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PUNCT iajs-3490 3 1 this this PRON iajs-3490 3 2 is be AUX iajs-3490 3 3 an an DET iajs-3490 3 4 open open ADJ iajs-3490 3 5 - - PUNCT iajs-3490 3 6 access access NOUN iajs-3490 3 7 article article NOUN iajs-3490 3 8 distributed distribute VERB iajs-3490 3 9 under under ADP iajs-3490 3 10 the the DET iajs-3490 3 11 terms term NOUN iajs-3490 3 12 of of ADP iajs-3490 3 13 the the DET iajs-3490 3 14 creative creative ADJ iajs-3490 3 15 commons common NOUN iajs-3490 3 16 attribution attribution NOUN iajs-3490 3 17 4.0 4.0 NUM iajs-3490 3 18 international international ADJ iajs-3490 3 19 license license NOUN iajs-3490 3 20 couple couple NOUN iajs-3490 3 21 stress stress NOUN iajs-3490 3 22 effects effect NOUN iajs-3490 3 23 on on ADP iajs-3490 3 24 peristaltic peristaltic ADJ iajs-3490 3 25 transport transport NOUN iajs-3490 3 26 of of ADP iajs-3490 3 27 peristaltic peristaltic ADJ iajs-3490 3 28 flow flow NOUN iajs-3490 3 29 of of ADP iajs-3490 3 30 carreau carreau PROPN iajs-3490 3 31 fluid fluid NOUN iajs-3490 3 32 in in ADP iajs-3490 3 33 an an DET iajs-3490 3 34 inclined inclined ADJ iajs-3490 3 35 asymmetric asymmetric ADJ iajs-3490 3 36 channel channel NOUN iajs-3490 3 37 with with ADP iajs-3490 3 38 porous porous ADJ iajs-3490 3 39 medium medium ADJ iajs-3490 3 40 hamza hamza PROPN iajs-3490 3 41 rashid rashid PROPN iajs-3490 3 42 dana dana PROPN iajs-3490 3 43 1 1 PROPN iajs-3490 3 44 * * PUNCT iajs-3490 3 45 and and CCONJ iajs-3490 3 46 liqaa liqaa PROPN iajs-3490 3 47 z. z. PROPN iajs-3490 3 48 hummady hummady PROPN iajs-3490 3 49 2 2 NUM iajs-3490 3 50 1,2 1,2 NUM iajs-3490 3 51 department department NOUN iajs-3490 3 52 of of ADP iajs-3490 3 53 mathematics mathematic NOUN iajs-3490 3 54 , , PUNCT iajs-3490 3 55 college college NOUN iajs-3490 3 56 of of ADP iajs-3490 3 57 science science NOUN iajs-3490 3 58 , , PUNCT iajs-3490 3 59 university university NOUN iajs-3490 3 60 of of ADP iajs-3490 3 61 baghdad baghdad PROPN iajs-3490 3 62 , , PUNCT iajs-3490 3 63 baghdad baghdad PROPN iajs-3490 3 64 , , PUNCT iajs-3490 3 65 iraq iraq PROPN iajs-3490 3 66 . . PUNCT iajs-3490 4 1 * * PUNCT iajs-3490 4 2 corresponding correspond VERB iajs-3490 4 3 author author NOUN iajs-3490 4 4 . . PUNCT iajs-3490 5 1 received receive VERB iajs-3490 5 2 : : PUNCT iajs-3490 5 3 14 14 NUM iajs-3490 5 4 may may PROPN iajs-3490 5 5 2023 2023 NUM iajs-3490 5 6 accepted accept VERB iajs-3490 5 7 : : PUNCT iajs-3490 5 8 14 14 NUM iajs-3490 5 9 august august PROPN iajs-3490 5 10 2023 2023 NUM iajs-3490 5 11 published publish VERB iajs-3490 5 12 : : PUNCT iajs-3490 5 13 20 20 NUM iajs-3490 5 14 july july PROPN iajs-3490 5 15 2025 2025 NUM iajs-3490 5 16 doi.org/10.30526/38.3.3490 doi.org/10.30526/38.3.3490 NOUN iajs-3490 5 17 abstract abstract ADV iajs-3490 5 18 in in ADP iajs-3490 5 19 this this DET iajs-3490 5 20 paper paper NOUN iajs-3490 5 21 , , PUNCT iajs-3490 5 22 we we PRON iajs-3490 5 23 share share VERB iajs-3490 5 24 a a DET iajs-3490 5 25 discussion discussion NOUN iajs-3490 5 26 of of ADP iajs-3490 5 27 the the DET iajs-3490 5 28 couple couple NOUN iajs-3490 5 29 tension tension NOUN iajs-3490 5 30 effect effect NOUN iajs-3490 5 31 on on ADP iajs-3490 5 32 the the DET iajs-3490 5 33 peristaltic peristaltic ADJ iajs-3490 5 34 transfer transfer NOUN iajs-3490 5 35 of of ADP iajs-3490 5 36 carreau carreau PROPN iajs-3490 5 37 peristaltic peristaltic ADJ iajs-3490 5 38 flow flow NOUN iajs-3490 5 39 of of ADP iajs-3490 5 40 fluid fluid NOUN iajs-3490 5 41 in in ADP iajs-3490 5 42 an an DET iajs-3490 5 43 inclined inclined ADJ iajs-3490 5 44 nonlinear nonlinear ADJ iajs-3490 5 45 canal canal NOUN iajs-3490 5 46 with with ADP iajs-3490 5 47 aporous aporous ADJ iajs-3490 5 48 medium medium NOUN iajs-3490 5 49 the the DET iajs-3490 5 50 carreau carreau PROPN iajs-3490 5 51 model model PROPN iajs-3490 5 52 's 's PART iajs-3490 5 53 constitutive constitutive ADJ iajs-3490 5 54 equation equation NOUN iajs-3490 5 55 is be AUX iajs-3490 5 56 selected select VERB iajs-3490 5 57 to to PART iajs-3490 5 58 represent represent VERB iajs-3490 5 59 solutions solution NOUN iajs-3490 5 60 to to ADP iajs-3490 5 61 these these DET iajs-3490 5 62 problems problem NOUN iajs-3490 5 63 are be AUX iajs-3490 5 64 obtained obtain VERB iajs-3490 5 65 a a DET iajs-3490 5 66 numerical numerical ADJ iajs-3490 5 67 method method NOUN iajs-3490 5 68 has have AUX iajs-3490 5 69 been be AUX iajs-3490 5 70 used use VERB iajs-3490 5 71 to to PART iajs-3490 5 72 answer answer VERB iajs-3490 5 73 the the DET iajs-3490 5 74 problems problem NOUN iajs-3490 5 75 and and CCONJ iajs-3490 5 76 consideration consideration NOUN iajs-3490 5 77 , , PUNCT iajs-3490 5 78 such such ADJ iajs-3490 5 79 as as ADP iajs-3490 5 80 perturbation perturbation NOUN iajs-3490 5 81 method method NOUN iajs-3490 5 82 . . PUNCT iajs-3490 6 1 closed close VERB iajs-3490 6 2 form form NOUN iajs-3490 6 3 dynamical dynamical ADJ iajs-3490 6 4 plus plus CCONJ iajs-3490 6 5 stream stream NOUN iajs-3490 6 6 function function NOUN iajs-3490 6 7 formulas formula NOUN iajs-3490 6 8 efficiency efficiency NOUN iajs-3490 6 9 are be AUX iajs-3490 6 10 pressure pressure NOUN iajs-3490 6 11 was be AUX iajs-3490 6 12 created create VERB iajs-3490 6 13 increase increase NOUN iajs-3490 6 14 per per ADP iajs-3490 6 15 wave wave NOUN iajs-3490 6 16 length length NOUN iajs-3490 6 17 has have AUX iajs-3490 6 18 been be AUX iajs-3490 6 19 estimated estimate VERB iajs-3490 6 20 numerically numerically ADV iajs-3490 6 21 on on ADP iajs-3490 6 22 the the DET iajs-3490 6 23 channel channel NOUN iajs-3490 6 24 walls wall NOUN iajs-3490 6 25 . . PUNCT iajs-3490 7 1 the the DET iajs-3490 7 2 hartman hartman PROPN iajs-3490 7 3 digits digits PROPN iajs-3490 7 4 impacts impact NOUN iajs-3490 7 5 ( ( PUNCT iajs-3490 7 6 ha ha INTJ iajs-3490 7 7 ) ) PUNCT iajs-3490 7 8 , , PUNCT iajs-3490 7 9 darcy darcy PROPN iajs-3490 7 10 digit digit NOUN iajs-3490 7 11 ( ( PUNCT iajs-3490 7 12 da da ADJ iajs-3490 7 13 ) ) PUNCT iajs-3490 7 14 , , PUNCT iajs-3490 7 15 amplitude amplitude NOUN iajs-3490 7 16 ratio ratio NOUN iajs-3490 7 17 ( ( PUNCT iajs-3490 7 18 e e NOUN iajs-3490 7 19 ) ) PUNCT iajs-3490 7 20 , , PUNCT iajs-3490 7 21 and and CCONJ iajs-3490 7 22 their their PRON iajs-3490 7 23 consequences consequence NOUN iajs-3490 7 24 . . PUNCT iajs-3490 8 1 the the DET iajs-3490 8 2 full full ADJ iajs-3490 8 3 effects effect NOUN iajs-3490 8 4 of of ADP iajs-3490 8 5 axial axial ADJ iajs-3490 8 6 velocity velocity NOUN iajs-3490 8 7 and and CCONJ iajs-3490 8 8 entrapment entrapment NOUN iajs-3490 8 9 are be AUX iajs-3490 8 10 carefully carefully ADV iajs-3490 8 11 examined examine VERB iajs-3490 8 12 and and CCONJ iajs-3490 8 13 graphically graphically ADV iajs-3490 8 14 represented represent VERB iajs-3490 8 15 . . PUNCT iajs-3490 9 1 numerical numerical PROPN iajs-3490 9 2 results result NOUN iajs-3490 9 3 have have AUX iajs-3490 9 4 been be AUX iajs-3490 9 5 computed compute VERB iajs-3490 9 6 by by ADP iajs-3490 9 7 using use VERB iajs-3490 9 8 mathematica mathematica PROPN iajs-3490 9 9 software software NOUN iajs-3490 9 10 for for ADP iajs-3490 9 11 all all DET iajs-3490 9 12 these these DET iajs-3490 9 13 problems problem NOUN iajs-3490 9 14 and and CCONJ iajs-3490 9 15 scheming scheme VERB iajs-3490 9 16 the the DET iajs-3490 9 17 graphs graph NOUN iajs-3490 9 18 . . 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PUNCT iajs-3490 12 1 the the DET iajs-3490 12 2 pressure pressure NOUN iajs-3490 12 3 of of ADP iajs-3490 12 4 rice rice NOUN iajs-3490 12 5 for for ADP iajs-3490 12 6 each each DET iajs-3490 12 7 wavelength wavelength NOUN iajs-3490 12 8 Ī“š‘ƒ Ī“š‘ƒ PROPN iajs-3490 12 9 increases increase VERB iajs-3490 12 10 in in ADP iajs-3490 12 11 magnitude magnitude NOUN iajs-3490 12 12 with with ADP iajs-3490 12 13 increasing increase VERB iajs-3490 12 14 values value NOUN iajs-3490 12 15 of of ADP iajs-3490 12 16 ( ( PUNCT iajs-3490 12 17 ha ha INTJ iajs-3490 12 18 ) ) PUNCT iajs-3490 12 19 . . PUNCT iajs-3490 13 1 keywords keyword NOUN iajs-3490 13 2 : : PUNCT iajs-3490 13 3 peristaltic peristaltic ADJ iajs-3490 13 4 flow flow NOUN iajs-3490 13 5 , , PUNCT iajs-3490 13 6 couple couple NOUN iajs-3490 13 7 stress stress NOUN iajs-3490 13 8 , , PUNCT iajs-3490 13 9 carreau carreau PROPN iajs-3490 13 10 . . PUNCT iajs-3490 14 1 1 1 X iajs-3490 14 2 . . X iajs-3490 14 3 introduction introduction NOUN iajs-3490 14 4 the the DET iajs-3490 14 5 studies study NOUN iajs-3490 14 6 of of ADP iajs-3490 14 7 non non ADJ iajs-3490 14 8 - - ADJ iajs-3490 14 9 newtonian newtonian ADJ iajs-3490 14 10 fluids fluid NOUN iajs-3490 14 11 are be AUX iajs-3490 14 12 not not PART iajs-3490 14 13 only only ADV iajs-3490 14 14 important important ADJ iajs-3490 14 15 but but CCONJ iajs-3490 14 16 sometimes sometimes ADV iajs-3490 14 17 essential essential ADJ iajs-3490 14 18 due due ADP iajs-3490 14 19 to to ADP iajs-3490 14 20 their their PRON iajs-3490 14 21 excessive excessive ADJ iajs-3490 14 22 presence presence NOUN iajs-3490 14 23 in in ADP iajs-3490 14 24 the the DET iajs-3490 14 25 universe universe NOUN iajs-3490 14 26 . . PUNCT iajs-3490 15 1 therefore therefore ADV iajs-3490 15 2 , , PUNCT iajs-3490 15 3 the the DET iajs-3490 15 4 analysis analysis NOUN iajs-3490 15 5 of of ADP iajs-3490 15 6 different different ADJ iajs-3490 15 7 non non ADJ iajs-3490 15 8 - - ADJ iajs-3490 15 9 newtonian newtonian ADJ iajs-3490 15 10 fluid fluid NOUN iajs-3490 15 11 flows flow NOUN iajs-3490 15 12 has have AUX iajs-3490 15 13 received receive VERB iajs-3490 15 14 a a DET iajs-3490 15 15 lot lot NOUN iajs-3490 15 16 of of ADP iajs-3490 15 17 attention attention NOUN iajs-3490 15 18 from from ADP iajs-3490 15 19 researchers researcher NOUN iajs-3490 15 20 . . PUNCT iajs-3490 16 1 particularly particularly ADV iajs-3490 16 2 peristaltic peristaltic ADJ iajs-3490 16 3 transport transport NOUN iajs-3490 16 4 of of ADP iajs-3490 16 5 these these DET iajs-3490 16 6 fluids fluid NOUN iajs-3490 16 7 was be AUX iajs-3490 16 8 discussed discuss VERB iajs-3490 16 9 ( ( PUNCT iajs-3490 16 10 1 1 NUM iajs-3490 16 11 - - SYM iajs-3490 16 12 3 3 NUM iajs-3490 16 13 ) ) PUNCT iajs-3490 16 14 peristalsis peristalsis NOUN iajs-3490 16 15 is be AUX iajs-3490 16 16 well well ADV iajs-3490 16 17 recognized recognize VERB iajs-3490 16 18 technique technique NOUN iajs-3490 16 19 in in ADP iajs-3490 16 20 which which PRON iajs-3490 16 21 a a DET iajs-3490 16 22 gradual gradual ADJ iajs-3490 16 23 wave wave NOUN iajs-3490 16 24 of of ADP iajs-3490 16 25 contraction contraction NOUN iajs-3490 16 26 or or CCONJ iajs-3490 16 27 expansion expansion NOUN iajs-3490 16 28 flows flow NOUN iajs-3490 16 29 along along ADP iajs-3490 16 30 the the DET iajs-3490 16 31 channel channel NOUN iajs-3490 16 32 walls wall NOUN iajs-3490 16 33 , , PUNCT iajs-3490 16 34 causing cause VERB iajs-3490 16 35 the the DET iajs-3490 16 36 contents content NOUN iajs-3490 16 37 of of ADP iajs-3490 16 38 the the DET iajs-3490 16 39 channel channel NOUN iajs-3490 16 40 to to PART iajs-3490 16 41 shift shift VERB iajs-3490 16 42 . . PUNCT iajs-3490 17 1 this this DET iajs-3490 17 2 phenomenon phenomenon NOUN iajs-3490 17 3 generally generally ADV iajs-3490 17 4 accurses accurse VERB iajs-3490 17 5 in in ADP iajs-3490 17 6 a a DET iajs-3490 17 7 number number NOUN iajs-3490 17 8 of of ADP iajs-3490 17 9 biological biological ADJ iajs-3490 17 10 , , PUNCT iajs-3490 17 11 medicinal medicinal ADJ iajs-3490 17 12 , , PUNCT iajs-3490 17 13 and and CCONJ iajs-3490 17 14 technical technical ADJ iajs-3490 17 15 applications application NOUN iajs-3490 17 16 ; ; PUNCT iajs-3490 17 17 similar similar ADJ iajs-3490 17 18 to to ADP iajs-3490 17 19 urinate urinate ADJ iajs-3490 17 20 transfer transfer NOUN iajs-3490 17 21 from from ADP iajs-3490 17 22 kidney kidney NOUN iajs-3490 17 23 to to PART iajs-3490 17 24 bladder bladder VERB iajs-3490 17 25 through through ADP iajs-3490 17 26 the the DET iajs-3490 17 27 ureter ureter ADJ iajs-3490 17 28 , , PUNCT iajs-3490 17 29 lymphatic lymphatic ADJ iajs-3490 17 30 vessel vessel NOUN iajs-3490 17 31 transport transport NOUN iajs-3490 17 32 , , PUNCT iajs-3490 17 33 heart heart NOUN iajs-3490 17 34 - - PUNCT iajs-3490 17 35 lung lung NOUN iajs-3490 17 36 machine machine NOUN iajs-3490 17 37 , , PUNCT iajs-3490 17 38 among among ADP iajs-3490 17 39 other other ADJ iajs-3490 17 40 things thing NOUN iajs-3490 17 41 . . PUNCT iajs-3490 18 1 many many ADJ iajs-3490 18 2 works work VERB iajs-3490 18 3 on on ADP iajs-3490 18 4 peristaltic peristaltic ADJ iajs-3490 18 5 flow flow NOUN iajs-3490 18 6 in in ADP iajs-3490 18 7 various various ADJ iajs-3490 18 8 geometries geometry NOUN iajs-3490 18 9 have have AUX iajs-3490 18 10 shown show VERB iajs-3490 18 11 that that SCONJ iajs-3490 18 12 the the DET iajs-3490 18 13 non non ADJ iajs-3490 18 14 - - ADJ iajs-3490 18 15 newtonian newtonian ADJ iajs-3490 18 16 behavior behavior NOUN iajs-3490 18 17 and and CCONJ iajs-3490 18 18 the the DET iajs-3490 18 19 non non ADJ iajs-3490 18 20 - - ADJ iajs-3490 18 21 newtonian newtonian ADJ iajs-3490 18 22 fluid fluid NOUN iajs-3490 18 23 flows flow NOUN iajs-3490 18 24 have have VERB iajs-3490 18 25 many many ADJ iajs-3490 18 26 applications application NOUN iajs-3490 18 27 in in ADP iajs-3490 18 28 engineering engineering NOUN iajs-3490 18 29 and and CCONJ iajs-3490 18 30 medicine medicine NOUN iajs-3490 18 31 , , PUNCT iajs-3490 18 32 have have AUX iajs-3490 18 33 examined examine VERB iajs-3490 18 34 the the DET iajs-3490 18 35 peristaltic peristaltic ADJ iajs-3490 18 36 flows flow NOUN iajs-3490 18 37 of of ADP iajs-3490 18 38 newtonian newtonian ADJ iajs-3490 18 39 and and CCONJ iajs-3490 18 40 non non ADJ iajs-3490 18 41 - - ADJ iajs-3490 18 42 newtonian newtonian ADJ iajs-3490 18 43 fluids fluid NOUN iajs-3490 18 44 in in ADP iajs-3490 18 45 symmetric symmetric ADJ iajs-3490 18 46 and and CCONJ iajs-3490 18 47 asymmetric asymmetric ADJ iajs-3490 18 48 channels channel NOUN iajs-3490 18 49 . . PUNCT iajs-3490 19 1 in in ADP iajs-3490 19 2 few few ADJ iajs-3490 19 3 other other ADJ iajs-3490 19 4 papers paper NOUN iajs-3490 19 5 , , PUNCT iajs-3490 19 6 ( ( PUNCT iajs-3490 19 7 5 5 X iajs-3490 19 8 ) ) PUNCT iajs-3490 19 9 several several ADJ iajs-3490 19 10 scholars scholar NOUN iajs-3490 19 11 in in ADP iajs-3490 19 12 particular particular ADJ iajs-3490 19 13 biological biological ADJ iajs-3490 19 14 https://orcid.org/0009-0002-4280-5870 https://orcid.org/0009-0002-4280-5870 NOUN iajs-3490 19 15 mailto:hamzafc51@gmail.com mailto:hamzafc51@gmail.com PROPN iajs-3490 19 16 https://orcid.org/0000-0001-8236-4120 https://orcid.org/0000-0001-8236-4120 PROPN iajs-3490 19 17 mailto:liqqa.hummady@sc.uobaghdad.edu.iq mailto:liqqa.hummady@sc.uobaghdad.edu.iq PROPN iajs-3490 19 18 https://orcid.org/0009-0002-4280-5870 https://orcid.org/0009-0002-4280-5870 PROPN iajs-3490 19 19 mailto:hamzafc51@gmail.com mailto:hamzafc51@gmail.com PROPN iajs-3490 19 20 https://orcid.org/0000-0001-8236-4120 https://orcid.org/0000-0001-8236-4120 PROPN iajs-3490 19 21 mailto:liqqa.hummady@sc.uobaghdad.edu.iq mailto:liqqa.hummady@sc.uobaghdad.edu.iq PROPN iajs-3490 19 22 https://orcid.org/0009-0002-4280-5870 https://orcid.org/0009-0002-4280-5870 PROPN iajs-3490 19 23 mailto:hamzafc51@gmail.com mailto:hamzafc51@gmail.com PROPN iajs-3490 19 24 https://orcid.org/0000-0001-8236-4120 https://orcid.org/0000-0001-8236-4120 PROPN iajs-3490 19 25 mailto:liqqa.hummady@sc.uobaghdad.edu.iq mailto:liqqa.hummady@sc.uobaghdad.edu.iq PROPN iajs-3490 19 26 https://orcid.org/0009-0002-4280-5870 https://orcid.org/0009-0002-4280-5870 PROPN iajs-3490 19 27 mailto:hamzafc51@gmail.com mailto:hamzafc51@gmail.com PROPN iajs-3490 19 28 https://orcid.org/0000-0001-8236-4120 https://orcid.org/0000-0001-8236-4120 PROPN iajs-3490 19 29 mailto:liqqa.hummady@sc.uobaghdad.edu.iq mailto:liqqa.hummady@sc.uobaghdad.edu.iq PROPN iajs-3490 19 30 https://orcid.org/0009-0002-4280-5870 https://orcid.org/0009-0002-4280-5870 PROPN iajs-3490 19 31 mailto:hamzafc51@gmail.com mailto:hamzafc51@gmail.com PROPN iajs-3490 19 32 https://orcid.org/0000-0001-8236-4120 https://orcid.org/0000-0001-8236-4120 PROPN iajs-3490 19 33 mailto:liqqa.hummady@sc.uobaghdad.edu.iq mailto:liqqa.hummady@sc.uobaghdad.edu.iq PROPN iajs-3490 19 34 https://orcid.org/0009-0002-4280-5870 https://orcid.org/0009-0002-4280-5870 PROPN iajs-3490 19 35 mailto:hamzafc51@gmail.com mailto:hamzafc51@gmail.com PROPN iajs-3490 19 36 https://orcid.org/0000-0001-8236-4120 https://orcid.org/0000-0001-8236-4120 PROPN iajs-3490 19 37 mailto:liqqa.hummady@sc.uobaghdad.edu.iq mailto:liqqa.hummady@sc.uobaghdad.edu.iq PROPN iajs-3490 19 38 ihjpas ihjpas PROPN iajs-3490 19 39 . . PUNCT iajs-3490 20 1 2025 2025 NUM iajs-3490 20 2 , , PUNCT iajs-3490 20 3 38(3 38(3 NUM iajs-3490 20 4 ) ) PUNCT iajs-3490 20 5 297 297 NUM iajs-3490 20 6 problems problem NOUN iajs-3490 20 7 dealing deal VERB iajs-3490 20 8 with with ADP iajs-3490 20 9 conductive conductive ADJ iajs-3490 20 10 fluids fluid NOUN iajs-3490 20 11 are be AUX iajs-3490 20 12 involved involve VERB iajs-3490 20 13 in in ADP iajs-3490 20 14 the the DET iajs-3490 20 15 effect effect NOUN iajs-3490 20 16 of of ADP iajs-3490 20 17 magnetic magnetic ADJ iajs-3490 20 18 field field NOUN iajs-3490 20 19 on on ADP iajs-3490 20 20 fluid fluid ADJ iajs-3490 20 21 flow flow NOUN iajs-3490 20 22 , , PUNCT iajs-3490 20 23 which which PRON iajs-3490 20 24 is be AUX iajs-3490 20 25 denoted denote VERB iajs-3490 20 26 by by ADP iajs-3490 20 27 magneto magneto PROPN iajs-3490 20 28 hydrodynamics hydrodynamic NOUN iajs-3490 20 29 ( ( PUNCT iajs-3490 20 30 mhd mhd NOUN iajs-3490 20 31 ) ) PUNCT iajs-3490 20 32 as as ADP iajs-3490 20 33 cancer cancer NOUN iajs-3490 20 34 therapy therapy NOUN iajs-3490 20 35 , , PUNCT iajs-3490 20 36 blood blood NOUN iajs-3490 20 37 pumping pump VERB iajs-3490 20 38 machines machine NOUN iajs-3490 20 39 , , PUNCT iajs-3490 20 40 polymer polymer NOUN iajs-3490 20 41 production production NOUN iajs-3490 20 42 , , PUNCT iajs-3490 20 43 and and CCONJ iajs-3490 20 44 metallurgy metallurgy NOUN iajs-3490 20 45 . . PUNCT iajs-3490 21 1 sensors sensor NOUN iajs-3490 21 2 , , PUNCT iajs-3490 21 3 magnetic magnetic ADJ iajs-3490 21 4 drug drug NOUN iajs-3490 21 5 , , PUNCT iajs-3490 21 6 and and CCONJ iajs-3490 21 7 engineering engineering NOUN iajs-3490 21 8 can can AUX iajs-3490 21 9 all all PRON iajs-3490 21 10 benefit benefit VERB iajs-3490 21 11 from from ADP iajs-3490 21 12 the the DET iajs-3490 21 13 mhd mhd NOUN iajs-3490 21 14 several several ADJ iajs-3490 21 15 studies study NOUN iajs-3490 21 16 have have AUX iajs-3490 21 17 been be AUX iajs-3490 21 18 steered steer VERB iajs-3490 21 19 on on ADP iajs-3490 21 20 mhd mhd NOUN iajs-3490 21 21 peristaltic peristaltic ADJ iajs-3490 21 22 transport transport NOUN iajs-3490 21 23 for for ADP iajs-3490 21 24 various various ADJ iajs-3490 21 25 fluid fluid ADJ iajs-3490 21 26 models model NOUN iajs-3490 21 27 and and CCONJ iajs-3490 21 28 states state NOUN iajs-3490 21 29 due due ADP iajs-3490 21 30 to to ADP iajs-3490 21 31 its its PRON iajs-3490 21 32 many many ADJ iajs-3490 21 33 uses use NOUN iajs-3490 21 34 ( ( PUNCT iajs-3490 21 35 6 6 NUM iajs-3490 21 36 - - SYM iajs-3490 21 37 9 9 NUM iajs-3490 21 38 ) ) PUNCT iajs-3490 21 39 peristalsis peristalsis NOUN iajs-3490 21 40 , , PUNCT iajs-3490 21 41 a a DET iajs-3490 21 42 characteristic characteristic NOUN iajs-3490 21 43 of of ADP iajs-3490 21 44 smooth smooth ADJ iajs-3490 21 45 muscles muscle NOUN iajs-3490 21 46 and and CCONJ iajs-3490 21 47 tubes tube NOUN iajs-3490 21 48 that that PRON iajs-3490 21 49 results result VERB iajs-3490 21 50 from from ADP iajs-3490 21 51 motor motor NOUN iajs-3490 21 52 activity activity NOUN iajs-3490 21 53 in in ADP iajs-3490 21 54 many many ADJ iajs-3490 21 55 biological biological ADJ iajs-3490 21 56 systems system NOUN iajs-3490 21 57 , , PUNCT iajs-3490 21 58 carries carry VERB iajs-3490 21 59 fluid fluid NOUN iajs-3490 21 60 through through ADP iajs-3490 21 61 channels channel NOUN iajs-3490 21 62 . . PUNCT iajs-3490 22 1 the the DET iajs-3490 22 2 governing govern VERB iajs-3490 22 3 analytical analytical ADJ iajs-3490 22 4 answers answer NOUN iajs-3490 22 5 have have AUX iajs-3490 22 6 been be AUX iajs-3490 22 7 obtained obtain VERB iajs-3490 22 8 utilizing utilize VERB iajs-3490 22 9 the the DET iajs-3490 22 10 presumption presumption NOUN iajs-3490 22 11 of of ADP iajs-3490 22 12 a a DET iajs-3490 22 13 long long ADJ iajs-3490 22 14 wave wave NOUN iajs-3490 22 15 - - PUNCT iajs-3490 22 16 size size NOUN iajs-3490 22 17 and and CCONJ iajs-3490 22 18 a a DET iajs-3490 22 19 small small ADJ iajs-3490 22 20 reynolds reynold NOUN iajs-3490 22 21 number number NOUN iajs-3490 22 22 to to PART iajs-3490 22 23 create create VERB iajs-3490 22 24 equations equation NOUN iajs-3490 22 25 for for ADP iajs-3490 22 26 continuity continuity NOUN iajs-3490 22 27 and and CCONJ iajs-3490 22 28 motion motion NOUN iajs-3490 22 29 . . PUNCT iajs-3490 23 1 studying study VERB iajs-3490 23 2 the the DET iajs-3490 23 3 impact impact NOUN iajs-3490 23 4 of of ADP iajs-3490 23 5 new new ADJ iajs-3490 23 6 factors factor NOUN iajs-3490 23 7 on on ADP iajs-3490 23 8 velocity velocity NOUN iajs-3490 23 9 , , PUNCT iajs-3490 23 10 pressure pressure NOUN iajs-3490 23 11 , , PUNCT iajs-3490 23 12 and and CCONJ iajs-3490 23 13 the the DET iajs-3490 23 14 trapping trap VERB iajs-3490 23 15 phenomena phenomenon NOUN iajs-3490 23 16 are be AUX iajs-3490 23 17 all all ADV iajs-3490 23 18 possible possible ADJ iajs-3490 23 19 . . PUNCT iajs-3490 24 1 2 2 X iajs-3490 24 2 . . X iajs-3490 24 3 materials material NOUN iajs-3490 24 4 and and CCONJ iajs-3490 24 5 methods method NOUN iajs-3490 24 6 consider consider VERB iajs-3490 24 7 the the DET iajs-3490 24 8 flow flow NOUN iajs-3490 24 9 of of ADP iajs-3490 24 10 a a DET iajs-3490 24 11 carreau carreau PROPN iajs-3490 24 12 asymmetric asymmetric ADJ iajs-3490 24 13 fluid fluid NOUN iajs-3490 24 14 in in ADP iajs-3490 24 15 two two NUM iajs-3490 24 16 dimensions dimension NOUN iajs-3490 24 17 , , PUNCT iajs-3490 24 18 canal canal NOUN iajs-3490 24 19 has have VERB iajs-3490 24 20 thickness thickness NOUN iajs-3490 24 21 ( ( PUNCT iajs-3490 24 22 e e NOUN iajs-3490 24 23 + + X iajs-3490 24 24 eā€² eā€² PROPN iajs-3490 24 25 ) ) PUNCT iajs-3490 24 26 . . PUNCT iajs-3490 25 1 asymmetrical asymmetrical ADJ iajs-3490 25 2 canals canal NOUN iajs-3490 25 3 are be AUX iajs-3490 25 4 created create VERB iajs-3490 25 5 thru thru ADP iajs-3490 25 6 altering alter VERB iajs-3490 25 7 wave wave NOUN iajs-3490 25 8 amplitudes amplitude NOUN iajs-3490 25 9 , , PUNCT iajs-3490 25 10 the the DET iajs-3490 25 11 geometries geometry NOUN iajs-3490 25 12 model model NOUN iajs-3490 25 13 is be AUX iajs-3490 25 14 : : PUNCT iajs-3490 25 15 ( ( PUNCT iajs-3490 25 16 x x X iajs-3490 25 17 , , PUNCT iajs-3490 25 18 t)=e t)=e NUM iajs-3490 25 19 upper upper ADJ iajs-3490 25 20 wall wall NOUN iajs-3490 25 21 ( ( PUNCT iajs-3490 25 22 1 1 NUM iajs-3490 25 23 ) ) PUNCT iajs-3490 25 24 ( ( PUNCT iajs-3490 25 25 x x X iajs-3490 25 26 , , PUNCT iajs-3490 25 27 t)= t)= X iajs-3490 25 28 lower low ADJ iajs-3490 25 29 wall wall NOUN iajs-3490 25 30 ( ( PUNCT iajs-3490 25 31 2 2 NUM iajs-3490 25 32 ) ) PUNCT iajs-3490 25 33 where where SCONJ iajs-3490 25 34 r1 r1 NOUN iajs-3490 25 35 , , PUNCT iajs-3490 25 36 r2 r2 PROPN iajs-3490 25 37 , , PUNCT iajs-3490 25 38 e e X iajs-3490 25 39 , , PUNCT iajs-3490 25 40 e e NOUN iajs-3490 25 41 ' ' X iajs-3490 25 42 , , PUNCT iajs-3490 25 43 Ī» Ī» PROPN iajs-3490 25 44 , , PUNCT iajs-3490 25 45 c c NOUN iajs-3490 25 46 , , PUNCT iajs-3490 25 47 , , PUNCT iajs-3490 25 48 t t PROPN iajs-3490 25 49 , , PUNCT iajs-3490 25 50 are be AUX iajs-3490 25 51 the the DET iajs-3490 25 52 waves wave NOUN iajs-3490 25 53 amplitudes amplitude NOUN iajs-3490 25 54 , , PUNCT iajs-3490 25 55 channels channel NOUN iajs-3490 25 56 ā€™ ' PUNCT iajs-3490 25 57 width width NOUN iajs-3490 25 58 , , PUNCT iajs-3490 25 59 wavelength wavelength NOUN iajs-3490 25 60 , , PUNCT iajs-3490 25 61 and and CCONJ iajs-3490 25 62 the the DET iajs-3490 25 63 speed speed NOUN iajs-3490 25 64 of of ADP iajs-3490 25 65 wave wave NOUN iajs-3490 25 66 , , PUNCT iajs-3490 25 67 ( ( PUNCT iajs-3490 25 68 0 0 NUM iajs-3490 25 69 ā‰¤ ā‰¤ NUM iajs-3490 25 70 ā‰¤ ā‰¤ NUM iajs-3490 25 71 Ļ€ Ļ€ NOUN iajs-3490 25 72 ) ) PUNCT iajs-3490 25 73 . . PUNCT iajs-3490 26 1 the the DET iajs-3490 26 2 rectangular rectangular ADJ iajs-3490 26 3 coordinating coordinating NOUN iajs-3490 26 4 system system NOUN iajs-3490 26 5 and and CCONJ iajs-3490 26 6 phase phase NOUN iajs-3490 26 7 difference difference NOUN iajs-3490 26 8 are be AUX iajs-3490 26 9 chosen choose VERB iajs-3490 26 10 . . PUNCT iajs-3490 27 1 so so ADV iajs-3490 27 2 that that SCONJ iajs-3490 27 3 the the DET iajs-3490 27 4 x x X iajs-3490 27 5 - - NOUN iajs-3490 27 6 axis axis NOUN iajs-3490 27 7 is be AUX iajs-3490 27 8 parallel parallel ADJ iajs-3490 27 9 to to ADP iajs-3490 27 10 the the DET iajs-3490 27 11 axis axis NOUN iajs-3490 27 12 of of ADP iajs-3490 27 13 the the DET iajs-3490 27 14 x x NOUN iajs-3490 27 15 - - NOUN iajs-3490 27 16 axis axis NOUN iajs-3490 27 17 and and CCONJ iajs-3490 27 18 the the DET iajs-3490 27 19 y y NOUN iajs-3490 27 20 - - PUNCT iajs-3490 27 21 axis axis NOUN iajs-3490 27 22 is be AUX iajs-3490 27 23 perpendicular perpendicular ADJ iajs-3490 27 24 to to ADP iajs-3490 27 25 the the DET iajs-3490 27 26 axis axis NOUN iajs-3490 27 27 of of ADP iajs-3490 27 28 x x NOUN iajs-3490 27 29 - - NOUN iajs-3490 27 30 axis axis ADJ iajs-3490 27 31 . . PUNCT iajs-3490 28 1 we we PRON iajs-3490 28 2 can can AUX iajs-3490 28 3 mention mention VERB iajs-3490 28 4 ( ( PUNCT iajs-3490 28 5 = = NOUN iajs-3490 28 6 0 0 NUM iajs-3490 28 7 ) ) PUNCT iajs-3490 28 8 denotes denote VERB iajs-3490 28 9 an an DET iajs-3490 28 10 equal equal ADJ iajs-3490 28 11 canal canal NOUN iajs-3490 28 12 thickness thickness NOUN iajs-3490 28 13 waveform waveform VERB iajs-3490 28 14 that that PRON iajs-3490 28 15 is be AUX iajs-3490 28 16 outside outside ADP iajs-3490 28 17 of of ADP iajs-3490 28 18 phase phase NOUN iajs-3490 28 19 , , PUNCT iajs-3490 28 20 whereas whereas SCONJ iajs-3490 28 21 ( ( PUNCT iajs-3490 28 22 = = SYM iajs-3490 28 23 Ļ€ Ļ€ X iajs-3490 28 24 ) ) PUNCT iajs-3490 28 25 denotes denote NOUN iajs-3490 28 26 in in ADP iajs-3490 28 27 - - PUNCT iajs-3490 28 28 phase phase NOUN iajs-3490 28 29 waves wave NOUN iajs-3490 28 30 . . PUNCT iajs-3490 29 1 furthermore furthermore ADV iajs-3490 29 2 , , PUNCT iajs-3490 29 3 r1 r1 PROPN iajs-3490 29 4 , , PUNCT iajs-3490 29 5 r2 r2 PROPN iajs-3490 29 6 , , PUNCT iajs-3490 29 7 e e X iajs-3490 29 8 , , PUNCT iajs-3490 29 9 e e NOUN iajs-3490 29 10 ' ' PUNCT iajs-3490 29 11 , , PUNCT iajs-3490 29 12 are be AUX iajs-3490 29 13 meet meet VERB iajs-3490 29 14 the the DET iajs-3490 29 15 condition condition NOUN iajs-3490 29 16 : : PUNCT iajs-3490 29 17 + + CCONJ iajs-3490 29 18 +2 +2 PROPN iajs-3490 29 19 ( ( PUNCT iajs-3490 29 20 e+e e+e NOUN iajs-3490 29 21 ' ' PUNCT iajs-3490 29 22 ( ( PUNCT iajs-3490 29 23 3 3 NUM iajs-3490 29 24 ) ) PUNCT iajs-3490 29 25 as as SCONJ iajs-3490 29 26 assumed assume VERB iajs-3490 29 27 , , PUNCT iajs-3490 29 28 there there PRON iajs-3490 29 29 is be VERB iajs-3490 29 30 no no DET iajs-3490 29 31 longitudinal longitudinal ADJ iajs-3490 29 32 walls wall NOUN iajs-3490 29 33 motion motion NOUN iajs-3490 29 34 . . PUNCT iajs-3490 30 1 this this DET iajs-3490 30 2 assumption assumption NOUN iajs-3490 30 3 constrains constrain VERB iajs-3490 30 4 wall wall NOUN iajs-3490 30 5 deformation deformation NOUN iajs-3490 30 6 . . PUNCT iajs-3490 31 1 , , PUNCT iajs-3490 31 2 however however ADV iajs-3490 31 3 , , PUNCT iajs-3490 31 4 this this PRON iajs-3490 31 5 does do AUX iajs-3490 31 6 n't not PART iajs-3490 31 7 imply imply VERB iajs-3490 31 8 that that SCONJ iajs-3490 31 9 the the DET iajs-3490 31 10 canal canal NOUN iajs-3490 31 11 is be AUX iajs-3490 31 12 rigid rigid ADJ iajs-3490 31 13 while while SCONJ iajs-3490 31 14 moving move VERB iajs-3490 31 15 longitudinally longitudinally ADV iajs-3490 31 16 . . PUNCT iajs-3490 32 1 3 3 X iajs-3490 32 2 . . NOUN iajs-3490 32 3 results result NOUN iajs-3490 32 4 to to PART iajs-3490 32 5 investigate investigate VERB iajs-3490 32 6 how how SCONJ iajs-3490 32 7 physical physical ADJ iajs-3490 32 8 characteristics characteristic NOUN iajs-3490 32 9 affect affect VERB iajs-3490 32 10 such such ADJ iajs-3490 32 11 as as ADP iajs-3490 32 12 effect effect NOUN iajs-3490 32 13 on on ADP iajs-3490 32 14 the the DET iajs-3490 32 15 plotted plot VERB iajs-3490 32 16 velocity velocity NOUN iajs-3490 32 17 ( ( PUNCT iajs-3490 32 18 u u NOUN iajs-3490 32 19 ) ) PUNCT iajs-3490 32 20 , , PUNCT iajs-3490 32 21 pressure pressure NOUN iajs-3490 32 22 rise rise NOUN iajs-3490 32 23 in in ADP iajs-3490 32 24 figures figure NOUN iajs-3490 32 25 ( ( PUNCT iajs-3490 32 26 1 1 NUM iajs-3490 32 27 and and CCONJ iajs-3490 32 28 2 2 NUM iajs-3490 32 29 ) ) PUNCT iajs-3490 32 30 are be AUX iajs-3490 32 31 clarified clarify VERB iajs-3490 32 32 graphically graphically ADV iajs-3490 32 33 by by ADP iajs-3490 32 34 " " PUNCT iajs-3490 32 35 mathematica mathematica PROPN iajs-3490 32 36 " " PUNCT iajs-3490 32 37 program program NOUN iajs-3490 32 38 figure figure NOUN iajs-3490 32 39 1 1 NUM iajs-3490 32 40 . . PUNCT iajs-3490 32 41 effectiveness effectiveness NOUN iajs-3490 32 42 of of ADP iajs-3490 32 43 various various ADJ iajs-3490 32 44 parameters parameter NOUN iajs-3490 32 45 of of ADP iajs-3490 32 46 da da NOUN iajs-3490 32 47 when when SCONJ iajs-3490 32 48 ha=3 ha=3 NOUN iajs-3490 32 49 , , PUNCT iajs-3490 32 50 = = NOUN iajs-3490 32 51 0.5 0.5 NUM iajs-3490 32 52 , , PUNCT iajs-3490 32 53 = = NOUN iajs-3490 32 54 4 4 NUM iajs-3490 32 55 , , PUNCT iajs-3490 32 56 = = NOUN iajs-3490 32 57 0.4 0.4 NUM iajs-3490 32 58 , , PUNCT iajs-3490 32 59 = = NOUN iajs-3490 32 60 0.5 0.5 NUM iajs-3490 32 61 , , PUNCT iajs-3490 32 62 z= z= NOUN iajs-3490 32 63 1 1 NUM iajs-3490 32 64 , , PUNCT iajs-3490 32 65 m= m= X iajs-3490 32 66 1 1 NUM iajs-3490 32 67 , , PUNCT iajs-3490 33 1 e e NOUN iajs-3490 33 2 * * PUNCT iajs-3490 33 3 = = SYM iajs-3490 33 4 0.5 0.5 NUM iajs-3490 33 5 . . PUNCT iajs-3490 33 6 ihjpas ihjpas PROPN iajs-3490 33 7 . . PUNCT iajs-3490 34 1 2025 2025 NUM iajs-3490 34 2 , , PUNCT iajs-3490 34 3 38(3 38(3 NUM iajs-3490 34 4 ) ) PUNCT iajs-3490 34 5 298 298 NUM iajs-3490 34 6 figure figure NOUN iajs-3490 34 7 2 2 NUM iajs-3490 34 8 . . PUNCT iajs-3490 35 1 the the DET iajs-3490 35 2 effectiveness effectiveness NOUN iajs-3490 35 3 of of ADP iajs-3490 35 4 various various ADJ iajs-3490 35 5 ( ( PUNCT iajs-3490 35 6 ha ha INTJ iajs-3490 35 7 ) ) PUNCT iajs-3490 35 8 values value NOUN iajs-3490 35 9 on on ADP iajs-3490 35 10 pressure pressure NOUN iajs-3490 35 11 ( ( PUNCT iajs-3490 35 12 Ī“p Ī“p INTJ iajs-3490 35 13 ) ) PUNCT iajs-3490 35 14 while while SCONJ iajs-3490 35 15 da=2 da=2 VERB iajs-3490 35 16 , , PUNCT iajs-3490 35 17 = = NOUN iajs-3490 35 18 0.5 0.5 NUM iajs-3490 35 19 , , PUNCT iajs-3490 35 20 = = NOUN iajs-3490 35 21 4 4 NUM iajs-3490 35 22 , , PUNCT iajs-3490 35 23 = = NOUN iajs-3490 35 24 0.4 0.4 NUM iajs-3490 35 25 , , PUNCT iajs-3490 35 26 = = NOUN iajs-3490 35 27 0.5 0.5 NUM iajs-3490 35 28 , , PUNCT iajs-3490 35 29 we=3 we=3 VERB iajs-3490 35 30 , , PUNCT iajs-3490 35 31 = = NOUN iajs-3490 35 32 0.5 0.5 NUM iajs-3490 35 33 , , PUNCT iajs-3490 35 34 re=0.2 re=0.2 NOUN iajs-3490 35 35 , , PUNCT iajs-3490 35 36 fr=0.2 fr=0.2 ADV iajs-3490 35 37 , , PUNCT iajs-3490 35 38 z= z= NOUN iajs-3490 35 39 0.2 0.2 NUM iajs-3490 35 40 , , PUNCT iajs-3490 35 41 m= m= X iajs-3490 35 42 0.2 0.2 NUM iajs-3490 35 43 , , PUNCT iajs-3490 35 44 e e X iajs-3490 35 45 * * PUNCT iajs-3490 35 46 = = SYM iajs-3490 35 47 0.5 0.5 NUM iajs-3490 35 48 , , PUNCT iajs-3490 35 49 n=1 n=1 PROPN iajs-3490 35 50 to to PART iajs-3490 35 51 solve solve VERB iajs-3490 35 52 the the DET iajs-3490 35 53 problem problem NOUN iajs-3490 35 54 and and CCONJ iajs-3490 35 55 find find VERB iajs-3490 35 56 the the DET iajs-3490 35 57 results result NOUN iajs-3490 35 58 , , PUNCT iajs-3490 35 59 we we PRON iajs-3490 35 60 get get VERB iajs-3490 35 61 the the DET iajs-3490 35 62 stream stream NOUN iajs-3490 35 63 function function NOUN iajs-3490 35 64 : : PUNCT iajs-3490 35 65 ( ( PUNCT iajs-3490 35 66 4 4 X iajs-3490 35 67 ) ) PUNCT iajs-3490 35 68 ( ( PUNCT iajs-3490 35 69 5 5 X iajs-3490 35 70 ) ) PUNCT iajs-3490 35 71 the the DET iajs-3490 35 72 answer answer NOUN iajs-3490 35 73 to to ADP iajs-3490 35 74 the the DET iajs-3490 35 75 motion motion NOUN iajs-3490 35 76 equation.is equation.is X iajs-3490 35 77 uncomplicated uncomplicated ADJ iajs-3490 35 78 . . PUNCT iajs-3490 36 1 and and CCONJ iajs-3490 36 2 may may AUX iajs-3490 36 3 also also ADV iajs-3490 36 4 be be AUX iajs-3490 36 5 written write VERB iajs-3490 36 6 āˆš āˆš ADP iajs-3490 36 7 āˆš āˆš PROPN iajs-3490 36 8 āˆš āˆš PROPN iajs-3490 36 9 āˆš āˆš NUM iajs-3490 36 10 āˆš āˆš NUM iajs-3490 36 11 āˆš āˆš NUM iajs-3490 36 12 āˆš āˆš NUM iajs-3490 36 13 āˆš āˆš NUM iajs-3490 36 14 āˆš āˆš NUM iajs-3490 36 15 āˆš āˆš NUM iajs-3490 36 16 āˆš āˆš NUM iajs-3490 36 17 āˆš āˆš NUM iajs-3490 36 18 āˆš āˆš NUM iajs-3490 36 19 āˆš āˆš NUM iajs-3490 36 20 āˆš āˆš NUM iajs-3490 36 21 āˆš āˆš NUM iajs-3490 36 22 āˆš āˆš NUM iajs-3490 36 23 āˆš āˆš NUM iajs-3490 36 24 āˆš āˆš NUM iajs-3490 36 25 āˆš āˆš NUM iajs-3490 36 26 āˆš āˆš NUM iajs-3490 36 27 āˆš āˆš NUM iajs-3490 36 28 āˆš āˆš NUM iajs-3490 36 29 āˆš āˆš NUM iajs-3490 36 30 āˆš āˆš NUM iajs-3490 36 31 āˆš āˆš NUM iajs-3490 36 32 āˆš āˆš NUM iajs-3490 36 33 āˆš āˆš NUM iajs-3490 36 34 āˆš āˆš NUM iajs-3490 36 35 āˆš āˆš NUM iajs-3490 36 36 āˆš āˆš PROPN iajs-3490 36 37 āˆš āˆš NUM iajs-3490 36 38 āˆš āˆš PROPN iajs-3490 36 39 ( ( PUNCT iajs-3490 36 40 6 6 NUM iajs-3490 36 41 ) ) PUNCT iajs-3490 36 42 from from ADP iajs-3490 36 43 eq eq ADP iajs-3490 36 44 . . PUNCT iajs-3490 37 1 ( ( PUNCT iajs-3490 37 2 26 26 NUM iajs-3490 37 3 ) ) PUNCT iajs-3490 37 4 in in ADP iajs-3490 37 5 eq eq ADP iajs-3490 37 6 . . PUNCT iajs-3490 38 1 ( ( PUNCT iajs-3490 38 2 30 30 NUM iajs-3490 38 3 ) ) PUNCT iajs-3490 38 4 we we PRON iajs-3490 38 5 get get VERB iajs-3490 38 6 : : PUNCT iajs-3490 38 7 ( ( PUNCT iajs-3490 38 8 ] ] PUNCT iajs-3490 38 9 . . PUNCT iajs-3490 39 1 ( ( PUNCT iajs-3490 39 2 7 7 NUM iajs-3490 39 3 ) ) PUNCT iajs-3490 39 4 from from ADP iajs-3490 39 5 eq eq ADP iajs-3490 39 6 . . PUNCT iajs-3490 40 1 ( ( PUNCT iajs-3490 40 2 31 31 NUM iajs-3490 40 3 ) ) PUNCT iajs-3490 40 4 we we PRON iajs-3490 40 5 get get VERB iajs-3490 40 6 : : PUNCT iajs-3490 40 7 . . PUNCT iajs-3490 41 1 ( ( PUNCT iajs-3490 41 2 8) 8) NUM iajs-3490 41 3 pressure pressure NOUN iajs-3490 41 4 rise rise NOUN iajs-3490 41 5 for for ADP iajs-3490 41 6 every every DET iajs-3490 41 7 wave wave NOUN iajs-3490 41 8 distance distance NOUN iajs-3490 41 9 ( ( PUNCT iajs-3490 41 10 is be AUX iajs-3490 41 11 definite definite ADJ iajs-3490 41 12 . . PUNCT iajs-3490 41 13 : : PUNCT iajs-3490 42 1 āˆ« āˆ« PROPN iajs-3490 42 2 ( ( PUNCT iajs-3490 42 3 9 9 NUM iajs-3490 42 4 ) ) PUNCT iajs-3490 42 5 within within ADP iajs-3490 42 6 the the DET iajs-3490 42 7 defined define VERB iajs-3490 42 8 frame frame NOUN iajs-3490 42 9 , , PUNCT iajs-3490 42 10 the the DET iajs-3490 42 11 provided provide VERB iajs-3490 42 12 axial axial ADJ iajs-3490 42 13 velocity velocity NOUN iajs-3490 42 14 segment segment NOUN iajs-3490 42 15 u(x u(x NOUN iajs-3490 42 16 . . PUNCT iajs-3490 42 17 , , PUNCT iajs-3490 42 18 y. y. PROPN iajs-3490 42 19 , , PUNCT iajs-3490 42 20 t. t. NOUN iajs-3490 42 21 ) ) PUNCT iajs-3490 42 22 -1 -1 PUNCT iajs-3490 43 1 = = PUNCT iajs-3490 43 2 ( ( PUNCT iajs-3490 43 3 10 10 NUM iajs-3490 43 4 ) ) PUNCT iajs-3490 43 5 4 4 NUM iajs-3490 43 6 . . PUNCT iajs-3490 44 1 discussion discussion NOUN iajs-3490 44 2 we we PRON iajs-3490 44 3 can can AUX iajs-3490 44 4 see see VERB iajs-3490 44 5 that that SCONJ iajs-3490 44 6 the the DET iajs-3490 44 7 impact impact NOUN iajs-3490 44 8 of of ADP iajs-3490 44 9 ( ( PUNCT iajs-3490 44 10 da da NOUN iajs-3490 44 11 ) ) PUNCT iajs-3490 44 12 on on ADP iajs-3490 44 13 velocity velocity NOUN iajs-3490 44 14 , , PUNCT iajs-3490 44 15 we we PRON iajs-3490 44 16 can can AUX iajs-3490 44 17 see see VERB iajs-3490 44 18 velocity velocity NOUN iajs-3490 44 19 decreases decrease NOUN iajs-3490 44 20 with with ADP iajs-3490 44 21 an an DET iajs-3490 44 22 increase increase NOUN iajs-3490 44 23 of of ADP iajs-3490 44 24 ( ( PUNCT iajs-3490 44 25 da da NOUN iajs-3490 44 26 ) ) PUNCT iajs-3490 44 27 . . PUNCT iajs-3490 45 1 the the DET iajs-3490 45 2 pressure pressure NOUN iajs-3490 45 3 rise rise NOUN iajs-3490 45 4 ( ( PUNCT iajs-3490 45 5 p p NOUN iajs-3490 45 6 ) ) PUNCT iajs-3490 45 7 increased increase VERB iajs-3490 45 8 ( ( PUNCT iajs-3490 45 9 p p NOUN iajs-3490 45 10 -10 -10 PROPN iajs-3490 45 11 , , PUNCT iajs-3490 45 12 q1 q1 NOUN iajs-3490 45 13 2 2 NUM iajs-3490 45 14 ) ) PUNCT iajs-3490 45 15 with with ADP iajs-3490 45 16 a a DET iajs-3490 45 17 rise rise NOUN iajs-3490 45 18 ( ( PUNCT iajs-3490 45 19 ha ha INTJ iajs-3490 45 20 ) ) PUNCT iajs-3490 45 21 is be AUX iajs-3490 45 22 the the DET iajs-3490 45 23 pumping pump VERB iajs-3490 45 24 rate rate NOUN iajs-3490 45 25 decreases decrease NOUN iajs-3490 45 26 in in ADP iajs-3490 45 27 a a DET iajs-3490 45 28 peristaltic peristaltic ADJ iajs-3490 45 29 pumping pumping NOUN iajs-3490 45 30 region region NOUN iajs-3490 45 31 where where SCONJ iajs-3490 45 32 ( ( PUNCT iajs-3490 45 33 p p NOUN iajs-3490 45 34 -10 -10 PROPN iajs-3490 45 35 , , PUNCT iajs-3490 45 36 q1 q1 NOUN iajs-3490 45 37 2 2 NUM iajs-3490 45 38 ) ) PUNCT iajs-3490 45 39 , , PUNCT iajs-3490 45 40 and and CCONJ iajs-3490 45 41 the the DET iajs-3490 45 42 opposite opposite NOUN iajs-3490 45 43 happens happen VERB iajs-3490 45 44 in in ADP iajs-3490 45 45 with with ADP iajs-3490 45 46 increasing increase VERB iajs-3490 45 47 ( ( PUNCT iajs-3490 45 48 da da ADJ iajs-3490 45 49 ) ) PUNCT iajs-3490 45 50 and and CCONJ iajs-3490 45 51 ( ( PUNCT iajs-3490 45 52 ) ) PUNCT iajs-3490 45 53 ihjpas ihjpas PROPN iajs-3490 45 54 . . PUNCT iajs-3490 46 1 2025 2025 NUM iajs-3490 46 2 , , PUNCT iajs-3490 46 3 38(3 38(3 NUM iajs-3490 46 4 ) ) PUNCT iajs-3490 46 5 299 299 NUM iajs-3490 46 6 5 5 NUM iajs-3490 46 7 . . PUNCT iajs-3490 46 8 conclusion conclusion NOUN iajs-3490 46 9 a a DET iajs-3490 46 10 mathematical mathematical ADJ iajs-3490 46 11 model model NOUN iajs-3490 46 12 was be AUX iajs-3490 46 13 used use VERB iajs-3490 46 14 to to PART iajs-3490 46 15 inspect inspect VERB iajs-3490 46 16 the the DET iajs-3490 46 17 peristaltic peristaltic ADJ iajs-3490 46 18 motion motion NOUN iajs-3490 46 19 of of ADP iajs-3490 46 20 carreau carreau PROPN iajs-3490 46 21 's 's PART iajs-3490 46 22 fluid fluid NOUN iajs-3490 46 23 in in ADP iajs-3490 46 24 an an DET iajs-3490 46 25 asymmetric asymmetric ADJ iajs-3490 46 26 porous porous ADJ iajs-3490 46 27 material material NOUN iajs-3490 46 28 . . PUNCT iajs-3490 47 1 where where SCONJ iajs-3490 47 2 this this DET iajs-3490 47 3 study study NOUN iajs-3490 47 4 was be AUX iajs-3490 47 5 conducted conduct VERB iajs-3490 47 6 to to PART iajs-3490 47 7 know know VERB iajs-3490 47 8 the the DET iajs-3490 47 9 consequence consequence NOUN iajs-3490 47 10 of of ADP iajs-3490 47 11 couple couple NOUN iajs-3490 47 12 stress stress NOUN iajs-3490 47 13 on on ADP iajs-3490 47 14 peristaltic peristaltic ADJ iajs-3490 47 15 transport transport NOUN iajs-3490 47 16 of of ADP iajs-3490 47 17 carreau carreau PROPN iajs-3490 47 18 fluid fluid ADJ iajs-3490 47 19 peristaltic peristaltic ADJ iajs-3490 47 20 current current NOUN iajs-3490 47 21 . . PUNCT iajs-3490 48 1 the the DET iajs-3490 48 2 results result NOUN iajs-3490 48 3 are be AUX iajs-3490 48 4 discussed discuss VERB iajs-3490 48 5 through through ADP iajs-3490 48 6 graphs graph NOUN iajs-3490 48 7 , , PUNCT iajs-3490 48 8 as as SCONJ iajs-3490 48 9 follows follow VERB iajs-3490 48 10 : : PUNCT iajs-3490 48 11 1 1 X iajs-3490 48 12 . . PUNCT iajs-3490 49 1 at at ADP iajs-3490 49 2 increasing increase VERB iajs-3490 49 3 the the DET iajs-3490 49 4 velocity velocity NOUN iajs-3490 49 5 increases increase NOUN iajs-3490 49 6 in in ADP iajs-3490 49 7 the the DET iajs-3490 49 8 focal focal ADJ iajs-3490 49 9 area area NOUN iajs-3490 49 10 withe withe PROPN iajs-3490 49 11 border border NOUN iajs-3490 49 12 canal canal NOUN iajs-3490 49 13 wall wall NOUN iajs-3490 49 14 but but CCONJ iajs-3490 49 15 the the DET iajs-3490 49 16 opposite opposite ADJ iajs-3490 49 17 occur occur VERB iajs-3490 49 18 for for ADP iajs-3490 49 19 increasing increase VERB iajs-3490 49 20 ( ( PUNCT iajs-3490 49 21 da da NOUN iajs-3490 49 22 ) ) PUNCT iajs-3490 49 23 . . PUNCT iajs-3490 50 1 and and CCONJ iajs-3490 50 2 the the DET iajs-3490 50 3 axial axial ADJ iajs-3490 50 4 velocity velocity NOUN iajs-3490 50 5 does do AUX iajs-3490 50 6 not not PART iajs-3490 50 7 change change VERB iajs-3490 50 8 with with ADP iajs-3490 50 9 increasing increase VERB iajs-3490 50 10 of of ADP iajs-3490 50 11 ( ( PUNCT iajs-3490 50 12 ha ha INTJ iajs-3490 50 13 ) ) PUNCT iajs-3490 50 14 . . PUNCT iajs-3490 51 1 2 2 X iajs-3490 51 2 . . X iajs-3490 51 3 the the DET iajs-3490 51 4 pressure pressure NOUN iajs-3490 51 5 of of ADP iajs-3490 51 6 rice rice NOUN iajs-3490 51 7 for for ADP iajs-3490 51 8 each each DET iajs-3490 51 9 wavelength wavelength NOUN iajs-3490 51 10 Ī“š‘ƒ Ī“š‘ƒ PROPN iajs-3490 51 11 increases increase VERB iajs-3490 51 12 in in ADP iajs-3490 51 13 magnitude magnitude NOUN iajs-3490 51 14 with with ADP iajs-3490 51 15 increasing increase VERB iajs-3490 51 16 values value NOUN iajs-3490 51 17 of of ADP iajs-3490 51 18 ( ( PUNCT iajs-3490 51 19 ha ha INTJ iajs-3490 51 20 ) ) PUNCT iajs-3490 51 21 , , PUNCT iajs-3490 51 22 acknowledgment acknowledgment NOUN iajs-3490 51 23 i i PRON iajs-3490 51 24 would would AUX iajs-3490 51 25 like like VERB iajs-3490 51 26 to to PART iajs-3490 51 27 extend extend VERB iajs-3490 51 28 my my PRON iajs-3490 51 29 sincere sincere ADJ iajs-3490 51 30 thanks thank NOUN iajs-3490 51 31 to to ADP iajs-3490 51 32 the the DET iajs-3490 51 33 distinguished distinguished PROPN iajs-3490 51 34 dr dr PROPN iajs-3490 51 35 . . PROPN iajs-3490 51 36 liqaa liqaa PROPN iajs-3490 51 37 z. z. PROPN iajs-3490 51 38 hummady hummady PROPN iajs-3490 51 39 who who PRON iajs-3490 51 40 did do AUX iajs-3490 51 41 not not PART iajs-3490 51 42 hesitate hesitate VERB iajs-3490 51 43 to to PART iajs-3490 51 44 provide provide VERB iajs-3490 51 45 any any DET iajs-3490 51 46 possible possible ADJ iajs-3490 51 47 assistance assistance NOUN iajs-3490 51 48 , , PUNCT iajs-3490 51 49 whether whether SCONJ iajs-3490 51 50 moral moral ADJ iajs-3490 51 51 or or CCONJ iajs-3490 51 52 scientific scientific ADJ iajs-3490 51 53 . . PUNCT iajs-3490 52 1 conflict conflict NOUN iajs-3490 52 2 of of ADP iajs-3490 52 3 interest interest NOUN iajs-3490 52 4 i i PRON iajs-3490 52 5 am be AUX iajs-3490 52 6 , , PUNCT iajs-3490 52 7 the the DET iajs-3490 52 8 researcher researcher NOUN iajs-3490 52 9 hamza hamza PROPN iajs-3490 52 10 rashid rashid PROPN iajs-3490 52 11 , , PUNCT iajs-3490 52 12 declare declare VERB iajs-3490 52 13 that that SCONJ iajs-3490 52 14 there there PRON iajs-3490 52 15 is be VERB iajs-3490 52 16 no no DET iajs-3490 52 17 conflict conflict NOUN iajs-3490 52 18 of of ADP iajs-3490 52 19 interest interest NOUN iajs-3490 52 20 . . PUNCT iajs-3490 53 1 funding funding NOUN iajs-3490 53 2 there there PRON iajs-3490 53 3 is be VERB iajs-3490 53 4 no no DET iajs-3490 53 5 funding funding NOUN iajs-3490 53 6 for for ADP iajs-3490 53 7 the the DET iajs-3490 53 8 article article NOUN iajs-3490 53 9 references reference VERB iajs-3490 53 10 1 1 NUM iajs-3490 53 11 . . PUNCT iajs-3490 54 1 asghar asghar PROPN iajs-3490 54 2 z z PROPN iajs-3490 54 3 , , PUNCT iajs-3490 54 4 ali ali PROPN iajs-3490 54 5 n. n. PROPN iajs-3490 54 6 mixed mix VERB iajs-3490 54 7 convective convective ADJ iajs-3490 54 8 heat heat NOUN iajs-3490 54 9 transfer transfer NOUN iajs-3490 54 10 analysis analysis NOUN iajs-3490 54 11 for for ADP iajs-3490 54 12 the the DET iajs-3490 54 13 peristaltic peristaltic ADJ iajs-3490 54 14 transport transport NOUN iajs-3490 54 15 of of ADP iajs-3490 54 16 viscoplastic viscoplastic ADJ iajs-3490 54 17 fluid fluid NOUN iajs-3490 54 18 . . PUNCT iajs-3490 55 1 aip aip PROPN iajs-3490 55 2 adv adv PROPN iajs-3490 55 3 . . PUNCT iajs-3490 56 1 2019;9.9:095001 2019;9.9:095001 NUM iajs-3490 56 2 . . PUNCT iajs-3490 57 1 https://doi.org/10.1063/1.5118846 https://doi.org/10.1063/1.5118846 PROPN iajs-3490 57 2 2 2 NUM iajs-3490 57 3 . . PUNCT iajs-3490 57 4 hussain hussain PROPN iajs-3490 57 5 s s PROPN iajs-3490 57 6 , , PUNCT iajs-3490 57 7 ali ali PROPN iajs-3490 57 8 n. n. PROPN iajs-3490 57 9 electro electro PROPN iajs-3490 57 10 - - PUNCT iajs-3490 57 11 kinetically kinetically ADV iajs-3490 57 12 modulated modulate VERB iajs-3490 57 13 peristaltic peristaltic ADJ iajs-3490 57 14 transport transport NOUN iajs-3490 57 15 of of ADP iajs-3490 57 16 multilayered multilayered ADJ iajs-3490 57 17 power power NOUN iajs-3490 57 18 - - PUNCT iajs-3490 57 19 law law NOUN iajs-3490 57 20 fluid fluid NOUN iajs-3490 57 21 in in ADP iajs-3490 57 22 an an DET iajs-3490 57 23 axisymmetric axisymmetric ADJ iajs-3490 57 24 tube tube NOUN iajs-3490 57 25 . . PUNCT iajs-3490 58 1 eur eur ADJ iajs-3490 58 2 . . PUNCT iajs-3490 59 1 phys phy NOUN iajs-3490 59 2 . . PUNCT iajs-3490 60 1 j. j. PROPN iajs-3490 60 2 plus plus PROPN iajs-3490 60 3 . . PUNCT iajs-3490 61 1 2020;135.4:1ā€“24 2020;135.4:1ā€“24 NUM iajs-3490 61 2 . . PUNCT iajs-3490 62 1 https://doi.org/10.1140/epjp/s13360-020-00331-w https://doi.org/10.1140/epjp/s13360-020-00331-w NOUN iajs-3490 62 2 3 3 NUM iajs-3490 62 3 . . NOUN iajs-3490 62 4 vajravelu vajravelu PROPN iajs-3490 62 5 k k PROPN iajs-3490 62 6 , , PUNCT iajs-3490 62 7 sreenadh sreenadh PROPN iajs-3490 62 8 s s PART iajs-3490 62 9 , , PUNCT iajs-3490 62 10 babu babu PROPN iajs-3490 62 11 vr vr PROPN iajs-3490 62 12 . . PROPN iajs-3490 62 13 peristaltic peristaltic ADJ iajs-3490 62 14 pumping pumping NOUN iajs-3490 62 15 of of ADP iajs-3490 62 16 a a DET iajs-3490 62 17 herschel herschel PROPN iajs-3490 62 18 ā€“ ā€“ PUNCT iajs-3490 62 19 bulkley bulkley NOUN iajs-3490 62 20 fluid fluid NOUN iajs-3490 62 21 in in ADP iajs-3490 62 22 a a DET iajs-3490 62 23 channel channel NOUN iajs-3490 62 24 . . PUNCT iajs-3490 63 1 appl appl PROPN iajs-3490 63 2 . . PROPN iajs-3490 63 3 math math PROPN iajs-3490 63 4 . . PUNCT iajs-3490 64 1 comput comput NOUN iajs-3490 64 2 . . 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