana-333 6 2 heat heat NOUN cana-333 6 3 transfer transfer NOUN cana-333 6 4 rate rate NOUN cana-333 6 5 was be AUX cana-333 6 6 thoroughly thoroughly ADV cana-333 6 7 evaluated evaluate VERB cana-333 6 8 and and CCONJ cana-333 6 9 compiled compile VERB cana-333 6 10 using use VERB cana-333 6 11 graphs graph NOUN cana-333 6 12 and and CCONJ cana-333 6 13 tables table NOUN cana-333 6 14 , , PUNCT cana-333 6 15 guaranteeing guarantee VERB cana-333 6 16 the the DET cana-333 6 17 accuracy accuracy NOUN cana-333 6 18 of of ADP cana-333 6 19 the the DET cana-333 6 20 results result NOUN cana-333 6 21 . . PUNCT cana-333 7 1 keywords keyword NOUN cana-333 7 2 : : PUNCT cana-333 7 3 unsteady unsteady ADJ cana-333 7 4 , , PUNCT cana-333 7 5 fluid fluid ADJ cana-333 7 6 , , PUNCT cana-333 7 7 porous porous ADJ cana-333 7 8 medium medium ADJ cana-333 7 9 , , PUNCT cana-333 7 10 flow flow NOUN cana-333 7 11 , , PUNCT cana-333 7 12 non non ADJ cana-333 7 13 - - ADJ cana-333 7 14 newtonian newtonian ADJ cana-333 7 15 fluid fluid NOUN cana-333 7 16 , , PUNCT cana-333 7 17 suction suction NOUN cana-333 7 18 / / SYM cana-333 7 19 injection injection NOUN cana-333 7 20 , , PUNCT cana-333 7 21 magneto magneto NOUN cana-333 7 22 - - PUNCT cana-333 7 23 hydrodynamic hydrodynamic ADJ cana-333 7 24 . . PUNCT cana-333 8 1 1 1 X cana-333 8 2 . . X cana-333 8 3 introduction introduction NOUN cana-333 8 4 universe universe NOUN cana-333 8 5 is be AUX cana-333 8 6 an an DET cana-333 8 7 un un ADJ cana-333 8 8 - - ADJ cana-333 8 9 parallel parallel ADJ cana-333 8 10 creation creation NOUN cana-333 8 11 of of ADP cana-333 8 12 nature nature NOUN cana-333 8 13 . . PUNCT cana-333 9 1 the the DET cana-333 9 2 earth earth NOUN cana-333 9 3 we we PRON cana-333 9 4 live live VERB cana-333 9 5 on on ADP cana-333 9 6 , , PUNCT cana-333 9 7 the the DET cana-333 9 8 sky sky NOUN cana-333 9 9 above above ADP cana-333 9 10 our our PRON cana-333 9 11 head head NOUN cana-333 9 12 studded stud VERB cana-333 9 13 with with ADP cana-333 9 14 innumerable innumerable ADJ cana-333 9 15 stars star NOUN cana-333 9 16 and and CCONJ cana-333 9 17 planets planet NOUN cana-333 9 18 . . PUNCT cana-333 10 1 moving move VERB cana-333 10 2 around around ADP cana-333 10 3 their their PRON cana-333 10 4 own own ADJ cana-333 10 5 axis axis NOUN cana-333 10 6 as as ADV cana-333 10 7 well well ADV cana-333 10 8 as as ADP cana-333 10 9 the the DET cana-333 10 10 sun sun NOUN cana-333 10 11 , , PUNCT cana-333 10 12 in in ADP cana-333 10 13 a a DET cana-333 10 14 relative relative ADJ cana-333 10 15 motion motion NOUN cana-333 10 16 , , PUNCT cana-333 10 17 under under ADP cana-333 10 18 a a DET cana-333 10 19 force force NOUN cana-333 10 20 keeping keep VERB cana-333 10 21 all all PRON cana-333 10 22 at at ADP cana-333 10 23 a a DET cana-333 10 24 specific specific ADJ cana-333 10 25 distance distance NOUN cana-333 10 26 , , PUNCT cana-333 10 27 maintaining maintain VERB cana-333 10 28 the the DET cana-333 10 29 equilibrium equilibrium NOUN cana-333 10 30 . . PUNCT cana-333 11 1 the the DET cana-333 11 2 earth earth NOUN cana-333 11 3 is be AUX cana-333 11 4 abundant abundant ADJ cana-333 11 5 in in ADP cana-333 11 6 several several ADJ cana-333 11 7 types type NOUN cana-333 11 8 of of ADP cana-333 11 9 matter matter NOUN cana-333 11 10 existing exist VERB cana-333 11 11 in in ADP cana-333 11 12 solid solid ADJ cana-333 11 13 , , PUNCT cana-333 11 14 liquid liquid ADJ cana-333 11 15 , , PUNCT cana-333 11 16 gaseous gaseous ADJ cana-333 11 17 or or CCONJ cana-333 11 18 plasma plasma NOUN cana-333 11 19 forms form NOUN cana-333 11 20 where where SCONJ cana-333 11 21 air air NOUN cana-333 11 22 and and CCONJ cana-333 11 23 water water NOUN cana-333 11 24 are be AUX cana-333 11 25 the the DET cana-333 11 26 most most ADV cana-333 11 27 essential essential ADJ cana-333 11 28 constituents constituent NOUN cana-333 11 29 of of ADP cana-333 11 30 life life NOUN cana-333 11 31 for for ADP cana-333 11 32 plants plant NOUN cana-333 11 33 , , PUNCT cana-333 11 34 trees tree NOUN cana-333 11 35 , , PUNCT cana-333 11 36 creatures creature NOUN cana-333 11 37 , , PUNCT cana-333 11 38 birds bird NOUN cana-333 11 39 , , PUNCT cana-333 11 40 animals animal NOUN cana-333 11 41 including include VERB cana-333 11 42 human human ADJ cana-333 11 43 beings being NOUN cana-333 11 44 and and CCONJ cana-333 11 45 help help VERB cana-333 11 46 their their PRON cana-333 11 47 growth growth NOUN cana-333 11 48 . . PUNCT cana-333 12 1 a a DET cana-333 12 2 number number NOUN cana-333 12 3 of of ADP cana-333 12 4 forces force NOUN cana-333 12 5 like like ADP cana-333 12 6 gravitation gravitation NOUN cana-333 12 7 , , PUNCT cana-333 12 8 frictions friction NOUN cana-333 12 9 etc etc X cana-333 12 10 . . X cana-333 12 11 are be AUX cana-333 12 12 regularly regularly ADV cana-333 12 13 influencing influence VERB cana-333 12 14 the the DET cana-333 12 15 state state NOUN cana-333 12 16 of of ADP cana-333 12 17 rest rest NOUN cana-333 12 18 or or CCONJ cana-333 12 19 of of ADP cana-333 12 20 uniform uniform ADJ cana-333 12 21 motion motion NOUN cana-333 12 22 of of ADP cana-333 12 23 all all DET cana-333 12 24 elements element NOUN cana-333 12 25 in in ADP cana-333 12 26 the the DET cana-333 12 27 system system NOUN cana-333 12 28 . . PUNCT cana-333 13 1 elements element NOUN cana-333 13 2 which which PRON cana-333 13 3 exist exist VERB cana-333 13 4 in in ADP cana-333 13 5 liquid liquid NOUN cana-333 13 6 , , PUNCT cana-333 13 7 gaseous gaseous ADJ cana-333 13 8 of of ADP cana-333 13 9 plasma plasma NOUN cana-333 13 10 form form NOUN cana-333 13 11 and and CCONJ cana-333 13 12 or or CCONJ cana-333 13 13 can can AUX cana-333 13 14 flow flow VERB cana-333 13 15 under under ADP cana-333 13 16 certain certain ADJ cana-333 13 17 conditions condition NOUN cana-333 13 18 are be AUX cana-333 13 19 said say VERB cana-333 13 20 to to PART cana-333 13 21 be be AUX cana-333 13 22 fluids fluid NOUN cana-333 13 23 . . PUNCT cana-333 14 1 a a DET cana-333 14 2 substance substance NOUN cana-333 14 3 which which PRON cana-333 14 4 continues continue VERB cana-333 14 5 to to PART cana-333 14 6 deform deform VERB cana-333 14 7 and and CCONJ cana-333 14 8 change change VERB cana-333 14 9 its its PRON cana-333 14 10 relative relative ADJ cana-333 14 11 position position NOUN cana-333 14 12 under under ADP cana-333 14 13 the the DET cana-333 14 14 effect effect NOUN cana-333 14 15 of of ADP cana-333 14 16 shear shear NOUN cana-333 14 17 force force NOUN cana-333 14 18 can can AUX cana-333 14 19 be be AUX cana-333 14 20 termed term VERB cana-333 14 21 as as ADP cana-333 14 22 fluid fluid ADJ cana-333 14 23 . . PUNCT cana-333 15 1 the the DET cana-333 15 2 study study NOUN cana-333 15 3 of of ADP cana-333 15 4 their their PRON cana-333 15 5 properties property NOUN cana-333 15 6 , , PUNCT cana-333 15 7 characteristics characteristic NOUN cana-333 15 8 as as ADV cana-333 15 9 well well ADV cana-333 15 10 as as ADP cana-333 15 11 physical physical ADJ cana-333 15 12 behaviour behaviour NOUN cana-333 15 13 is be AUX cana-333 15 14 a a DET cana-333 15 15 subject subject NOUN cana-333 15 16 of of ADP cana-333 15 17 science science NOUN cana-333 15 18 and and CCONJ cana-333 15 19 comes come VERB cana-333 15 20 under under ADP cana-333 15 21 fluid fluid ADJ cana-333 15 22 mechanics mechanic NOUN cana-333 15 23 known know VERB cana-333 15 24 to to PART cana-333 15 25 be be AUX cana-333 15 26 fluid fluid ADJ cana-333 15 27 dynamics dynamic NOUN cana-333 15 28 . . PUNCT cana-333 16 1 convection convection NOUN cana-333 16 2 is be AUX cana-333 16 3 considered consider VERB cana-333 16 4 to to PART cana-333 16 5 be be AUX cana-333 16 6 the the DET cana-333 16 7 dominant dominant ADJ cana-333 16 8 mechanism mechanism NOUN cana-333 16 9 . . PUNCT cana-333 17 1 it it PRON cana-333 17 2 has have VERB cana-333 17 3 its its PRON cana-333 17 4 application application NOUN cana-333 17 5 in in ADP cana-333 17 6 chemical chemical ADJ cana-333 17 7 engineering engineering NOUN cana-333 17 8 , , PUNCT cana-333 17 9 geothermal geothermal ADJ cana-333 17 10 and and CCONJ cana-333 17 11 oil oil NOUN cana-333 17 12 reservoir reservoir NOUN cana-333 17 13 modelling modelling NOUN cana-333 17 14 . . PUNCT cana-333 18 1 there there PRON cana-333 18 2 can can AUX cana-333 18 3 be be AUX cana-333 18 4 free free ADJ cana-333 18 5 or or CCONJ cana-333 18 6 forced force VERB cana-333 18 7 convection convection NOUN cana-333 18 8 . . PUNCT cana-333 19 1 free free ADJ cana-333 19 2 convection convection NOUN cana-333 19 3 flow flow NOUN cana-333 19 4 is be AUX cana-333 19 5 the the DET cana-333 19 6 outcome outcome NOUN cana-333 19 7 of of ADP cana-333 19 8 the the DET cana-333 19 9 fluid fluid ADJ cana-333 19 10 body body NOUN cana-333 19 11 forces force NOUN cana-333 19 12 proportional proportional ADJ cana-333 19 13 to to ADP cana-333 19 14 mass mass NOUN cana-333 19 15 or or CCONJ cana-333 19 16 density density NOUN cana-333 19 17 of of ADP cana-333 19 18 fluid fluid NOUN cana-333 19 19 . . PUNCT cana-333 20 1 buoyant buoyant ADJ cana-333 20 2 force force NOUN cana-333 20 3 determines determine VERB cana-333 20 4 the the DET cana-333 20 5 pattern pattern NOUN cana-333 20 6 of of ADP cana-333 20 7 flow flow NOUN cana-333 20 8 . . PUNCT cana-333 21 1 rise rise NOUN cana-333 21 2 of of ADP cana-333 21 3 smoke smoke NOUN cana-333 21 4 from from ADP cana-333 21 5 fire fire NOUN cana-333 21 6 is be AUX cana-333 21 7 an an DET cana-333 21 8 example example NOUN cana-333 21 9 of of ADP cana-333 21 10 such such ADJ cana-333 21 11 convection convection NOUN cana-333 21 12 . . PUNCT cana-333 22 1 in in ADP cana-333 22 2 case case NOUN cana-333 22 3 the the DET cana-333 22 4 fluid fluid ADJ cana-333 22 5 motion motion NOUN cana-333 22 6 is be AUX cana-333 22 7 artificially artificially ADV cana-333 22 8 created create VERB cana-333 22 9 using use VERB cana-333 22 10 external external ADJ cana-333 22 11 force force NOUN cana-333 22 12 like like ADP cana-333 22 13 wind wind NOUN cana-333 22 14 , , PUNCT cana-333 22 15 fan fan NOUN cana-333 22 16 , , PUNCT cana-333 22 17 blower blower NOUN cana-333 22 18 or or CCONJ cana-333 22 19 pump pump VERB cana-333 22 20 the the DET cana-333 22 21 convection convection NOUN cana-333 22 22 is be AUX cana-333 22 23 forced force VERB cana-333 22 24 one one NUM cana-333 22 25 . . PUNCT cana-333 23 1 on on ADP cana-333 23 2 the the DET cana-333 23 3 other other ADJ cana-333 23 4 hand hand NOUN cana-333 23 5 those those PRON cana-333 23 6 found find VERB cana-333 23 7 in in ADP cana-333 23 8 nature nature NOUN cana-333 23 9 are be AUX cana-333 23 10 known know VERB cana-333 23 11 to to PART cana-333 23 12 be be AUX cana-333 23 13 free free ADJ cana-333 23 14 convections convection NOUN cana-333 23 15 . . PUNCT cana-333 24 1 such such ADJ cana-333 24 2 flows flow NOUN cana-333 24 3 are be AUX cana-333 24 4 also also ADV cana-333 24 5 experienced experience VERB cana-333 24 6 in in ADP cana-333 24 7 industrial industrial ADJ cana-333 24 8 field field NOUN cana-333 24 9 like like ADP cana-333 24 10 filtration filtration NOUN cana-333 24 11 process process NOUN cana-333 24 12 , , PUNCT cana-333 24 13 food food NOUN cana-333 24 14 communications communication NOUN cana-333 24 15 on on ADP cana-333 24 16 applied apply VERB cana-333 24 17 nonlinear nonlinear ADJ cana-333 24 18 analysis analysis NOUN cana-333 24 19 issn issn NOUN cana-333 24 20 : : PUNCT cana-333 24 21 1074 1074 NUM cana-333 24 22 - - PUNCT cana-333 24 23 133x 133x NUM cana-333 24 24 vol vol NOUN cana-333 24 25 31 31 NUM cana-333 24 26 no no NOUN cana-333 24 27 . . NOUN cana-333 24 28 1 1 NUM cana-333 24 29 ( ( PUNCT cana-333 24 30 2024 2024 NUM cana-333 24 31 ) ) PUNCT cana-333 24 32 105 105 NUM cana-333 24 33 https://internationalpubls.com https://internationalpubls.com X cana-333 24 34 industries industry NOUN cana-333 24 35 , , PUNCT cana-333 24 36 metallurgical metallurgical ADJ cana-333 24 37 process process NOUN cana-333 24 38 , , PUNCT cana-333 24 39 textile textile NOUN cana-333 24 40 industries industry NOUN cana-333 24 41 , , PUNCT cana-333 24 42 nuclear nuclear ADJ cana-333 24 43 reactors reactor NOUN cana-333 24 44 and and CCONJ cana-333 24 45 solar solar ADJ cana-333 24 46 energy energy NOUN cana-333 24 47 collectors collector NOUN cana-333 24 48 . . PUNCT cana-333 25 1 prior prior ADV cana-333 25 2 to to ADP cana-333 25 3 the the DET cana-333 25 4 study study NOUN cana-333 25 5 of of ADP cana-333 25 6 flows flow NOUN cana-333 25 7 through through ADP cana-333 25 8 porous porous ADJ cana-333 25 9 medium medium NOUN cana-333 25 10 , , PUNCT cana-333 25 11 the the DET cana-333 25 12 study study NOUN cana-333 25 13 is be AUX cana-333 25 14 carried carry VERB cana-333 25 15 out out ADP cana-333 25 16 in in ADP cana-333 25 17 the the DET cana-333 25 18 wake wake NOUN cana-333 25 19 of of ADP cana-333 25 20 a a DET cana-333 25 21 number number NOUN cana-333 25 22 of of ADP cana-333 25 23 forces force NOUN cana-333 25 24 acting act VERB cana-333 25 25 on on ADP cana-333 25 26 the the DET cana-333 25 27 fluid fluid NOUN cana-333 25 28 , , PUNCT cana-333 25 29 effecting effect VERB cana-333 25 30 monitoring monitoring NOUN cana-333 25 31 and and CCONJ cana-333 25 32 controlling control VERB cana-333 25 33 its its PRON cana-333 25 34 flow flow NOUN cana-333 25 35 . . PUNCT cana-333 26 1 various various ADJ cana-333 26 2 concepts concept NOUN cana-333 26 3 , , PUNCT cana-333 26 4 principals principal NOUN cana-333 26 5 , , PUNCT cana-333 26 6 laws law NOUN cana-333 26 7 like like ADP cana-333 26 8 conservation conservation NOUN cana-333 26 9 of of ADP cana-333 26 10 energy energy NOUN cana-333 26 11 , , PUNCT cana-333 26 12 mass mass NOUN cana-333 26 13 and and CCONJ cana-333 26 14 momentum momentum NOUN cana-333 26 15 including include VERB cana-333 26 16 law law NOUN cana-333 26 17 of of ADP cana-333 26 18 viscosity viscosity NOUN cana-333 26 19 , , PUNCT cana-333 26 20 thermodynamics thermodynamic NOUN cana-333 26 21 , , PUNCT cana-333 26 22 mathematical mathematical ADJ cana-333 26 23 applications application NOUN cana-333 26 24 , , PUNCT cana-333 26 25 in in ADP cana-333 26 26 addition addition NOUN cana-333 26 27 boundary boundary ADJ cana-333 26 28 conditions condition NOUN cana-333 26 29 and and CCONJ cana-333 26 30 limitations limitation NOUN cana-333 26 31 are be AUX cana-333 26 32 operative operative ADJ cana-333 26 33 at at ADP cana-333 26 34 appropriate appropriate ADJ cana-333 26 35 situations situation NOUN cana-333 26 36 . . PUNCT cana-333 27 1 in in ADP cana-333 27 2 present present ADJ cana-333 27 3 times time NOUN cana-333 27 4 multifarious multifarious ADJ cana-333 27 5 problems problem NOUN cana-333 27 6 and and CCONJ cana-333 27 7 their their PRON cana-333 27 8 complex complex ADJ cana-333 27 9 nature nature NOUN cana-333 27 10 poses pose VERB cana-333 27 11 new new ADJ cana-333 27 12 challenges challenge NOUN cana-333 27 13 in in ADP cana-333 27 14 every every DET cana-333 27 15 field field NOUN cana-333 27 16 dealing deal VERB cana-333 27 17 with with ADP cana-333 27 18 fluid fluid ADJ cana-333 27 19 flow flow NOUN cana-333 27 20 , , PUNCT cana-333 27 21 simulation simulation NOUN cana-333 27 22 of of ADP cana-333 27 23 ocean ocean PROPN cana-333 27 24 currents current NOUN cana-333 27 25 , , PUNCT cana-333 27 26 artificial artificial ADJ cana-333 27 27 kidney kidney NOUN cana-333 27 28 and and CCONJ cana-333 27 29 heart heart NOUN cana-333 27 30 mechanism mechanism NOUN cana-333 27 31 and and CCONJ cana-333 27 32 blood blood NOUN cana-333 27 33 flow flow NOUN cana-333 27 34 in in ADP cana-333 27 35 veins vein NOUN cana-333 27 36 and and CCONJ cana-333 27 37 arteries artery NOUN cana-333 27 38 . . PUNCT cana-333 28 1 to to PART cana-333 28 2 solve solve VERB cana-333 28 3 fluid fluid ADJ cana-333 28 4 dynamics dynamic NOUN cana-333 28 5 problems problem NOUN cana-333 28 6 , , PUNCT cana-333 28 7 numerous numerous ADJ cana-333 28 8 properties property NOUN cana-333 28 9 of of ADP cana-333 28 10 fluid fluid ADJ cana-333 28 11 like like ADP cana-333 28 12 temperature temperature NOUN cana-333 28 13 , , PUNCT cana-333 28 14 pressure pressure NOUN cana-333 28 15 , , PUNCT cana-333 28 16 velocity velocity NOUN cana-333 28 17 and and CCONJ cana-333 28 18 density density NOUN cana-333 28 19 as as ADP cana-333 28 20 functions function NOUN cana-333 28 21 of of ADP cana-333 28 22 time time NOUN cana-333 28 23 and and CCONJ cana-333 28 24 space space NOUN cana-333 28 25 are be AUX cana-333 28 26 calculated calculate VERB cana-333 28 27 in in ADP cana-333 28 28 addition addition NOUN cana-333 28 29 to to ADP cana-333 28 30 some some DET cana-333 28 31 parameters parameter NOUN cana-333 28 32 and and CCONJ cana-333 28 33 terms term NOUN cana-333 28 34 . . PUNCT cana-333 29 1 during during ADP cana-333 29 2 the the DET cana-333 29 3 past past ADJ cana-333 29 4 few few ADJ cana-333 29 5 years year NOUN cana-333 29 6 , , PUNCT cana-333 29 7 it it PRON cana-333 29 8 's be AUX cana-333 29 9 been be AUX cana-333 29 10 noticed notice VERB cana-333 29 11 that that SCONJ cana-333 29 12 fluids fluid NOUN cana-333 29 13 of of ADP cana-333 29 14 non non ADJ cana-333 29 15 - - ADJ cana-333 29 16 newtonian newtonian ADJ cana-333 29 17 features feature NOUN cana-333 29 18 have have AUX cana-333 29 19 earned earn VERB cana-333 29 20 increasing increase VERB cana-333 29 21 significance significance NOUN cana-333 29 22 for for ADP cana-333 29 23 their their PRON cana-333 29 24 application application NOUN cana-333 29 25 in in ADP cana-333 29 26 several several ADJ cana-333 29 27 engineering engineering NOUN cana-333 29 28 and and CCONJ cana-333 29 29 technical technical ADJ cana-333 29 30 fields field NOUN cana-333 29 31 . . PUNCT cana-333 30 1 more more ADJ cana-333 30 2 and and CCONJ cana-333 30 3 more more ADJ cana-333 30 4 researchers researcher NOUN cana-333 30 5 have have AUX cana-333 30 6 come come VERB cana-333 30 7 to to PART cana-333 30 8 be be AUX cana-333 30 9 fascinated fascinated ADJ cana-333 30 10 to to PART cana-333 30 11 adopt adopt VERB cana-333 30 12 studies study NOUN cana-333 30 13 pertaining pertain VERB cana-333 30 14 to to ADP cana-333 30 15 such such ADJ cana-333 30 16 form form NOUN cana-333 30 17 of of ADP cana-333 30 18 fluids fluid NOUN cana-333 30 19 , , PUNCT cana-333 30 20 which which PRON cana-333 30 21 do do AUX cana-333 30 22 not not PART cana-333 30 23 obey obey VERB cana-333 30 24 the the DET cana-333 30 25 laws law NOUN cana-333 30 26 of of ADP cana-333 30 27 viscosity viscosity NOUN cana-333 30 28 , , PUNCT cana-333 30 29 moreover moreover ADV cana-333 30 30 , , PUNCT cana-333 30 31 show show NOUN cana-333 30 32 of of ADP cana-333 30 33 a a DET cana-333 30 34 link link NOUN cana-333 30 35 between between ADP cana-333 30 36 strain strain NOUN cana-333 30 37 and and CCONJ cana-333 30 38 stress stress NOUN cana-333 30 39 rate rate NOUN cana-333 30 40 of of ADP cana-333 30 41 nonlinear nonlinear ADJ cana-333 30 42 nature nature NOUN cana-333 30 43 . . PUNCT cana-333 31 1 because because SCONJ cana-333 31 2 of of ADP cana-333 31 3 their their PRON cana-333 31 4 complex complex ADJ cana-333 31 5 nature nature NOUN cana-333 31 6 , , PUNCT cana-333 31 7 various various ADJ cana-333 31 8 types type NOUN cana-333 31 9 of of ADP cana-333 31 10 fluids fluid NOUN cana-333 31 11 together together ADV cana-333 31 12 with with ADP cana-333 31 13 ketchup ketchup NOUN cana-333 31 14 , , PUNCT cana-333 31 15 paints paint NOUN cana-333 31 16 , , PUNCT cana-333 31 17 shampoo shampoo NOUN cana-333 31 18 , , PUNCT cana-333 31 19 and and CCONJ cana-333 31 20 polymer polymer NOUN cana-333 31 21 solutions solution NOUN cana-333 31 22 have have AUX cana-333 31 23 posed pose VERB cana-333 31 24 a a DET cana-333 31 25 project project NOUN cana-333 31 26 to to ADP cana-333 31 27 engineers engineer NOUN cana-333 31 28 , , PUNCT cana-333 31 29 mathematicians mathematician NOUN cana-333 31 30 , , PUNCT cana-333 31 31 and and CCONJ cana-333 31 32 physicists physicist NOUN cana-333 31 33 to to PART cana-333 31 34 examine examine VERB cana-333 31 35 on on ADP cana-333 31 36 those those DET cana-333 31 37 fluids fluid NOUN cana-333 31 38 . . PUNCT cana-333 32 1 a a DET cana-333 32 2 number number NOUN cana-333 32 3 of of ADP cana-333 32 4 fashions fashion NOUN cana-333 32 5 play play VERB cana-333 32 6 fundamental fundamental ADJ cana-333 32 7 position position NOUN cana-333 32 8 in in ADP cana-333 32 9 their their PRON cana-333 32 10 take take NOUN cana-333 32 11 a a DET cana-333 32 12 look look NOUN cana-333 32 13 at at ADP cana-333 32 14 however however ADV cana-333 32 15 no no DET cana-333 32 16 unmarried unmarried ADJ cana-333 32 17 version version NOUN cana-333 32 18 has have AUX cana-333 32 19 yet yet ADV cana-333 32 20 been be AUX cana-333 32 21 determined determine VERB cana-333 32 22 that that PRON cana-333 32 23 may may AUX cana-333 32 24 show show VERB cana-333 32 25 to to PART cana-333 32 26 be be AUX cana-333 32 27 multi multi ADJ cana-333 32 28 - - NOUN cana-333 32 29 function function NOUN cana-333 32 30 . . PUNCT cana-333 33 1 2 2 X cana-333 33 2 . . X cana-333 33 3 literature literature NOUN cana-333 33 4 review review PROPN cana-333 33 5 [ [ X cana-333 33 6 1 1 X cana-333 33 7 ] ] PUNCT cana-333 33 8 this this DET cana-333 33 9 paper paper NOUN cana-333 33 10 mainly mainly ADV cana-333 33 11 aims aim VERB cana-333 33 12 at at ADP cana-333 33 13 the the DET cana-333 33 14 combined combine VERB cana-333 33 15 impact impact NOUN cana-333 33 16 of of ADP cana-333 33 17 both both CCONJ cana-333 33 18 free free ADJ cana-333 33 19 convective convective ADJ cana-333 33 20 heating heating NOUN cana-333 33 21 as as ADV cana-333 33 22 well well ADV cana-333 33 23 as as ADP cana-333 33 24 mass mass ADJ cana-333 33 25 transfer transfer NOUN cana-333 33 26 of of ADP cana-333 33 27 stable stable ADJ cana-333 33 28 two two NUM cana-333 33 29 dimensional dimensional ADJ cana-333 33 30 laminar laminar NOUN cana-333 33 31 , , PUNCT cana-333 33 32 polar polar ADJ cana-333 33 33 fluid fluid NOUN cana-333 33 34 through through ADP cana-333 33 35 a a DET cana-333 33 36 porous porous ADJ cana-333 33 37 medium medium NOUN cana-333 33 38 , , PUNCT cana-333 33 39 with with ADP cana-333 33 40 internal internal ADJ cana-333 33 41 heat heat NOUN cana-333 33 42 generation generation NOUN cana-333 33 43 and and CCONJ cana-333 33 44 first first ADJ cana-333 33 45 order order NOUN cana-333 33 46 chemical chemical NOUN cana-333 33 47 reaction reaction NOUN cana-333 33 48 . . PUNCT cana-333 34 1 the the DET cana-333 34 2 highly highly ADV cana-333 34 3 non non ADJ cana-333 34 4 liner liner NOUN cana-333 34 5 couple couple NOUN cana-333 34 6 differential differential ADJ cana-333 34 7 equations equation NOUN cana-333 34 8 that that PRON cana-333 34 9 control control VERB cana-333 34 10 boundary boundary ADJ cana-333 34 11 layer layer NOUN cana-333 34 12 flow flow NOUN cana-333 34 13 are be AUX cana-333 34 14 resolved resolve VERB cana-333 34 15 using use VERB cana-333 34 16 the the DET cana-333 34 17 two two NUM cana-333 34 18 term term NOUN cana-333 34 19 ( ( PUNCT cana-333 34 20 eckert eckert PROPN cana-333 34 21 number number PROPN cana-333 34 22 e e NOUN cana-333 34 23 ) ) PUNCT cana-333 34 24 method.[2 method.[2 NOUN cana-333 34 25 ] ] PUNCT cana-333 34 26 for for ADP cana-333 34 27 investigating investigate VERB cana-333 34 28 numerically numerically ADV cana-333 34 29 the the DET cana-333 34 30 multiphase multiphase NOUN cana-333 34 31 problem problem NOUN cana-333 34 32 concerning concern VERB cana-333 34 33 both both CCONJ cana-333 34 34 newtonian newtonian NOUN cana-333 34 35 as as ADV cana-333 34 36 well well ADV cana-333 34 37 as as ADP cana-333 34 38 nonnewtonian nonnewtonian NOUN cana-333 34 39 flows flow VERB cana-333 34 40 , , PUNCT cana-333 34 41 on on ADP cana-333 34 42 improved improved ADJ cana-333 34 43 isph isph NOUN cana-333 34 44 algorithm algorithm NOUN cana-333 34 45 has have AUX cana-333 34 46 been be AUX cana-333 34 47 utilised utilise VERB cana-333 34 48 . . PUNCT cana-333 35 1 [ [ X cana-333 35 2 3 3 X cana-333 35 3 ] ] X cana-333 35 4 investigation investigation NOUN cana-333 35 5 was be AUX cana-333 35 6 made make VERB cana-333 35 7 to to PART cana-333 35 8 know know VERB cana-333 35 9 the the DET cana-333 35 10 result result NOUN cana-333 35 11 of of ADP cana-333 35 12 free free ADJ cana-333 35 13 convection convection NOUN cana-333 35 14 of of ADP cana-333 35 15 conducting conduct VERB cana-333 35 16 viscoelastic viscoelastic ADJ cana-333 35 17 incompressible incompressible ADJ cana-333 35 18 fluid fluid NOUN cana-333 35 19 in in ADP cana-333 35 20 the the DET cana-333 35 21 matter matter NOUN cana-333 35 22 of of ADP cana-333 35 23 heat heat NOUN cana-333 35 24 and and CCONJ cana-333 35 25 mass mass NOUN cana-333 35 26 transfer transfer NOUN cana-333 35 27 on on ADP cana-333 35 28 vertical vertical ADJ cana-333 35 29 plate plate NOUN cana-333 35 30 in in ADP cana-333 35 31 porous porous ADJ cana-333 35 32 medium medium NOUN cana-333 35 33 while while SCONJ cana-333 35 34 a a DET cana-333 35 35 homogeneous homogeneous ADJ cana-333 35 36 transverse transverse NOUN cana-333 35 37 magnetic magnetic ADJ cana-333 35 38 field field NOUN cana-333 35 39 was be AUX cana-333 35 40 acting act VERB cana-333 35 41 with with ADP cana-333 35 42 heat heat NOUN cana-333 35 43 source source NOUN cana-333 35 44 having have VERB cana-333 35 45 time time NOUN cana-333 35 46 dependent dependent ADJ cana-333 35 47 permeability.[4 permeability.[4 NOUN cana-333 35 48 ] ] PUNCT cana-333 35 49 this this DET cana-333 35 50 paper paper NOUN cana-333 35 51 studies study NOUN cana-333 35 52 jeffrey jeffrey PROPN cana-333 35 53 ’s ’s PART cana-333 35 54 non non ADJ cana-333 35 55 - - ADJ cana-333 35 56 newtonian newtonian ADJ cana-333 35 57 incompressible incompressible ADJ cana-333 35 58 fluid fluid NOUN cana-333 35 59 , , PUNCT cana-333 35 60 boundary boundary ADJ cana-333 35 61 layer layer NOUN cana-333 35 62 flow flow NOUN cana-333 35 63 of of ADP cana-333 35 64 nonliner nonliner PROPN cana-333 35 65 equilibrium equilibrium NOUN cana-333 35 66 nature nature NOUN cana-333 35 67 across across ADP cana-333 35 68 a a DET cana-333 35 69 porous porous ADJ cana-333 35 70 plate plate NOUN cana-333 35 71 in in ADP cana-333 35 72 non non ADJ cana-333 35 73 - - ADJ cana-333 35 74 darcy darcy ADJ cana-333 35 75 porous porous ADJ cana-333 35 76 medium medium NOUN cana-333 35 77 , , PUNCT cana-333 35 78 using use VERB cana-333 35 79 indirect indirect ADJ cana-333 35 80 keller keller PROPN cana-333 35 81 box box PROPN cana-333 35 82 finite finite ADJ cana-333 35 83 difference difference NOUN cana-333 35 84 technique technique NOUN cana-333 35 85 . . PUNCT cana-333 36 1 the the DET cana-333 36 2 transformed transform VERB cana-333 36 3 conservation conservation NOUN cana-333 36 4 equations equation NOUN cana-333 36 5 are be AUX cana-333 36 6 solved solve VERB cana-333 36 7 numerically numerically ADV cana-333 36 8 using use VERB cana-333 36 9 reverse reverse ADJ cana-333 36 10 plate plate NOUN cana-333 36 11 under under ADP cana-333 36 12 appropriate appropriate ADJ cana-333 36 13 boundary boundary ADJ cana-333 36 14 conditions condition NOUN cana-333 36 15 . . PUNCT cana-333 37 1 [ [ X cana-333 37 2 5]this 5]this NUM cana-333 37 3 paper paper NOUN cana-333 37 4 carries carry VERB cana-333 37 5 out out ADP cana-333 37 6 study study NOUN cana-333 37 7 into into ADP cana-333 37 8 free free ADJ cana-333 37 9 convective convective ADJ cana-333 37 10 mhd mhd PROPN cana-333 37 11 casson casson PROPN cana-333 37 12 fluid fluid NOUN cana-333 37 13 flow flow NOUN cana-333 37 14 conducting conduct VERB cana-333 37 15 electrically electrically ADV cana-333 37 16 past past ADP cana-333 37 17 an an DET cana-333 37 18 oscillating oscillate VERB cana-333 37 19 plate plate NOUN cana-333 37 20 placed place VERB cana-333 37 21 vertically vertically ADV cana-333 37 22 in in ADP cana-333 37 23 porous porous ADJ cana-333 37 24 medium medium NOUN cana-333 37 25 under under ADP cana-333 37 26 appropriate appropriate ADJ cana-333 37 27 boundary boundary ADJ cana-333 37 28 conditions condition NOUN cana-333 37 29 . . PUNCT cana-333 38 1 the the DET cana-333 38 2 problem problem NOUN cana-333 38 3 is be AUX cana-333 38 4 solved solve VERB cana-333 38 5 analytically analytically ADV cana-333 38 6 , , PUNCT cana-333 38 7 solving solve VERB cana-333 38 8 the the DET cana-333 38 9 partial partial ADJ cana-333 38 10 differential differential NOUN cana-333 38 11 equations equation NOUN cana-333 38 12 numerically numerically ADV cana-333 38 13 .[6 .[6 PUNCT cana-333 38 14 ] ] PUNCT cana-333 38 15 examination examination NOUN cana-333 38 16 into into ADP cana-333 38 17 free free ADJ cana-333 38 18 convective convective NOUN cana-333 38 19 , , PUNCT cana-333 38 20 unstable unstable ADJ cana-333 38 21 mhd mhd NOUN cana-333 38 22 casson casson PROPN cana-333 38 23 fluid fluid NOUN cana-333 38 24 flow flow NOUN cana-333 38 25 across across ADP cana-333 38 26 oscillating oscillate VERB cana-333 38 27 vertical vertical ADJ cana-333 38 28 plate plate NOUN cana-333 38 29 has have AUX cana-333 38 30 been be AUX cana-333 38 31 conducted conduct VERB cana-333 38 32 to to PART cana-333 38 33 know know VERB cana-333 38 34 the the DET cana-333 38 35 thermal thermal NOUN cana-333 38 36 as as ADV cana-333 38 37 well well ADV cana-333 38 38 as as ADP cana-333 38 39 viscous viscous ADJ cana-333 38 40 dissipation dissipation NOUN cana-333 38 41 effect effect NOUN cana-333 38 42 , , PUNCT cana-333 38 43 while while SCONJ cana-333 38 44 facing face VERB cana-333 38 45 transverse transverse NOUN cana-333 38 46 magnetic magnetic ADJ cana-333 38 47 field field NOUN cana-333 38 48 . . PUNCT cana-333 39 1 homotopy homotopy VERB cana-333 39 2 analysis analysis NOUN cana-333 39 3 method method NOUN cana-333 39 4 ( ( PUNCT cana-333 39 5 ham ham PROPN cana-333 39 6 t t PROPN cana-333 39 7 is be AUX cana-333 39 8 utilized utilize VERB cana-333 39 9 to to PART cana-333 39 10 solve solve VERB cana-333 39 11 governing govern VERB cana-333 39 12 nonlinear nonlinear ADJ cana-333 39 13 boundary boundary ADJ cana-333 39 14 layer layer NOUN cana-333 39 15 equations equation NOUN cana-333 39 16 . . PUNCT cana-333 40 1 [ [ X cana-333 40 2 7 7 X cana-333 40 3 ] ] X cana-333 40 4 a a DET cana-333 40 5 micro micro ADJ cana-333 40 6 polar polar PROPN cana-333 40 7 mhd mhd NOUN cana-333 40 8 fluid fluid NOUN cana-333 40 9 flow flow NOUN cana-333 40 10 past past ADP cana-333 40 11 an an DET cana-333 40 12 oscillating oscillate VERB cana-333 40 13 infinite infinite ADJ cana-333 40 14 vertical vertical ADJ cana-333 40 15 plate plate NOUN cana-333 40 16 placed place VERB cana-333 40 17 in in ADP cana-333 40 18 porous porous ADJ cana-333 40 19 medium medium NOUN cana-333 40 20 has have AUX cana-333 40 21 been be AUX cana-333 40 22 analysed analyse VERB cana-333 40 23 . . PUNCT cana-333 41 1 free free ADJ cana-333 41 2 convection convection NOUN cana-333 41 3 takes take VERB cana-333 41 4 place place NOUN cana-333 41 5 on on ADP cana-333 41 6 the the DET cana-333 41 7 plate plate NOUN cana-333 41 8 because because SCONJ cana-333 41 9 of of ADP cana-333 41 10 differences difference NOUN cana-333 41 11 in in ADP cana-333 41 12 temperature temperature NOUN cana-333 41 13 and and CCONJ cana-333 41 14 concentration concentration NOUN cana-333 41 15 . . PUNCT cana-333 42 1 as as ADP cana-333 42 2 a a DET cana-333 42 3 result result NOUN cana-333 42 4 the the DET cana-333 42 5 effects effect NOUN cana-333 42 6 of of ADP cana-333 42 7 both both CCONJ cana-333 42 8 radiant radiant ADJ cana-333 42 9 heat heat NOUN cana-333 42 10 and and CCONJ cana-333 42 11 mass mass NOUN cana-333 42 12 transfer transfer NOUN cana-333 42 13 take take VERB cana-333 42 14 place place NOUN cana-333 42 15 . . PUNCT cana-333 43 1 [ [ X cana-333 43 2 8 8 NUM cana-333 43 3 ] ] X cana-333 43 4 general general ADJ cana-333 43 5 solution solution NOUN cana-333 43 6 for for ADP cana-333 43 7 velocity velocity NOUN cana-333 43 8 , , PUNCT cana-333 43 9 temperature temperature NOUN cana-333 43 10 , , PUNCT cana-333 43 11 as as ADV cana-333 43 12 well well ADV cana-333 43 13 communications communication NOUN cana-333 43 14 on on ADP cana-333 43 15 applied apply VERB cana-333 43 16 nonlinear nonlinear ADJ cana-333 43 17 analysis analysis NOUN cana-333 43 18 issn issn NOUN cana-333 43 19 : : PUNCT cana-333 43 20 1074 1074 NUM cana-333 43 21 - - PUNCT cana-333 43 22 133x 133x NUM cana-333 43 23 vol vol NOUN cana-333 43 24 31 31 NUM cana-333 43 25 no no NOUN cana-333 43 26 . . NOUN cana-333 43 27 1 1 NUM cana-333 43 28 ( ( PUNCT cana-333 43 29 2024 2024 NUM cana-333 43 30 ) ) PUNCT cana-333 43 31 106 106 NUM cana-333 43 32 https://internationalpubls.com https://internationalpubls.com X cana-333 43 33 as as SCONJ cana-333 43 34 nusselt nusselt NOUN cana-333 43 35 number number NOUN cana-333 43 36 is be AUX cana-333 43 37 obtained obtain VERB cana-333 43 38 facing face VERB cana-333 43 39 heat heat NOUN cana-333 43 40 source source NOUN cana-333 43 41 and and CCONJ cana-333 43 42 shear shear NOUN cana-333 43 43 stress stress NOUN cana-333 43 44 . . PUNCT cana-333 44 1 fluid fluid ADJ cana-333 44 2 velocity velocity NOUN cana-333 44 3 is be AUX cana-333 44 4 taken take VERB cana-333 44 5 to to PART cana-333 44 6 be be AUX cana-333 44 7 the the DET cana-333 44 8 sum sum NOUN cana-333 44 9 of of ADP cana-333 44 10 mechanical mechanical ADJ cana-333 44 11 and and CCONJ cana-333 44 12 thermal thermal ADJ cana-333 44 13 components component NOUN cana-333 44 14 . . PUNCT cana-333 45 1 they they PRON cana-333 45 2 are be AUX cana-333 45 3 capable capable ADJ cana-333 45 4 of of ADP cana-333 45 5 providing provide VERB cana-333 45 6 precise precise ADJ cana-333 45 7 solution solution NOUN cana-333 45 8 for for ADP cana-333 45 9 any any DET cana-333 45 10 movement movement NOUN cana-333 45 11 of of ADP cana-333 45 12 this this DET cana-333 45 13 type type NOUN cana-333 45 14 of of ADP cana-333 45 15 technical technical ADJ cana-333 45 16 importance importance NOUN cana-333 45 17 . . PUNCT cana-333 46 1 thermal thermal ADJ cana-333 46 2 and and CCONJ cana-333 46 3 mechanical mechanical ADJ cana-333 46 4 effects effect NOUN cana-333 46 5 are be AUX cana-333 46 6 considered consider VERB cana-333 46 7 important important ADJ cana-333 46 8 . . PUNCT cana-333 47 1 the the DET cana-333 47 2 effect effect NOUN cana-333 47 3 of of ADP cana-333 47 4 physical physical ADJ cana-333 47 5 parameters parameter NOUN cana-333 47 6 on on ADP cana-333 47 7 temperature temperature NOUN cana-333 47 8 as as ADV cana-333 47 9 well well ADV cana-333 47 10 as as ADP cana-333 47 11 velocity velocity NOUN cana-333 47 12 is be AUX cana-333 47 13 underlined underline VERB cana-333 47 14 graphically graphically ADV cana-333 47 15 for for ADP cana-333 47 16 a a DET cana-333 47 17 slope slope NOUN cana-333 47 18 - - PUNCT cana-333 47 19 type type NOUN cana-333 47 20 heating heating NOUN cana-333 47 21 plate plate NOUN cana-333 47 22 which which PRON cana-333 47 23 adds add VERB cana-333 47 24 regular regular ADJ cana-333 47 25 accelerating accelerate VERB cana-333 47 26 shear shear ADJ cana-333 47 27 stress stress NOUN cana-333 47 28 to to ADP cana-333 47 29 the the DET cana-333 47 30 liquid liquid NOUN cana-333 47 31 . . PUNCT cana-333 48 1 [ [ X cana-333 48 2 9 9 NUM cana-333 48 3 ] ] PUNCT cana-333 48 4 navier navier NOUN cana-333 48 5 slip slip AUX cana-333 48 6 electrically electrically ADV cana-333 48 7 conducting conduct VERB cana-333 48 8 third third ADJ cana-333 48 9 order order NOUN cana-333 48 10 fluid fluid NOUN cana-333 48 11 through through ADP cana-333 48 12 a a DET cana-333 48 13 porous porous ADJ cana-333 48 14 medium medium NOUN cana-333 48 15 , , PUNCT cana-333 48 16 with with ADP cana-333 48 17 convective convective ADJ cana-333 48 18 boundary boundary ADJ cana-333 48 19 condition condition NOUN cana-333 48 20 . . PUNCT cana-333 49 1 newton newton PROPN cana-333 49 2 's 's PART cana-333 49 3 law law NOUN cana-333 49 4 of of ADP cana-333 49 5 cooling cooling NOUN cana-333 49 6 is be AUX cana-333 49 7 observed observe VERB cana-333 49 8 in in ADP cana-333 49 9 heat heat NOUN cana-333 49 10 exchange exchange NOUN cana-333 49 11 of of ADP cana-333 49 12 surfaces surface NOUN cana-333 49 13 with with ADP cana-333 49 14 the the DET cana-333 49 15 surrounding surround VERB cana-333 49 16 environment environment NOUN cana-333 49 17 . . PUNCT cana-333 50 1 heat heat NOUN cana-333 50 2 transfer transfer NOUN cana-333 50 3 characteristics characteristic NOUN cana-333 50 4 are be AUX cana-333 50 5 analysed analyse VERB cana-333 50 6 graphically graphically ADV cana-333 50 7 . . PUNCT cana-333 51 1 a a DET cana-333 51 2 lower low ADJ cana-333 51 3 wall wall NOUN cana-333 51 4 slip slip NOUN cana-333 51 5 parameter parameter NOUN cana-333 51 6 is be AUX cana-333 51 7 found find VERB cana-333 51 8 to to PART cana-333 51 9 increase increase VERB cana-333 51 10 fluid fluid ADJ cana-333 51 11 velocity velocity NOUN cana-333 51 12 profile profile NOUN cana-333 51 13 . . PUNCT cana-333 52 1 the the DET cana-333 52 2 chemical chemical ADJ cana-333 52 3 kinetics kinetic NOUN cana-333 52 4 of of ADP cana-333 52 5 the the DET cana-333 52 6 flow flow NOUN cana-333 52 7 system system NOUN cana-333 52 8 is be AUX cana-333 52 9 assumed assume VERB cana-333 52 10 to to PART cana-333 52 11 be be AUX cana-333 52 12 exothermic exothermic ADJ cana-333 52 13 and and CCONJ cana-333 52 14 asymmetric asymmetric ADJ cana-333 52 15 convective convective NOUN cana-333 52 16 . . PUNCT cana-333 53 1 the the DET cana-333 53 2 governing govern VERB cana-333 53 3 equations equation NOUN cana-333 53 4 solved solve VERB cana-333 53 5 numerically numerically ADV cana-333 53 6 with with ADP cana-333 53 7 the the DET cana-333 53 8 help help NOUN cana-333 53 9 of of ADP cana-333 53 10 semi semi ADJ cana-333 53 11 - - ADJ cana-333 53 12 implicit implicit ADJ cana-333 53 13 finite finite ADJ cana-333 53 14 difference difference NOUN cana-333 53 15 scheme scheme NOUN cana-333 53 16 . . PUNCT cana-333 54 1 [ [ X cana-333 54 2 10 10 NUM cana-333 54 3 ] ] SYM cana-333 54 4 optically optically ADV cana-333 54 5 thick thick ADJ cana-333 54 6 radiation radiation NOUN cana-333 54 7 boundary boundary NOUN cana-333 54 8 is be AUX cana-333 54 9 considered consider VERB cana-333 54 10 in in ADP cana-333 54 11 this this DET cana-333 54 12 investigation investigation NOUN cana-333 54 13 in in ADP cana-333 54 14 which which PRON cana-333 54 15 the the DET cana-333 54 16 radiating radiate VERB cana-333 54 17 heat heat NOUN cana-333 54 18 flux flux NOUN cana-333 54 19 expression expression NOUN cana-333 54 20 is be AUX cana-333 54 21 simplified simplify VERB cana-333 54 22 by by ADP cana-333 54 23 the the DET cana-333 54 24 use use NOUN cana-333 54 25 of of ADP cana-333 54 26 rosseland rosseland PROPN cana-333 54 27 approximation approximation NOUN cana-333 54 28 . . PUNCT cana-333 55 1 entropy entropy PROPN cana-333 55 2 generation generation NOUN cana-333 55 3 in in ADP cana-333 55 4 magneto magneto ADJ cana-333 55 5 - - PUNCT cana-333 55 6 hydrodynamic hydrodynamic ADJ cana-333 55 7 continuous continuous ADJ cana-333 55 8 flow flow NOUN cana-333 55 9 of of ADP cana-333 55 10 incompressible incompressible ADJ cana-333 55 11 matter matter NOUN cana-333 55 12 . . PUNCT cana-333 56 1 non non ADJ cana-333 56 2 - - ADJ cana-333 56 3 newtonian newtonian ADJ cana-333 56 4 casson casson PROPN cana-333 56 5 fluid fluid NOUN cana-333 56 6 conduction conduction NOUN cana-333 56 7 through through ADP cana-333 56 8 horizontal horizontal ADJ cana-333 56 9 pre pre ADJ cana-333 56 10 - - ADJ cana-333 56 11 filled filled ADJ cana-333 56 12 porous porous ADJ cana-333 56 13 channel channel NOUN cana-333 56 14 is be AUX cana-333 56 15 materialised materialise VERB cana-333 56 16 while while SCONJ cana-333 56 17 a a DET cana-333 56 18 uniform uniform ADJ cana-333 56 19 transverse transverse NOUN cana-333 56 20 magnetic magnetic ADJ cana-333 56 21 field field NOUN cana-333 56 22 along along ADP cana-333 56 23 with with ADP cana-333 56 24 constant constant ADJ cana-333 56 25 pressure pressure NOUN cana-333 56 26 is be AUX cana-333 56 27 acting act VERB cana-333 56 28 with with ADP cana-333 56 29 thermal thermal ADJ cana-333 56 30 radiation radiation NOUN cana-333 56 31 gradient gradient NOUN cana-333 56 32 . . PUNCT cana-333 57 1 the the DET cana-333 57 2 fluid fluid NOUN cana-333 57 3 contains contain VERB cana-333 57 4 copper copper NOUN cana-333 57 5 ( ( PUNCT cana-333 57 6 cu cu NOUN cana-333 57 7 ) ) PUNCT cana-333 57 8 nano nano NOUN cana-333 57 9 particles particle NOUN cana-333 57 10 . . PUNCT cana-333 58 1 [ [ X cana-333 58 2 11 11 NUM cana-333 58 3 ] ] PUNCT cana-333 58 4 the the DET cana-333 58 5 study study NOUN cana-333 58 6 involves involve VERB cana-333 58 7 natural natural ADJ cana-333 58 8 convective convective ADJ cana-333 58 9 flow flow NOUN cana-333 58 10 of of ADP cana-333 58 11 mhd mhd NOUN cana-333 58 12 unsteady unsteady ADJ cana-333 58 13 nature nature NOUN cana-333 58 14 concerning concern VERB cana-333 58 15 rotating rotate VERB cana-333 58 16 water water NOUN cana-333 58 17 - - PUNCT cana-333 58 18 b b NOUN cana-333 58 19 fluid fluid NOUN cana-333 58 20 across across ADP cana-333 58 21 oscillating oscillate VERB cana-333 58 22 plate plate NOUN cana-333 58 23 facing face VERB cana-333 58 24 fluctuating fluctuate VERB cana-333 58 25 wall wall NOUN cana-333 58 26 temperature temperature NOUN cana-333 58 27 and and CCONJ cana-333 58 28 concentration concentration NOUN cana-333 58 29 difference difference NOUN cana-333 58 30 , , PUNCT cana-333 58 31 give give VERB cana-333 58 32 rise rise NOUN cana-333 58 33 to to ADP cana-333 58 34 pressure pressure NOUN cana-333 58 35 field field NOUN cana-333 58 36 . . PUNCT cana-333 59 1 [ [ X cana-333 59 2 12 12 NUM cana-333 59 3 ] ] PUNCT cana-333 59 4 in in ADP cana-333 59 5 this this DET cana-333 59 6 experiment experiment NOUN cana-333 59 7 mhd mhd NOUN cana-333 59 8 free free ADJ cana-333 59 9 convective convective ADJ cana-333 59 10 flow flow NOUN cana-333 59 11 pertaining pertain VERB cana-333 59 12 to to ADP cana-333 59 13 viscoelastic viscoelastic NOUN cana-333 59 14 , , PUNCT cana-333 59 15 electrically electrically ADV cana-333 59 16 conducting conduct VERB cana-333 59 17 fluid fluid NOUN cana-333 59 18 past past ADP cana-333 59 19 a a DET cana-333 59 20 vertical vertical ADJ cana-333 59 21 porous porous ADJ cana-333 59 22 plate plate NOUN cana-333 59 23 placed place VERB cana-333 59 24 in in ADP cana-333 59 25 porous porous ADJ cana-333 59 26 medium medium NOUN cana-333 59 27 is be AUX cana-333 59 28 under under ADP cana-333 59 29 consideration consideration NOUN cana-333 59 30 . . PUNCT cana-333 60 1 continuous continuous ADJ cana-333 60 2 suction suction NOUN cana-333 60 3 and and CCONJ cana-333 60 4 heat heat NOUN cana-333 60 5 source source NOUN cana-333 60 6 including include VERB cana-333 60 7 transverse transverse NOUN cana-333 60 8 magnetic magnetic ADJ cana-333 60 9 field field NOUN cana-333 60 10 was be AUX cana-333 60 11 effective effective ADJ cana-333 60 12 . . PUNCT cana-333 61 1 boussinesq boussinesq ADJ cana-333 61 2 approximation approximation NOUN cana-333 61 3 was be AUX cana-333 61 4 utilised utilise VERB cana-333 61 5 to to PART cana-333 61 6 derive derive VERB cana-333 61 7 governing govern VERB cana-333 61 8 equations equation NOUN cana-333 61 9 of of ADP cana-333 61 10 the the DET cana-333 61 11 flow flow NOUN cana-333 61 12 field field NOUN cana-333 61 13 for for ADP cana-333 61 14 energy energy NOUN cana-333 61 15 dissipation dissipation NOUN cana-333 61 16 . . PUNCT cana-333 62 1 [ [ X cana-333 62 2 13 13 NUM cana-333 62 3 ] ] PUNCT cana-333 62 4 the the DET cana-333 62 5 study study NOUN cana-333 62 6 involves involve VERB cana-333 62 7 heat heat NOUN cana-333 62 8 transfer transfer NOUN cana-333 62 9 and and CCONJ cana-333 62 10 fluid fluid NOUN cana-333 62 11 flow flow NOUN cana-333 62 12 concerning concern VERB cana-333 62 13 pseudo pseudo NOUN cana-333 62 14 plastic plastic NOUN cana-333 62 15 nonnewtonian nonnewtonian NOUN cana-333 62 16 nano nano NOUN cana-333 62 17 fluid fluid NOUN cana-333 62 18 using use VERB cana-333 62 19 injection injection NOUN cana-333 62 20 and and CCONJ cana-333 62 21 suction suction NOUN cana-333 62 22 through through ADP cana-333 62 23 permeable permeable ADJ cana-333 62 24 surface surface NOUN cana-333 62 25 . . PUNCT cana-333 63 1 similarity similarity NOUN cana-333 63 2 solution solution NOUN cana-333 63 3 method method NOUN cana-333 63 4 is be AUX cana-333 63 5 used use VERB cana-333 63 6 to to PART cana-333 63 7 transfer transfer VERB cana-333 63 8 governing govern VERB cana-333 63 9 partial partial ADJ cana-333 63 10 differential differential ADJ cana-333 63 11 equations equation NOUN cana-333 63 12 into into ADP cana-333 63 13 ordinary ordinary ADJ cana-333 63 14 differential differential ADJ cana-333 63 15 equations equation NOUN cana-333 63 16 . . PUNCT cana-333 64 1 these these DET cana-333 64 2 equations equation NOUN cana-333 64 3 were be AUX cana-333 64 4 further far ADV cana-333 64 5 solved solve VERB cana-333 64 6 with with ADP cana-333 64 7 the the DET cana-333 64 8 help help NOUN cana-333 64 9 of of ADP cana-333 64 10 runga runga NOUN cana-333 64 11 - - PUNCT cana-333 64 12 kutta kutta PROPN cana-333 64 13 fehlbrg fehlbrg NOUN cana-333 64 14 fourth fourth ADJ cana-333 64 15 and and CCONJ cana-333 64 16 fifth fifth ADJ cana-333 64 17 order order NOUN cana-333 64 18 method method NOUN cana-333 64 19 ( ( PUNCT cana-333 64 20 rkf-45 rkf-45 NOUN cana-333 64 21 ) ) PUNCT cana-333 64 22 . . PUNCT cana-333 65 1 this this DET cana-333 65 2 system system NOUN cana-333 65 3 providing provide VERB cana-333 65 4 better well ADJ cana-333 65 5 heat heat NOUN cana-333 65 6 transfer transfer NOUN cana-333 65 7 efficiency efficiency NOUN cana-333 65 8 as as ADP cana-333 65 9 compared compare VERB cana-333 65 10 to to ADP cana-333 65 11 impermeable impermeable ADJ cana-333 65 12 plate plate NOUN cana-333 65 13 . . PUNCT cana-333 66 1 [ [ X cana-333 66 2 14 14 NUM cana-333 66 3 ] ] PUNCT cana-333 66 4 this this DET cana-333 66 5 study study NOUN cana-333 66 6 investigates investigate VERB cana-333 66 7 heat heat NOUN cana-333 66 8 source source NOUN cana-333 66 9 effect effect NOUN cana-333 66 10 on on ADP cana-333 66 11 mhd mhd PROPN cana-333 66 12 casson casson PROPN cana-333 66 13 fluid fluid NOUN cana-333 66 14 through through ADP cana-333 66 15 vertically vertically ADV cana-333 66 16 moving move VERB cana-333 66 17 porous porous ADJ cana-333 66 18 plate plate NOUN cana-333 66 19 . . PUNCT cana-333 67 1 differential differential ADJ cana-333 67 2 equations equation NOUN cana-333 67 3 non non ADJ cana-333 67 4 - - ADJ cana-333 67 5 linearly linearly ADV cana-333 67 6 related relate VERB cana-333 67 7 to to ADP cana-333 67 8 dimensions dimension NOUN cana-333 67 9 are be AUX cana-333 67 10 converted convert VERB cana-333 67 11 with with ADP cana-333 67 12 the the DET cana-333 67 13 help help NOUN cana-333 67 14 of of ADP cana-333 67 15 similarity similarity NOUN cana-333 67 16 variables variable NOUN cana-333 67 17 . . PUNCT cana-333 68 1 the the DET cana-333 68 2 transformed transform VERB cana-333 68 3 equations equation NOUN cana-333 68 4 solved solve VERB cana-333 68 5 with with ADP cana-333 68 6 the the DET cana-333 68 7 help help NOUN cana-333 68 8 of of ADP cana-333 68 9 glerkin glerkin PROPN cana-333 68 10 finite finite PROPN cana-333 68 11 element element NOUN cana-333 68 12 technique technique NOUN cana-333 68 13 . . PUNCT cana-333 69 1 the the DET cana-333 69 2 result result NOUN cana-333 69 3 shows show VERB cana-333 69 4 that that SCONJ cana-333 69 5 for for SCONJ cana-333 69 6 heat heat NOUN cana-333 69 7 source source NOUN cana-333 69 8 parameter parameter NOUN cana-333 69 9 increase increase NOUN cana-333 69 10 velocity velocity NOUN cana-333 69 11 and and CCONJ cana-333 69 12 temperature temperature NOUN cana-333 69 13 profile profile NOUN cana-333 69 14 increase increase NOUN cana-333 69 15 . . PUNCT cana-333 70 1 [ [ X cana-333 70 2 15 15 NUM cana-333 70 3 ] ] X cana-333 70 4 a a DET cana-333 70 5 study study NOUN cana-333 70 6 on on ADP cana-333 70 7 effect effect NOUN cana-333 70 8 of of ADP cana-333 70 9 chemical chemical ADJ cana-333 70 10 reaction reaction NOUN cana-333 70 11 on on ADP cana-333 70 12 laminar laminar ADJ cana-333 70 13 fluid fluid ADJ cana-333 70 14 cross cross NOUN cana-333 70 15 flow flow NOUN cana-333 70 16 and and CCONJ cana-333 70 17 thermal thermal ADJ cana-333 70 18 mass mass NOUN cana-333 70 19 transfer transfer NOUN cana-333 70 20 is be AUX cana-333 70 21 conducted conduct VERB cana-333 70 22 which which PRON cana-333 70 23 reveals reveal VERB cana-333 70 24 certain certain ADJ cana-333 70 25 important important ADJ cana-333 70 26 characteristics characteristic NOUN cana-333 70 27 of of ADP cana-333 70 28 liquids liquid NOUN cana-333 70 29 namely namely ADV cana-333 70 30 variable variable ADJ cana-333 70 31 thermal thermal ADJ cana-333 70 32 conductivity conductivity NOUN cana-333 70 33 and and CCONJ cana-333 70 34 its its PRON cana-333 70 35 dependences dependence NOUN cana-333 70 36 on on ADP cana-333 70 37 temperature temperature NOUN cana-333 70 38 field field NOUN cana-333 70 39 . . PUNCT cana-333 71 1 fluid fluid ADJ cana-333 71 2 movement movement NOUN cana-333 71 3 is be AUX cana-333 71 4 supposed suppose VERB cana-333 71 5 to to PART cana-333 71 6 be be AUX cana-333 71 7 caused cause VERB cana-333 71 8 by by ADP cana-333 71 9 stress stress NOUN cana-333 71 10 plate plate NOUN cana-333 71 11 kept keep VERB cana-333 71 12 in in ADP cana-333 71 13 porous porous ADJ cana-333 71 14 medium medium NOUN cana-333 71 15 . . PUNCT cana-333 72 1 [ [ X cana-333 72 2 16 16 NUM cana-333 72 3 ] ] PUNCT cana-333 72 4 examined examine VERB cana-333 72 5 magneto magneto PROPN cana-333 72 6 hydrodynamic hydrodynamic PROPN cana-333 72 7 convective convective ADJ cana-333 72 8 non non ADJ cana-333 72 9 - - ADJ cana-333 72 10 newtonian newtonian ADJ cana-333 72 11 casson casson PROPN cana-333 72 12 flow flow NOUN cana-333 72 13 for for ADP cana-333 72 14 mass mass ADJ cana-333 72 15 and and CCONJ cana-333 72 16 heat heat NOUN cana-333 72 17 transfer transfer NOUN cana-333 72 18 . . PUNCT cana-333 73 1 fluid fluid NOUN cana-333 73 2 was be AUX cana-333 73 3 made make VERB cana-333 73 4 to to PART cana-333 73 5 flow flow VERB cana-333 73 6 across across ADP cana-333 73 7 oscillating oscillate VERB cana-333 73 8 permeable permeable ADJ cana-333 73 9 straight straight ADV cana-333 73 10 up up ADP cana-333 73 11 plate plate NOUN cana-333 73 12 with with ADP cana-333 73 13 thermal thermal ADJ cana-333 73 14 diffusion diffusion NOUN cana-333 73 15 ( ( PUNCT cana-333 73 16 soret soret NOUN cana-333 73 17 ) ) PUNCT cana-333 73 18 . . PUNCT cana-333 74 1 to to PART cana-333 74 2 overcome overcome VERB cana-333 74 3 the the DET cana-333 74 4 nondimensional nondimensional ADJ cana-333 74 5 pde pde NOUN cana-333 74 6 ’s ’s NOUN cana-333 74 7 in in ADP cana-333 74 8 the the DET cana-333 74 9 fluid fluid ADJ cana-333 74 10 concentration concentration NOUN cana-333 74 11 . . PUNCT cana-333 75 1 velocity velocity NOUN cana-333 75 2 including include VERB cana-333 75 3 temperature temperature NOUN cana-333 75 4 distribution distribution NOUN cana-333 75 5 , , PUNCT cana-333 75 6 ( ( PUNCT cana-333 75 7 fem fem NOUN cana-333 75 8 ) ) PUNCT cana-333 75 9 finite finite PROPN cana-333 75 10 element element NOUN cana-333 75 11 approach approach NOUN cana-333 75 12 was be AUX cana-333 75 13 adopted adopt VERB cana-333 75 14 in in ADP cana-333 75 15 the the DET cana-333 75 16 presence presence NOUN cana-333 75 17 of of ADP cana-333 75 18 different different ADJ cana-333 75 19 dimensional dimensional ADJ cana-333 75 20 variables variable NOUN cana-333 75 21 . . PUNCT cana-333 76 1 [ [ X cana-333 76 2 17 17 NUM cana-333 76 3 ] ] PUNCT cana-333 76 4 the the DET cana-333 76 5 study study NOUN cana-333 76 6 involves involve VERB cana-333 76 7 numerical numerical ADJ cana-333 76 8 approach approach NOUN cana-333 76 9 in in ADP cana-333 76 10 the the DET cana-333 76 11 matter matter NOUN cana-333 76 12 of of ADP cana-333 76 13 newtonian newtonian ADJ cana-333 76 14 mhd mhd NOUN cana-333 76 15 fluid fluid NOUN cana-333 76 16 flow flow NOUN cana-333 76 17 across across ADP cana-333 76 18 porous porous ADJ cana-333 76 19 medium medium NOUN cana-333 76 20 . . PUNCT cana-333 77 1 a a DET cana-333 77 2 good good ADJ cana-333 77 3 number number NOUN cana-333 77 4 of of ADP cana-333 77 5 investigation investigation NOUN cana-333 77 6 have have AUX cana-333 77 7 been be AUX cana-333 77 8 made make VERB cana-333 77 9 in in ADP cana-333 77 10 thermal thermal ADJ cana-333 77 11 equilibrium equilibrium NOUN cana-333 77 12 through through ADP cana-333 77 13 in in ADP cana-333 77 14 real real ADJ cana-333 77 15 applications application NOUN cana-333 77 16 the the DET cana-333 77 17 model model NOUN cana-333 77 18 exists exist VERB cana-333 77 19 without without ADP cana-333 77 20 equilibrium equilibrium NOUN cana-333 77 21 state state NOUN cana-333 77 22 and and CCONJ cana-333 77 23 local local ADJ cana-333 77 24 thermal thermal ADJ cana-333 77 25 imbalance imbalance NOUN cana-333 77 26 accurately accurately ADV cana-333 77 27 communications communication VERB cana-333 77 28 on on ADP cana-333 77 29 applied apply VERB cana-333 77 30 nonlinear nonlinear ADJ cana-333 77 31 analysis analysis NOUN cana-333 77 32 issn issn NOUN cana-333 77 33 : : PUNCT cana-333 77 34 1074 1074 NUM cana-333 77 35 - - PUNCT cana-333 77 36 133x 133x NUM cana-333 77 37 vol vol NOUN cana-333 77 38 31 31 NUM cana-333 77 39 no no NOUN cana-333 77 40 . . NOUN cana-333 77 41 1 1 NUM cana-333 77 42 ( ( PUNCT cana-333 77 43 2024 2024 NUM cana-333 77 44 ) ) PUNCT cana-333 77 45 107 107 NUM cana-333 77 46 https://internationalpubls.com https://internationalpubls.com X cana-333 77 47 projects project VERB cana-333 77 48 the the DET cana-333 77 49 thermal thermal ADJ cana-333 77 50 hydro hydro NOUN cana-333 77 51 flow flow NOUN cana-333 77 52 . . PUNCT cana-333 78 1 [ [ X cana-333 78 2 18 18 NUM cana-333 78 3 ] ] PUNCT cana-333 78 4 examined examine VERB cana-333 78 5 impact impact NOUN cana-333 78 6 of of ADP cana-333 78 7 naviers navier NOUN cana-333 78 8 slip slip VERB cana-333 78 9 on on ADP cana-333 78 10 laminar laminar ADJ cana-333 78 11 boundary boundary ADJ cana-333 78 12 layer layer NOUN cana-333 78 13 flow flow NOUN cana-333 78 14 including include VERB cana-333 78 15 thermal thermal ADJ cana-333 78 16 radiation radiation NOUN cana-333 78 17 on on ADP cana-333 78 18 continuous continuous ADJ cana-333 78 19 non non ADJ cana-333 78 20 - - ADJ cana-333 78 21 newtonian newtonian ADJ cana-333 78 22 fluid fluid ADJ cana-333 78 23 flow flow NOUN cana-333 78 24 related relate VERB cana-333 78 25 to to ADP cana-333 78 26 viscous viscous ADJ cana-333 78 27 incompressible incompressible ADJ cana-333 78 28 nano nano NOUN cana-333 78 29 fluid fluid NOUN cana-333 78 30 , , PUNCT cana-333 78 31 through through ADP cana-333 78 32 permeable permeable ADJ cana-333 78 33 , , PUNCT cana-333 78 34 stretching/ stretching/ NUM cana-333 78 35 shrinking shrink VERB cana-333 78 36 plate plate NOUN cana-333 78 37 . . PUNCT cana-333 79 1 3 3 X cana-333 79 2 . . X cana-333 79 3 analytical analytical ADJ cana-333 79 4 solution solution NOUN cana-333 79 5 of of ADP cana-333 79 6 the the DET cana-333 79 7 problem problem NOUN cana-333 79 8 3.1 3.1 NUM cana-333 79 9 mathematical mathematical ADJ cana-333 79 10 interpretation interpretation NOUN cana-333 79 11 of of ADP cana-333 79 12 flow flow NOUN cana-333 79 13 study study NOUN cana-333 79 14 has have AUX cana-333 79 15 been be AUX cana-333 79 16 carried carry VERB cana-333 79 17 out out ADP cana-333 79 18 to to PART cana-333 79 19 know know VERB cana-333 79 20 the the DET cana-333 79 21 impact impact NOUN cana-333 79 22 of of ADP cana-333 79 23 electrically electrically ADV cana-333 79 24 conducting conducting NOUN cana-333 79 25 , , PUNCT cana-333 79 26 convective convective ADJ cana-333 79 27 flow flow NOUN cana-333 79 28 of of ADP cana-333 79 29 non non ADJ cana-333 79 30 newtonian newtonian ADJ cana-333 79 31 viscous viscous ADJ cana-333 79 32 fluid fluid NOUN cana-333 79 33 , , PUNCT cana-333 79 34 in in ADP cana-333 79 35 porous porous ADJ cana-333 79 36 medium medium NOUN cana-333 79 37 , , PUNCT cana-333 79 38 past past ADP cana-333 79 39 a a DET cana-333 79 40 semi semi ADJ cana-333 79 41 - - ADJ cana-333 79 42 infinite infinite ADJ cana-333 79 43 plate plate NOUN cana-333 79 44 of of ADP cana-333 79 45 porous porous ADJ cana-333 79 46 nature nature NOUN cana-333 79 47 placed place VERB cana-333 79 48 in in ADP cana-333 79 49 oscillating oscillate VERB cana-333 79 50 state state NOUN cana-333 79 51 , , PUNCT cana-333 79 52 with with ADP cana-333 79 53 transverse transverse NOUN cana-333 79 54 magnetic magnetic ADJ cana-333 79 55 field field NOUN cana-333 79 56 𝐡0 𝐡0 NOUN cana-333 79 57 acting act VERB cana-333 79 58 on on ADP cana-333 79 59 it it PRON cana-333 79 60 . . PUNCT cana-333 80 1 velocity velocity NOUN cana-333 80 2 u u NOUN cana-333 80 3 is be AUX cana-333 80 4 shown show VERB cana-333 80 5 to to PART cana-333 80 6 have have AUX cana-333 80 7 been be AUX cana-333 80 8 taken take VERB cana-333 80 9 along along ADP cana-333 80 10 x x PUNCT cana-333 80 11 axis axis NOUN cana-333 80 12 and and CCONJ cana-333 80 13 velocity velocity NOUN cana-333 80 14 v v NOUN cana-333 80 15 along along ADP cana-333 80 16 the the DET cana-333 80 17 direction direction NOUN cana-333 80 18 of of ADP cana-333 80 19 y y PROPN cana-333 80 20 axis axis NOUN cana-333 80 21 , , PUNCT cana-333 80 22 both both PRON cana-333 80 23 being be AUX cana-333 80 24 perpendicular perpendicular ADJ cana-333 80 25 to to ADP cana-333 80 26 the the DET cana-333 80 27 plate plate NOUN cana-333 80 28 . . PUNCT cana-333 81 1 physical physical ADJ cana-333 81 2 quantities quantity NOUN cana-333 81 3 involved involve VERB cana-333 81 4 are be AUX cana-333 81 5 taken take VERB cana-333 81 6 to to PART cana-333 81 7 be be AUX cana-333 81 8 functions function NOUN cana-333 81 9 of of ADP cana-333 81 10 y y PROPN cana-333 81 11 and and CCONJ cana-333 81 12 t t PROPN cana-333 81 13 , , PUNCT cana-333 81 14 with with ADP cana-333 81 15 negligible negligible ADJ cana-333 81 16 induced induced ADJ cana-333 81 17 magnetic magnetic ADJ cana-333 81 18 field field NOUN cana-333 81 19 . . PUNCT cana-333 82 1 pressure pressure NOUN cana-333 82 2 is be AUX cana-333 82 3 considered consider VERB cana-333 82 4 constant constant ADJ cana-333 82 5 and and CCONJ cana-333 82 6 reynolds reynold NOUN cana-333 82 7 number number NOUN cana-333 82 8 very very ADV cana-333 82 9 small small ADJ cana-333 82 10 . . PUNCT cana-333 83 1 suction suction NOUN cana-333 83 2 velocity velocity NOUN cana-333 83 3 at at ADP cana-333 83 4 the the DET cana-333 83 5 plate plate NOUN cana-333 83 6 taken take VERB cana-333 83 7 as as ADP cana-333 83 8 𝑉0 𝑉0 NOUN cana-333 83 9 . . PUNCT cana-333 84 1 considering consider VERB cana-333 84 2 y=0 y=0 PRON cana-333 84 3 , , PUNCT cana-333 84 4 v=βˆ’π‘‰0 v=βˆ’π‘‰0 ADJ cana-333 84 5 , , PUNCT cana-333 84 6 continuity continuity NOUN cana-333 84 7 equation equation NOUN cana-333 84 8 will will AUX cana-333 84 9 be be AUX cana-333 84 10 πœ•π‘£ πœ•π‘£ NOUN cana-333 84 11 πœ•π‘¦ πœ•π‘¦ NOUN cana-333 84 12 = = SYM cana-333 84 13 0 0 NUM cana-333 84 14 … … PUNCT cana-333 84 15 … … PUNCT cana-333 84 16 . . PUNCT cana-333 85 1 ( ( PUNCT cana-333 85 2 1 1 X cana-333 85 3 ) ) PUNCT cana-333 85 4 πœ•π‘’ πœ•π‘’ NOUN cana-333 85 5 πœ•π‘‘ πœ•π‘‘ NOUN cana-333 85 6 + + CCONJ cana-333 85 7 v v ADJ cana-333 85 8 πœ•π‘’ πœ•π‘’ NOUN cana-333 85 9 πœ•π‘¦ πœ•π‘¦ NOUN cana-333 86 1 = = SYM cana-333 86 2 πœ— πœ— ADP cana-333 86 3 πœ•2𝑒 πœ•2𝑒 NUM cana-333 86 4 πœ•π‘¦2 πœ•π‘¦2 ADJ cana-333 86 5 + + CCONJ cana-333 86 6 π‘˜0 π‘˜0 ADP cana-333 86 7 𝜌 𝜌 X cana-333 86 8 ( ( PUNCT cana-333 86 9 πœ•3𝑒 πœ•3𝑒 PROPN cana-333 86 10 πœ•π‘‘πœ•π‘¦2+v πœ•π‘‘πœ•π‘¦2+v PROPN cana-333 86 11 πœ•3𝑒 πœ•3𝑒 PROPN cana-333 86 12 πœ•π‘¦3 πœ•π‘¦3 PROPN cana-333 86 13 ) ) PUNCT cana-333 87 1 + + ADP cana-333 87 2 𝑔𝛽(𝑇 𝑔𝛽(𝑇 PROPN cana-333 87 3 βˆ’ βˆ’ PROPN cana-333 87 4 π‘‡βˆž π‘‡βˆž PROPN cana-333 87 5 ) ) PUNCT cana-333 87 6 βˆ’ βˆ’ PROPN cana-333 87 7 πœ— πœ— NUM cana-333 87 8 π‘˜0 π‘˜0 X cana-333 87 9 𝑒 𝑒 PRON cana-333 87 10 βˆ’ βˆ’ PROPN cana-333 87 11 𝜎𝐡0 𝜎𝐡0 PROPN cana-333 87 12 2𝑒 2𝑒 NUM cana-333 87 13 𝜌 𝜌 ADP cana-333 87 14 … … PUNCT cana-333 87 15 … … PUNCT cana-333 87 16 … … PUNCT cana-333 87 17 .(2 .(2 NUM cana-333 87 18 ) ) PUNCT cana-333 88 1 πœ•π‘‡ πœ•π‘‡ PUNCT cana-333 88 2 πœ•π‘‘ πœ•π‘‘ NOUN cana-333 88 3 + + CCONJ cana-333 88 4 πœ•π‘‡ πœ•π‘‡ NOUN cana-333 88 5 πœ•π‘¦ πœ•π‘¦ NOUN cana-333 88 6 = = SYM cana-333 88 7 k k PROPN cana-333 88 8 πœ•2𝑇 πœ•2𝑇 PROPN cana-333 88 9 πœ•π‘¦2 πœ•π‘¦2 PROPN cana-333 88 10 + + CCONJ cana-333 88 11 π‘˜0 π‘˜0 PART cana-333 88 12 𝜌 𝜌 DET cana-333 88 13 πœ•3𝑇 πœ•3𝑇 ADJ cana-333 88 14 πœ•π‘‘πœ•π‘¦2 πœ•π‘‘πœ•π‘¦2 ADJ cana-333 88 15 βˆ’s βˆ’s NOUN cana-333 88 16 [ [ X cana-333 88 17 t t X cana-333 88 18 βˆ’π‘‡βˆž βˆ’π‘‡βˆž X cana-333 88 19 ] ] X cana-333 88 20 … … PUNCT cana-333 88 21 …… …… X cana-333 88 22 . . PUNCT cana-333 89 1 ( ( PUNCT cana-333 89 2 3 3 X cana-333 89 3 ) ) PUNCT cana-333 89 4 the the DET cana-333 89 5 related relate VERB cana-333 89 6 boundary boundary ADJ cana-333 89 7 conditions condition NOUN cana-333 89 8 are be AUX cana-333 89 9 y y NOUN cana-333 89 10 = = SYM cana-333 89 11 0 0 NUM cana-333 89 12 : : PUNCT cana-333 89 13 u u NOUN cana-333 89 14 = = NOUN cana-333 89 15 𝑉0 𝑉0 X cana-333 89 16 π‘π‘œπ‘ π‘€π‘‘ π‘π‘œπ‘ π‘€π‘‘ NOUN cana-333 89 17 , , PUNCT cana-333 89 18 t t PROPN cana-333 89 19 = = SYM cana-333 89 20 π‘‡βˆž π‘‡βˆž PROPN cana-333 89 21 + + CCONJ cana-333 89 22 ( ( PUNCT cana-333 89 23 π‘‡πœ” π‘‡πœ” PROPN cana-333 89 24 βˆ’π‘‡βˆž βˆ’π‘‡βˆž NOUN cana-333 89 25 ) ) PUNCT cana-333 89 26 π‘’βˆ’π‘–πœ”π‘‘ π‘’βˆ’π‘–πœ”π‘‘ NOUN cana-333 89 27 ] ] PUNCT cana-333 89 28 yβ†’βˆž yβ†’βˆž ADV cana-333 89 29 : : PUNCT cana-333 89 30 u u NOUN cana-333 89 31 β‡Ύ β‡Ύ PROPN cana-333 89 32 0 0 NUM cana-333 89 33 , , PUNCT cana-333 90 1 tβ†’ tβ†’ X cana-333 90 2 π‘‡βˆž π‘‡βˆž PROPN cana-333 90 3 ] ] PUNCT cana-333 90 4 … … PUNCT cana-333 90 5 … … PUNCT cana-333 90 6 …… …… NOUN cana-333 90 7 …… …… NOUN cana-333 90 8 . . PUNCT cana-333 91 1 ( ( PUNCT cana-333 91 2 4 4 X cana-333 91 3 ) ) PUNCT cana-333 91 4 here here ADV cana-333 91 5 g g PROPN cana-333 91 6 is be AUX cana-333 91 7 gravitational gravitational ADJ cana-333 91 8 force force NOUN cana-333 91 9 , , PUNCT cana-333 91 10 s s VERB cana-333 91 11 heat heat NOUN cana-333 91 12 source source NOUN cana-333 91 13 parameter parameter NOUN cana-333 91 14 , , PUNCT cana-333 91 15 u u NOUN cana-333 91 16 the the DET cana-333 91 17 flow flow NOUN cana-333 91 18 velocity velocity NOUN cana-333 91 19 component component NOUN cana-333 91 20 in in ADP cana-333 91 21 the the DET cana-333 91 22 xdirection xdirection NOUN cana-333 91 23 , , PUNCT cana-333 91 24 k k PROPN cana-333 91 25 is be AUX cana-333 91 26 thermal thermal ADJ cana-333 91 27 diffusivity diffusivity NOUN cana-333 91 28 , , PUNCT cana-333 91 29 density density NOUN cana-333 91 30 ρ ρ PROPN cana-333 91 31 , , PUNCT cana-333 91 32 t t PROPN cana-333 91 33 for for ADP cana-333 91 34 temperature temperature NOUN cana-333 91 35 , , PUNCT cana-333 91 36 v v ADP cana-333 91 37 kinematic kinematic ADJ cana-333 91 38 viscosity viscosity NOUN cana-333 91 39 , , PUNCT cana-333 91 40 Ξ² Ξ² X cana-333 91 41 stands stand VERB cana-333 91 42 for for ADP cana-333 91 43 volumetric volumetric ADJ cana-333 91 44 heat heat NOUN cana-333 91 45 transfer transfer NOUN cana-333 91 46 expansion expansion NOUN cana-333 91 47 coefficient coefficient NOUN cana-333 91 48 , , PUNCT cana-333 91 49 π‘‡βˆž π‘‡βˆž PROPN cana-333 91 50 stands stand VERB cana-333 91 51 for for ADP cana-333 91 52 fluid fluid ADJ cana-333 91 53 temperature temperature NOUN cana-333 91 54 remote remote NOUN cana-333 91 55 from from ADP cana-333 91 56 the the DET cana-333 91 57 plate plate NOUN cana-333 91 58 . . PUNCT cana-333 92 1 3 3 X cana-333 92 2 . . NOUN cana-333 92 3 2 2 NUM cana-333 92 4 evolving evolve VERB cana-333 92 5 the the DET cana-333 92 6 dimensionless dimensionless NOUN cana-333 92 7 quantities quantity NOUN cana-333 92 8 π‘‘βˆ— π‘‘βˆ— NOUN cana-333 92 9 = = SYM cana-333 92 10 𝑉0 𝑉0 NOUN cana-333 92 11 2 2 NUM cana-333 92 12 𝑑 𝑑 NOUN cana-333 92 13 πœ— πœ— NOUN cana-333 92 14 , , PUNCT cana-333 92 15 𝑉0 𝑉0 PROPN cana-333 92 16 βˆ—= βˆ—= PROPN cana-333 92 17 𝑉0 𝑉0 NOUN cana-333 92 18 πœ— πœ— PROPN cana-333 92 19 , , PUNCT cana-333 92 20 πœ”βˆ—= πœ”βˆ—= PROPN cana-333 92 21 πœ—πœ” πœ—πœ” PRON cana-333 92 22 𝑉0 𝑉0 NOUN cana-333 92 23 2 2 NUM cana-333 92 24 π‘¦βˆ—= π‘¦βˆ—= PROPN cana-333 92 25 𝑉0 𝑉0 NOUN cana-333 92 26 𝑦 𝑦 ADP cana-333 92 27 πœ— πœ— NOUN cana-333 92 28 , , PUNCT cana-333 92 29 π‘’βˆ— π‘’βˆ— NOUN cana-333 92 30 = = PUNCT cana-333 92 31 𝑒 𝑒 X cana-333 92 32 𝑉0 𝑉0 NOUN cana-333 92 33 , , PUNCT cana-333 92 34 π‘†βˆ— π‘†βˆ— X cana-333 92 35 = = PUNCT cana-333 92 36 πœ—π‘† πœ—π‘† NOUN cana-333 92 37 𝑉0 𝑉0 NOUN cana-333 92 38 2 2 NUM cana-333 92 39 π‘‡βˆ—= π‘‡βˆ—= SYM cana-333 92 40 t t NOUN cana-333 92 41 βˆ’π‘‡βˆž βˆ’π‘‡βˆž PUNCT cana-333 92 42 π‘‡πœ” π‘‡πœ” PROPN cana-333 92 43 βˆ’π‘‡βˆž βˆ’π‘‡βˆž PUNCT cana-333 92 44 , , PUNCT cana-333 93 1 m m VERB cana-333 93 2 = = VERB cana-333 93 3 𝐡0 𝐡0 ADJ cana-333 93 4 𝑉0 𝑉0 PROPN cana-333 94 1 ( ( PUNCT cana-333 94 2 πœ—πœŽ πœ—πœŽ ADP cana-333 94 3 𝜌 𝜌 X cana-333 94 4 ) ) PUNCT cana-333 94 5 1/2 1/2 NUM cana-333 94 6 , , PUNCT cana-333 94 7 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-333 94 8 = = PUNCT cana-333 94 9 πœ—πœŒπΆπ‘ πœ—πœŒπΆπ‘ PROPN cana-333 94 10 π‘˜ π‘˜ PRON cana-333 94 11 πΊπ‘Ÿ πΊπ‘Ÿ PROPN cana-333 94 12 = = PUNCT cana-333 94 13 πœ—gΞ² πœ—gΞ² PROPN cana-333 94 14 π‘‡πœ”βˆ’π‘‡βˆž π‘‡πœ”βˆ’π‘‡βˆž NOUN cana-333 94 15 𝑉0 𝑉0 NOUN cana-333 94 16 3 3 NUM cana-333 94 17 , , PUNCT cana-333 95 1 𝐾𝑝 𝐾𝑝 PROPN cana-333 95 2 = = SYM cana-333 95 3 π‘˜0𝑉0 π‘˜0𝑉0 ADJ cana-333 95 4 2 2 NUM cana-333 95 5 πœ—2 πœ—2 NOUN cana-333 95 6 , , PUNCT cana-333 95 7 𝑅𝑐 𝑅𝑐 PROPN cana-333 95 8 = = PUNCT cana-333 95 9 π‘˜0𝑉0 π‘˜0𝑉0 ADV cana-333 95 10 2 2 NUM cana-333 95 11 πœŒπœ—2 πœŒπœ—2 NOUN cana-333 95 12 here here ADV cana-333 95 13 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-333 95 14 , , PUNCT cana-333 95 15 πΊπ‘Ÿ πΊπ‘Ÿ PROPN cana-333 95 16 , , PUNCT cana-333 95 17 m m VERB cana-333 95 18 describe describe VERB cana-333 95 19 prandtl prandtl NOUN cana-333 95 20 number number NOUN cana-333 95 21 , , PUNCT cana-333 95 22 grashof grashof ADJ cana-333 95 23 number number NOUN cana-333 95 24 and and CCONJ cana-333 95 25 magnetic magnetic ADJ cana-333 95 26 parameter parameter NOUN cana-333 95 27 respectively respectively ADV cana-333 95 28 . . PUNCT cana-333 96 1 equations equation NOUN cana-333 96 2 ( ( PUNCT cana-333 96 3 2 2 NUM cana-333 96 4 ) ) PUNCT cana-333 96 5 , , PUNCT cana-333 96 6 ( ( PUNCT cana-333 96 7 3 3 X cana-333 96 8 ) ) PUNCT cana-333 96 9 and and CCONJ cana-333 96 10 related relate VERB cana-333 96 11 boundary boundary ADJ cana-333 96 12 condition condition NOUN cana-333 96 13 ( ( PUNCT cana-333 96 14 4 4 X cana-333 96 15 ) ) PUNCT cana-333 96 16 reduce reduce VERB cana-333 96 17 to to ADP cana-333 96 18 , , PUNCT cana-333 96 19 πœ•π‘’βˆ— πœ•π‘’βˆ— VERB cana-333 96 20 πœ•π‘‘βˆ— πœ•π‘‘βˆ— NOUN cana-333 96 21 βˆ’ βˆ’ NOUN cana-333 96 22 πœ•π‘’βˆ— πœ•π‘’βˆ— NOUN cana-333 96 23 πœ•π‘¦βˆ— πœ•π‘¦βˆ— ADV cana-333 96 24 = = PUNCT cana-333 96 25 𝑅𝑐 𝑅𝑐 ADP cana-333 96 26 ( ( PUNCT cana-333 96 27 πœ•3π‘’βˆ— πœ•3π‘’βˆ— NOUN cana-333 96 28 πœ•π‘‘βˆ—πœ•π‘¦βˆ—2 πœ•π‘‘βˆ—πœ•π‘¦βˆ—2 NUM cana-333 96 29 βˆ’ βˆ’ NOUN cana-333 96 30 πœ•3π‘’βˆ— πœ•3π‘’βˆ— NOUN cana-333 96 31 πœ•π‘¦βˆ—3 πœ•π‘¦βˆ—3 PROPN cana-333 96 32 ) ) PUNCT cana-333 96 33 + + NUM cana-333 96 34 πœ•2π‘’βˆ— πœ•2π‘’βˆ— NOUN cana-333 96 35 πœ•π‘¦βˆ—2+πΊπ‘Ÿπ‘‡βˆ— πœ•π‘¦βˆ—2+πΊπ‘Ÿπ‘‡βˆ— ADP cana-333 97 1 βˆ’ βˆ’ PROPN cana-333 97 2 [ [ PUNCT cana-333 97 3 1 1 NUM cana-333 97 4 𝐾𝑝 𝐾𝑝 NOUN cana-333 97 5 + + ADJ cana-333 97 6 𝑀2]π‘’βˆ— 𝑀2]π‘’βˆ— NOUN cana-333 97 7 … … SYM cana-333 97 8 …… …… NOUN cana-333 97 9 … … PUNCT cana-333 97 10 .. .. PUNCT cana-333 97 11 ( ( PUNCT cana-333 97 12 5 5 X cana-333 97 13 ) ) PUNCT cana-333 97 14 πœ•π‘‡βˆ— πœ•π‘‡βˆ— NOUN cana-333 97 15 πœ•π‘‘βˆ— πœ•π‘‘βˆ— PROPN cana-333 97 16 βˆ’ βˆ’ PROPN cana-333 97 17 πœ•π‘‡βˆ— πœ•π‘‡βˆ— NOUN cana-333 97 18 πœ•π‘¦βˆ— πœ•π‘¦βˆ— ADV cana-333 97 19 = = SYM cana-333 97 20 1 1 NUM cana-333 97 21 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-333 97 22 πœ•2 πœ•2 NOUN cana-333 97 23 π‘‡βˆ— π‘‡βˆ— NOUN cana-333 98 1 πœ•π‘¦βˆ—2 πœ•π‘¦βˆ—2 NOUN cana-333 98 2 – – PUNCT cana-333 98 3 π‘†βˆ—π‘‡βˆ— π‘†βˆ—π‘‡βˆ— NOUN cana-333 98 4 + + NOUN cana-333 98 5 𝑅𝑐 𝑅𝑐 PROPN cana-333 98 6 πœ•3 πœ•3 NOUN cana-333 98 7 π‘‡βˆ— π‘‡βˆ— NOUN cana-333 98 8 πœ•π‘‘βˆ—πœ•π‘¦βˆ—2 πœ•π‘‘βˆ—πœ•π‘¦βˆ—2 NOUN cana-333 98 9 … … PUNCT cana-333 98 10 … … SYM cana-333 98 11 …… …… NOUN cana-333 98 12 ( ( PUNCT cana-333 98 13 6 6 NUM cana-333 98 14 ) ) PUNCT cana-333 98 15 ( ( PUNCT cana-333 98 16 dropping drop VERB cana-333 98 17 sign sign NOUN cana-333 98 18 βˆ— βˆ— NOUN cana-333 98 19 for for ADP cana-333 98 20 convenience convenience NOUN cana-333 98 21 ) ) PUNCT cana-333 98 22 communications communication NOUN cana-333 98 23 on on ADP cana-333 98 24 applied apply VERB cana-333 98 25 nonlinear nonlinear ADJ cana-333 98 26 analysis analysis NOUN cana-333 98 27 issn issn NOUN cana-333 98 28 : : PUNCT cana-333 98 29 1074 1074 NUM cana-333 98 30 - - PUNCT cana-333 98 31 133x 133x NUM cana-333 98 32 vol vol NOUN cana-333 98 33 31 31 NUM cana-333 98 34 no no NOUN cana-333 98 35 . . NOUN cana-333 98 36 1 1 NUM cana-333 98 37 ( ( PUNCT cana-333 98 38 2024 2024 NUM cana-333 98 39 ) ) PUNCT cana-333 98 40 108 108 NUM cana-333 98 41 https://internationalpubls.com https://internationalpubls.com X cana-333 98 42 the the DET cana-333 98 43 conforming conform VERB cana-333 98 44 conditions condition NOUN cana-333 98 45 of of ADP cana-333 98 46 boundary boundary NOUN cana-333 98 47 are be AUX cana-333 98 48 u u NOUN cana-333 98 49 = = NOUN cana-333 98 50 cos cos ADJ cana-333 98 51 𝑀𝑑 𝑀𝑑 X cana-333 98 52 , , PUNCT cana-333 98 53 t t PROPN cana-333 98 54 = = SYM cana-333 98 55 π‘’βˆ’π‘–πœ”π‘‘ π‘’βˆ’π‘–πœ”π‘‘ NOUN cana-333 98 56 at at ADP cana-333 98 57 y y PROPN cana-333 98 58 = = PROPN cana-333 98 59 0 0 NUM cana-333 98 60 … … PUNCT cana-333 98 61 … … PUNCT cana-333 98 62 …… …… NOUN cana-333 98 63 ( ( PUNCT cana-333 98 64 7 7 NUM cana-333 98 65 ) ) PUNCT cana-333 98 66 uβ†’0 uβ†’0 NUM cana-333 98 67 , , PUNCT cana-333 98 68 tβ†’ tβ†’ X cana-333 98 69 0 0 NUM cana-333 98 70 as as ADP cana-333 98 71 yβ†’βˆž yβ†’βˆž NOUN cana-333 98 72 4 4 NUM cana-333 98 73 . . PUNCT cana-333 98 74 solving solve VERB cana-333 98 75 the the DET cana-333 98 76 equations equation NOUN cana-333 98 77 dropping drop VERB cana-333 98 78 βˆ— βˆ— NOUN cana-333 98 79 and and CCONJ cana-333 98 80 solving solve VERB cana-333 98 81 non non ADJ cana-333 98 82 - - ADJ cana-333 98 83 linear linear ADJ cana-333 98 84 partial partial ADJ cana-333 98 85 differential differential NOUN cana-333 98 86 equation equation NOUN cana-333 98 87 ( ( PUNCT cana-333 98 88 5 5 NUM cana-333 98 89 ) ) PUNCT cana-333 98 90 , , PUNCT cana-333 98 91 ( ( PUNCT cana-333 98 92 6 6 NUM cana-333 98 93 ) ) PUNCT cana-333 98 94 including include VERB cana-333 98 95 boundary boundary ADJ cana-333 98 96 condition condition NOUN cana-333 98 97 ( ( PUNCT cana-333 98 98 7 7 NUM cana-333 98 99 ) ) PUNCT cana-333 98 100 , , PUNCT cana-333 98 101 u u NOUN cana-333 98 102 = = SYM cana-333 98 103 π‘’π‘œπ‘’π‘–πœ”π‘‘+ π‘’π‘œπ‘’π‘–πœ”π‘‘+ PROPN cana-333 98 104 𝑒1π‘’βˆ’π‘–πœ”π‘‘ 𝑒1π‘’βˆ’π‘–πœ”π‘‘ NOUN cana-333 98 105 … … PUNCT cana-333 98 106 … … SYM cana-333 98 107 …… …… NOUN cana-333 98 108 ( ( PUNCT cana-333 98 109 8) 8) NUM cana-333 98 110 t t NOUN cana-333 98 111 = = SYM cana-333 98 112 𝑇0π‘’π‘–πœ”π‘‘ 𝑇0π‘’π‘–πœ”π‘‘ PROPN cana-333 98 113 + + NUM cana-333 98 114 𝑇1π‘’βˆ’π‘–πœ”π‘‘ 𝑇1π‘’βˆ’π‘–πœ”π‘‘ NOUN cana-333 98 115 … … PUNCT cana-333 98 116 … … PUNCT cana-333 98 117 …… …… X cana-333 98 118 ( ( PUNCT cana-333 98 119 9 9 NUM cana-333 98 120 ) ) PUNCT cana-333 98 121 where where SCONJ cana-333 98 122 𝑒𝑖 𝑒𝑖 INTJ cana-333 98 123 , , PUNCT cana-333 98 124 𝑇𝑖 𝑇𝑖 PROPN cana-333 98 125 ( ( PUNCT cana-333 98 126 i i NOUN cana-333 98 127 = = NOUN cana-333 98 128 0 0 NUM cana-333 98 129 , , PUNCT cana-333 98 130 1 1 NUM cana-333 98 131 ) ) PUNCT cana-333 98 132 are be AUX cana-333 98 133 functions function NOUN cana-333 98 134 of of ADP cana-333 98 135 y y PRON cana-333 98 136 only only ADV cana-333 98 137 and and CCONJ cana-333 98 138 𝑒0 𝑒0 PROPN cana-333 98 139 𝑒1 𝑒1 PROPN cana-333 98 140 , , PUNCT cana-333 98 141 𝑇0 𝑇0 NOUN cana-333 98 142 , , PUNCT cana-333 98 143 𝑇1 𝑇1 NOUN cana-333 98 144 are be AUX cana-333 98 145 unknown unknown ADJ cana-333 98 146 , , PUNCT cana-333 98 147 to to PART cana-333 98 148 be be AUX cana-333 98 149 determined determine VERB cana-333 98 150 . . PUNCT cana-333 99 1 equating equate VERB cana-333 99 2 harmonic harmonic ADJ cana-333 99 3 and and CCONJ cana-333 99 4 non non ADJ cana-333 99 5 - - ADJ cana-333 99 6 harmonic harmonic ADJ cana-333 99 7 terms term NOUN cana-333 99 8 and and CCONJ cana-333 99 9 putting put VERB cana-333 99 10 the the DET cana-333 99 11 values value NOUN cana-333 99 12 of of ADP cana-333 99 13 equations equation NOUN cana-333 99 14 ( ( PUNCT cana-333 99 15 5 5 NUM cana-333 99 16 ) ) PUNCT cana-333 99 17 and and CCONJ cana-333 99 18 ( ( PUNCT cana-333 99 19 6 6 NUM cana-333 99 20 ) ) PUNCT cana-333 99 21 from from ADP cana-333 99 22 equations equation NOUN cana-333 99 23 ( ( PUNCT cana-333 99 24 8) 8) NUM cana-333 99 25 , , PUNCT cana-333 99 26 ( ( PUNCT cana-333 99 27 9 9 NUM cana-333 99 28 ) ) PUNCT cana-333 99 29 obtained obtain VERB cana-333 99 30 ordinary ordinary ADJ cana-333 99 31 differential differential ADJ cana-333 99 32 equations equation NOUN cana-333 99 33 are be AUX cana-333 99 34 given give VERB cana-333 99 35 as as ADP cana-333 99 36 : : PUNCT cana-333 99 37 𝑅𝑐 𝑅𝑐 PROPN cana-333 99 38 𝑑3𝑒0 𝑑3𝑒0 VERB cana-333 99 39 𝑑𝑦3 𝑑𝑦3 NOUN cana-333 99 40 + + CCONJ cana-333 99 41 ( ( PUNCT cana-333 99 42 1 1 NUM cana-333 99 43 + + CCONJ cana-333 99 44 π‘…π‘πœ”π‘– π‘…π‘πœ”π‘– PROPN cana-333 99 45 ) ) PUNCT cana-333 100 1 𝑑2𝑒0 𝑑2𝑒0 X cana-333 100 2 𝑑𝑦2 𝑑𝑦2 NOUN cana-333 100 3 βˆ’ βˆ’ NOUN cana-333 100 4 𝑑𝑒0 𝑑𝑒0 NOUN cana-333 100 5 𝑑𝑦 𝑑𝑦 NOUN cana-333 100 6 + + CCONJ cana-333 100 7 ( ( PUNCT cana-333 100 8 1 1 NUM cana-333 101 1 𝐾𝑝 𝐾𝑝 ADJ cana-333 101 2 + + NUM cana-333 101 3 𝑀2 𝑀2 PROPN cana-333 101 4 + + CCONJ cana-333 101 5 π‘–πœ” π‘–πœ” PROPN cana-333 101 6 ) ) PUNCT cana-333 101 7 𝑒0 𝑒0 PROPN cana-333 101 8 = = PUNCT cana-333 102 1 πΊπ‘Ÿ πΊπ‘Ÿ PROPN cana-333 102 2 𝑇 𝑇 PROPN cana-333 102 3 0 0 NUM cana-333 102 4 … … SYM cana-333 102 5 …… …… NOUN cana-333 102 6 … … PUNCT cana-333 102 7 ( ( PUNCT cana-333 102 8 10 10 NUM cana-333 102 9 ) ) PUNCT cana-333 102 10 𝑅𝑐 𝑅𝑐 PROPN cana-333 102 11 𝑑3𝑒1 𝑑3𝑒1 NOUN cana-333 102 12 𝑑𝑦3 𝑑𝑦3 NOUN cana-333 102 13 βˆ’(1 βˆ’(1 NOUN cana-333 102 14 βˆ’ βˆ’ PROPN cana-333 102 15 π‘…π‘πœ”π‘– π‘…π‘πœ”π‘– PROPN cana-333 102 16 ) ) PUNCT cana-333 102 17 𝑑2𝑒1 𝑑2𝑒1 PROPN cana-333 102 18 𝑑𝑦2 𝑑𝑦2 X cana-333 102 19 βˆ’ βˆ’ X cana-333 102 20 𝑑𝑒1 𝑑𝑒1 PROPN cana-333 102 21 𝑑𝑦 𝑑𝑦 NOUN cana-333 102 22 + + CCONJ cana-333 102 23 ( ( PUNCT cana-333 102 24 1 1 NUM cana-333 103 1 𝐾𝑝 𝐾𝑝 ADJ cana-333 103 2 + + NUM cana-333 103 3 𝑀2 𝑀2 PROPN cana-333 103 4 βˆ’ βˆ’ PROPN cana-333 103 5 π‘–πœ” π‘–πœ” SYM cana-333 103 6 ) ) PUNCT cana-333 103 7 𝑒1 𝑒1 PROPN cana-333 103 8 = = PROPN cana-333 104 1 πΊπ‘Ÿ πΊπ‘Ÿ ADP cana-333 104 2 𝑇1 𝑇1 NOUN cana-333 104 3 … … PUNCT cana-333 104 4 … … PUNCT cana-333 104 5 … … PUNCT cana-333 104 6 ( ( PUNCT cana-333 104 7 11 11 NUM cana-333 104 8 ) ) PUNCT cana-333 104 9 𝑑2𝑇0 𝑑2𝑇0 X cana-333 104 10 𝑑𝑦2 𝑑𝑦2 X cana-333 104 11 + + CCONJ cana-333 104 12 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-333 104 13 1+π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” 1+π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” PROPN cana-333 104 14 𝑑𝑇0 𝑑𝑇0 NOUN cana-333 104 15 𝑑𝑦 𝑑𝑦 ADP cana-333 104 16 βˆ’ βˆ’ PROPN cana-333 105 1 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-333 105 2 ( ( PUNCT cana-333 105 3 𝑆+π‘–πœ” 𝑆+π‘–πœ” PROPN cana-333 105 4 ) ) PUNCT cana-333 105 5 1+π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” 1+π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” NUM cana-333 105 6 𝑇0 𝑇0 NOUN cana-333 105 7 = = SYM cana-333 105 8 0 0 NUM cana-333 105 9 … … PUNCT cana-333 105 10 …… …… NOUN cana-333 105 11 ( ( PUNCT cana-333 105 12 12 12 NUM cana-333 105 13 ) ) PUNCT cana-333 105 14 𝑑2𝑇1 𝑑2𝑇1 NUM cana-333 105 15 𝑑𝑦2 𝑑𝑦2 PRON cana-333 105 16 + + CCONJ cana-333 105 17 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-333 105 18 1βˆ’π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” 1βˆ’π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” PROPN cana-333 105 19 𝑑𝑇1 𝑑𝑇1 PROPN cana-333 105 20 𝑑𝑦 𝑑𝑦 ADP cana-333 105 21 βˆ’ βˆ’ PROPN cana-333 105 22 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-333 105 23 ( ( PUNCT cana-333 105 24 π‘†βˆ’π‘–πœ” π‘†βˆ’π‘–πœ” PROPN cana-333 105 25 ) ) PUNCT cana-333 105 26 1βˆ’π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” 1βˆ’π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” NUM cana-333 105 27 𝑇1 𝑇1 NOUN cana-333 105 28 = = SYM cana-333 105 29 0 0 NUM cana-333 105 30 … … PUNCT cana-333 105 31 ( ( PUNCT cana-333 105 32 13 13 NUM cana-333 105 33 ) ) PUNCT cana-333 105 34 the the DET cana-333 105 35 resultant resultant NOUN cana-333 105 36 boundary boundary ADJ cana-333 105 37 conditions condition NOUN cana-333 105 38 are be AUX cana-333 105 39 , , PUNCT cana-333 105 40 at at ADP cana-333 105 41 y y PROPN cana-333 105 42 = = SYM cana-333 105 43 0 0 NUM cana-333 105 44 𝑒0 𝑒0 PROPN cana-333 105 45 = = NOUN cana-333 105 46 1 1 NUM cana-333 105 47 2 2 NUM cana-333 105 48 𝑒1 𝑒1 NOUN cana-333 105 49 = = NOUN cana-333 105 50 1 1 NUM cana-333 105 51 2 2 NUM cana-333 105 52 … … PUNCT cana-333 105 53 …… …… NOUN cana-333 105 54 ( ( PUNCT cana-333 105 55 14 14 NUM cana-333 105 56 ) ) PUNCT cana-333 105 57 at at ADP cana-333 105 58 yβ†’βˆž yβ†’βˆž ADJ cana-333 105 59 𝑒0 𝑒0 PROPN cana-333 105 60 = = SYM cana-333 105 61 0 0 NUM cana-333 105 62 𝑒1 𝑒1 NOUN cana-333 105 63 = = NOUN cana-333 105 64 0 0 NUM cana-333 105 65 … … PUNCT cana-333 105 66 … … PUNCT cana-333 105 67 … … PUNCT cana-333 105 68 . . PUNCT cana-333 106 1 ( ( PUNCT cana-333 106 2 15 15 NUM cana-333 106 3 ) ) PUNCT cana-333 106 4 at at ADP cana-333 106 5 y y PROPN cana-333 106 6 = = SYM cana-333 106 7 0 0 NUM cana-333 106 8 𝑇0 𝑇0 NOUN cana-333 106 9 = = SYM cana-333 106 10 0 0 NUM cana-333 106 11 𝑇1 𝑇1 NOUN cana-333 106 12 = = SYM cana-333 106 13 1 1 NUM cana-333 106 14 … … PUNCT cana-333 106 15 … … PUNCT cana-333 106 16 … … PUNCT cana-333 106 17 . . PUNCT cana-333 107 1 ( ( PUNCT cana-333 107 2 16 16 NUM cana-333 107 3 ) ) PUNCT cana-333 107 4 at at ADP cana-333 107 5 yβ†’βˆž yβ†’βˆž NOUN cana-333 107 6 𝑇0 𝑇0 NOUN cana-333 108 1 = = SYM cana-333 108 2 0 0 NUM cana-333 108 3 𝑇1 𝑇1 NOUN cana-333 108 4 = = SYM cana-333 108 5 0 0 NUM cana-333 108 6 … … PUNCT cana-333 108 7 …… …… NOUN cana-333 108 8 ( ( PUNCT cana-333 108 9 17 17 NUM cana-333 108 10 ) ) PUNCT cana-333 108 11 from from ADP cana-333 108 12 equation equation NOUN cana-333 108 13 ( ( PUNCT cana-333 108 14 12 12 NUM cana-333 108 15 ) ) PUNCT cana-333 108 16 and and CCONJ cana-333 108 17 ( ( PUNCT cana-333 108 18 13 13 NUM cana-333 108 19 ) ) PUNCT cana-333 108 20 , , PUNCT cana-333 108 21 obtained obtain VERB cana-333 108 22 ordinary ordinary ADJ cana-333 108 23 differential differential ADJ cana-333 108 24 equations equation NOUN cana-333 108 25 ( ( PUNCT cana-333 108 26 16 16 NUM cana-333 108 27 ) ) PUNCT cana-333 108 28 and and CCONJ cana-333 108 29 ( ( PUNCT cana-333 108 30 17 17 NUM cana-333 108 31 ) ) PUNCT cana-333 108 32 with with ADP cana-333 108 33 prescribed prescribe VERB cana-333 108 34 boundary boundary ADJ cana-333 108 35 conditions condition NOUN cana-333 108 36 which which PRON cana-333 108 37 are be AUX cana-333 108 38 solved solve VERB cana-333 108 39 as as ADP cana-333 108 40 under under ADV cana-333 108 41 : : PUNCT cana-333 108 42 𝑇0 𝑇0 NOUN cana-333 108 43 = = SYM cana-333 108 44 0 0 PUNCT cana-333 108 45 … … PUNCT cana-333 108 46 … … PUNCT cana-333 108 47 ( ( PUNCT cana-333 108 48 18 18 NUM cana-333 108 49 ) ) PUNCT cana-333 108 50 𝑇1 𝑇1 NOUN cana-333 108 51 = = SYM cana-333 108 52 exp exp NOUN cana-333 108 53 ( ( PUNCT cana-333 108 54 -π‘š3 -π‘š3 PROPN cana-333 108 55 𝑦 𝑦 NOUN cana-333 108 56 ) ) PUNCT cana-333 108 57 … … PUNCT cana-333 108 58 …… …… X cana-333 108 59 ( ( PUNCT cana-333 108 60 19 19 NUM cana-333 108 61 ) ) PUNCT cana-333 108 62 where where SCONJ cana-333 108 63 π‘š3 π‘š3 NOUN cana-333 108 64 = = SYM cana-333 108 65 a+√𝐴2 a+√𝐴2 PROPN cana-333 108 66 + + PROPN cana-333 108 67 4b 4b X cana-333 108 68 2 2 NUM cana-333 108 69 where where SCONJ cana-333 108 70 a a DET cana-333 108 71 = = SYM cana-333 108 72 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-333 108 73 1βˆ’π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” 1βˆ’π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” PROPN cana-333 108 74 , , PUNCT cana-333 108 75 b= b= NOUN cana-333 108 76 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-333 108 77 ( ( PUNCT cana-333 108 78 π‘†βˆ’π‘–πœ” π‘†βˆ’π‘–πœ” PROPN cana-333 108 79 ) ) PUNCT cana-333 108 80 1βˆ’π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” 1βˆ’π‘ƒπ‘Ÿπ‘…π‘π‘–πœ” NUM cana-333 108 81 5 5 NUM cana-333 108 82 . . PUNCT cana-333 108 83 method method NOUN cana-333 108 84 used use VERB cana-333 108 85 the the DET cana-333 108 86 equations equation NOUN cana-333 108 87 ( ( PUNCT cana-333 108 88 10 10 NUM cana-333 108 89 ) ) PUNCT cana-333 108 90 and and CCONJ cana-333 108 91 ( ( PUNCT cana-333 108 92 11 11 NUM cana-333 108 93 ) ) PUNCT cana-333 108 94 are be AUX cana-333 108 95 not not PART cana-333 108 96 solvable solvable ADJ cana-333 108 97 by by ADP cana-333 108 98 using use VERB cana-333 108 99 the the DET cana-333 108 100 given give VERB cana-333 108 101 boundary boundary ADJ cana-333 108 102 conditions condition NOUN cana-333 108 103 ( ( PUNCT cana-333 108 104 14 14 NUM cana-333 108 105 ) ) PUNCT cana-333 108 106 and and CCONJ cana-333 108 107 ( ( PUNCT cana-333 108 108 15 15 NUM cana-333 108 109 ) ) PUNCT cana-333 108 110 . . PUNCT cana-333 109 1 hence hence ADV cana-333 109 2 the the DET cana-333 109 3 perturbation perturbation NOUN cana-333 109 4 method method NOUN cana-333 109 5 has have AUX cana-333 109 6 been be AUX cana-333 109 7 applied apply VERB cana-333 109 8 using use VERB cana-333 109 9 rc rc PROPN cana-333 109 10 ( ( PUNCT cana-333 109 11 rc rc X cana-333 109 12 < < X cana-333 109 13 1 1 NUM cana-333 109 14 ) ) PUNCT cana-333 109 15 , , PUNCT cana-333 109 16 the the DET cana-333 109 17 elastic elastic ADJ cana-333 109 18 parameter parameter NOUN cana-333 109 19 as as ADP cana-333 109 20 the the DET cana-333 109 21 perturbation perturbation NOUN cana-333 109 22 parameter parameter NOUN cana-333 109 23 . . PUNCT cana-333 110 1 𝑒0 𝑒0 PROPN cana-333 110 2 = = PUNCT cana-333 110 3 𝑒00(𝑦 𝑒00(𝑦 ADJ cana-333 110 4 ) ) PUNCT cana-333 110 5 + + CCONJ cana-333 110 6 𝑅𝑐𝑒01(𝑦 𝑅𝑐𝑒01(𝑦 PROPN cana-333 110 7 ) ) PUNCT cana-333 110 8 … … PUNCT cana-333 110 9 … … PUNCT cana-333 110 10 … … PUNCT cana-333 110 11 … … PUNCT cana-333 110 12 …… …… NOUN cana-333 110 13 …… …… NOUN cana-333 110 14 …… …… NOUN cana-333 110 15 …… …… NOUN cana-333 110 16 ( ( PUNCT cana-333 110 17 20 20 NUM cana-333 110 18 ) ) PUNCT cana-333 110 19 𝑒1 𝑒1 NOUN cana-333 110 20 = = PROPN cana-333 110 21 𝑒10(𝑦 𝑒10(𝑦 NOUN cana-333 110 22 ) ) PUNCT cana-333 110 23 + + CCONJ cana-333 110 24 𝑅𝑐𝑒11(𝑦 𝑅𝑐𝑒11(𝑦 NUM cana-333 110 25 ) ) PUNCT cana-333 110 26 … … PUNCT cana-333 110 27 … … PUNCT cana-333 110 28 … … PUNCT cana-333 110 29 … … PUNCT cana-333 110 30 …… …… NOUN cana-333 110 31 …… …… NOUN cana-333 110 32 …… …… NOUN cana-333 110 33 …… …… NOUN cana-333 110 34 .(21 .(21 PRON cana-333 110 35 ) ) PUNCT cana-333 110 36 substituting substitute VERB cana-333 110 37 equation equation NOUN cana-333 110 38 ( ( PUNCT cana-333 110 39 20 20 NUM cana-333 110 40 ) ) PUNCT cana-333 110 41 and and CCONJ cana-333 110 42 ( ( PUNCT cana-333 110 43 21 21 NUM cana-333 110 44 ) ) PUNCT cana-333 110 45 into into ADP cana-333 110 46 equations equation NOUN cana-333 110 47 ( ( PUNCT cana-333 110 48 10 10 NUM cana-333 110 49 ) ) PUNCT cana-333 110 50 and and CCONJ cana-333 110 51 ( ( PUNCT cana-333 110 52 11 11 NUM cana-333 110 53 ) ) PUNCT cana-333 110 54 respectively respectively ADV cana-333 110 55 , , PUNCT cana-333 110 56 equating equate VERB cana-333 110 57 the the DET cana-333 110 58 coefficients coefficient NOUN cana-333 110 59 of of ADP cana-333 110 60 𝑅𝑐 𝑅𝑐 PROPN cana-333 110 61 0and 0and NOUN cana-333 110 62 𝑅𝑐 𝑅𝑐 PROPN cana-333 110 63 1 1 NUM cana-333 110 64 to to ADP cana-333 110 65 zero zero NUM cana-333 110 66 , , PUNCT cana-333 110 67 we we PRON cana-333 110 68 get get VERB cana-333 110 69 the the DET cana-333 110 70 following follow VERB cana-333 110 71 set set NOUN cana-333 110 72 of of ADP cana-333 110 73 equations equation NOUN cana-333 110 74 . . PUNCT cana-333 111 1 communications communication NOUN cana-333 111 2 on on ADP cana-333 111 3 applied apply VERB cana-333 111 4 nonlinear nonlinear ADJ cana-333 111 5 analysis analysis NOUN cana-333 111 6 issn issn NOUN cana-333 111 7 : : PUNCT cana-333 111 8 1074 1074 NUM cana-333 111 9 - - PUNCT cana-333 111 10 133x 133x NUM cana-333 111 11 vol vol NOUN cana-333 111 12 31 31 NUM cana-333 111 13 no no NOUN cana-333 111 14 . . NOUN cana-333 111 15 1 1 NUM cana-333 111 16 ( ( PUNCT cana-333 111 17 2024 2024 NUM cana-333 111 18 ) ) PUNCT cana-333 111 19 109 109 NUM cana-333 111 20 https://internationalpubls.com https://internationalpubls.com X cana-333 111 21 zeroth zeroth PRON cana-333 111 22 order order NOUN cana-333 111 23 equations equation NOUN cana-333 111 24 𝑒00 𝑒00 VERB cana-333 112 1 β€²β€² β€²β€² PROPN cana-333 112 2 βˆ’ βˆ’ PROPN cana-333 112 3 𝑒00 𝑒00 NOUN cana-333 113 1 β€² β€² NUM cana-333 113 2 βˆ’ βˆ’ PROPN cana-333 114 1 ( ( PUNCT cana-333 114 2 1 1 NUM cana-333 114 3 𝐾𝑝 𝐾𝑝 ADJ cana-333 114 4 + + NUM cana-333 114 5 𝑀2 𝑀2 PROPN cana-333 114 6 + + CCONJ cana-333 114 7 π‘–πœ” π‘–πœ” X cana-333 114 8 ) ) PUNCT cana-333 114 9 𝑒00 𝑒00 NOUN cana-333 114 10 = = SYM cana-333 114 11 0 0 NUM cana-333 114 12 … … PUNCT cana-333 114 13 … … PUNCT cana-333 114 14 … … PUNCT cana-333 114 15 … … PUNCT cana-333 114 16 … … PUNCT cana-333 114 17 …… …… NOUN cana-333 114 18 …… …… NOUN cana-333 114 19 …… …… NOUN cana-333 114 20 …… …… NOUN cana-333 114 21 … … PUNCT cana-333 114 22 ( ( PUNCT cana-333 114 23 22 22 NUM cana-333 114 24 ) ) PUNCT cana-333 114 25 𝑒10 𝑒10 NOUN cana-333 114 26 β€²β€² β€²β€² PROPN cana-333 114 27 βˆ’ βˆ’ NOUN cana-333 114 28 𝑒10 𝑒10 INTJ cana-333 115 1 β€² β€² NUM cana-333 115 2 βˆ’ βˆ’ PROPN cana-333 115 3 ( ( PUNCT cana-333 115 4 1 1 NUM cana-333 116 1 𝐾𝑝 𝐾𝑝 ADJ cana-333 116 2 + + NUM cana-333 116 3 𝑀2 𝑀2 PROPN cana-333 116 4 βˆ’ βˆ’ PROPN cana-333 116 5 π‘–πœ” π‘–πœ” SYM cana-333 116 6 ) ) PUNCT cana-333 116 7 𝑒10 𝑒10 PROPN cana-333 116 8 = = SYM cana-333 116 9 βˆ’πΊπ‘Ÿπ‘’π‘₯𝑝. βˆ’πΊπ‘Ÿπ‘’π‘₯𝑝. NUM cana-333 116 10 ( ( PUNCT cana-333 116 11 βˆ’π‘š3𝑦 βˆ’π‘š3𝑦 X cana-333 116 12 ) ) PUNCT cana-333 116 13 … … PUNCT cana-333 116 14 … … PUNCT cana-333 116 15 … … SYM cana-333 116 16 …… …… NOUN cana-333 116 17 … … PUNCT cana-333 116 18 … … PUNCT cana-333 116 19 ( ( PUNCT cana-333 116 20 23 23 NUM cana-333 116 21 ) ) PUNCT cana-333 116 22 first first ADJ cana-333 116 23 order order NOUN cana-333 116 24 equations equation NOUN cana-333 116 25 𝑒00 𝑒00 PRON cana-333 116 26 β€²β€²β€² β€²β€²β€² VERB cana-333 116 27 βˆ’ βˆ’ PROPN cana-333 117 1 𝑒01 𝑒01 NOUN cana-333 118 1 β€²β€² β€²β€² PROPN cana-333 118 2 βˆ’ βˆ’ PROPN cana-333 119 1 π‘–πœ”π‘’00 π‘–πœ”π‘’00 PROPN cana-333 119 2 β€²β€² β€²β€² PROPN cana-333 119 3 βˆ’ βˆ’ NOUN cana-333 119 4 𝑒01 𝑒01 NOUN cana-333 119 5 β€² β€² NUM cana-333 120 1 + + CCONJ cana-333 120 2 ( ( PUNCT cana-333 120 3 1 1 NUM cana-333 120 4 𝐾𝑝 𝐾𝑝 ADJ cana-333 120 5 + + NUM cana-333 120 6 𝑀2 𝑀2 PROPN cana-333 120 7 + + CCONJ cana-333 120 8 π‘–πœ” π‘–πœ” PROPN cana-333 120 9 ) ) PUNCT cana-333 120 10 𝑒01 𝑒01 NOUN cana-333 120 11 = = SYM cana-333 120 12 0 0 NUM cana-333 120 13 … … PUNCT cana-333 120 14 … … SYM cana-333 120 15 …… …… NOUN cana-333 120 16 … … PUNCT cana-333 120 17 … … SYM cana-333 120 18 .(24 .(24 NUM cana-333 120 19 ) ) PUNCT cana-333 121 1 𝑒10 𝑒10 ADV cana-333 121 2 β€²β€²β€² β€²β€²β€² INTJ cana-333 122 1 βˆ’ βˆ’ PUNCT cana-333 122 2 𝑒11 𝑒11 NOUN cana-333 122 3 β€²β€² β€²β€² PROPN cana-333 122 4 + + CCONJ cana-333 122 5 π‘–πœ”π‘’10 π‘–πœ”π‘’10 PROPN cana-333 122 6 β€²β€² β€²β€² PROPN cana-333 122 7 βˆ’ βˆ’ PROPN cana-333 122 8 𝑒11 𝑒11 NOUN cana-333 122 9 β€² β€² NUM cana-333 123 1 + + CCONJ cana-333 124 1 ( ( PUNCT cana-333 124 2 1 1 NUM cana-333 124 3 𝐾𝑝 𝐾𝑝 ADJ cana-333 124 4 + + NUM cana-333 124 5 𝑀2 𝑀2 PROPN cana-333 124 6 βˆ’ βˆ’ PROPN cana-333 124 7 π‘–πœ” π‘–πœ” NOUN cana-333 124 8 ) ) PUNCT cana-333 124 9 𝑒11 𝑒11 NOUN cana-333 124 10 = = NOUN cana-333 124 11 0 0 NUM cana-333 124 12 …… …… NOUN cana-333 124 13 …… …… NOUN cana-333 124 14 … … PUNCT cana-333 124 15 … … PUNCT cana-333 124 16 .. .. PUNCT cana-333 124 17 ( ( PUNCT cana-333 124 18 25 25 NUM cana-333 124 19 ) ) PUNCT cana-333 124 20 using use VERB cana-333 124 21 the the DET cana-333 124 22 perturbation perturbation NOUN cana-333 124 23 the the DET cana-333 124 24 boundary boundary ADJ cana-333 124 25 conditions condition NOUN cana-333 124 26 are be AUX cana-333 124 27 reduced reduce VERB cana-333 124 28 as as SCONJ cana-333 124 29 follows follow VERB cana-333 124 30 : : PUNCT cana-333 124 31 at at ADP cana-333 124 32 y=0 y=0 X cana-333 124 33 𝑒00 𝑒00 NOUN cana-333 124 34 = = SYM cana-333 124 35 0 0 NUM cana-333 124 36 𝑒01 𝑒01 NOUN cana-333 124 37 = = SYM cana-333 125 1 0 0 NUM cana-333 125 2 𝑒10 𝑒10 NOUN cana-333 125 3 = = SYM cana-333 125 4 1 1 NUM cana-333 125 5 2 2 NUM cana-333 125 6 𝑒11 𝑒11 NOUN cana-333 125 7 = = SYM cana-333 125 8 0 0 NUM cana-333 125 9 … … PUNCT cana-333 125 10 … … SYM cana-333 125 11 …… …… NOUN cana-333 125 12 … … PUNCT cana-333 125 13 ( ( PUNCT cana-333 125 14 26 26 NUM cana-333 125 15 ) ) PUNCT cana-333 125 16 at at ADP cana-333 125 17 yβ†’ yβ†’ X cana-333 125 18 ∞ ∞ PROPN cana-333 125 19 𝑒00 𝑒00 PROPN cana-333 125 20 = = NOUN cana-333 125 21 0 0 NUM cana-333 125 22 𝑒01 𝑒01 NOUN cana-333 125 23 = = SYM cana-333 125 24 0 0 NUM cana-333 125 25 𝑒10 𝑒10 NOUN cana-333 125 26 = = SYM cana-333 125 27 0 0 NUM cana-333 125 28 𝑒11 𝑒11 NOUN cana-333 125 29 = = SYM cana-333 125 30 0 0 NUM cana-333 125 31 … … NUM cana-333 125 32 …… …… NOUN cana-333 125 33 … … PUNCT cana-333 125 34 … … PUNCT cana-333 125 35 … … PUNCT cana-333 125 36 ( ( PUNCT cana-333 125 37 27 27 NUM cana-333 125 38 ) ) PUNCT cana-333 125 39 solving solve VERB cana-333 125 40 these these DET cana-333 125 41 differential differential ADJ cana-333 125 42 equations equation NOUN cana-333 125 43 by by ADP cana-333 125 44 using use VERB cana-333 125 45 the the DET cana-333 125 46 boundary boundary ADJ cana-333 125 47 conditions condition NOUN cana-333 125 48 we we PRON cana-333 125 49 get get VERB cana-333 125 50 the the DET cana-333 125 51 following follow VERB cana-333 125 52 results result NOUN cana-333 125 53 u u NOUN cana-333 125 54 = = PUNCT cana-333 125 55 ( ( PUNCT cana-333 125 56 c5 c5 PROPN cana-333 125 57 exp.(-m5y)+ exp.(-m5y)+ PROPN cana-333 125 58 rc rc PROPN cana-333 125 59 c9 c9 PROPN cana-333 125 60 ( ( PUNCT cana-333 125 61 exp.(-m9y)-exp.(-m5y exp.(-m9y)-exp.(-m5y NOUN cana-333 125 62 ) ) PUNCT cana-333 125 63 ) ) PUNCT cana-333 125 64 ) ) PUNCT cana-333 125 65 eiΟ‰t eiΟ‰t VERB cana-333 126 1 + + PROPN cana-333 126 2 ( ( PUNCT cana-333 126 3 c7(exp.(-m7y)-exp.(-m3y c7(exp.(-m7y)-exp.(-m3y PROPN cana-333 126 4 ) ) PUNCT cana-333 126 5 ) ) PUNCT cana-333 127 1 + + PUNCT cana-333 127 2 rc(c11 rc(c11 ADJ cana-333 127 3 exp.(m11y)+a2 exp.(m11y)+a2 PROPN cana-333 127 4 exp.(-m7y)+a3exp.(-m3y))))e exp.(-m7y)+a3exp.(-m3y))))e PROPN cana-333 127 5 - - PUNCT cana-333 127 6 iΟ‰t iΟ‰t NOUN cana-333 127 7 … … PUNCT cana-333 127 8 …… …… X cana-333 127 9 .(28 .(28 SYM cana-333 127 10 ) ) PUNCT cana-333 127 11 t t PROPN cana-333 127 12 = = PUNCT cana-333 127 13 exp.(-m3y)e exp.(-m3y)e PROPN cana-333 127 14 - - PUNCT cana-333 127 15 iΟ‰t iΟ‰t NOUN cana-333 127 16 . . PUNCT cana-333 128 1 … … PUNCT cana-333 128 2 … … PUNCT cana-333 128 3 … … PUNCT cana-333 128 4 … … PUNCT cana-333 128 5 … … PUNCT cana-333 128 6 …… …… NOUN cana-333 128 7 …… …… NOUN cana-333 128 8 …… …… NOUN cana-333 128 9 … … PUNCT cana-333 128 10 … … SYM cana-333 128 11 … … PUNCT cana-333 128 12 … … PUNCT cana-333 128 13 .. .. PUNCT cana-333 128 14 ( ( PUNCT cana-333 128 15 29 29 NUM cana-333 128 16 ) ) PUNCT cana-333 129 1 where where SCONJ cana-333 129 2 π‘š5 π‘š5 NOUN cana-333 129 3 = = PUNCT cana-333 129 4 1+√ 1+√ NUM cana-333 129 5 1 1 NUM cana-333 129 6 𝐾𝑝 𝐾𝑝 NOUN cana-333 129 7 + + NOUN cana-333 129 8 𝑀2+iΟ‰ 𝑀2+iΟ‰ NOUN cana-333 129 9 2 2 NUM cana-333 129 10 , , PUNCT cana-333 129 11 π‘š7= π‘š7= PROPN cana-333 129 12 1+√ 1+√ NUM cana-333 129 13 1 1 NUM cana-333 129 14 𝐾𝑝 𝐾𝑝 NOUN cana-333 129 15 + + ADJ cana-333 129 16 𝑀2βˆ’iΟ‰ 𝑀2βˆ’iΟ‰ NOUN cana-333 129 17 2 2 NUM cana-333 129 18 , , PUNCT cana-333 129 19 π‘š9 π‘š9 NOUN cana-333 129 20 = = SYM cana-333 129 21 π‘š5 π‘š5 NOUN cana-333 129 22 , , PUNCT cana-333 129 23 π‘š11 π‘š11 NOUN cana-333 129 24 = = SYM cana-333 129 25 π‘š7 π‘š7 NOUN cana-333 129 26 𝐢7 𝐢7 NOUN cana-333 130 1 = = PUNCT cana-333 130 2 βˆ’πΊπ‘Ÿ βˆ’πΊπ‘Ÿ NOUN cana-333 130 3 π‘š3 π‘š3 ADP cana-333 130 4 2 2 NUM cana-333 130 5 βˆ’ βˆ’ NOUN cana-333 130 6 π‘š3 π‘š3 NOUN cana-333 130 7 βˆ’ βˆ’ PROPN cana-333 131 1 ( ( PUNCT cana-333 131 2 1 1 NUM cana-333 131 3 𝐾𝑝 𝐾𝑝 ADJ cana-333 131 4 + + NUM cana-333 131 5 𝑀2 𝑀2 PROPN cana-333 131 6 βˆ’ βˆ’ PROPN cana-333 131 7 π‘–πœ” π‘–πœ” PROPN cana-333 131 8 ) ) PUNCT cana-333 131 9 𝐢9 𝐢9 NOUN cana-333 131 10 = = PROPN cana-333 131 11 π‘š5 π‘š5 PROPN cana-333 131 12 2(π‘š5 2(π‘š5 PROPN cana-333 131 13 + + CCONJ cana-333 131 14 π‘–πœ” π‘–πœ” PROPN cana-333 131 15 ) ) PUNCT cana-333 131 16 2(π‘š5 2(π‘š5 NOUN cana-333 131 17 2 2 NUM cana-333 131 18 βˆ’ βˆ’ NOUN cana-333 131 19 π‘š5 π‘š5 NOUN cana-333 131 20 βˆ’ βˆ’ PROPN cana-333 131 21 ( ( PUNCT cana-333 131 22 1 1 NUM cana-333 132 1 𝐾𝑝 𝐾𝑝 ADJ cana-333 132 2 + + NUM cana-333 132 3 𝑀2 𝑀2 PROPN cana-333 132 4 + + CCONJ cana-333 132 5 π‘–πœ” π‘–πœ” X cana-333 132 6 ) ) PUNCT cana-333 132 7 a1 a1 PROPN cana-333 132 8 = = PROPN cana-333 132 9 c7 c7 PROPN cana-333 132 10 , , PUNCT cana-333 132 11 c11=-a2 c11=-a2 ADJ cana-333 132 12 - - PUNCT cana-333 132 13 a3 a3 NOUN cana-333 132 14 𝐴2 𝐴2 PROPN cana-333 132 15 = = SYM cana-333 132 16 𝐴1π‘š7 𝐴1π‘š7 PROPN cana-333 132 17 2(βˆ’π‘š7+π‘–πœ” 2(βˆ’π‘š7+π‘–πœ” NUM cana-333 132 18 ) ) PUNCT cana-333 132 19 ( ( PUNCT cana-333 132 20 π‘š7 π‘š7 NOUN cana-333 132 21 2βˆ’π‘š7βˆ’ 2βˆ’π‘š7βˆ’ NUM cana-333 132 22 ( ( PUNCT cana-333 132 23 1 1 NUM cana-333 133 1 𝐾𝑝 𝐾𝑝 NOUN cana-333 133 2 + + ADJ cana-333 133 3 𝑀2βˆ’π‘–πœ” 𝑀2βˆ’π‘–πœ” ADJ cana-333 133 4 ) ) PUNCT cana-333 133 5 𝐴3 𝐴3 PROPN cana-333 133 6 = = PUNCT cana-333 133 7 𝐴1π‘š3 𝐴1π‘š3 PROPN cana-333 133 8 2(π‘š3 2(π‘š3 NUM cana-333 133 9 βˆ’ βˆ’ NOUN cana-333 133 10 π‘–πœ” π‘–πœ” SYM cana-333 133 11 ) ) PUNCT cana-333 133 12 ( ( PUNCT cana-333 133 13 π‘š3 π‘š3 NOUN cana-333 133 14 2 2 NUM cana-333 133 15 βˆ’ βˆ’ NOUN cana-333 133 16 π‘š3 π‘š3 NOUN cana-333 133 17 βˆ’ βˆ’ PROPN cana-333 134 1 ( ( PUNCT cana-333 134 2 1 1 NUM cana-333 134 3 𝐾𝑝 𝐾𝑝 ADJ cana-333 134 4 + + NUM cana-333 134 5 𝑀2 𝑀2 PROPN cana-333 134 6 βˆ’ βˆ’ PROPN cana-333 134 7 π‘–πœ” π‘–πœ” SYM cana-333 134 8 ) ) PUNCT cana-333 134 9 6 6 NUM cana-333 134 10 . . PUNCT cana-333 135 1 results result VERB cana-333 135 2 discussion discussion NOUN cana-333 135 3 present present ADJ cana-333 135 4 study study NOUN cana-333 135 5 involves involve VERB cana-333 135 6 impact impact NOUN cana-333 135 7 of of ADP cana-333 135 8 heat heat NOUN cana-333 135 9 source source NOUN cana-333 135 10 on on ADP cana-333 135 11 convective convective ADJ cana-333 135 12 mhd mhd NOUN cana-333 135 13 flow flow NOUN cana-333 135 14 concerning concern VERB cana-333 135 15 viscous viscous ADJ cana-333 135 16 non non ADJ cana-333 135 17 newtonian newtonian ADJ cana-333 135 18 fluid fluid NOUN cana-333 135 19 . . PUNCT cana-333 136 1 it it PRON cana-333 136 2 is be AUX cana-333 136 3 allowed allow VERB cana-333 136 4 to to PART cana-333 136 5 flow flow VERB cana-333 136 6 past past ADP cana-333 136 7 a a DET cana-333 136 8 semi semi ADJ cana-333 136 9 - - ADJ cana-333 136 10 infinite infinite ADJ cana-333 136 11 porous porous ADJ cana-333 136 12 plate plate NOUN cana-333 136 13 which which PRON cana-333 136 14 is be AUX cana-333 136 15 in in ADP cana-333 136 16 oscillating oscillate VERB cana-333 136 17 position position NOUN cana-333 136 18 and and CCONJ cana-333 136 19 acted act VERB cana-333 136 20 upon upon SCONJ cana-333 136 21 by by ADP cana-333 136 22 transverse transverse NOUN cana-333 136 23 magnetic magnetic ADJ cana-333 136 24 field field NOUN cana-333 136 25 . . PUNCT cana-333 137 1 analytically analytically ADV cana-333 137 2 derived derive VERB cana-333 137 3 mathematical mathematical ADJ cana-333 137 4 expressions expression NOUN cana-333 137 5 related relate VERB cana-333 137 6 to to ADP cana-333 137 7 velocity velocity NOUN cana-333 137 8 and and CCONJ cana-333 137 9 temperature temperature NOUN cana-333 137 10 , , PUNCT cana-333 137 11 solving solve VERB cana-333 137 12 field field NOUN cana-333 137 13 equations equation NOUN cana-333 137 14 . . PUNCT cana-333 138 1 figures figure NOUN cana-333 138 2 1 1 NUM cana-333 138 3 - - SYM cana-333 138 4 5 5 NUM cana-333 138 5 describe describe VERB cana-333 138 6 the the DET cana-333 138 7 velocity velocity NOUN cana-333 138 8 field field NOUN cana-333 138 9 u u NOUN cana-333 138 10 under under ADP cana-333 138 11 the the DET cana-333 138 12 effect effect NOUN cana-333 138 13 of of ADP cana-333 138 14 parameters parameter NOUN cana-333 138 15 gr gr ADP cana-333 138 16 , , PUNCT cana-333 138 17 kp kp PROPN cana-333 138 18 , , PUNCT cana-333 138 19 pr pr INTJ cana-333 138 20 , , PUNCT cana-333 138 21 s s PART cana-333 138 22 and and CCONJ cana-333 138 23 m m VERB cana-333 138 24 .figure .figure ADJ cana-333 138 25 6 6 NUM cana-333 138 26 - - SYM cana-333 138 27 7 7 NUM cana-333 138 28 describe describe VERB cana-333 138 29 temperature temperature NOUN cana-333 138 30 field field NOUN cana-333 138 31 t t NOUN cana-333 138 32 under under ADP cana-333 138 33 the the DET cana-333 138 34 effect effect NOUN cana-333 138 35 of of ADP cana-333 138 36 parameters parameter NOUN cana-333 138 37 s s PART cana-333 138 38 and and CCONJ cana-333 138 39 pr pr NOUN cana-333 138 40 . . PUNCT cana-333 139 1 figure figure NOUN cana-333 140 1 -1 -1 ADJ cana-333 140 2 , , PUNCT cana-333 140 3 it it PRON cana-333 140 4 depicts depict VERB cana-333 140 5 the the DET cana-333 140 6 variation variation NOUN cana-333 140 7 in in ADP cana-333 140 8 velocity velocity NOUN cana-333 140 9 field field NOUN cana-333 140 10 u u NOUN cana-333 140 11 due due ADP cana-333 140 12 to to ADP cana-333 140 13 varying vary VERB cana-333 140 14 values value NOUN cana-333 140 15 of of ADP cana-333 140 16 grashof grashof ADJ cana-333 140 17 number number NOUN cana-333 140 18 , , PUNCT cana-333 140 19 gr gr NOUN cana-333 140 20 , , PUNCT cana-333 140 21 velocity velocity NOUN cana-333 140 22 field field NOUN cana-333 140 23 u u NOUN cana-333 140 24 is be AUX cana-333 140 25 taken take VERB cana-333 140 26 against against ADP cana-333 140 27 y y PRON cana-333 140 28 which which PRON cana-333 140 29 means mean VERB cana-333 140 30 velocity velocity NOUN cana-333 140 31 field field NOUN cana-333 140 32 u u NOUN cana-333 140 33 decreases decrease VERB cana-333 140 34 sharply sharply ADV cana-333 140 35 for for ADP cana-333 140 36 increase increase NOUN cana-333 140 37 in in ADP cana-333 140 38 y y PROPN cana-333 140 39 communications communication NOUN cana-333 140 40 on on ADP cana-333 140 41 applied apply VERB cana-333 140 42 nonlinear nonlinear ADJ cana-333 140 43 analysis analysis NOUN cana-333 140 44 issn issn NOUN cana-333 140 45 : : PUNCT cana-333 140 46 1074 1074 NUM cana-333 140 47 - - PUNCT cana-333 140 48 133x 133x NUM cana-333 140 49 vol vol NOUN cana-333 140 50 31 31 NUM cana-333 140 51 no no NOUN cana-333 140 52 . . NOUN cana-333 140 53 1 1 NUM cana-333 140 54 ( ( PUNCT cana-333 140 55 2024 2024 NUM cana-333 140 56 ) ) PUNCT cana-333 140 57 110 110 NUM cana-333 140 58 https://internationalpubls.com https://internationalpubls.com X cana-333 140 59 approaches approach VERB cana-333 140 60 zero zero NUM cana-333 140 61 at at ADP cana-333 140 62 the the DET cana-333 140 63 boundary boundary NOUN cana-333 140 64 . . PUNCT cana-333 141 1 figure figure NOUN cana-333 142 1 -2 -2 INTJ cana-333 142 2 , , PUNCT cana-333 142 3 it it PRON cana-333 142 4 depicts depict VERB cana-333 142 5 the the DET cana-333 142 6 variation variation NOUN cana-333 142 7 in in ADP cana-333 142 8 velocity velocity NOUN cana-333 142 9 field field NOUN cana-333 142 10 u u NOUN cana-333 142 11 due due ADP cana-333 142 12 to to ADP cana-333 142 13 varying vary VERB cana-333 142 14 values value NOUN cana-333 142 15 of of ADP cana-333 142 16 kp kp NOUN cana-333 142 17 , , PUNCT cana-333 142 18 permeability permeability NOUN cana-333 142 19 parameter parameter NOUN cana-333 142 20 , , PUNCT cana-333 142 21 velocity velocity NOUN cana-333 142 22 field field NOUN cana-333 142 23 u u NOUN cana-333 142 24 is be AUX cana-333 142 25 plotted plot VERB cana-333 142 26 against against ADP cana-333 142 27 y y PRON cana-333 142 28 which which PRON cana-333 142 29 means mean VERB cana-333 142 30 velocity velocity NOUN cana-333 142 31 field field NOUN cana-333 142 32 u u NOUN cana-333 142 33 increases increase VERB cana-333 142 34 sharply sharply ADV cana-333 142 35 for for ADP cana-333 142 36 increase increase NOUN cana-333 142 37 in in ADP cana-333 142 38 y y PROPN cana-333 142 39 approaches approach NOUN cana-333 142 40 zero zero NUM cana-333 142 41 at at ADP cana-333 142 42 the the DET cana-333 142 43 boundary boundary NOUN cana-333 142 44 . . PUNCT cana-333 143 1 figure3 figure3 PROPN cana-333 143 2 , , PUNCT cana-333 143 3 it it PRON cana-333 143 4 depicts depict VERB cana-333 143 5 the the DET cana-333 143 6 variation variation NOUN cana-333 143 7 in in ADP cana-333 143 8 velocity velocity NOUN cana-333 143 9 field field NOUN cana-333 143 10 u u NOUN cana-333 143 11 due due ADP cana-333 143 12 to to ADP cana-333 143 13 varying vary VERB cana-333 143 14 values value NOUN cana-333 143 15 of of ADP cana-333 143 16 prandtl prandtl NOUN cana-333 143 17 number number NOUN cana-333 143 18 pr pr NOUN cana-333 143 19 , , PUNCT cana-333 143 20 velocity velocity NOUN cana-333 143 21 field field NOUN cana-333 143 22 u u NOUN cana-333 143 23 is be AUX cana-333 143 24 plotted plot VERB cana-333 143 25 against against ADP cana-333 143 26 y y PRON cana-333 143 27 which which PRON cana-333 143 28 means mean VERB cana-333 143 29 velocity velocity NOUN cana-333 143 30 field field NOUN cana-333 143 31 u u NOUN cana-333 143 32 increases increase VERB cana-333 143 33 sharply sharply ADV cana-333 143 34 for for ADP cana-333 143 35 increase increase NOUN cana-333 143 36 in in ADP cana-333 143 37 y y PROPN cana-333 143 38 and and CCONJ cana-333 143 39 tends tend VERB cana-333 143 40 to to ADP cana-333 143 41 zero zero NUM cana-333 143 42 at at ADP cana-333 143 43 the the DET cana-333 143 44 boundary boundary NOUN cana-333 143 45 . . PUNCT cana-333 144 1 figure4 figure4 ADJ cana-333 144 2 , , PUNCT cana-333 144 3 it it PRON cana-333 144 4 depicts depict VERB cana-333 144 5 the the DET cana-333 144 6 variation variation NOUN cana-333 144 7 in in ADP cana-333 144 8 velocity velocity NOUN cana-333 144 9 field field NOUN cana-333 144 10 u u NOUN cana-333 144 11 due due ADP cana-333 144 12 to to ADP cana-333 144 13 varying vary VERB cana-333 144 14 values value NOUN cana-333 144 15 of of ADP cana-333 144 16 s s PROPN cana-333 144 17 , , PUNCT cana-333 144 18 heat heat NOUN cana-333 144 19 source source NOUN cana-333 144 20 parameter parameter NOUN cana-333 144 21 , , PUNCT cana-333 144 22 velocity velocity NOUN cana-333 144 23 field field NOUN cana-333 144 24 u u NOUN cana-333 144 25 is be AUX cana-333 144 26 taken take VERB cana-333 144 27 against against ADP cana-333 144 28 y y PRON cana-333 144 29 which which PRON cana-333 144 30 means mean VERB cana-333 144 31 velocity velocity NOUN cana-333 144 32 field field NOUN cana-333 144 33 u u NOUN cana-333 144 34 increases increase VERB cana-333 144 35 sharply sharply ADV cana-333 144 36 for for ADP cana-333 144 37 increase increase NOUN cana-333 144 38 in in ADP cana-333 144 39 y y PROPN cana-333 144 40 and and CCONJ cana-333 144 41 approaches approach VERB cana-333 144 42 zero zero NUM cana-333 144 43 at at ADP cana-333 144 44 the the DET cana-333 144 45 boundary boundary NOUN cana-333 144 46 . . PUNCT cana-333 145 1 figure5 figure5 NOUN cana-333 145 2 , , PUNCT cana-333 145 3 it it PRON cana-333 145 4 depicts depict VERB cana-333 145 5 the the DET cana-333 145 6 variation variation NOUN cana-333 145 7 in in ADP cana-333 145 8 velocity velocity NOUN cana-333 145 9 field field NOUN cana-333 145 10 u u NOUN cana-333 145 11 due due ADP cana-333 145 12 to to ADP cana-333 145 13 varying vary VERB cana-333 145 14 values value NOUN cana-333 145 15 of of ADP cana-333 145 16 m m PROPN cana-333 145 17 , , PUNCT cana-333 145 18 magnetic magnetic ADJ cana-333 145 19 parameter parameter NOUN cana-333 145 20 , , PUNCT cana-333 145 21 velocity velocity NOUN cana-333 145 22 field field NOUN cana-333 145 23 u u NOUN cana-333 145 24 is be AUX cana-333 145 25 plotted plot VERB cana-333 145 26 against against ADP cana-333 145 27 y y PRON cana-333 145 28 which which PRON cana-333 145 29 means mean VERB cana-333 145 30 velocity velocity NOUN cana-333 145 31 field field NOUN cana-333 145 32 u u NOUN cana-333 145 33 decreases decrease VERB cana-333 145 34 sharply sharply ADV cana-333 145 35 for for ADP cana-333 145 36 increase increase NOUN cana-333 145 37 in in ADP cana-333 145 38 y y PROPN cana-333 145 39 and and CCONJ cana-333 145 40 finally finally ADV cana-333 145 41 approaches approach VERB cana-333 145 42 zero zero NUM cana-333 145 43 at at ADP cana-333 145 44 the the DET cana-333 145 45 boundary boundary NOUN cana-333 145 46 . . PUNCT cana-333 146 1 figure-6 figure-6 ADV cana-333 146 2 , , PUNCT cana-333 146 3 it it PRON cana-333 146 4 depicts depict VERB cana-333 146 5 the the DET cana-333 146 6 variation variation NOUN cana-333 146 7 in in ADP cana-333 146 8 temperature temperature NOUN cana-333 146 9 field field NOUN cana-333 146 10 u u NOUN cana-333 146 11 due due ADP cana-333 146 12 to to ADP cana-333 146 13 varying vary VERB cana-333 146 14 values value NOUN cana-333 146 15 of of ADP cana-333 146 16 heat heat NOUN cana-333 146 17 source source NOUN cana-333 146 18 parameter parameter NOUN cana-333 146 19 , , PUNCT cana-333 146 20 s s NOUN cana-333 146 21 , , PUNCT cana-333 146 22 temperature temperature NOUN cana-333 146 23 field field NOUN cana-333 146 24 t t PROPN cana-333 146 25 is be AUX cana-333 146 26 plotted plot VERB cana-333 146 27 against against ADP cana-333 146 28 y y PRON cana-333 146 29 which which PRON cana-333 146 30 means mean VERB cana-333 146 31 temperature temperature NOUN cana-333 146 32 field field NOUN cana-333 146 33 t t NOUN cana-333 146 34 decreases decrease VERB cana-333 146 35 sharply sharply ADV cana-333 146 36 for for ADP cana-333 146 37 increase increase NOUN cana-333 146 38 in in ADP cana-333 146 39 value value NOUN cana-333 146 40 of of ADP cana-333 146 41 y y PROPN cana-333 146 42 and and CCONJ cana-333 146 43 approaches approach VERB cana-333 146 44 zero zero NUM cana-333 146 45 at at ADP cana-333 146 46 the the DET cana-333 146 47 boundary boundary NOUN cana-333 146 48 . . PUNCT cana-333 147 1 figure-7 figure-7 NUM cana-333 147 2 , , PUNCT cana-333 147 3 it it PRON cana-333 147 4 depicts depict VERB cana-333 147 5 the the DET cana-333 147 6 variation variation NOUN cana-333 147 7 in in ADP cana-333 147 8 temperature temperature NOUN cana-333 147 9 field field NOUN cana-333 147 10 u u NOUN cana-333 147 11 due due ADP cana-333 147 12 to to ADP cana-333 147 13 varying vary VERB cana-333 147 14 values value NOUN cana-333 147 15 of of ADP cana-333 147 16 prandtl prandtl NOUN cana-333 147 17 number number NOUN cana-333 147 18 , , PUNCT cana-333 147 19 pr pr NOUN cana-333 147 20 , , PUNCT cana-333 147 21 temperature temperature NOUN cana-333 147 22 field field NOUN cana-333 147 23 t t PROPN cana-333 147 24 is be AUX cana-333 147 25 plotted plot VERB cana-333 147 26 against against ADP cana-333 147 27 y y PRON cana-333 147 28 which which PRON cana-333 147 29 means mean VERB cana-333 147 30 temperature temperature NOUN cana-333 147 31 field field NOUN cana-333 147 32 t t NOUN cana-333 147 33 decreases decrease VERB cana-333 147 34 sharply sharply ADV cana-333 147 35 for for ADP cana-333 147 36 increase increase NOUN cana-333 147 37 in in ADP cana-333 147 38 value value NOUN cana-333 147 39 of of ADP cana-333 147 40 y y PROPN cana-333 147 41 and and CCONJ cana-333 147 42 approaches approach VERB cana-333 147 43 zero zero NUM cana-333 147 44 at at ADP cana-333 147 45 the the DET cana-333 147 46 boundary boundary NOUN cana-333 147 47 . . PUNCT cana-333 148 1 table-1 table-1 NUM cana-333 148 2 . . PUNCT cana-333 149 1 it it PRON cana-333 149 2 exhibits exhibit VERB cana-333 149 3 skin skin NOUN cana-333 149 4 - - PUNCT cana-333 149 5 friction friction NOUN cana-333 149 6 value value NOUN cana-333 149 7 𝐢𝑓 𝐢𝑓 PROPN cana-333 149 8 which which PRON cana-333 149 9 increases increase VERB cana-333 149 10 with with ADP cana-333 149 11 increase increase NOUN cana-333 149 12 in in ADP cana-333 149 13 heat heat NOUN cana-333 149 14 source source NOUN cana-333 149 15 parameter parameter PROPN cana-333 149 16 s. s. PROPN cana-333 149 17 nusselt nusselt PROPN cana-333 149 18 number number NOUN cana-333 149 19 decreases decrease VERB cana-333 149 20 on on ADP cana-333 149 21 increase increase NOUN cana-333 149 22 of of ADP cana-333 149 23 heat heat NOUN cana-333 149 24 source source NOUN cana-333 149 25 parameter parameter NOUN cana-333 149 26 , , PUNCT cana-333 149 27 s. s. PROPN cana-333 149 28 table-2 table-2 PROPN cana-333 149 29 . . PUNCT cana-333 150 1 it it PRON cana-333 150 2 shows show VERB cana-333 150 3 an an DET cana-333 150 4 increase increase NOUN cana-333 150 5 in in ADP cana-333 150 6 skin skin NOUN cana-333 150 7 friction friction NOUN cana-333 150 8 𝐢𝑓 𝐢𝑓 PROPN cana-333 150 9 for for ADP cana-333 150 10 increase increase NOUN cana-333 150 11 in in ADP cana-333 150 12 prandtl prandtl NOUN cana-333 150 13 number number NOUN cana-333 150 14 but but CCONJ cana-333 150 15 nusselt nusselt NOUN cana-333 150 16 number number NOUN cana-333 150 17 , , PUNCT cana-333 150 18 nu nu NOUN cana-333 150 19 decreases decrease VERB cana-333 150 20 with with ADP cana-333 150 21 increase increase NOUN cana-333 150 22 in in ADP cana-333 150 23 prandtl prandtl NOUN cana-333 150 24 number number NOUN cana-333 150 25 pr pr NOUN cana-333 150 26 . . PUNCT cana-333 151 1 table-3 table-3 PRON cana-333 151 2 shows show VERB cana-333 151 3 that that PRON cana-333 151 4 increase increase NOUN cana-333 151 5 in in ADP cana-333 151 6 ( ( PUNCT cana-333 151 7 kp kp INTJ cana-333 151 8 ) ) PUNCT cana-333 151 9 permeability permeability NOUN cana-333 151 10 parameter parameter NOUN cana-333 151 11 brings bring VERB cana-333 151 12 about about ADP cana-333 151 13 increase increase NOUN cana-333 151 14 in in ADP cana-333 151 15 skin skin NOUN cana-333 151 16 friction friction NOUN cana-333 152 1 𝐢𝑓 𝐢𝑓 PROPN cana-333 153 1 but but CCONJ cana-333 153 2 there there PRON cana-333 153 3 occurs occur VERB cana-333 153 4 no no DET cana-333 153 5 change change NOUN cana-333 153 6 in in ADP cana-333 153 7 value value NOUN cana-333 153 8 of of ADP cana-333 153 9 nusselt nusselt NOUN cana-333 153 10 number number NOUN cana-333 153 11 due due ADP cana-333 153 12 to to PART cana-333 153 13 increase increase VERB cana-333 153 14 in in ADP cana-333 153 15 kp kp NOUN cana-333 153 16 . . PUNCT cana-333 154 1 table-4 table-4 PROPN cana-333 154 2 . . PUNCT cana-333 155 1 increase increase NOUN cana-333 155 2 in in ADP cana-333 155 3 m m PROPN cana-333 155 4 , , PUNCT cana-333 155 5 magnetic magnetic ADJ cana-333 155 6 parameter parameter NOUN cana-333 155 7 causes cause VERB cana-333 155 8 decrease decrease NOUN cana-333 155 9 in in ADP cana-333 155 10 skin skin NOUN cana-333 155 11 - - PUNCT cana-333 155 12 friction friction NOUN cana-333 155 13 𝐢𝑓 𝐢𝑓 PROPN cana-333 155 14 but but CCONJ cana-333 155 15 its its PRON cana-333 155 16 increase increase NOUN cana-333 155 17 brings bring VERB cana-333 155 18 about about ADP cana-333 155 19 no no DET cana-333 155 20 change change NOUN cana-333 155 21 in in ADP cana-333 155 22 nusselt nusselt NOUN cana-333 155 23 number number NOUN cana-333 155 24 . . PUNCT cana-333 156 1 table-5 table-5 PROPN cana-333 156 2 . . PUNCT cana-333 156 3 increasing increase VERB cana-333 156 4 value value NOUN cana-333 156 5 of of ADP cana-333 156 6 grashof grashof ADJ cana-333 156 7 number number NOUN cana-333 156 8 causes cause VERB cana-333 156 9 decrease decrease NOUN cana-333 156 10 in in ADP cana-333 156 11 𝐢𝑓 𝐢𝑓 PROPN cana-333 156 12 whereas whereas SCONJ cana-333 156 13 no no DET cana-333 156 14 change change NOUN cana-333 156 15 occurs occur VERB cana-333 156 16 in in ADP cana-333 156 17 case case NOUN cana-333 156 18 of of ADP cana-333 156 19 nusselt nusselt NOUN cana-333 156 20 number number NOUN cana-333 156 21 . . PUNCT cana-333 157 1 figure-1 figure-1 PROPN cana-333 157 2 . . PUNCT cana-333 158 1 at at ADP cana-333 158 2 s=0.1 s=0.1 NOUN cana-333 158 3 , , PUNCT cana-333 158 4 m=2 m=2 PROPN cana-333 158 5 , , PUNCT cana-333 158 6 pr=1,kp=0.1,w=0.2 pr=1,kp=0.1,w=0.2 PROPN cana-333 158 7 , , PUNCT cana-333 158 8 exp=2.7183 exp=2.7183 NUM cana-333 158 9 , , PUNCT cana-333 158 10 t=0.5 t=0.5 X cana-333 158 11 , , PUNCT cana-333 158 12 rc=0.1,gr=0.3 rc=0.1,gr=0.3 PROPN cana-333 158 13 grashof grashof ADJ cana-333 158 14 number number NOUN cana-333 158 15 brings bring VERB cana-333 158 16 about about ADP cana-333 158 17 variation variation NOUN cana-333 158 18 in in ADP cana-333 158 19 velocity velocity NOUN cana-333 158 20 communications communication NOUN cana-333 158 21 on on ADP cana-333 158 22 applied apply VERB cana-333 158 23 nonlinear nonlinear ADJ cana-333 158 24 analysis analysis NOUN cana-333 158 25 issn issn NOUN cana-333 158 26 : : PUNCT cana-333 158 27 1074 1074 NUM cana-333 158 28 - - PUNCT cana-333 158 29 133x 133x NUM cana-333 158 30 vol vol NOUN cana-333 158 31 31 31 NUM cana-333 158 32 no no NOUN cana-333 158 33 . . NOUN cana-333 158 34 1 1 NUM cana-333 158 35 ( ( PUNCT cana-333 158 36 2024 2024 NUM cana-333 158 37 ) ) PUNCT cana-333 158 38 111 111 NUM cana-333 158 39 https://internationalpubls.com https://internationalpubls.com X cana-333 158 40 figure-2 figure-2 PROPN cana-333 158 41 . . PUNCT cana-333 159 1 at at ADP cana-333 159 2 s=0.1 s=0.1 NOUN cana-333 159 3 , , PUNCT cana-333 159 4 m=2 m=2 PROPN cana-333 159 5 , , PUNCT cana-333 159 6 pr=1,kp=0.1,w=0.2 pr=1,kp=0.1,w=0.2 PROPN cana-333 159 7 , , PUNCT cana-333 159 8 exp=2.7183 exp=2.7183 NUM cana-333 159 9 , , PUNCT cana-333 159 10 t=0.5 t=0.5 X cana-333 159 11 , , PUNCT cana-333 159 12 rc=0.1,gr=0.3 rc=0.1,gr=0.3 PROPN cana-333 159 13 permeability permeability NOUN cana-333 159 14 parameter parameter NOUN cana-333 159 15 brings bring VERB cana-333 159 16 about about ADP cana-333 159 17 variation variation NOUN cana-333 159 18 in in ADP cana-333 159 19 velocity velocity NOUN cana-333 159 20 figure-3 figure-3 NUM cana-333 159 21 . . PUNCT cana-333 160 1 at at ADP cana-333 160 2 s=0.1 s=0.1 NOUN cana-333 160 3 , , PUNCT cana-333 160 4 m=2 m=2 PROPN cana-333 160 5 , , PUNCT cana-333 160 6 pr=1,kp=0.1,w=0.2 pr=1,kp=0.1,w=0.2 PROPN cana-333 160 7 , , PUNCT cana-333 160 8 exp=2.7183 exp=2.7183 NUM cana-333 160 9 , , PUNCT cana-333 160 10 t=0.5 t=0.5 X cana-333 160 11 , , PUNCT cana-333 160 12 rc=0.1,gr=0.3 rc=0.1,gr=0.3 PROPN cana-333 160 13 prandtl prandtl NOUN cana-333 160 14 number number NOUN cana-333 160 15 brings bring VERB cana-333 160 16 about about ADP cana-333 160 17 variation variation NOUN cana-333 160 18 in in ADP cana-333 160 19 velocity velocity NOUN cana-333 160 20 figure-4 figure-4 PROPN cana-333 160 21 . . PUNCT cana-333 161 1 at at ADP cana-333 161 2 s=0.1 s=0.1 NOUN cana-333 161 3 , , PUNCT cana-333 161 4 m=2 m=2 PROPN cana-333 161 5 , , PUNCT cana-333 161 6 pr=1,kp=0.1,w=0.2 pr=1,kp=0.1,w=0.2 PROPN cana-333 161 7 , , PUNCT cana-333 161 8 exp=2.7183 exp=2.7183 NUM cana-333 161 9 , , PUNCT cana-333 161 10 t=0.5 t=0.5 X cana-333 161 11 , , PUNCT cana-333 161 12 rc=0.1,gr=0.3 rc=0.1,gr=0.3 PROPN cana-333 161 13 heat heat NOUN cana-333 161 14 source source NOUN cana-333 161 15 parameter parameter NOUN cana-333 161 16 brings bring VERB cana-333 161 17 about about ADP cana-333 161 18 variation variation NOUN cana-333 161 19 in in ADP cana-333 161 20 velocity velocity NOUN cana-333 161 21 communications communication NOUN cana-333 161 22 on on ADP cana-333 161 23 applied apply VERB cana-333 161 24 nonlinear nonlinear ADJ cana-333 161 25 analysis analysis NOUN cana-333 161 26 issn issn NOUN cana-333 161 27 : : PUNCT cana-333 161 28 1074 1074 NUM cana-333 161 29 - - PUNCT cana-333 161 30 133x 133x NUM cana-333 161 31 vol vol NOUN cana-333 161 32 31 31 NUM cana-333 161 33 no no NOUN cana-333 161 34 . . NOUN cana-333 161 35 1 1 NUM cana-333 161 36 ( ( PUNCT cana-333 161 37 2024 2024 NUM cana-333 161 38 ) ) PUNCT cana-333 161 39 112 112 NUM cana-333 161 40 https://internationalpubls.com https://internationalpubls.com X cana-333 161 41 figure-5 figure-5 PROPN cana-333 161 42 . . PUNCT cana-333 162 1 at at ADP cana-333 162 2 s=0.1 s=0.1 NOUN cana-333 162 3 , , PUNCT cana-333 162 4 m=2 m=2 PROPN cana-333 162 5 , , PUNCT cana-333 162 6 pr=1,kp=0.1,w=0.2 pr=1,kp=0.1,w=0.2 PROPN cana-333 162 7 , , PUNCT cana-333 162 8 exp=2.7183 exp=2.7183 NUM cana-333 162 9 , , PUNCT cana-333 162 10 t=0.5 t=0.5 X cana-333 162 11 , , PUNCT cana-333 162 12 rc=0.1,gr=0.3 rc=0.1,gr=0.3 PROPN cana-333 162 13 magnetic magnetic ADJ cana-333 162 14 parameter parameter NOUN cana-333 162 15 brings bring VERB cana-333 162 16 about about ADP cana-333 162 17 variation variation NOUN cana-333 162 18 in in ADP cana-333 162 19 velocity velocity NOUN cana-333 162 20 figure-6 figure-6 PROPN cana-333 162 21 . . PUNCT cana-333 163 1 at at ADP cana-333 163 2 s=0.1 s=0.1 NOUN cana-333 163 3 , , PUNCT cana-333 163 4 m=2 m=2 PROPN cana-333 163 5 , , PUNCT cana-333 163 6 pr=1,kp=0.1,w=0.2 pr=1,kp=0.1,w=0.2 PROPN cana-333 163 7 , , PUNCT cana-333 163 8 exp=2.7183 exp=2.7183 NUM cana-333 163 9 , , PUNCT cana-333 163 10 t=0.5 t=0.5 X cana-333 163 11 , , PUNCT cana-333 163 12 rc=0.1,gr=0.3 rc=0.1,gr=0.3 PROPN cana-333 163 13 heat heat NOUN cana-333 163 14 source source NOUN cana-333 163 15 parameter parameter NOUN cana-333 163 16 brings bring VERB cana-333 163 17 about about ADP cana-333 163 18 variation variation NOUN cana-333 163 19 in in ADP cana-333 163 20 temperature temperature NOUN cana-333 163 21 figure-7 figure-7 PROPN cana-333 163 22 . . PUNCT cana-333 164 1 at at ADP cana-333 164 2 s=0.1 s=0.1 NOUN cana-333 164 3 , , PUNCT cana-333 164 4 m=2 m=2 PROPN cana-333 164 5 , , PUNCT cana-333 164 6 pr=1,kp=0.1,w=0.2 pr=1,kp=0.1,w=0.2 PROPN cana-333 164 7 , , PUNCT cana-333 164 8 exp=2.7183 exp=2.7183 NUM cana-333 164 9 , , PUNCT cana-333 164 10 t=0.5 t=0.5 X cana-333 164 11 , , PUNCT cana-333 164 12 rc=0.1,gr=0.3 rc=0.1,gr=0.3 PROPN cana-333 164 13 communications communication NOUN cana-333 164 14 on on ADP cana-333 164 15 applied apply VERB cana-333 164 16 nonlinear nonlinear ADJ cana-333 164 17 analysis analysis NOUN cana-333 164 18 issn issn NOUN cana-333 164 19 : : PUNCT cana-333 164 20 1074 1074 NUM cana-333 164 21 - - PUNCT cana-333 164 22 133x 133x NUM cana-333 164 23 vol vol NOUN cana-333 164 24 31 31 NUM cana-333 164 25 no no NOUN cana-333 164 26 . . NOUN cana-333 164 27 1 1 NUM cana-333 164 28 ( ( PUNCT cana-333 164 29 2024 2024 NUM cana-333 164 30 ) ) PUNCT cana-333 164 31 113 113 NUM cana-333 164 32 https://internationalpubls.com https://internationalpubls.com X cana-333 164 33 prandtl prandtl NOUN cana-333 164 34 number number NOUN cana-333 164 35 brings bring VERB cana-333 164 36 about about ADP cana-333 164 37 variation variation NOUN cana-333 164 38 in in ADP cana-333 164 39 temperature temperature NOUN cana-333 164 40 . . PUNCT cana-333 165 1 table table NOUN cana-333 165 2 1 1 NUM cana-333 165 3 . . PUNCT cana-333 165 4 effect effect NOUN cana-333 165 5 of of ADP cana-333 165 6 s s PRON cana-333 165 7 on on ADP cana-333 165 8 skin skin NOUN cana-333 165 9 friction friction NOUN cana-333 165 10 , , PUNCT cana-333 165 11 nusselt nusselt NOUN cana-333 165 12 number number NOUN cana-333 165 13 , , PUNCT cana-333 165 14 t= t= NOUN cana-333 165 15 0.5 0.5 NUM cana-333 165 16 , , PUNCT cana-333 165 17 exp=2.7183 exp=2.7183 NUM cana-333 165 18 , , PUNCT cana-333 165 19 w=0.2 w=0.2 X cana-333 165 20 s s AUX cana-333 165 21 pr pr X cana-333 165 22 kp kp PROPN cana-333 165 23 m m VERB cana-333 165 24 gr gr PROPN cana-333 165 25 rc rc PROPN cana-333 165 26 cf cf NOUN cana-333 165 27 nu nu PROPN cana-333 165 28 0.1 0.1 NUM cana-333 165 29 1 1 NUM cana-333 165 30 0.1 0.1 NUM cana-333 165 31 2 2 NUM cana-333 165 32 0.3 0.3 NUM cana-333 165 33 0.1 0.1 NUM cana-333 165 34 -2.1949 -2.1949 NOUN cana-333 165 35 -1.0891 -1.0891 NOUN cana-333 165 36 0.2 0.2 NUM cana-333 165 37 1 1 NUM cana-333 165 38 0.1 0.1 NUM cana-333 165 39 2 2 NUM cana-333 165 40 0.3 0.3 NUM cana-333 165 41 0.1 0.1 NUM cana-333 165 42 -2.1936 -2.1936 NOUN cana-333 165 43 -1.1675 -1.1675 VERB cana-333 165 44 0.3 0.3 NUM cana-333 165 45 1 1 NUM cana-333 165 46 0.1 0.1 NUM cana-333 165 47 2 2 NUM cana-333 165 48 0.3 0.3 NUM cana-333 165 49 0.1 0.1 NUM cana-333 165 50 -2.1925 -2.1925 NOUN cana-333 165 51 -1.2377 -1.2377 NOUN cana-333 165 52 table table NOUN cana-333 165 53 2 2 NUM cana-333 165 54 . . PUNCT cana-333 165 55 effect effect NOUN cana-333 165 56 of of ADP cana-333 165 57 pr pr NOUN cana-333 165 58 on on ADP cana-333 165 59 skin skin NOUN cana-333 165 60 friction friction NOUN cana-333 165 61 , , PUNCT cana-333 165 62 nusselt nusselt NOUN cana-333 165 63 number number NOUN cana-333 165 64 , , PUNCT cana-333 165 65 t= t= NOUN cana-333 165 66 0.5 0.5 NUM cana-333 165 67 , , PUNCT cana-333 165 68 exp=2.7183 exp=2.7183 NUM cana-333 165 69 , , PUNCT cana-333 165 70 w=0.2 w=0.2 X cana-333 165 71 s s AUX cana-333 165 72 pr pr X cana-333 165 73 kp kp PROPN cana-333 165 74 m m VERB cana-333 165 75 gr gr PROPN cana-333 165 76 rc rc PROPN cana-333 165 77 cf cf NOUN cana-333 165 78 nu nu PROPN cana-333 165 79 0.1 0.1 NUM cana-333 165 80 1 1 NUM cana-333 165 81 0.1 0.1 NUM cana-333 165 82 2 2 NUM cana-333 165 83 0.3 0.3 NUM cana-333 165 84 0.1 0.1 NUM cana-333 165 85 -2.1949 -2.1949 NOUN cana-333 165 86 -1.0891 -1.0891 NOUN cana-333 165 87 0.1 0.1 NUM cana-333 165 88 2.5 2.5 NUM cana-333 165 89 0.1 0.1 NUM cana-333 165 90 2 2 NUM cana-333 165 91 0.3 0.3 NUM cana-333 165 92 0.1 0.1 NUM cana-333 165 93 -2.1635 -2.1635 NOUN cana-333 165 94 -2.5863 -2.5863 NOUN cana-333 165 95 0.1 0.1 NUM cana-333 165 96 9 9 NUM cana-333 165 97 0.1 0.1 NUM cana-333 165 98 2 2 NUM cana-333 165 99 0.3 0.3 NUM cana-333 165 100 0.1 0.1 NUM cana-333 165 101 -2.1168 -2.1168 NOUN cana-333 165 102 -8.8073 -8.8073 NOUN cana-333 165 103 table table NOUN cana-333 165 104 3 3 NUM cana-333 165 105 . . PUNCT cana-333 165 106 effect effect NOUN cana-333 165 107 of of ADP cana-333 165 108 kp kp PROPN cana-333 165 109 on on ADP cana-333 165 110 skin skin NOUN cana-333 165 111 friction friction NOUN cana-333 165 112 , , PUNCT cana-333 165 113 nusselt nusselt NOUN cana-333 165 114 number number NOUN cana-333 165 115 , , PUNCT cana-333 165 116 t= t= NOUN cana-333 165 117 0.5 0.5 NUM cana-333 165 118 , , PUNCT cana-333 165 119 exp=2.7183 exp=2.7183 NUM cana-333 165 120 , , PUNCT cana-333 165 121 w=0.2 w=0.2 X cana-333 165 122 s s AUX cana-333 165 123 pr pr X cana-333 165 124 kp kp PROPN cana-333 165 125 m m VERB cana-333 165 126 gr gr PROPN cana-333 165 127 rc rc PROPN cana-333 165 128 cf cf NOUN cana-333 165 129 nu nu PROPN cana-333 165 130 0.1 0.1 NUM cana-333 165 131 1 1 NUM cana-333 165 132 0.1 0.1 NUM cana-333 165 133 2 2 NUM cana-333 165 134 0.3 0.3 NUM cana-333 165 135 0.1 0.1 NUM cana-333 165 136 -2.1949 -2.1949 NOUN cana-333 165 137 -1.0891 -1.0891 NOUN cana-333 165 138 0.1 0.1 NUM cana-333 165 139 1 1 NUM cana-333 165 140 0.3 0.3 NUM cana-333 165 141 2 2 NUM cana-333 165 142 0.3 0.3 NUM cana-333 165 143 0.1 0.1 NUM cana-333 165 144 -1.7072 -1.7072 NOUN cana-333 165 145 -1.0891 -1.0891 NOUN cana-333 165 146 0.1 0.1 NUM cana-333 165 147 1 1 NUM cana-333 165 148 0.6 0.6 NUM cana-333 165 149 2 2 NUM cana-333 165 150 0.3 0.3 NUM cana-333 165 151 0.1 0.1 NUM cana-333 165 152 -1.5562 -1.5562 ADJ cana-333 165 153 -0.0891 -0.0891 ADJ cana-333 165 154 table table NOUN cana-333 165 155 4 4 NUM cana-333 165 156 . . PUNCT cana-333 165 157 effect effect NOUN cana-333 165 158 of of ADP cana-333 165 159 m m PROPN cana-333 165 160 on on ADP cana-333 165 161 skin skin NOUN cana-333 165 162 friction friction NOUN cana-333 165 163 , , PUNCT cana-333 165 164 nusselt nusselt NOUN cana-333 165 165 number number NOUN cana-333 165 166 , , PUNCT cana-333 165 167 t= t= NOUN cana-333 165 168 0.5 0.5 NUM cana-333 165 169 , , PUNCT cana-333 165 170 exp=2.7183 exp=2.7183 NUM cana-333 165 171 , , PUNCT cana-333 165 172 w=0.2 w=0.2 X cana-333 165 173 s s AUX cana-333 165 174 pr pr X cana-333 165 175 kp kp PROPN cana-333 165 176 m m VERB cana-333 165 177 gr gr PROPN cana-333 165 178 rc rc PROPN cana-333 165 179 cf cf NOUN cana-333 165 180 nu nu PROPN cana-333 165 181 0.1 0.1 NUM cana-333 165 182 1 1 NUM cana-333 165 183 0.1 0.1 NUM cana-333 165 184 2 2 NUM cana-333 165 185 0.3 0.3 NUM cana-333 165 186 0.1 0.1 NUM cana-333 165 187 -2.1949 -2.1949 NOUN cana-333 165 188 -1.0891 -1.0891 NOUN cana-333 165 189 0.1 0.1 NUM cana-333 165 190 1 1 NUM cana-333 165 191 0.1 0.1 NUM cana-333 165 192 4 4 NUM cana-333 165 193 0.3 0.3 NUM cana-333 165 194 0.1 0.1 NUM cana-333 165 195 -2.8498 -2.8498 NOUN cana-333 165 196 -1.0891 -1.0891 NOUN cana-333 165 197 0.1 0.1 NUM cana-333 165 198 1 1 NUM cana-333 165 199 0.1 0.1 NUM cana-333 165 200 5 5 NUM cana-333 165 201 0.3 0.3 NUM cana-333 165 202 0.1 0.1 NUM cana-333 165 203 -3.2482 -3.2482 PUNCT cana-333 165 204 -1.0891 -1.0891 PROPN cana-333 165 205 table table NOUN cana-333 165 206 5 5 NUM cana-333 165 207 . . PUNCT cana-333 165 208 effect effect NOUN cana-333 165 209 of of ADP cana-333 165 210 gr gr NOUN cana-333 165 211 on on ADP cana-333 165 212 skin skin NOUN cana-333 165 213 friction friction NOUN cana-333 165 214 , , PUNCT cana-333 165 215 nusselt nusselt NOUN cana-333 165 216 number number NOUN cana-333 165 217 , , PUNCT cana-333 165 218 t= t= NOUN cana-333 165 219 0.5 0.5 NUM cana-333 165 220 , , PUNCT cana-333 165 221 exp=2.7183 exp=2.7183 NUM cana-333 165 222 , , PUNCT cana-333 165 223 w=0.2 w=0.2 X cana-333 165 224 s s AUX cana-333 165 225 pr pr X cana-333 165 226 kp kp PROPN cana-333 165 227 m m VERB cana-333 165 228 gr gr PROPN cana-333 165 229 rc rc PROPN cana-333 165 230 cf cf NOUN cana-333 165 231 nu nu PROPN cana-333 165 232 0.1 0.1 NUM cana-333 165 233 1 1 NUM cana-333 165 234 0.1 0.1 NUM cana-333 165 235 2 2 NUM cana-333 165 236 0.3 0.3 NUM cana-333 165 237 0.1 0.1 NUM cana-333 165 238 -2.1949 -2.1949 NOUN cana-333 165 239 -1.0891 -1.0891 NOUN cana-333 165 240 0.2 0.2 NUM cana-333 165 241 1 1 NUM cana-333 165 242 0.1 0.1 NUM cana-333 165 243 2 2 NUM cana-333 165 244 0.7 0.7 NUM cana-333 165 245 0.1 0.1 NUM cana-333 165 246 -2.2857 -2.2857 NOUN cana-333 165 247 -1.0891 -1.0891 NOUN cana-333 165 248 0.3 0.3 NUM cana-333 165 249 1 1 NUM cana-333 165 250 0.1 0.1 NUM cana-333 165 251 2 2 NUM cana-333 165 252 0.9 0.9 NUM cana-333 165 253 0.1 0.1 NUM cana-333 165 254 -2.3311 -2.3311 NOUN cana-333 165 255 -1.0891 -1.0891 NOUN cana-333 165 256 7 7 NUM cana-333 165 257 . . X cana-333 165 258 conclusion conclusion NOUN cana-333 165 259 β€’ β€’ NOUN cana-333 165 260 velocity velocity NOUN cana-333 165 261 profile profile NOUN cana-333 165 262 value value NOUN cana-333 165 263 decreases decrease VERB cana-333 165 264 for for ADP cana-333 165 265 increase increase NOUN cana-333 165 266 in in ADP cana-333 165 267 grashof grashof ADJ cana-333 165 268 number number NOUN cana-333 165 269 . . PUNCT cana-333 166 1 β€’ β€’ NOUN cana-333 166 2 velocity velocity NOUN cana-333 166 3 field field NOUN cana-333 166 4 value value NOUN cana-333 166 5 decreases decrease VERB cana-333 166 6 for for ADP cana-333 166 7 increase increase NOUN cana-333 166 8 in in ADP cana-333 166 9 magnetic magnetic ADJ cana-333 166 10 parameter parameter NOUN cana-333 166 11 ( ( PUNCT cana-333 166 12 m m NOUN cana-333 166 13 ) ) PUNCT cana-333 166 14 value value NOUN cana-333 166 15 . . PUNCT cana-333 167 1 β€’ β€’ NOUN cana-333 167 2 velocity velocity NOUN cana-333 167 3 field field NOUN cana-333 167 4 increases increase VERB cana-333 167 5 for for ADP cana-333 167 6 increasing increase VERB cana-333 167 7 prandtl prandtl NOUN cana-333 167 8 number number NOUN cana-333 167 9 ( ( PUNCT cana-333 167 10 pr pr NOUN cana-333 167 11 ) ) PUNCT cana-333 167 12 , , PUNCT cana-333 167 13 heat heat NOUN cana-333 167 14 source source NOUN cana-333 167 15 ( ( PUNCT cana-333 167 16 s s NOUN cana-333 167 17 ) ) PUNCT cana-333 167 18 and and CCONJ cana-333 167 19 permeability permeability NOUN cana-333 167 20 ( ( PUNCT cana-333 167 21 kp kp PROPN cana-333 167 22 ) ) PUNCT cana-333 167 23 . . PUNCT cana-333 168 1 β€’ β€’ NOUN cana-333 168 2 skin skin NOUN cana-333 168 3 - - PUNCT cana-333 168 4 friction friction NOUN cana-333 168 5 decreases decrease NOUN cana-333 168 6 for for ADP cana-333 168 7 increase increase NOUN cana-333 168 8 of of ADP cana-333 168 9 magnetic magnetic ADJ cana-333 168 10 field field NOUN cana-333 168 11 , , PUNCT cana-333 168 12 m m PRON cana-333 168 13 and and CCONJ cana-333 168 14 grashof grashof ADJ cana-333 168 15 number number NOUN cana-333 168 16 , , PUNCT cana-333 168 17 gr gr NOUN cana-333 168 18 . . NOUN cana-333 168 19 β€’ β€’ NOUN cana-333 168 20 nusselt nusselt NOUN cana-333 168 21 number number NOUN cana-333 168 22 faces face NOUN cana-333 168 23 decrease decrease NOUN cana-333 168 24 due due ADJ cana-333 168 25 to to PART cana-333 168 26 increase increase VERB cana-333 168 27 in in ADP cana-333 168 28 prandlt prandlt PROPN cana-333 168 29 number number NOUN cana-333 168 30 pr pr NOUN cana-333 168 31 and and CCONJ cana-333 168 32 heat heat NOUN cana-333 168 33 source source NOUN cana-333 168 34 parameter parameter PROPN cana-333 168 35 s. s. PROPN cana-333 168 36 communications communications PROPN cana-333 168 37 on on ADP cana-333 168 38 applied apply VERB cana-333 168 39 nonlinear nonlinear ADJ cana-333 168 40 analysis analysis NOUN cana-333 168 41 issn issn NOUN cana-333 168 42 : : PUNCT cana-333 168 43 1074 1074 NUM cana-333 168 44 - - PUNCT cana-333 168 45 133x 133x NUM cana-333 168 46 vol vol NOUN cana-333 168 47 31 31 NUM cana-333 168 48 no no NOUN cana-333 168 49 . . NOUN cana-333 168 50 1 1 NUM cana-333 168 51 ( ( PUNCT cana-333 168 52 2024 2024 NUM cana-333 168 53 ) ) PUNCT cana-333 168 54 114 114 NUM cana-333 168 55 https://internationalpubls.com https://internationalpubls.com X cana-333 168 56 β€’ β€’ NOUN cana-333 168 57 skin skin NOUN cana-333 168 58 friction friction NOUN cana-333 168 59 increases increase VERB cana-333 168 60 as as ADP cana-333 168 61 heat heat NOUN cana-333 168 62 source source NOUN cana-333 168 63 ( ( PUNCT cana-333 168 64 s s NOUN cana-333 168 65 ) ) PUNCT cana-333 168 66 , , PUNCT cana-333 168 67 prandtl prandtl NOUN cana-333 168 68 number number NOUN cana-333 168 69 ( ( PUNCT cana-333 168 70 pr pr NOUN cana-333 168 71 ) ) PUNCT cana-333 168 72 and and CCONJ cana-333 168 73 permeability permeability NOUN cana-333 168 74 ( ( PUNCT cana-333 168 75 kp kp INTJ cana-333 168 76 ) ) PUNCT cana-333 168 77 increase increase NOUN cana-333 168 78 . . PUNCT cana-333 169 1 β€’ β€’ NOUN cana-333 169 2 temperature temperature NOUN cana-333 169 3 profile profile NOUN cana-333 169 4 faces face VERB cana-333 169 5 decrease decrease VERB cana-333 169 6 due due ADJ cana-333 169 7 to to PART cana-333 169 8 increase increase VERB cana-333 169 9 in in ADP cana-333 169 10 s s PROPN cana-333 169 11 , , PUNCT cana-333 169 12 heat heat NOUN cana-333 169 13 source source NOUN cana-333 169 14 parameter parameter NOUN cana-333 169 15 , , PUNCT cana-333 169 16 pr pr NOUN cana-333 169 17 , , PUNCT cana-333 169 18 prandlt prandlt PROPN cana-333 169 19 number number NOUN cana-333 169 20 . . PUNCT cana-333 170 1 references reference NOUN cana-333 170 2 [ [ X cana-333 170 3 1 1 NUM cana-333 170 4 ] ] X cana-333 170 5 patil patil PROPN cana-333 170 6 , , PUNCT cana-333 170 7 p. p. NOUN cana-333 170 8 m. m. NOUN cana-333 170 9 , , PUNCT cana-333 170 10 & & CCONJ cana-333 170 11 kulkarni kulkarni PROPN cana-333 170 12 , , PUNCT cana-333 170 13 p. p. PROPN cana-333 170 14 s. s. PROPN cana-333 170 15 ( ( PUNCT cana-333 170 16 2008 2008 NUM cana-333 170 17 ) ) PUNCT cana-333 170 18 . . PUNCT cana-333 171 1 effects effect NOUN cana-333 171 2 of of ADP cana-333 171 3 chemical chemical ADJ cana-333 171 4 reaction reaction NOUN cana-333 171 5 on on ADP cana-333 171 6 free free ADJ cana-333 171 7 convective convective ADJ cana-333 171 8 flow flow NOUN cana-333 171 9 of of ADP cana-333 171 10 a a DET cana-333 171 11 polar polar ADJ cana-333 171 12 fluid fluid NOUN cana-333 171 13 through through ADP cana-333 171 14 a a DET cana-333 171 15 porous porous ADJ cana-333 171 16 medium medium NOUN cana-333 171 17 in in ADP cana-333 171 18 the the DET cana-333 171 19 presence presence NOUN cana-333 171 20 of of ADP cana-333 171 21 internal internal ADJ cana-333 171 22 heat heat NOUN cana-333 171 23 generation generation NOUN cana-333 171 24 . . PUNCT cana-333 172 1 international international ADJ cana-333 172 2 journal journal PROPN cana-333 172 3 of of ADP cana-333 172 4 thermal thermal ADJ cana-333 172 5 sciences science NOUN cana-333 172 6 , , PUNCT cana-333 172 7 47(8 47(8 NOUN cana-333 172 8 ) ) PUNCT cana-333 172 9 , , PUNCT cana-333 172 10 1043 1043 NUM cana-333 172 11 - - SYM cana-333 172 12 1054 1054 NUM cana-333 172 13 . . PUNCT cana-333 173 1 [ [ X cana-333 173 2 2 2 NUM cana-333 173 3 ] ] X cana-333 173 4 zainali zainali NUM cana-333 173 5 , , PUNCT cana-333 173 6 a. a. NOUN cana-333 173 7 , , PUNCT cana-333 173 8 tofighi tofighi PROPN cana-333 173 9 , , PUNCT cana-333 173 10 n. n. NOUN cana-333 173 11 , , PUNCT cana-333 173 12 shadloo shadloo NOUN cana-333 173 13 , , PUNCT cana-333 173 14 m. m. NOUN cana-333 173 15 s. s. PROPN cana-333 173 16 , , PUNCT cana-333 173 17 & & CCONJ cana-333 173 18 yildiz yildiz PROPN cana-333 173 19 , , PUNCT cana-333 173 20 m. m. NOUN cana-333 173 21 ( ( PUNCT cana-333 173 22 2013 2013 NUM cana-333 173 23 ) ) PUNCT cana-333 173 24 . . PUNCT cana-333 174 1 numerical numerical PROPN cana-333 174 2 investigation investigation NOUN cana-333 174 3 of of ADP cana-333 174 4 newtonian newtonian ADJ cana-333 174 5 and and CCONJ cana-333 174 6 non non ADJ cana-333 174 7 - - ADJ cana-333 174 8 newtonian newtonian ADJ cana-333 174 9 multiphase multiphase NOUN cana-333 174 10 flows flow NOUN cana-333 174 11 using use VERB cana-333 174 12 isph isph NOUN cana-333 174 13 method method NOUN cana-333 174 14 . . PUNCT cana-333 175 1 computer computer NOUN cana-333 175 2 methods method NOUN cana-333 175 3 in in ADP cana-333 175 4 applied applied ADJ cana-333 175 5 mechanics mechanic NOUN cana-333 175 6 and and CCONJ cana-333 175 7 engineering engineering NOUN cana-333 175 8 , , PUNCT cana-333 175 9 254 254 NUM cana-333 175 10 , , PUNCT cana-333 175 11 99 99 NUM cana-333 175 12 - - SYM cana-333 175 13 113 113 NUM cana-333 175 14 . . PUNCT cana-333 176 1 [ [ X cana-333 176 2 3 3 NUM cana-333 176 3 ] ] PUNCT cana-333 176 4 mohanty mohanty PROPN cana-333 176 5 , , PUNCT cana-333 176 6 b. b. PROPN cana-333 176 7 , , PUNCT cana-333 176 8 mishra mishra PROPN cana-333 176 9 , , PUNCT cana-333 176 10 s. s. PROPN cana-333 176 11 r. r. PROPN cana-333 176 12 , , PUNCT cana-333 176 13 & & CCONJ cana-333 176 14 pattnaik pattnaik PROPN cana-333 176 15 , , PUNCT cana-333 176 16 h. h. PROPN cana-333 176 17 b. b. PROPN cana-333 176 18 ( ( PUNCT cana-333 176 19 2014 2014 NUM cana-333 176 20 ) ) PUNCT cana-333 176 21 . . PUNCT cana-333 177 1 mhd mhd NOUN cana-333 177 2 flow flow NOUN cana-333 177 3 of of ADP cana-333 177 4 a a DET cana-333 177 5 viscoelastic viscoelastic ADJ cana-333 177 6 fluid fluid NOUN cana-333 177 7 through through ADP cana-333 177 8 non non ADJ cana-333 177 9 homogeneous homogeneous ADJ cana-333 177 10 porous porous ADJ cana-333 177 11 medium medium NOUN cana-333 177 12 with with ADP cana-333 177 13 oscillatory oscillatory ADJ cana-333 177 14 suction suction NOUN cana-333 177 15 and and CCONJ cana-333 177 16 heat heat NOUN cana-333 177 17 source source NOUN cana-333 177 18 / / SYM cana-333 177 19 sink sink NOUN cana-333 177 20 . . PUNCT cana-333 178 1 int int PROPN cana-333 179 1 j j PROPN cana-333 179 2 math math PROPN cana-333 179 3 educ educ PROPN cana-333 179 4 , , PUNCT cana-333 179 5 4 4 NUM cana-333 179 6 , , PUNCT cana-333 179 7 21 21 NUM cana-333 179 8 - - SYM cana-333 179 9 34 34 NUM cana-333 179 10 . . PUNCT cana-333 180 1 [ [ X cana-333 180 2 4 4 NUM cana-333 180 3 ] ] X cana-333 180 4 prasad prasad PROPN cana-333 180 5 , , PUNCT cana-333 180 6 v. v. PROPN cana-333 180 7 r. r. PROPN cana-333 180 8 , , PUNCT cana-333 180 9 gaffar gaffar PROPN cana-333 180 10 , , PUNCT cana-333 180 11 s. s. PROPN cana-333 180 12 a. a. PROPN cana-333 180 13 , , PUNCT cana-333 180 14 reddy reddy PROPN cana-333 180 15 , , PUNCT cana-333 180 16 e. e. PROPN cana-333 180 17 k. k. PROPN cana-333 180 18 , , PUNCT cana-333 180 19 & & CCONJ cana-333 180 20 bΓ©g bΓ©g PROPN cana-333 180 21 , , PUNCT cana-333 180 22 o. o. NOUN cana-333 180 23 a. a. NOUN cana-333 180 24 ( ( PUNCT cana-333 180 25 2014 2014 NUM cana-333 180 26 ) ) PUNCT cana-333 180 27 . . PUNCT cana-333 181 1 numerical numerical PROPN cana-333 181 2 study study PROPN cana-333 181 3 of of ADP cana-333 181 4 nonnewtonian nonnewtonian ADJ cana-333 181 5 boundary boundary ADJ cana-333 181 6 layer layer NOUN cana-333 181 7 flow flow NOUN cana-333 181 8 of of ADP cana-333 181 9 jeffreys jeffreys PROPN cana-333 181 10 fluid fluid NOUN cana-333 181 11 past past ADP cana-333 181 12 a a DET cana-333 181 13 vertical vertical ADJ cana-333 181 14 porous porous ADJ cana-333 181 15 plate plate NOUN cana-333 181 16 in in ADP cana-333 181 17 a a DET cana-333 181 18 non non ADJ cana-333 181 19 - - ADJ cana-333 181 20 darcy darcy ADJ cana-333 181 21 porous porous ADJ cana-333 181 22 medium medium NOUN cana-333 181 23 . . PUNCT cana-333 182 1 international international ADJ cana-333 182 2 journal journal NOUN cana-333 182 3 for for ADP cana-333 182 4 computational computational ADJ cana-333 182 5 methods method NOUN cana-333 182 6 in in ADP cana-333 182 7 engineering engineering NOUN cana-333 182 8 science science NOUN cana-333 182 9 and and CCONJ cana-333 182 10 mechanics mechanic NOUN cana-333 182 11 , , PUNCT cana-333 182 12 15(4 15(4 NUM cana-333 182 13 ) ) PUNCT cana-333 182 14 , , PUNCT cana-333 182 15 372 372 NUM cana-333 182 16 - - SYM cana-333 182 17 389 389 NUM cana-333 182 18 . . PUNCT cana-333 183 1 [ [ X cana-333 183 2 5 5 NUM cana-333 183 3 ] ] X cana-333 183 4 khalid khalid PROPN cana-333 183 5 , , PUNCT cana-333 183 6 a. a. PROPN cana-333 183 7 , , PUNCT cana-333 183 8 khan khan PROPN cana-333 183 9 , , PUNCT cana-333 183 10 i. i. PROPN cana-333 183 11 , , PUNCT cana-333 183 12 khan khan PROPN cana-333 183 13 , , PUNCT cana-333 183 14 a. a. PROPN cana-333 183 15 , , PUNCT cana-333 183 16 & & CCONJ cana-333 183 17 shafie shafie NOUN cana-333 183 18 , , PUNCT cana-333 183 19 s. s. PROPN cana-333 183 20 ( ( PUNCT cana-333 183 21 2015 2015 NUM cana-333 183 22 ) ) PUNCT cana-333 183 23 . . PUNCT cana-333 184 1 unsteady unsteady PROPN cana-333 184 2 mhd mhd PROPN cana-333 184 3 free free ADJ cana-333 184 4 convection convection NOUN cana-333 184 5 flow flow NOUN cana-333 184 6 of of ADP cana-333 184 7 casson casson PROPN cana-333 184 8 fluid fluid NOUN cana-333 184 9 past past NOUN cana-333 184 10 over over ADP cana-333 184 11 an an DET cana-333 184 12 oscillating oscillate VERB cana-333 184 13 vertical vertical ADJ cana-333 184 14 plate plate NOUN cana-333 184 15 embedded embed VERB cana-333 184 16 in in ADP cana-333 184 17 a a DET cana-333 184 18 porous porous ADJ cana-333 184 19 medium medium NOUN cana-333 184 20 . . PUNCT cana-333 185 1 engineering engineering NOUN cana-333 185 2 science science NOUN cana-333 185 3 and and CCONJ cana-333 185 4 technology technology NOUN cana-333 185 5 , , PUNCT cana-333 185 6 an an DET cana-333 185 7 international international ADJ cana-333 185 8 journal journal NOUN cana-333 185 9 , , PUNCT cana-333 185 10 18(3 18(3 NUM cana-333 185 11 ) ) PUNCT cana-333 185 12 , , PUNCT cana-333 185 13 309 309 NUM cana-333 185 14 - - SYM cana-333 185 15 317 317 NUM cana-333 185 16 . . PUNCT cana-333 186 1 [ [ X cana-333 186 2 6 6 NUM cana-333 186 3 ] ] PUNCT cana-333 186 4 narahari narahari NOUN cana-333 186 5 , , PUNCT cana-333 186 6 m. m. NOUN cana-333 186 7 , , PUNCT cana-333 186 8 & & CCONJ cana-333 186 9 kamran kamran PROPN cana-333 186 10 , , PUNCT cana-333 186 11 m. m. NOUN cana-333 186 12 ( ( PUNCT cana-333 186 13 2016 2016 NUM cana-333 186 14 ) ) PUNCT cana-333 186 15 . . PUNCT cana-333 186 16 mhd mhd PROPN cana-333 186 17 natural natural ADJ cana-333 186 18 convection convection NOUN cana-333 186 19 flow flow NOUN cana-333 186 20 past past ADP cana-333 186 21 an an DET cana-333 186 22 impulsively impulsively ADV cana-333 186 23 started start VERB cana-333 186 24 infinite infinite ADJ cana-333 186 25 vertical vertical ADJ cana-333 186 26 porous porous ADJ cana-333 186 27 plate plate NOUN cana-333 186 28 with with ADP cana-333 186 29 newtonian newtonian ADJ cana-333 186 30 heating heating NOUN cana-333 186 31 in in ADP cana-333 186 32 the the DET cana-333 186 33 presence presence NOUN cana-333 186 34 of of ADP cana-333 186 35 radiation radiation NOUN cana-333 186 36 . . PUNCT cana-333 187 1 international international ADJ cana-333 187 2 journal journal PROPN cana-333 187 3 of of ADP cana-333 187 4 numerical numerical ADJ cana-333 187 5 methods method NOUN cana-333 187 6 for for ADP cana-333 187 7 heat heat NOUN cana-333 187 8 & & CCONJ cana-333 187 9 fluid fluid ADJ cana-333 187 10 flow flow NOUN cana-333 187 11 , , PUNCT cana-333 187 12 26(6 26(6 NOUN cana-333 187 13 ) ) PUNCT cana-333 187 14 , , PUNCT cana-333 187 15 1932 1932 NUM cana-333 187 16 - - SYM cana-333 187 17 1953 1953 NUM cana-333 187 18 . . PUNCT cana-333 188 1 [ [ X cana-333 188 2 7 7 NUM cana-333 188 3 ] ] X cana-333 188 4 sheikh sheikh NOUN cana-333 188 5 , , PUNCT cana-333 188 6 n. n. PROPN cana-333 188 7 a. a. PROPN cana-333 188 8 , , PUNCT cana-333 188 9 ali ali PROPN cana-333 188 10 , , PUNCT cana-333 188 11 f. f. PROPN cana-333 188 12 , , PUNCT cana-333 188 13 khan khan PROPN cana-333 188 14 , , PUNCT cana-333 188 15 i. i. PROPN cana-333 188 16 , , PUNCT cana-333 188 17 saqib saqib NOUN cana-333 188 18 , , PUNCT cana-333 188 19 m. m. NOUN cana-333 188 20 , , PUNCT cana-333 188 21 & & CCONJ cana-333 188 22 khan khan PROPN cana-333 188 23 , , PUNCT cana-333 188 24 a. a. NOUN cana-333 188 25 ( ( PUNCT cana-333 188 26 2017 2017 NUM cana-333 188 27 ) ) PUNCT cana-333 188 28 . . PUNCT cana-333 189 1 mhd mhd NOUN cana-333 189 2 flow flow NOUN cana-333 189 3 of of ADP cana-333 189 4 micropolar micropolar ADJ cana-333 189 5 fluid fluid NOUN cana-333 189 6 over over ADP cana-333 189 7 an an DET cana-333 189 8 oscillating oscillate VERB cana-333 189 9 vertical vertical ADJ cana-333 189 10 plate plate NOUN cana-333 189 11 embedded embed VERB cana-333 189 12 in in ADP cana-333 189 13 porous porous ADJ cana-333 189 14 media medium NOUN cana-333 189 15 with with ADP cana-333 189 16 constant constant ADJ cana-333 189 17 temperature temperature NOUN cana-333 189 18 and and CCONJ cana-333 189 19 concentration concentration NOUN cana-333 189 20 . . PUNCT cana-333 190 1 mathematical mathematical ADJ cana-333 190 2 problems problem NOUN cana-333 190 3 in in ADP cana-333 190 4 engineering,2017 engineering,2017 NOUN cana-333 190 5 . . PUNCT cana-333 191 1 [ [ X cana-333 191 2 8 8 NUM cana-333 191 3 ] ] X cana-333 191 4 fetecau fetecau PROPN cana-333 191 5 , , PUNCT cana-333 191 6 c. c. PROPN cana-333 191 7 , , PUNCT cana-333 191 8 akhtar akhtar PROPN cana-333 191 9 , , PUNCT cana-333 191 10 s. s. PROPN cana-333 191 11 , , PUNCT cana-333 191 12 pop pop PROPN cana-333 191 13 , , PUNCT cana-333 191 14 i. i. NOUN cana-333 191 15 , , PUNCT cana-333 191 16 & & CCONJ cana-333 191 17 fetecau fetecau PROPN cana-333 191 18 , , PUNCT cana-333 191 19 c. c. PROPN cana-333 191 20 ( ( PUNCT cana-333 191 21 2017 2017 NUM cana-333 191 22 ) ) PUNCT cana-333 191 23 . . PUNCT cana-333 192 1 unsteady unsteady ADJ cana-333 192 2 general general ADJ cana-333 192 3 solution solution NOUN cana-333 192 4 for for ADP cana-333 192 5 mhd mhd X cana-333 192 6 natural natural ADJ cana-333 192 7 convection convection NOUN cana-333 192 8 flow flow NOUN cana-333 192 9 with with ADP cana-333 192 10 radiative radiative ADJ cana-333 192 11 effects effect NOUN cana-333 192 12 , , PUNCT cana-333 192 13 heat heat NOUN cana-333 192 14 source source NOUN cana-333 192 15 and and CCONJ cana-333 192 16 shear shear NOUN cana-333 192 17 stress stress NOUN cana-333 192 18 on on ADP cana-333 192 19 the the DET cana-333 192 20 boundary boundary NOUN cana-333 192 21 . . PUNCT cana-333 193 1 international international ADJ cana-333 193 2 journal journal PROPN cana-333 193 3 of of ADP cana-333 193 4 numerical numerical ADJ cana-333 193 5 methods method NOUN cana-333 193 6 for for ADP cana-333 193 7 heat heat NOUN cana-333 193 8 & & CCONJ cana-333 193 9 fluid fluid ADJ cana-333 193 10 flow flow NOUN cana-333 193 11 , , PUNCT cana-333 193 12 27(6 27(6 NUM cana-333 193 13 ) ) PUNCT cana-333 193 14 , , PUNCT cana-333 193 15 12661281 12661281 NUM cana-333 194 1 [ [ X cana-333 194 2 9 9 NUM cana-333 194 3 ] ] X cana-333 194 4 rundora rundora PROPN cana-333 194 5 , , PUNCT cana-333 194 6 l. l. PROPN cana-333 194 7 , , PUNCT cana-333 194 8 & & CCONJ cana-333 194 9 makinde makinde PROPN cana-333 194 10 , , PUNCT cana-333 194 11 o. o. PROPN cana-333 194 12 d. d. PROPN cana-333 194 13 ( ( PUNCT cana-333 194 14 2018 2018 NUM cana-333 194 15 ) ) PUNCT cana-333 194 16 . . PUNCT cana-333 195 1 unsteady unsteady ADJ cana-333 195 2 mhd mhd PROPN cana-333 195 3 flow flow NOUN cana-333 195 4 of of ADP cana-333 195 5 non non ADJ cana-333 195 6 - - ADJ cana-333 195 7 newtonian newtonian ADJ cana-333 195 8 fluid fluid NOUN cana-333 195 9 in in ADP cana-333 195 10 a a DET cana-333 195 11 channel channel NOUN cana-333 195 12 filled fill VERB cana-333 195 13 with with ADP cana-333 195 14 a a DET cana-333 195 15 saturated saturate VERB cana-333 195 16 porous porous ADJ cana-333 195 17 medium medium NOUN cana-333 195 18 with with ADP cana-333 195 19 asymmetric asymmetric ADJ cana-333 195 20 navier navier NOUN cana-333 195 21 slip slip NOUN cana-333 195 22 and and CCONJ cana-333 195 23 convective convective ADJ cana-333 195 24 heating heating NOUN cana-333 195 25 . . PUNCT cana-333 196 1 appl appl PROPN cana-333 196 2 . . PROPN cana-333 196 3 math math PROPN cana-333 196 4 , , PUNCT cana-333 196 5 12(3 12(3 NUM cana-333 196 6 ) ) PUNCT cana-333 196 7 , , PUNCT cana-333 196 8 483 483 NUM cana-333 196 9 - - SYM cana-333 196 10 493 493 NUM cana-333 196 11 . . PUNCT cana-333 197 1 [ [ X cana-333 197 2 10 10 NUM cana-333 197 3 ] ] X cana-333 197 4 das das PROPN cana-333 197 5 , , PUNCT cana-333 197 6 s. s. PROPN cana-333 197 7 , , PUNCT cana-333 197 8 sarkar sarkar PROPN cana-333 197 9 , , PUNCT cana-333 197 10 s. s. PROPN cana-333 197 11 , , PUNCT cana-333 197 12 & & CCONJ cana-333 197 13 jana jana PROPN cana-333 197 14 , , PUNCT cana-333 197 15 r. r. PROPN cana-333 197 16 n. n. PROPN cana-333 197 17 ( ( PUNCT cana-333 197 18 2018 2018 NUM cana-333 197 19 ) ) PUNCT cana-333 197 20 . . PUNCT cana-333 197 21 entropy entropy PROPN cana-333 197 22 generation generation NOUN cana-333 197 23 analysis analysis NOUN cana-333 197 24 of of ADP cana-333 197 25 mhd mhd NOUN cana-333 197 26 slip slip NOUN cana-333 197 27 flow flow NOUN cana-333 197 28 of of ADP cana-333 197 29 non non ADJ cana-333 197 30 - - ADJ cana-333 197 31 newtonian newtonian ADJ cana-333 197 32 cu cu PROPN cana-333 197 33 - - PUNCT cana-333 197 34 casson casson PROPN cana-333 197 35 nanofluid nanofluid PROPN cana-333 197 36 in in ADP cana-333 197 37 a a DET cana-333 197 38 porous porous ADJ cana-333 197 39 microchannel microchannel NOUN cana-333 197 40 filled fill VERB cana-333 197 41 with with ADP cana-333 197 42 saturated saturate VERB cana-333 197 43 porous porous ADJ cana-333 197 44 medium medium NOUN cana-333 197 45 considering consider VERB cana-333 197 46 thermal thermal ADJ cana-333 197 47 radiation radiation NOUN cana-333 197 48 . . PUNCT cana-333 198 1 journal journal NOUN cana-333 198 2 of of ADP cana-333 198 3 nanofluids nanofluid NOUN cana-333 198 4 , , PUNCT cana-333 198 5 7(6 7(6 NUM cana-333 198 6 ) ) PUNCT cana-333 198 7 , , PUNCT cana-333 198 8 1217 1217 NUM cana-333 198 9 - - SYM cana-333 198 10 1232 1232 NUM cana-333 198 11 . . PUNCT cana-333 199 1 [ [ X cana-333 199 2 11 11 NUM cana-333 199 3 ] ] X cana-333 199 4 singh singh PROPN cana-333 199 5 , , PUNCT cana-333 199 6 j. j. PROPN cana-333 199 7 k. k. PROPN cana-333 199 8 , , PUNCT cana-333 199 9 joshi joshi PROPN cana-333 199 10 , , PUNCT cana-333 199 11 n. n. PROPN cana-333 199 12 , , PUNCT cana-333 199 13 & & CCONJ cana-333 199 14 rohidas rohidas PROPN cana-333 199 15 , , PUNCT cana-333 199 16 p. p. NOUN cana-333 199 17 ( ( PUNCT cana-333 199 18 2018 2018 NUM cana-333 199 19 ) ) PUNCT cana-333 199 20 . . PUNCT cana-333 200 1 unsteady unsteady ADJ cana-333 200 2 mhd mhd PROPN cana-333 200 3 natural natural ADJ cana-333 200 4 convective convective ADJ cana-333 200 5 flow flow NOUN cana-333 200 6 of of ADP cana-333 200 7 a a DET cana-333 200 8 rotating rotate VERB cana-333 200 9 walters’-b walters’-b VERB cana-333 200 10 fluid fluid NOUN cana-333 200 11 over over ADP cana-333 200 12 an an DET cana-333 200 13 oscillating oscillate VERB cana-333 200 14 plate plate NOUN cana-333 200 15 with with ADP cana-333 200 16 fluctuating fluctuate VERB cana-333 200 17 wall wall NOUN cana-333 200 18 temperature temperature NOUN cana-333 200 19 and and CCONJ cana-333 200 20 concentration concentration NOUN cana-333 200 21 . . PUNCT cana-333 201 1 journal journal NOUN cana-333 201 2 of of ADP cana-333 201 3 mechanics mechanic NOUN cana-333 201 4 , , PUNCT cana-333 201 5 34(4 34(4 NUM cana-333 201 6 ) ) PUNCT cana-333 201 7 , , PUNCT cana-333 201 8 519 519 NUM cana-333 201 9 - - SYM cana-333 201 10 532 532 NUM cana-333 201 11 . . PUNCT cana-333 202 1 communications communication NOUN cana-333 202 2 on on ADP cana-333 202 3 applied apply VERB cana-333 202 4 nonlinear nonlinear ADJ cana-333 202 5 analysis analysis NOUN cana-333 202 6 issn issn NOUN cana-333 202 7 : : PUNCT cana-333 202 8 1074 1074 NUM cana-333 202 9 - - PUNCT cana-333 202 10 133x 133x NUM cana-333 202 11 vol vol NOUN cana-333 202 12 31 31 NUM cana-333 202 13 no no NOUN cana-333 202 14 . . NOUN cana-333 202 15 1 1 NUM cana-333 202 16 ( ( PUNCT cana-333 202 17 2024 2024 NUM cana-333 202 18 ) ) PUNCT cana-333 202 19 115 115 NUM cana-333 202 20 https://internationalpubls.com https://internationalpubls.com X cana-333 203 1 [ [ X cana-333 203 2 12 12 NUM cana-333 203 3 ] ] X cana-333 203 4 deb deb PROPN cana-333 203 5 , , PUNCT cana-333 203 6 h. h. PROPN cana-333 203 7 r. r. PROPN cana-333 203 8 ( ( PUNCT cana-333 203 9 2019 2019 NUM cana-333 203 10 ) ) PUNCT cana-333 203 11 . . PUNCT cana-333 204 1 free free ADJ cana-333 204 2 convective convective ADJ cana-333 204 3 mhd mhd NOUN cana-333 204 4 flow flow NOUN cana-333 204 5 of of ADP cana-333 204 6 a a DET cana-333 204 7 visco visco ADJ cana-333 204 8 - - ADJ cana-333 204 9 elastic elastic ADJ cana-333 204 10 fluid fluid NOUN cana-333 204 11 past past ADP cana-333 204 12 a a DET cana-333 204 13 vertical vertical ADJ cana-333 204 14 porous porous ADJ cana-333 204 15 plate plate NOUN cana-333 204 16 through through ADP cana-333 204 17 a a DET cana-333 204 18 porous porous ADJ cana-333 204 19 medium medium NOUN cana-333 204 20 with with ADP cana-333 204 21 constant constant ADJ cana-333 204 22 suction suction NOUN cana-333 204 23 and and CCONJ cana-333 204 24 heat heat NOUN cana-333 204 25 source source NOUN cana-333 204 26 . . PUNCT cana-333 205 1 international international ADJ cana-333 205 2 journal journal PROPN cana-333 205 3 of of ADP cana-333 205 4 engineering engineering NOUN cana-333 205 5 , , PUNCT cana-333 205 6 science science NOUN cana-333 205 7 and and CCONJ cana-333 205 8 mathematics mathematic NOUN cana-333 205 9 , , PUNCT cana-333 205 10 8(1 8(1 NOUN cana-333 205 11 ) ) PUNCT cana-333 205 12 , , PUNCT cana-333 205 13 27 27 NUM cana-333 205 14 - - SYM cana-333 205 15 40 40 NUM cana-333 205 16 . . PUNCT cana-333 206 1 [ [ X cana-333 206 2 13 13 NUM cana-333 206 3 ] ] PUNCT cana-333 206 4 maleki maleki NOUN cana-333 206 5 , , PUNCT cana-333 206 6 h. h. PROPN cana-333 206 7 , , PUNCT cana-333 206 8 safaei safaei NOUN cana-333 206 9 , , PUNCT cana-333 206 10 m. m. NOUN cana-333 206 11 r. r. PROPN cana-333 206 12 , , PUNCT cana-333 206 13 alrashed alrashe VERB cana-333 206 14 , , PUNCT cana-333 206 15 a. a. NOUN cana-333 206 16 a. a. PROPN cana-333 206 17 , , PUNCT cana-333 206 18 & & CCONJ cana-333 206 19 kasaeian kasaeian PROPN cana-333 206 20 , , PUNCT cana-333 206 21 a. a. NOUN cana-333 206 22 ( ( PUNCT cana-333 206 23 2019 2019 NUM cana-333 206 24 ) ) PUNCT cana-333 206 25 . . PUNCT cana-333 207 1 flow flow NOUN cana-333 207 2 and and CCONJ cana-333 207 3 heat heat NOUN cana-333 207 4 transfer transfer NOUN cana-333 207 5 in in ADP cana-333 207 6 non non ADJ cana-333 207 7 - - ADJ cana-333 207 8 newtonian newtonian ADJ cana-333 207 9 nanofluids nanofluid NOUN cana-333 207 10 over over ADP cana-333 207 11 porous porous ADJ cana-333 207 12 surfaces surface NOUN cana-333 207 13 . . PUNCT cana-333 208 1 journal journal NOUN cana-333 208 2 of of ADP cana-333 208 3 thermal thermal ADJ cana-333 208 4 analysis analysis NOUN cana-333 208 5 and and CCONJ cana-333 208 6 calorimetry calorimetry NOUN cana-333 208 7 , , PUNCT cana-333 208 8 135 135 NUM cana-333 208 9 , , PUNCT cana-333 208 10 1655 1655 NUM cana-333 208 11 - - SYM cana-333 208 12 1666 1666 NUM cana-333 208 13 . . PUNCT cana-333 209 1 [ [ X cana-333 209 2 14 14 NUM cana-333 209 3 ] ] X cana-333 209 4 goud goud PROPN cana-333 209 5 , , PUNCT cana-333 209 6 b. b. PROPN cana-333 209 7 s. s. PROPN cana-333 209 8 , , PUNCT cana-333 209 9 kumar kumar PROPN cana-333 209 10 , , PUNCT cana-333 209 11 p. p. PROPN cana-333 209 12 p. p. PROPN cana-333 209 13 , , PUNCT cana-333 209 14 & & CCONJ cana-333 209 15 malga malga PROPN cana-333 209 16 , , PUNCT cana-333 209 17 b. b. PROPN cana-333 209 18 s. s. PROPN cana-333 209 19 ( ( PUNCT cana-333 209 20 2020 2020 NUM cana-333 209 21 ) ) PUNCT cana-333 209 22 . . PUNCT cana-333 210 1 effect effect NOUN cana-333 210 2 of of ADP cana-333 210 3 heat heat NOUN cana-333 210 4 source source NOUN cana-333 210 5 on on ADP cana-333 210 6 an an DET cana-333 210 7 unsteady unsteady ADJ cana-333 210 8 mhd mhd NOUN cana-333 210 9 free free ADJ cana-333 210 10 convection convection NOUN cana-333 210 11 flow flow NOUN cana-333 210 12 of of ADP cana-333 210 13 casson casson PROPN cana-333 210 14 fluid fluid NOUN cana-333 210 15 past past ADP cana-333 210 16 a a DET cana-333 210 17 vertical vertical ADJ cana-333 210 18 oscillating oscillate VERB cana-333 210 19 plate plate NOUN cana-333 210 20 in in ADP cana-333 210 21 porous porous ADJ cana-333 210 22 medium medium NOUN cana-333 210 23 using use VERB cana-333 210 24 finite finite ADJ cana-333 210 25 element element NOUN cana-333 210 26 analysis analysis NOUN cana-333 210 27 . . PUNCT cana-333 211 1 partial partial ADJ cana-333 211 2 differential differential ADJ cana-333 211 3 equations equation NOUN cana-333 211 4 in in ADP cana-333 211 5 applied applied ADJ cana-333 211 6 mathematics mathematic NOUN cana-333 211 7 , , PUNCT cana-333 211 8 2 2 NUM cana-333 211 9 , , PUNCT cana-333 211 10 100015 100015 NUM cana-333 211 11 . . PUNCT cana-333 212 1 [ [ X cana-333 212 2 15 15 NUM cana-333 212 3 ] ] X cana-333 212 4 megahed megahe VERB cana-333 212 5 , , PUNCT cana-333 212 6 a. a. NOUN cana-333 212 7 m. m. NOUN cana-333 212 8 , , PUNCT cana-333 212 9 & & CCONJ cana-333 212 10 abbas abbas PROPN cana-333 212 11 , , PUNCT cana-333 212 12 w. w. PROPN cana-333 212 13 ( ( PUNCT cana-333 212 14 2022 2022 NUM cana-333 212 15 ) ) PUNCT cana-333 212 16 . . PUNCT cana-333 213 1 non non ADJ cana-333 213 2 - - ADJ cana-333 213 3 newtonian newtonian ADJ cana-333 213 4 cross cross ADJ cana-333 213 5 fluid fluid NOUN cana-333 213 6 flow flow NOUN cana-333 213 7 through through ADP cana-333 213 8 a a DET cana-333 213 9 porous porous ADJ cana-333 213 10 medium medium NOUN cana-333 213 11 with with ADP cana-333 213 12 regard regard NOUN cana-333 213 13 to to ADP cana-333 213 14 the the DET cana-333 213 15 effect effect NOUN cana-333 213 16 of of ADP cana-333 213 17 chemical chemical ADJ cana-333 213 18 reaction reaction NOUN cana-333 213 19 and and CCONJ cana-333 213 20 thermal thermal ADJ cana-333 213 21 stratification stratification NOUN cana-333 213 22 phenomenon phenomenon NOUN cana-333 213 23 . . PUNCT cana-333 214 1 case case NOUN cana-333 214 2 studies study NOUN cana-333 214 3 in in ADP cana-333 214 4 thermal thermal ADJ cana-333 214 5 engineering engineering NOUN cana-333 214 6 , , PUNCT cana-333 214 7 29 29 NUM cana-333 214 8 , , PUNCT cana-333 214 9 101715 101715 NUM cana-333 214 10 . . PUNCT cana-333 215 1 [ [ X cana-333 215 2 16 16 NUM cana-333 215 3 ] ] X cana-333 215 4 prameela prameela PROPN cana-333 215 5 , , PUNCT cana-333 215 6 m. m. NOUN cana-333 215 7 , , PUNCT cana-333 215 8 gangadhar gangadhar PROPN cana-333 215 9 , , PUNCT cana-333 215 10 k. k. PROPN cana-333 215 11 , , PUNCT cana-333 215 12 & & CCONJ cana-333 215 13 reddy reddy PROPN cana-333 215 14 , , PUNCT cana-333 215 15 g. g. PROPN cana-333 215 16 j. j. PROPN cana-333 215 17 ( ( PUNCT cana-333 215 18 2022 2022 NUM cana-333 215 19 ) ) PUNCT cana-333 215 20 . . PUNCT cana-333 216 1 mhd mhd PROPN cana-333 216 2 free free PROPN cana-333 216 3 convective convective ADJ cana-333 216 4 non non ADJ cana-333 216 5 - - ADJ cana-333 216 6 newtonian newtonian ADJ cana-333 216 7 casson casson PROPN cana-333 216 8 fluid fluid NOUN cana-333 216 9 flow flow NOUN cana-333 216 10 over over ADP cana-333 216 11 an an DET cana-333 216 12 oscillating oscillate VERB cana-333 216 13 vertical vertical ADJ cana-333 216 14 plate plate NOUN cana-333 216 15 . . PUNCT cana-333 217 1 partial partial ADJ cana-333 217 2 differential differential ADJ cana-333 217 3 equations equation NOUN cana-333 217 4 in in ADP cana-333 217 5 applied applied ADJ cana-333 217 6 mathematics mathematic NOUN cana-333 217 7 , , PUNCT cana-333 217 8 5 5 NUM cana-333 217 9 , , PUNCT cana-333 217 10 100366 100366 NUM cana-333 217 11 . . PUNCT cana-333 218 1 [ [ X cana-333 218 2 17 17 NUM cana-333 218 3 ] ] X cana-333 218 4 siddabasappa siddabasappa NOUN cana-333 218 5 , , PUNCT cana-333 218 6 c. c. PROPN cana-333 218 7 , , PUNCT cana-333 218 8 kalpana kalpana PROPN cana-333 218 9 , , PUNCT cana-333 218 10 g. g. PROPN cana-333 218 11 , , PUNCT cana-333 218 12 & & CCONJ cana-333 218 13 babitha babitha PROPN cana-333 218 14 . . PUNCT cana-333 219 1 ( ( PUNCT cana-333 219 2 2023 2023 NUM cana-333 219 3 ) ) PUNCT cana-333 219 4 . . PUNCT cana-333 220 1 a a DET cana-333 220 2 numerical numerical ADJ cana-333 220 3 study study NOUN cana-333 220 4 on on ADP cana-333 220 5 heat heat NOUN cana-333 220 6 transfer transfer NOUN cana-333 220 7 and and CCONJ cana-333 220 8 mhd mhd NOUN cana-333 220 9 flow flow NOUN cana-333 220 10 of of ADP cana-333 220 11 a a DET cana-333 220 12 newtonian newtonian NOUN cana-333 220 13 through through ADP cana-333 220 14 a a DET cana-333 220 15 porous porous ADJ cana-333 220 16 channel channel NOUN cana-333 220 17 β€” β€” PUNCT cana-333 220 18 local local ADJ cana-333 220 19 thermal thermal ADJ cana-333 220 20 nonequilibrium nonequilibrium NOUN cana-333 220 21 model model NOUN cana-333 220 22 . . PUNCT cana-333 221 1 heat heat NOUN cana-333 221 2 transfer transfer NOUN cana-333 221 3 , , PUNCT cana-333 221 4 52(1 52(1 NOUN cana-333 221 5 ) ) PUNCT cana-333 221 6 , , PUNCT cana-333 221 7 949 949 NUM cana-333 221 8 - - SYM cana-333 221 9 967 967 NUM cana-333 221 10 . . PUNCT cana-333 222 1 [ [ X cana-333 222 2 18 18 NUM cana-333 222 3 ] ] PUNCT cana-333 222 4 maranna maranna NOUN cana-333 222 5 , , PUNCT cana-333 222 6 t. t. PROPN cana-333 222 7 , , PUNCT cana-333 222 8 sachhin sachhin PROPN cana-333 222 9 , , PUNCT cana-333 222 10 s. s. PROPN cana-333 222 11 m. m. PROPN cana-333 222 12 , , PUNCT cana-333 222 13 mahabaleshwar mahabaleshwar PROPN cana-333 222 14 , , PUNCT cana-333 222 15 u. u. PROPN cana-333 222 16 s. s. PROPN cana-333 222 17 , , PUNCT cana-333 222 18 & & CCONJ cana-333 222 19 hatami hatami PROPN cana-333 222 20 , , PUNCT cana-333 222 21 m. m. NOUN cana-333 222 22 ( ( PUNCT cana-333 222 23 2023 2023 NUM cana-333 222 24 ) ) PUNCT cana-333 222 25 . . PUNCT cana-333 223 1 impact impact NOUN cana-333 223 2 of of ADP cana-333 223 3 navier navier NOUN cana-333 223 4 ’s ’s PART cana-333 223 5 slip slip NOUN cana-333 223 6 and and CCONJ cana-333 223 7 mhd mhd VERB cana-333 223 8 on on ADP cana-333 223 9 laminar laminar ADJ cana-333 223 10 boundary boundary ADJ cana-333 223 11 layer layer NOUN cana-333 223 12 flow flow NOUN cana-333 223 13 with with ADP cana-333 223 14 heat heat NOUN cana-333 223 15 transfer transfer NOUN cana-333 223 16 for for ADP cana-333 223 17 non non ADJ cana-333 223 18 - - ADJ cana-333 223 19 newtonian newtonian ADJ cana-333 223 20 nanofluid nanofluid NOUN cana-333 223 21 over over ADP cana-333 223 22 a a DET cana-333 223 23 porous porous ADJ cana-333 223 24 media medium NOUN cana-333 223 25 . . PUNCT cana-333 224 1 scientific scientific ADJ cana-333 224 2 reports report NOUN cana-333 224 3 , , PUNCT cana-333 224 4 13(1 13(1 NUM cana-333 224 5 ) ) PUNCT cana-333 224 6 , , PUNCT cana-333 224 7 12634 12634 NUM cana-333 224 8 . . PUNCT