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PUNCT iajs-2987 2 1 36(2)2023 36(2)2023 NUM iajs-2987 2 2 314 314 NUM iajs-2987 2 3 this this DET iajs-2987 2 4 work work NOUN iajs-2987 2 5 is be AUX iajs-2987 2 6 licensed license VERB iajs-2987 2 7 under under ADP iajs-2987 2 8 a a DET iajs-2987 2 9 creative creative ADJ iajs-2987 2 10 commons common NOUN iajs-2987 2 11 attribution attribution NOUN iajs-2987 2 12 4.0 4.0 NUM iajs-2987 2 13 international international ADJ iajs-2987 2 14 license license NOUN iajs-2987 2 15 abstract abstract NOUN iajs-2987 2 16 the the DET iajs-2987 2 17 purpose purpose NOUN iajs-2987 2 18 of of ADP iajs-2987 2 19 this this DET iajs-2987 2 20 research research NOUN iajs-2987 2 21 is be AUX iajs-2987 2 22 to to PART iajs-2987 2 23 investigate investigate VERB iajs-2987 2 24 the the DET iajs-2987 2 25 effects effect NOUN iajs-2987 2 26 of of ADP iajs-2987 2 27 rotation rotation NOUN iajs-2987 2 28 on on ADP iajs-2987 2 29 heat heat NOUN iajs-2987 2 30 transfer transfer NOUN iajs-2987 2 31 using use VERB iajs-2987 2 32 inclination inclination NOUN iajs-2987 2 33 magnetohydrodynamics magnetohydrodynamic NOUN iajs-2987 2 34 for for ADP iajs-2987 2 35 a a DET iajs-2987 2 36 couple couple NOUN iajs-2987 2 37 - - PUNCT iajs-2987 2 38 stress stress NOUN iajs-2987 2 39 fluid fluid NOUN iajs-2987 2 40 in in ADP iajs-2987 2 41 a a DET iajs-2987 2 42 non non ADJ iajs-2987 2 43 - - ADJ iajs-2987 2 44 uniform uniform ADJ iajs-2987 2 45 canal canal NOUN iajs-2987 2 46 . . PUNCT iajs-2987 3 1 when when SCONJ iajs-2987 3 2 the the DET iajs-2987 3 3 reynolds reynolds PROPN iajs-2987 3 4 number number NOUN iajs-2987 3 5 is be AUX iajs-2987 3 6 low low ADJ iajs-2987 3 7 and and CCONJ iajs-2987 3 8 the the DET iajs-2987 3 9 wavelength wavelength NOUN iajs-2987 3 10 is be AUX iajs-2987 3 11 long long ADJ iajs-2987 3 12 , , PUNCT iajs-2987 3 13 math math NOUN iajs-2987 3 14 formulas formula NOUN iajs-2987 3 15 are be AUX iajs-2987 3 16 used use VERB iajs-2987 3 17 to to PART iajs-2987 3 18 describe describe VERB iajs-2987 3 19 the the DET iajs-2987 3 20 stream stream NOUN iajs-2987 3 21 function function NOUN iajs-2987 3 22 , , PUNCT iajs-2987 3 23 as as ADV iajs-2987 3 24 well well ADV iajs-2987 3 25 as as ADP iajs-2987 3 26 the the DET iajs-2987 3 27 gradient gradient NOUN iajs-2987 3 28 of of ADP iajs-2987 3 29 pressure pressure NOUN iajs-2987 3 30 , , PUNCT iajs-2987 3 31 temperature temperature NOUN iajs-2987 3 32 , , PUNCT iajs-2987 3 33 pressure pressure NOUN iajs-2987 3 34 rise rise NOUN iajs-2987 3 35 and and CCONJ iajs-2987 3 36 axial axial ADJ iajs-2987 3 37 velocity velocity NOUN iajs-2987 3 38 per per ADP iajs-2987 3 39 wavelength wavelength NOUN iajs-2987 3 40 , , PUNCT iajs-2987 3 41 which which PRON iajs-2987 3 42 have have AUX iajs-2987 3 43 been be AUX iajs-2987 3 44 calculated calculate VERB iajs-2987 3 45 analytically analytically ADV iajs-2987 3 46 . . PUNCT iajs-2987 4 1 the the DET iajs-2987 4 2 many many ADJ iajs-2987 4 3 parameters parameter NOUN iajs-2987 4 4 in in ADP iajs-2987 4 5 the the DET iajs-2987 4 6 current current ADJ iajs-2987 4 7 model model NOUN iajs-2987 4 8 are be AUX iajs-2987 4 9 assigned assign VERB iajs-2987 4 10 a a DET iajs-2987 4 11 definite definite ADJ iajs-2987 4 12 set set NOUN iajs-2987 4 13 of of ADP iajs-2987 4 14 values value NOUN iajs-2987 4 15 . . PUNCT iajs-2987 5 1 it it PRON iajs-2987 5 2 has have AUX iajs-2987 5 3 been be AUX iajs-2987 5 4 noticed notice VERB iajs-2987 5 5 that that SCONJ iajs-2987 5 6 both both CCONJ iajs-2987 5 7 the the DET iajs-2987 5 8 pressure pressure NOUN iajs-2987 5 9 rise rise NOUN iajs-2987 5 10 and and CCONJ iajs-2987 5 11 the the DET iajs-2987 5 12 pressure pressure NOUN iajs-2987 5 13 gradient gradient NOUN iajs-2987 5 14 decrease decrease NOUN iajs-2987 5 15 with with ADP iajs-2987 5 16 the the DET iajs-2987 5 17 rise rise NOUN iajs-2987 5 18 of of ADP iajs-2987 5 19 the the DET iajs-2987 5 20 rotation rotation NOUN iajs-2987 5 21 and and CCONJ iajs-2987 5 22 couple couple NOUN iajs-2987 5 23 stress stress NOUN iajs-2987 5 24 , , PUNCT iajs-2987 5 25 while while SCONJ iajs-2987 5 26 they they PRON iajs-2987 5 27 increase increase VERB iajs-2987 5 28 with with ADP iajs-2987 5 29 an an DET iajs-2987 5 30 increase increase NOUN iajs-2987 5 31 in in ADP iajs-2987 5 32 viscosity viscosity NOUN iajs-2987 5 33 and and CCONJ iajs-2987 5 34 hartmann hartmann PROPN iajs-2987 5 35 number number NOUN iajs-2987 5 36 . . PUNCT iajs-2987 6 1 the the DET iajs-2987 6 2 explanation explanation NOUN iajs-2987 6 3 of of ADP iajs-2987 6 4 parameters parameter NOUN iajs-2987 6 5 is be AUX iajs-2987 6 6 shown show VERB iajs-2987 6 7 graphically graphically ADV iajs-2987 6 8 by by ADP iajs-2987 6 9 a a DET iajs-2987 6 10 series series NOUN iajs-2987 6 11 of of ADP iajs-2987 6 12 figures figure NOUN iajs-2987 6 13 using use VERB iajs-2987 6 14 " " PUNCT iajs-2987 6 15 mathematica mathematica PROPN iajs-2987 6 16 " " PUNCT iajs-2987 6 17 . . PUNCT iajs-2987 7 1 keywords keyword NOUN iajs-2987 7 2 : : PUNCT iajs-2987 7 3 non non ADJ iajs-2987 7 4 - - ADJ iajs-2987 7 5 uniform uniform ADJ iajs-2987 7 6 channel channel NOUN iajs-2987 7 7 , , PUNCT iajs-2987 7 8 rotation rotation NOUN iajs-2987 7 9 , , PUNCT iajs-2987 7 10 inclined inclined ADJ iajs-2987 7 11 mhd mhd NOUN iajs-2987 7 12 , , PUNCT iajs-2987 7 13 couple couple NOUN iajs-2987 7 14 stress stress NOUN iajs-2987 7 15 , , PUNCT iajs-2987 7 16 porous porous ADJ iajs-2987 7 17 medium medium ADJ iajs-2987 7 18 1 1 NUM iajs-2987 7 19 . . PUNCT iajs-2987 8 1 introduction introduction NOUN iajs-2987 8 2 using use VERB iajs-2987 8 3 a a DET iajs-2987 8 4 couple couple NOUN iajs-2987 8 5 stress stress NOUN iajs-2987 8 6 fluids fluid NOUN iajs-2987 8 7 as as ADP iajs-2987 8 8 a a DET iajs-2987 8 9 model model NOUN iajs-2987 8 10 for for ADP iajs-2987 8 11 describing describe VERB iajs-2987 8 12 biologically biologically ADV iajs-2987 8 13 complicated complicated ADJ iajs-2987 8 14 fluids fluid NOUN iajs-2987 8 15 , , PUNCT iajs-2987 8 16 such such ADJ iajs-2987 8 17 as as ADP iajs-2987 8 18 colloidal colloidal NOUN iajs-2987 8 19 fluids fluid NOUN iajs-2987 8 20 , , PUNCT iajs-2987 8 21 polymeric polymeric ADJ iajs-2987 8 22 suspensions suspension NOUN iajs-2987 8 23 , , PUNCT iajs-2987 8 24 animal animal NOUN iajs-2987 8 25 and and CCONJ iajs-2987 8 26 human human ADJ iajs-2987 8 27 blood blood NOUN iajs-2987 8 28 , , PUNCT iajs-2987 8 29 and and CCONJ iajs-2987 8 30 lubrication lubrication NOUN iajs-2987 8 31 , , PUNCT iajs-2987 8 32 is be AUX iajs-2987 8 33 extremely extremely ADV iajs-2987 8 34 beneficial beneficial ADJ iajs-2987 8 35 in in ADP iajs-2987 8 36 understanding understand VERB iajs-2987 8 37 a a DET iajs-2987 8 38 wide wide ADJ iajs-2987 8 39 range range NOUN iajs-2987 8 40 of of ADP iajs-2987 8 41 physical physical ADJ iajs-2987 8 42 issues issue NOUN iajs-2987 8 43 . . PUNCT iajs-2987 9 1 one one NUM iajs-2987 9 2 of of ADP iajs-2987 9 3 the the DET iajs-2987 9 4 numerous numerous ADJ iajs-2987 9 5 models model NOUN iajs-2987 9 6 created create VERB iajs-2987 9 7 to to PART iajs-2987 9 8 describe describe VERB iajs-2987 9 9 the the DET iajs-2987 9 10 reaction reaction NOUN iajs-2987 9 11 explanation explanation NOUN iajs-2987 9 12 of of ADP iajs-2987 9 13 non non ADJ iajs-2987 9 14 - - ADJ iajs-2987 9 15 newtonian newtonian ADJ iajs-2987 9 16 fluids fluid NOUN iajs-2987 9 17 is be AUX iajs-2987 9 18 the the DET iajs-2987 9 19 couple couple NOUN iajs-2987 9 20 stress stress ADJ iajs-2987 9 21 fluid fluid NOUN iajs-2987 9 22 model model NOUN iajs-2987 9 23 . . PUNCT iajs-2987 10 1 nonnewtonian nonnewtonian PROPN iajs-2987 10 2 fluids fluid NOUN iajs-2987 10 3 , , PUNCT iajs-2987 10 4 such such ADJ iajs-2987 10 5 as as ADP iajs-2987 10 6 couple couple NOUN iajs-2987 10 7 stress stress NOUN iajs-2987 10 8 fluids fluid NOUN iajs-2987 10 9 , , PUNCT iajs-2987 10 10 are be AUX iajs-2987 10 11 those those PRON iajs-2987 10 12 in in ADP iajs-2987 10 13 which which PRON iajs-2987 10 14 particle particle NOUN iajs-2987 10 15 size size NOUN iajs-2987 10 16 is be AUX iajs-2987 10 17 taken take VERB iajs-2987 10 18 into into ADP iajs-2987 10 19 account account NOUN iajs-2987 10 20 and and CCONJ iajs-2987 10 21 studied study VERB iajs-2987 10 22 by by ADP iajs-2987 10 23 [ [ PUNCT iajs-2987 10 24 1 1 NUM iajs-2987 10 25 - - SYM iajs-2987 10 26 4 4 NUM iajs-2987 10 27 ] ] PUNCT iajs-2987 10 28 . . 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PUNCT iajs-2987 12 1 murad murad NOUN iajs-2987 12 2 and and CCONJ iajs-2987 12 3 abdulhadi abdulhadi NOUN iajs-2987 13 1 [ [ X iajs-2987 13 2 6 6 NUM iajs-2987 13 3 ] ] PUNCT iajs-2987 13 4 analysis analysis NOUN iajs-2987 13 5 of of ADP iajs-2987 13 6 mixed mixed ADJ iajs-2987 13 7 convective convective ADJ iajs-2987 13 8 heat heat NOUN iajs-2987 13 9 transfer transfer NOUN iajs-2987 13 10 for for ADP iajs-2987 13 11 peristaltic peristaltic ADJ iajs-2987 13 12 transport transport NOUN iajs-2987 13 13 of of ADP iajs-2987 13 14 viscoplastic viscoplastic ADJ iajs-2987 13 15 fluid fluid NOUN iajs-2987 13 16 : : PUNCT iajs-2987 13 17 perturbation perturbation NOUN iajs-2987 13 18 and and CCONJ iajs-2987 13 19 numerical numerical ADJ iajs-2987 13 20 studies study NOUN iajs-2987 13 21 . . PUNCT iajs-2987 14 1 abdulla abdulla PROPN iajs-2987 14 2 and and CCONJ iajs-2987 14 3 hummady hummady ADJ iajs-2987 14 4 [ [ X iajs-2987 14 5 7 7 NUM iajs-2987 14 6 ] ] PUNCT iajs-2987 14 7 considered consider VERB iajs-2987 14 8 the the DET iajs-2987 14 9 influence influence NOUN iajs-2987 14 10 of of ADP iajs-2987 14 11 sliding slide VERB iajs-2987 14 12 speed speed NOUN iajs-2987 14 13 on on ADP iajs-2987 14 14 channel channel NOUN iajs-2987 14 15 walls wall NOUN iajs-2987 14 16 and and CCONJ iajs-2987 14 17 the the DET iajs-2987 14 18 effect effect NOUN iajs-2987 14 19 of of ADP iajs-2987 14 20 nonlinear nonlinear ADJ iajs-2987 14 21 particle particle NOUN iajs-2987 14 22 size size NOUN iajs-2987 14 23 . . PUNCT iajs-2987 15 1 to to PART iajs-2987 15 2 make make VERB iajs-2987 15 3 things thing NOUN iajs-2987 15 4 even even ADV iajs-2987 15 5 more more ADV iajs-2987 15 6 complicated complicated ADJ iajs-2987 15 7 , , PUNCT iajs-2987 15 8 non non ADJ iajs-2987 15 9 - - ADJ iajs-2987 15 10 newtonian newtonian ADJ iajs-2987 15 11 fluids fluid NOUN iajs-2987 15 12 ca can AUX iajs-2987 15 13 n't not PART iajs-2987 15 14 be be AUX iajs-2987 15 15 studied study VERB iajs-2987 15 16 with with ADP iajs-2987 15 17 non non ADJ iajs-2987 15 18 - - ADJ iajs-2987 15 19 slip slip ADJ iajs-2987 15 20 boundary boundary ADJ iajs-2987 15 21 conditions condition NOUN iajs-2987 15 22 because because SCONJ iajs-2987 15 23 it it PRON iajs-2987 15 24 's be AUX iajs-2987 15 25 doi.org/10.30526/36.2.2987 doi.org/10.30526/36.2.2987 NOUN iajs-2987 15 26 article article NOUN iajs-2987 15 27 history history NOUN iajs-2987 15 28 : : PUNCT iajs-2987 15 29 received receive VERB iajs-2987 15 30 23 23 NUM iajs-2987 15 31 august august PROPN iajs-2987 15 32 2022 2022 NUM iajs-2987 15 33 , , PUNCT iajs-2987 15 34 accepted accept VERB iajs-2987 15 35 9 9 NUM iajs-2987 15 36 october october NOUN iajs-2987 15 37 2022 2022 NUM iajs-2987 15 38 , , PUNCT iajs-2987 15 39 published publish VERB iajs-2987 15 40 in in ADP iajs-2987 15 41 april april PROPN iajs-2987 15 42 2023 2023 NUM iajs-2987 15 43 . . PUNCT iajs-2987 16 1 ibn ibn PROPN iajs-2987 16 2 al al PROPN iajs-2987 16 3 - - PUNCT iajs-2987 16 4 haitham haitham PROPN iajs-2987 16 5 journal journal PROPN iajs-2987 16 6 for for ADP iajs-2987 16 7 pure pure ADJ iajs-2987 16 8 and and CCONJ iajs-2987 16 9 applied applied ADJ iajs-2987 16 10 sciences sciences PROPN iajs-2987 16 11 journal journal PROPN iajs-2987 16 12 homepage homepage NOUN iajs-2987 16 13 : : PUNCT iajs-2987 16 14 jih.uobaghdad.edu.iq jih.uobaghdad.edu.iq VERB iajs-2987 16 15 the the DET iajs-2987 16 16 effect effect NOUN iajs-2987 16 17 of of ADP iajs-2987 16 18 rotation rotation NOUN iajs-2987 16 19 on on ADP iajs-2987 16 20 the the DET iajs-2987 16 21 heat heat NOUN iajs-2987 16 22 transfer transfer NOUN iajs-2987 16 23 of of ADP iajs-2987 16 24 a a DET iajs-2987 16 25 couple couple NOUN iajs-2987 16 26 stress stress NOUN iajs-2987 16 27 fluid fluid NOUN iajs-2987 16 28 in in ADP iajs-2987 16 29 a a DET iajs-2987 16 30 nonuniform nonuniform NOUN iajs-2987 16 31 inclined incline VERB iajs-2987 16 32 asymmetrical asymmetrical ADJ iajs-2987 16 33 channel channel NOUN iajs-2987 16 34 with with ADP iajs-2987 16 35 inclined inclined ADJ iajs-2987 16 36 mhd mhd PROPN iajs-2987 16 37 hanaa hanaa PROPN iajs-2987 16 38 abdulhussein abdulhussein PROPN iajs-2987 16 39 department department PROPN iajs-2987 16 40 of of ADP iajs-2987 16 41 mathematics mathematics PROPN iajs-2987 16 42 , , PUNCT iajs-2987 16 43 college college NOUN iajs-2987 16 44 of of ADP iajs-2987 16 45 science science NOUN iajs-2987 16 46 , , PUNCT iajs-2987 16 47 university university NOUN iajs-2987 16 48 of of ADP iajs-2987 16 49 baghdad baghdad PROPN iajs-2987 16 50 , , PUNCT iajs-2987 16 51 baghdad baghdad PROPN iajs-2987 16 52 , , PUNCT iajs-2987 16 53 iraq iraq PROPN iajs-2987 16 54 . . PUNCT iajs-2987 17 1 hshatty@uowasit.edu.iq hshatty@uowasit.edu.iq PROPN iajs-2987 17 2 ahmed ahmed PROPN iajs-2987 17 3 m. m. PROPN iajs-2987 17 4 abdulhadi abdulhadi PROPN iajs-2987 17 5 department department PROPN iajs-2987 17 6 of of ADP iajs-2987 17 7 mathematics mathematics PROPN iajs-2987 17 8 , , PUNCT iajs-2987 17 9 college college NOUN iajs-2987 17 10 of of ADP iajs-2987 17 11 science science NOUN iajs-2987 17 12 , , PUNCT iajs-2987 17 13 university university NOUN iajs-2987 17 14 of of ADP iajs-2987 17 15 baghdad baghdad PROPN iajs-2987 17 16 , , PUNCT iajs-2987 17 17 baghdad baghdad PROPN iajs-2987 17 18 , , PUNCT iajs-2987 17 19 iraq iraq PROPN iajs-2987 17 20 . . PUNCT iajs-2987 18 1 ahm6161@yahoo.com ahm6161@yahoo.com X iajs-2987 19 1 https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ PROPN iajs-2987 19 2 mailto:hshatty@uowasit.edu.iq mailto:hshatty@uowasit.edu.iq PROPN iajs-2987 19 3 mailto:ahm6161@yahoo.com mailto:ahm6161@yahoo.com PROPN iajs-2987 19 4 ihjpas ihjpa VERB iajs-2987 19 5 . . PUNCT iajs-2987 20 1 36(2)2023 36(2)2023 NUM iajs-2987 20 2 315 315 NUM iajs-2987 20 3 easy easy ADJ iajs-2987 20 4 to to PART iajs-2987 20 5 see see VERB iajs-2987 20 6 how how SCONJ iajs-2987 20 7 the the DET iajs-2987 20 8 walls wall NOUN iajs-2987 20 9 slide slide VERB iajs-2987 20 10 . . PUNCT iajs-2987 21 1 in in ADP iajs-2987 21 2 technology technology NOUN iajs-2987 21 3 , , PUNCT iajs-2987 21 4 boundary boundary ADJ iajs-2987 21 5 slip slip NOUN iajs-2987 21 6 condition condition NOUN iajs-2987 21 7 fluids fluid NOUN iajs-2987 21 8 can can AUX iajs-2987 21 9 be be AUX iajs-2987 21 10 used use VERB iajs-2987 21 11 to to PART iajs-2987 21 12 polish polish VERB iajs-2987 21 13 artificial artificial ADJ iajs-2987 21 14 hearts heart NOUN iajs-2987 21 15 . . PUNCT iajs-2987 22 1 see see VERB iajs-2987 22 2 [ [ X iajs-2987 22 3 8 8 NUM iajs-2987 22 4 - - SYM iajs-2987 22 5 13 13 NUM iajs-2987 22 6 ] ] PUNCT iajs-2987 22 7 for for ADP iajs-2987 22 8 a a DET iajs-2987 22 9 list list NOUN iajs-2987 22 10 of of ADP iajs-2987 22 11 studies study NOUN iajs-2987 22 12 that that PRON iajs-2987 22 13 use use VERB iajs-2987 22 14 this this DET iajs-2987 22 15 condition condition NOUN iajs-2987 22 16 . . PUNCT iajs-2987 23 1 researchers researcher NOUN iajs-2987 23 2 have have AUX iajs-2987 23 3 recently recently ADV iajs-2987 23 4 looked look VERB iajs-2987 23 5 into into ADP iajs-2987 23 6 how how SCONJ iajs-2987 23 7 a a DET iajs-2987 23 8 magnetic magnetic ADJ iajs-2987 23 9 field field NOUN iajs-2987 23 10 and and CCONJ iajs-2987 23 11 rotation rotation NOUN iajs-2987 23 12 affect affect VERB iajs-2987 23 13 how how SCONJ iajs-2987 23 14 fluid fluid ADJ iajs-2987 23 15 moves move NOUN iajs-2987 23 16 through through ADP iajs-2987 23 17 an an DET iajs-2987 23 18 asymmetric asymmetric ADJ iajs-2987 23 19 channel channel NOUN iajs-2987 23 20 , , PUNCT iajs-2987 23 21 abd abd NOUN iajs-2987 23 22 - - PUNCT iajs-2987 23 23 alla alla NOUN iajs-2987 23 24 and and CCONJ iajs-2987 23 25 abo abo NOUN iajs-2987 23 26 - - PUNCT iajs-2987 23 27 dahab dahab NOUN iajs-2987 23 28 [ [ X iajs-2987 23 29 14 14 NUM iajs-2987 23 30 ] ] PUNCT iajs-2987 23 31 . . PUNCT iajs-2987 24 1 the the DET iajs-2987 24 2 effects effect NOUN iajs-2987 24 3 of of ADP iajs-2987 24 4 rotation rotation NOUN iajs-2987 24 5 and and CCONJ iajs-2987 24 6 mhd mhd NOUN iajs-2987 24 7 on on ADP iajs-2987 24 8 an an DET iajs-2987 24 9 asymmetric asymmetric ADJ iajs-2987 24 10 channel channel NOUN iajs-2987 24 11 through through ADP iajs-2987 24 12 a a DET iajs-2987 24 13 porous porous ADJ iajs-2987 24 14 medium medium NOUN iajs-2987 24 15 where where SCONJ iajs-2987 24 16 a a DET iajs-2987 24 17 jeffrey jeffrey PROPN iajs-2987 24 18 fluid fluid NOUN iajs-2987 24 19 flows flow NOUN iajs-2987 24 20 nonlinearly nonlinearly ADV iajs-2987 24 21 have have AUX iajs-2987 24 22 been be AUX iajs-2987 24 23 looked look VERB iajs-2987 24 24 at at ADP iajs-2987 24 25 by by ADP iajs-2987 24 26 abdulhadi abdulhadi NOUN iajs-2987 24 27 and and CCONJ iajs-2987 24 28 al al PROPN iajs-2987 24 29 - - PROPN iajs-2987 24 30 hadad hadad PROPN iajs-2987 24 31 [ [ X iajs-2987 24 32 15 15 NUM iajs-2987 24 33 ] ] PUNCT iajs-2987 24 34 . . PUNCT iajs-2987 25 1 in in ADP iajs-2987 25 2 porous porous ADJ iajs-2987 25 3 media medium NOUN iajs-2987 25 4 with with ADP iajs-2987 25 5 non non ADJ iajs-2987 25 6 - - ADJ iajs-2987 25 7 symmetric symmetric ADJ iajs-2987 25 8 canals canal NOUN iajs-2987 25 9 , , PUNCT iajs-2987 25 10 rotating rotate VERB iajs-2987 25 11 waveform waveform NOUN iajs-2987 25 12 motion motion NOUN iajs-2987 25 13 in in ADP iajs-2987 25 14 two two NUM iajs-2987 25 15 - - PUNCT iajs-2987 25 16 dimensional dimensional ADJ iajs-2987 25 17 channels channel NOUN iajs-2987 25 18 of of ADP iajs-2987 25 19 non non ADJ iajs-2987 25 20 - - ADJ iajs-2987 25 21 newtonian newtonian ADJ iajs-2987 25 22 fluid fluid NOUN iajs-2987 25 23 was be AUX iajs-2987 25 24 explored explore VERB iajs-2987 25 25 by by ADP iajs-2987 25 26 alshareef alshareef VERB iajs-2987 25 27 [ [ X iajs-2987 25 28 16 16 NUM iajs-2987 25 29 ] ] PUNCT iajs-2987 25 30 . . PUNCT iajs-2987 26 1 for for ADP iajs-2987 26 2 viscoplastic viscoplastic ADJ iajs-2987 26 3 fluid fluid ADJ iajs-2987 26 4 and and CCONJ iajs-2987 26 5 variable variable ADJ iajs-2987 26 6 viscosity viscosity NOUN iajs-2987 26 7 on on ADP iajs-2987 26 8 peristalsis peristalsis NOUN iajs-2987 26 9 , , PUNCT iajs-2987 26 10 they they PRON iajs-2987 26 11 discussed discuss VERB iajs-2987 26 12 the the DET iajs-2987 26 13 influence influence NOUN iajs-2987 26 14 of of ADP iajs-2987 26 15 rotation rotation NOUN iajs-2987 26 16 of of ADP iajs-2987 26 17 the the DET iajs-2987 26 18 mixture mixture NOUN iajs-2987 26 19 on on ADP iajs-2987 26 20 convection convection NOUN iajs-2987 26 21 heat heat NOUN iajs-2987 26 22 transfer transfer NOUN iajs-2987 26 23 analysis analysis NOUN iajs-2987 26 24 by by ADP iajs-2987 26 25 [ [ X iajs-2987 26 26 17 17 NUM iajs-2987 26 27 , , PUNCT iajs-2987 26 28 18 18 NUM iajs-2987 26 29 ] ] PUNCT iajs-2987 26 30 . . PUNCT iajs-2987 27 1 this this DET iajs-2987 27 2 study study NOUN iajs-2987 27 3 's 's PART iajs-2987 27 4 objective objective NOUN iajs-2987 27 5 is be AUX iajs-2987 27 6 to to PART iajs-2987 27 7 examine examine VERB iajs-2987 27 8 the the DET iajs-2987 27 9 effects effect NOUN iajs-2987 27 10 of of ADP iajs-2987 27 11 rotation rotation NOUN iajs-2987 27 12 on on ADP iajs-2987 27 13 heat heat NOUN iajs-2987 27 14 transfer transfer NOUN iajs-2987 27 15 with with ADP iajs-2987 27 16 inclination inclination NOUN iajs-2987 27 17 magnetohydrodynamics magnetohydrodynamic NOUN iajs-2987 27 18 in in ADP iajs-2987 27 19 a a DET iajs-2987 27 20 non non ADJ iajs-2987 27 21 - - ADJ iajs-2987 27 22 uniform uniform ADJ iajs-2987 27 23 channel channel NOUN iajs-2987 27 24 containing contain VERB iajs-2987 27 25 a a DET iajs-2987 27 26 couple couple NOUN iajs-2987 27 27 stress stress NOUN iajs-2987 27 28 fluid fluid NOUN iajs-2987 27 29 . . PUNCT iajs-2987 28 1 the the DET iajs-2987 28 2 equation equation NOUN iajs-2987 28 3 for for ADP iajs-2987 28 4 the the DET iajs-2987 28 5 governing govern VERB iajs-2987 28 6 equation equation NOUN iajs-2987 28 7 is be AUX iajs-2987 28 8 examined examine VERB iajs-2987 28 9 using use VERB iajs-2987 28 10 low low ADJ iajs-2987 28 11 reynolds reynold NOUN iajs-2987 28 12 approximations approximation NOUN iajs-2987 28 13 and and CCONJ iajs-2987 28 14 long long ADJ iajs-2987 28 15 - - PUNCT iajs-2987 28 16 wavelength wavelength NOUN iajs-2987 28 17 assumptions assumption NOUN iajs-2987 28 18 , , PUNCT iajs-2987 28 19 respectively respectively ADV iajs-2987 28 20 . . PUNCT iajs-2987 29 1 graphs graph NOUN iajs-2987 29 2 are be AUX iajs-2987 29 3 used use VERB iajs-2987 29 4 to to PART iajs-2987 29 5 show show VERB iajs-2987 29 6 the the DET iajs-2987 29 7 impact impact NOUN iajs-2987 29 8 of of ADP iajs-2987 29 9 various various ADJ iajs-2987 29 10 factors factor NOUN iajs-2987 29 11 on on ADP iajs-2987 29 12 fluid fluid ADJ iajs-2987 29 13 flow flow NOUN iajs-2987 29 14 . . PUNCT iajs-2987 30 1 2 2 X iajs-2987 30 2 . . X iajs-2987 30 3 mathematical mathematical ADJ iajs-2987 30 4 formulation formulation NOUN iajs-2987 30 5 consider consider VERB iajs-2987 30 6 that that SCONJ iajs-2987 30 7 the the DET iajs-2987 30 8 effect effect NOUN iajs-2987 30 9 of of ADP iajs-2987 30 10 a a DET iajs-2987 30 11 magnetic magnetic ADJ iajs-2987 30 12 field field NOUN iajs-2987 30 13 and and CCONJ iajs-2987 30 14 rotation rotation NOUN iajs-2987 30 15 on on ADP iajs-2987 30 16 heat heat NOUN iajs-2987 30 17 transfer transfer NOUN iajs-2987 30 18 can can AUX iajs-2987 30 19 be be AUX iajs-2987 30 20 explained explain VERB iajs-2987 30 21 by by ADP iajs-2987 30 22 a a DET iajs-2987 30 23 porous porous ADJ iajs-2987 30 24 medium medium NOUN iajs-2987 30 25 with with ADP iajs-2987 30 26 an an DET iajs-2987 30 27 inclined inclined ADJ iajs-2987 30 28 asymmetry asymmetry NOUN iajs-2987 30 29 of of ADP iajs-2987 30 30 the the DET iajs-2987 30 31 couple couple NOUN iajs-2987 30 32 stress stress NOUN iajs-2987 30 33 fluid fluid NOUN iajs-2987 30 34 . . PUNCT iajs-2987 31 1 let let VERB iajs-2987 31 2 's us PRON iajs-2987 31 3 say say VERB iajs-2987 31 4 π‘Œβˆ—Μ… π‘Œβˆ—Μ… NOUN iajs-2987 31 5 = = SYM iajs-2987 31 6 β„Ž1Μƒ β„Ž1Μƒ X iajs-2987 31 7 ( ( PUNCT iajs-2987 31 8 x x SYM iajs-2987 31 9 Μƒ Μƒ PROPN iajs-2987 31 10 , , PUNCT iajs-2987 31 11 t t PROPN iajs-2987 31 12 Μƒ Μƒ PROPN iajs-2987 31 13 ) ) PUNCT iajs-2987 31 14 and and CCONJ iajs-2987 31 15 π‘Œβˆ—Μ… π‘Œβˆ—Μ… PROPN iajs-2987 31 16 = = SYM iajs-2987 31 17 β„Ž2Μƒ β„Ž2Μƒ PROPN iajs-2987 31 18 ( ( PUNCT iajs-2987 31 19 x x SYM iajs-2987 31 20 Μƒ Μƒ PROPN iajs-2987 31 21 , , PUNCT iajs-2987 31 22 t t PROPN iajs-2987 31 23 Μƒ Μƒ PROPN iajs-2987 31 24 ) ) PUNCT iajs-2987 31 25 here here ADV iajs-2987 31 26 is be AUX iajs-2987 31 27 a a DET iajs-2987 31 28 representation representation NOUN iajs-2987 31 29 of of ADP iajs-2987 31 30 the the DET iajs-2987 31 31 channel channel NOUN iajs-2987 31 32 's 's PART iajs-2987 31 33 top top ADJ iajs-2987 31 34 and and CCONJ iajs-2987 31 35 bottom bottom ADJ iajs-2987 31 36 walls wall NOUN iajs-2987 31 37 . . PUNCT iajs-2987 32 1 β„Ž1Μƒ β„Ž1Μƒ X iajs-2987 32 2 ( ( PUNCT iajs-2987 32 3 x x SYM iajs-2987 32 4 Μƒ Μƒ PROPN iajs-2987 32 5 , , PUNCT iajs-2987 32 6 t t PROPN iajs-2987 32 7 Μƒ Μƒ ADV iajs-2987 32 8 ) ) PUNCT iajs-2987 33 1 = = NOUN iajs-2987 33 2 𝑑1 𝑑1 NOUN iajs-2987 33 3 + + CCONJ iajs-2987 33 4 ( ( PUNCT iajs-2987 33 5 οΏ½ οΏ½ PROPN iajs-2987 33 6 Μƒ Μƒ PROPN iajs-2987 33 7 οΏ½ οΏ½ NOUN iajs-2987 33 8 βˆ’ βˆ’ ADP iajs-2987 33 9 𝑐 𝑐 PROPN iajs-2987 33 10 οΏ½ οΏ½ PROPN iajs-2987 33 11 Μƒ Μƒ PROPN iajs-2987 33 12 οΏ½ οΏ½ PROPN iajs-2987 33 13 ) ) PUNCT iajs-2987 33 14 tan tan PROPN iajs-2987 33 15 οΏ½ οΏ½ PROPN iajs-2987 33 16 Μƒ Μƒ PROPN iajs-2987 33 17 οΏ½ οΏ½ PROPN iajs-2987 33 18 + + CCONJ iajs-2987 33 19 π‘Ž1 π‘Ž1 PROPN iajs-2987 33 20 βˆ— βˆ— NOUN iajs-2987 33 21 cos cos PROPN iajs-2987 33 22 [ [ PUNCT iajs-2987 33 23 2πœ‹ 2πœ‹ NUM iajs-2987 33 24 πœ† πœ† X iajs-2987 33 25 ( ( PUNCT iajs-2987 33 26 οΏ½ οΏ½ PROPN iajs-2987 33 27 Μƒ Μƒ NOUN iajs-2987 33 28 οΏ½ οΏ½ NOUN iajs-2987 33 29 βˆ’ βˆ’ ADP iajs-2987 33 30 𝑐 𝑐 PROPN iajs-2987 33 31 οΏ½ οΏ½ PROPN iajs-2987 33 32 Μƒ Μƒ PROPN iajs-2987 33 33 οΏ½ οΏ½ PROPN iajs-2987 33 34 ) ) PUNCT iajs-2987 33 35 ] ] PUNCT iajs-2987 33 36 ( ( PUNCT iajs-2987 33 37 1 1 X iajs-2987 33 38 ) ) PUNCT iajs-2987 33 39 β„Ž2Μƒ β„Ž2Μƒ PROPN iajs-2987 34 1 ( ( PUNCT iajs-2987 34 2 x x X iajs-2987 34 3 Μƒ Μƒ ADV iajs-2987 34 4 , , PUNCT iajs-2987 34 5 t t PROPN iajs-2987 34 6 Μƒ Μƒ PROPN iajs-2987 34 7 ) ) PUNCT iajs-2987 35 1 = = PUNCT iajs-2987 35 2 βˆ’π‘‘2 βˆ’π‘‘2 NOUN iajs-2987 35 3 βˆ’ βˆ’ PROPN iajs-2987 35 4 ( ( PUNCT iajs-2987 35 5 οΏ½ οΏ½ PROPN iajs-2987 35 6 Μƒ Μƒ PROPN iajs-2987 35 7 οΏ½ οΏ½ NOUN iajs-2987 35 8 βˆ’ βˆ’ ADP iajs-2987 35 9 𝑐 𝑐 PROPN iajs-2987 35 10 οΏ½ οΏ½ PROPN iajs-2987 35 11 Μƒ Μƒ PROPN iajs-2987 35 12 οΏ½ οΏ½ PROPN iajs-2987 35 13 ) ) PUNCT iajs-2987 35 14 tan tan PROPN iajs-2987 35 15 οΏ½ οΏ½ PROPN iajs-2987 35 16 Μƒ Μƒ PROPN iajs-2987 35 17 οΏ½ οΏ½ PROPN iajs-2987 35 18 βˆ’ βˆ’ PROPN iajs-2987 35 19 π‘Ž2 π‘Ž2 NOUN iajs-2987 35 20 βˆ— βˆ— X iajs-2987 35 21 cos cos PROPN iajs-2987 36 1 [ [ PUNCT iajs-2987 36 2 2πœ‹ 2πœ‹ NUM iajs-2987 36 3 πœ† πœ† X iajs-2987 36 4 ( ( PUNCT iajs-2987 36 5 οΏ½ οΏ½ PROPN iajs-2987 36 6 Μƒ Μƒ NOUN iajs-2987 36 7 οΏ½ οΏ½ NOUN iajs-2987 36 8 βˆ’ βˆ’ ADP iajs-2987 36 9 𝑐 𝑐 PROPN iajs-2987 36 10 οΏ½ οΏ½ PROPN iajs-2987 36 11 Μƒ Μƒ PROPN iajs-2987 36 12 οΏ½ οΏ½ PROPN iajs-2987 36 13 ) ) PUNCT iajs-2987 37 1 + + NUM iajs-2987 37 2 πœ™ πœ™ X iajs-2987 37 3 Β° Β° NOUN iajs-2987 37 4 ] ] X iajs-2987 37 5 ( ( PUNCT iajs-2987 37 6 2 2 X iajs-2987 37 7 ) ) PUNCT iajs-2987 37 8 where where SCONJ iajs-2987 37 9 π‘Ž1 π‘Ž1 PROPN iajs-2987 37 10 βˆ—π‘Žπ‘›π‘‘ βˆ—π‘Žπ‘›π‘‘ ADJ iajs-2987 37 11 π‘Ž2 π‘Ž2 NOUN iajs-2987 37 12 βˆ— βˆ— NOUN iajs-2987 37 13 are be AUX iajs-2987 37 14 the the DET iajs-2987 37 15 amplitudes amplitude NOUN iajs-2987 37 16 of of ADP iajs-2987 37 17 waves wave NOUN iajs-2987 37 18 Ξ» Ξ» PROPN iajs-2987 37 19 is be AUX iajs-2987 37 20 wavelength wavelength NOUN iajs-2987 37 21 , , PUNCT iajs-2987 37 22 οΏ½ οΏ½ PROPN iajs-2987 37 23 Μƒ Μƒ PROPN iajs-2987 37 24 οΏ½ οΏ½ PROPN iajs-2987 37 25 is be AUX iajs-2987 37 26 the the DET iajs-2987 37 27 time time NOUN iajs-2987 37 28 c c NOUN iajs-2987 37 29 is be AUX iajs-2987 37 30 wave wave NOUN iajs-2987 37 31 speed speed NOUN iajs-2987 37 32 , , PUNCT iajs-2987 37 33 ( ( PUNCT iajs-2987 37 34 0 0 NUM iajs-2987 37 35 ≀ ≀ NUM iajs-2987 38 1 πœ™ πœ™ NOUN iajs-2987 38 2 Β° Β° NOUN iajs-2987 38 3 ≀ ≀ NUM iajs-2987 38 4 πœ‹ πœ‹ NOUN iajs-2987 38 5 ) ) PUNCT iajs-2987 38 6 the the DET iajs-2987 38 7 phase phase NOUN iajs-2987 38 8 difference difference NOUN iajs-2987 38 9 πœ™ πœ™ NOUN iajs-2987 38 10 Β° Β° NOUN iajs-2987 38 11 between between ADP iajs-2987 38 12 the the DET iajs-2987 38 13 walls wall NOUN iajs-2987 38 14 of of ADP iajs-2987 38 15 the the DET iajs-2987 38 16 channel channel NOUN iajs-2987 38 17 the the DET iajs-2987 38 18 rectangular rectangular ADJ iajs-2987 38 19 cartesian cartesian ADJ iajs-2987 38 20 coordinates coordinate NOUN iajs-2987 38 21 are be AUX iajs-2987 38 22 used use VERB iajs-2987 38 23 οΏ½ οΏ½ PROPN iajs-2987 38 24 Μƒ Μƒ PROPN iajs-2987 38 25 οΏ½ οΏ½ PROPN iajs-2987 38 26 and and CCONJ iajs-2987 38 27 οΏ½ οΏ½ PROPN iajs-2987 38 28 Μƒ Μƒ PROPN iajs-2987 38 29 οΏ½ οΏ½ PROPN iajs-2987 38 30 . . PUNCT iajs-2987 39 1 the the DET iajs-2987 39 2 channel channel NOUN iajs-2987 39 3 's 's PART iajs-2987 39 4 axis axis NOUN iajs-2987 39 5 is be AUX iajs-2987 39 6 measured measure VERB iajs-2987 39 7 by by ADP iajs-2987 39 8 οΏ½ οΏ½ PROPN iajs-2987 39 9 Μƒ Μƒ PROPN iajs-2987 39 10 οΏ½ οΏ½ PROPN iajs-2987 39 11 , , PUNCT iajs-2987 39 12 and and CCONJ iajs-2987 39 13 the the DET iajs-2987 39 14 transverse transverse NOUN iajs-2987 39 15 axis axis NOUN iajs-2987 39 16 is be AUX iajs-2987 39 17 measured measure VERB iajs-2987 39 18 by by ADP iajs-2987 39 19 οΏ½ οΏ½ PROPN iajs-2987 39 20 Μƒ Μƒ PROPN iajs-2987 39 21 οΏ½ οΏ½ PROPN iajs-2987 39 22 , , PUNCT iajs-2987 39 23 which which PRON iajs-2987 39 24 is be AUX iajs-2987 39 25 perpendicular perpendicular ADJ iajs-2987 39 26 to to ADP iajs-2987 39 27 οΏ½ οΏ½ PROPN iajs-2987 39 28 Μƒ Μƒ PROPN iajs-2987 39 29 οΏ½ οΏ½ PROPN iajs-2987 39 30 . . PUNCT iajs-2987 40 1 the the DET iajs-2987 40 2 constant constant ADJ iajs-2987 40 3 heights height NOUN iajs-2987 40 4 of of ADP iajs-2987 40 5 the the DET iajs-2987 40 6 upper upper ADJ iajs-2987 40 7 and and CCONJ iajs-2987 40 8 lower low ADJ iajs-2987 40 9 walls wall NOUN iajs-2987 40 10 of of ADP iajs-2987 40 11 the the DET iajs-2987 40 12 channel channel NOUN iajs-2987 40 13 from from ADP iajs-2987 40 14 the the DET iajs-2987 40 15 central central ADJ iajs-2987 40 16 line line NOUN iajs-2987 40 17 are be AUX iajs-2987 40 18 denoted denote VERB iajs-2987 40 19 by by ADP iajs-2987 40 20 𝑑1π‘Žπ‘›π‘‘ 𝑑1π‘Žπ‘›π‘‘ NOUN iajs-2987 40 21 𝑑2 𝑑2 NOUN iajs-2987 40 22 , , PUNCT iajs-2987 40 23 respectively respectively ADV iajs-2987 40 24 . . PUNCT iajs-2987 41 1 it it PRON iajs-2987 41 2 's be AUX iajs-2987 41 3 worth worth ADJ iajs-2987 41 4 noting note VERB iajs-2987 41 5 that that SCONJ iajs-2987 41 6 πœ™ πœ™ NOUN iajs-2987 41 7 Β° Β° NOUN iajs-2987 41 8 = = SYM iajs-2987 41 9 0 0 NUM iajs-2987 41 10 corresponds correspond VERB iajs-2987 41 11 to to ADP iajs-2987 41 12 an an DET iajs-2987 41 13 asymmetry asymmetry NOUN iajs-2987 41 14 with with ADP iajs-2987 41 15 out out ADV iajs-2987 41 16 - - PUNCT iajs-2987 41 17 of of ADP iajs-2987 41 18 - - PUNCT iajs-2987 41 19 phase phase NOUN iajs-2987 41 20 waves wave NOUN iajs-2987 41 21 , , PUNCT iajs-2987 41 22 whereas whereas SCONJ iajs-2987 41 23 πœ™ πœ™ X iajs-2987 41 24 Β° Β° NOUN iajs-2987 41 25 = = SYM iajs-2987 41 26 πœ‹ πœ‹ NOUN iajs-2987 41 27 relates relate VERB iajs-2987 41 28 to to ADP iajs-2987 41 29 waves wave NOUN iajs-2987 41 30 that that PRON iajs-2987 41 31 are be AUX iajs-2987 41 32 in in ADP iajs-2987 41 33 phase phase NOUN iajs-2987 41 34 . . PUNCT iajs-2987 42 1 furthermore furthermore ADV iajs-2987 42 2 , , PUNCT iajs-2987 42 3 𝑑1 𝑑1 NOUN iajs-2987 42 4 , , PUNCT iajs-2987 42 5 𝑑2 𝑑2 PROPN iajs-2987 42 6 , , PUNCT iajs-2987 42 7 π‘Ž2 π‘Ž2 NOUN iajs-2987 42 8 βˆ— βˆ— NOUN iajs-2987 42 9 , , PUNCT iajs-2987 42 10 π‘Ž1 π‘Ž1 INTJ iajs-2987 42 11 βˆ—and βˆ—and NOUN iajs-2987 42 12 πœ™ πœ™ NOUN iajs-2987 42 13 Β° Β° NOUN iajs-2987 42 14 satisfy satisfy VERB iajs-2987 42 15 the the DET iajs-2987 42 16 condition condition NOUN iajs-2987 42 17 ; ; PUNCT iajs-2987 42 18 π‘Ž1 π‘Ž1 ADP iajs-2987 42 19 βˆ—2 βˆ—2 SYM iajs-2987 42 20 + + CCONJ iajs-2987 42 21 π‘Ž2 π‘Ž2 PROPN iajs-2987 42 22 βˆ—2 βˆ—2 PROPN iajs-2987 42 23 + + SYM iajs-2987 42 24 2π‘Ž1 2π‘Ž1 NUM iajs-2987 42 25 βˆ—π‘Ž2 βˆ—π‘Ž2 ADJ iajs-2987 42 26 βˆ—π‘π‘œπ‘ πœ™ βˆ—π‘π‘œπ‘ πœ™ PROPN iajs-2987 42 27 Β° Β° ADJ iajs-2987 42 28 ≀ ≀ NOUN iajs-2987 42 29 ( ( PUNCT iajs-2987 42 30 𝑑1 𝑑1 NOUN iajs-2987 42 31 + + CCONJ iajs-2987 42 32 𝑑2 𝑑2 NOUN iajs-2987 42 33 ) ) PUNCT iajs-2987 42 34 2 2 NUM iajs-2987 42 35 . . X iajs-2987 43 1 the the DET iajs-2987 43 2 governing govern VERB iajs-2987 43 3 equations equation NOUN iajs-2987 43 4 . . PUNCT iajs-2987 44 1 βˆ‚uΜƒ βˆ‚uΜƒ NOUN iajs-2987 44 2 βˆ‚xΜƒ βˆ‚xΜƒ ADV iajs-2987 44 3 + + CCONJ iajs-2987 44 4 βˆ‚vΜƒ βˆ‚vΜƒ ADJ iajs-2987 44 5 βˆ‚yΜƒ βˆ‚yΜƒ NOUN iajs-2987 44 6 = = SYM iajs-2987 44 7 0 0 NUM iajs-2987 44 8 ( ( PUNCT iajs-2987 44 9 3 3 NUM iajs-2987 44 10 ) ) PUNCT iajs-2987 44 11 𝜌 𝜌 X iajs-2987 44 12 ( ( PUNCT iajs-2987 44 13 πœ•uΜƒ πœ•uΜƒ NOUN iajs-2987 44 14 πœ• πœ• NOUN iajs-2987 44 15 οΏ½ οΏ½ PROPN iajs-2987 44 16 Μƒ Μƒ PROPN iajs-2987 44 17 οΏ½ οΏ½ PROPN iajs-2987 44 18 + + CCONJ iajs-2987 44 19 uΜƒ uΜƒ PROPN iajs-2987 44 20 πœ•uΜƒ πœ•uΜƒ NOUN iajs-2987 44 21 πœ• πœ• NOUN iajs-2987 44 22 οΏ½ οΏ½ PROPN iajs-2987 44 23 Μƒ Μƒ PROPN iajs-2987 44 24 οΏ½ οΏ½ PROPN iajs-2987 44 25 + + CCONJ iajs-2987 44 26 vΜƒ vΜƒ PROPN iajs-2987 44 27 πœ•uΜƒ πœ•uΜƒ NOUN iajs-2987 44 28 πœ• πœ• NOUN iajs-2987 44 29 οΏ½ οΏ½ PROPN iajs-2987 44 30 Μƒ Μƒ PROPN iajs-2987 44 31 οΏ½ οΏ½ PROPN iajs-2987 44 32 ) ) PUNCT iajs-2987 44 33 βˆ’ βˆ’ ADP iajs-2987 45 1 𝜌 𝜌 ADP iajs-2987 45 2 οΏ½ οΏ½ PROPN iajs-2987 45 3 Μ€ Μ€ ADJ iajs-2987 45 4 οΏ½ οΏ½ PROPN iajs-2987 45 5 ( ( PUNCT iajs-2987 45 6 οΏ½ οΏ½ PROPN iajs-2987 45 7 Μ€ Μ€ VERB iajs-2987 45 8 οΏ½ οΏ½ PROPN iajs-2987 45 9 οΏ½ οΏ½ PROPN iajs-2987 45 10 Μƒ Μƒ PROPN iajs-2987 45 11 οΏ½ οΏ½ NOUN iajs-2987 45 12 + + CCONJ iajs-2987 45 13 2 2 NUM iajs-2987 45 14 πœ•vΜƒ πœ•vΜƒ NOUN iajs-2987 45 15 πœ• πœ• PROPN iajs-2987 45 16 οΏ½ οΏ½ PROPN iajs-2987 45 17 Μƒ Μƒ PROPN iajs-2987 45 18 οΏ½ οΏ½ PROPN iajs-2987 45 19 ) ) PUNCT iajs-2987 45 20 = = SYM iajs-2987 45 21 βˆ’ βˆ’ ADP iajs-2987 45 22 πœ•pΜƒ πœ•pΜƒ NOUN iajs-2987 45 23 πœ•xΜƒ πœ•xΜƒ ADJ iajs-2987 45 24 + + CCONJ iajs-2987 45 25 πœ‡βˆ‡2 πœ‡βˆ‡2 PROPN iajs-2987 45 26 οΏ½ οΏ½ PROPN iajs-2987 45 27 Μƒ Μƒ PROPN iajs-2987 45 28 οΏ½ οΏ½ PROPN iajs-2987 45 29 βˆ’ βˆ’ PROPN iajs-2987 45 30 πœ‚βˆ‡4 πœ‚βˆ‡4 PROPN iajs-2987 45 31 οΏ½ οΏ½ PROPN iajs-2987 45 32 Μƒ Μƒ PROPN iajs-2987 45 33 οΏ½ οΏ½ PROPN iajs-2987 45 34 βˆ’ βˆ’ PROPN iajs-2987 45 35 οΏ½ οΏ½ PROPN iajs-2987 45 36 Μƒ Μƒ PROPN iajs-2987 45 37 οΏ½ οΏ½ NOUN iajs-2987 45 38 π΅βˆ— π΅βˆ— NUM iajs-2987 45 39 2 2 NUM iajs-2987 45 40 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 45 41 Ο† Ο† PROPN iajs-2987 45 42 ( ( PUNCT iajs-2987 45 43 uΜƒ uΜƒ PROPN iajs-2987 45 44 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 45 45 Ο† Ο† PROPN iajs-2987 45 46 βˆ’ βˆ’ PROPN iajs-2987 45 47 vΜƒ vΜƒ PROPN iajs-2987 45 48 𝑠𝑖𝑛 𝑠𝑖𝑛 NOUN iajs-2987 45 49 Ο† Ο† PROPN iajs-2987 45 50 ) ) PUNCT iajs-2987 45 51 βˆ’ βˆ’ PROPN iajs-2987 45 52 πœ‡ πœ‡ ADP iajs-2987 45 53 π‘˜ π‘˜ PROPN iajs-2987 45 54 Β° Β° PROPN iajs-2987 45 55 uΜƒ uΜƒ PROPN iajs-2987 45 56 + + CCONJ iajs-2987 45 57 𝜌g 𝜌g PRON iajs-2987 45 58 οΏ½ οΏ½ PROPN iajs-2987 45 59 Μ‡ Μ‡ PROPN iajs-2987 45 60 οΏ½ οΏ½ PROPN iajs-2987 45 61 ( ( PUNCT iajs-2987 45 62 t t PROPN iajs-2987 45 63 βˆ’ βˆ’ PROPN iajs-2987 45 64 t t PROPN iajs-2987 45 65 Β° Β° PROPN iajs-2987 45 66 )𝑠𝑖𝑛 )𝑠𝑖𝑛 PROPN iajs-2987 45 67 οΏ½ οΏ½ PROPN iajs-2987 45 68 Μƒ Μƒ PROPN iajs-2987 45 69 οΏ½ οΏ½ PROPN iajs-2987 45 70 + + CCONJ iajs-2987 45 71 πœŒπ‘”π‘ π‘–π‘›Ξ±Μƒ πœŒπ‘”π‘ π‘–π‘›Ξ±Μƒ X iajs-2987 45 72 ( ( PUNCT iajs-2987 45 73 4 4 NUM iajs-2987 45 74 ) ) PUNCT iajs-2987 45 75 𝜌 𝜌 X iajs-2987 45 76 ( ( PUNCT iajs-2987 45 77 πœ•vΜƒ πœ•vΜƒ PROPN iajs-2987 45 78 πœ• πœ• PROPN iajs-2987 45 79 οΏ½ οΏ½ PROPN iajs-2987 45 80 Μƒ Μƒ PROPN iajs-2987 45 81 οΏ½ οΏ½ PROPN iajs-2987 45 82 + + SYM iajs-2987 45 83 uΜƒ uΜƒ PROPN iajs-2987 45 84 βˆ‚vΜƒ βˆ‚vΜƒ NOUN iajs-2987 45 85 βˆ‚xΜƒ βˆ‚xΜƒ ADV iajs-2987 45 86 + + CCONJ iajs-2987 45 87 vΜƒ vΜƒ PROPN iajs-2987 45 88 βˆ‚vΜƒ βˆ‚vΜƒ ADP iajs-2987 45 89 βˆ‚yΜƒ βˆ‚yΜƒ NUM iajs-2987 45 90 ) ) PUNCT iajs-2987 46 1 βˆ’ βˆ’ ADP iajs-2987 47 1 𝜌 𝜌 ADP iajs-2987 47 2 οΏ½ οΏ½ PROPN iajs-2987 47 3 Μ€ Μ€ ADJ iajs-2987 47 4 οΏ½ οΏ½ PROPN iajs-2987 47 5 ( ( PUNCT iajs-2987 47 6 οΏ½ οΏ½ PROPN iajs-2987 47 7 Μ€ Μ€ VERB iajs-2987 47 8 οΏ½ οΏ½ PROPN iajs-2987 47 9 οΏ½ οΏ½ PROPN iajs-2987 47 10 Μƒ Μƒ PROPN iajs-2987 47 11 οΏ½ οΏ½ NOUN iajs-2987 47 12 βˆ’ βˆ’ NUM iajs-2987 47 13 2 2 NUM iajs-2987 47 14 πœ•uΜƒ πœ•uΜƒ NOUN iajs-2987 47 15 πœ• πœ• NOUN iajs-2987 47 16 οΏ½ οΏ½ PROPN iajs-2987 47 17 Μƒ Μƒ PROPN iajs-2987 47 18 οΏ½ οΏ½ PROPN iajs-2987 47 19 ) ) PUNCT iajs-2987 48 1 = = SYM iajs-2987 49 1 βˆ’ βˆ’ ADP iajs-2987 49 2 πœ•pΜƒ πœ•pΜƒ X iajs-2987 49 3 πœ•yΜƒ πœ•yΜƒ NOUN iajs-2987 49 4 + + CCONJ iajs-2987 49 5 πœ‡βˆ‡2vΜƒ πœ‡βˆ‡2vΜƒ VERB iajs-2987 49 6 βˆ’ βˆ’ PROPN iajs-2987 49 7 πœ‚βˆ‡4vΜƒ πœ‚βˆ‡4vΜƒ PROPN iajs-2987 49 8 + + CCONJ iajs-2987 49 9 οΏ½ οΏ½ PROPN iajs-2987 49 10 Μƒ Μƒ PROPN iajs-2987 49 11 οΏ½ οΏ½ NOUN iajs-2987 49 12 π΅βˆ— π΅βˆ— NUM iajs-2987 49 13 2 2 NUM iajs-2987 49 14 𝑠𝑖𝑛 𝑠𝑖𝑛 NOUN iajs-2987 49 15 Ο† Ο† PROPN iajs-2987 49 16 ( ( PUNCT iajs-2987 49 17 uΜƒ uΜƒ PROPN iajs-2987 49 18 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 49 19 Ο† Ο† PROPN iajs-2987 49 20 βˆ’ βˆ’ PROPN iajs-2987 49 21 vΜƒ vΜƒ PROPN iajs-2987 49 22 𝑠𝑖𝑛 𝑠𝑖𝑛 NOUN iajs-2987 49 23 Ο† Ο† PROPN iajs-2987 49 24 ) ) PUNCT iajs-2987 49 25 βˆ’ βˆ’ PROPN iajs-2987 49 26 πœ‡ πœ‡ ADP iajs-2987 49 27 π‘˜ π‘˜ PROPN iajs-2987 49 28 Β° Β° ADJ iajs-2987 49 29 vΜƒ vΜƒ PROPN iajs-2987 49 30 βˆ’ βˆ’ PROPN iajs-2987 49 31 πœŒπ‘”π‘π‘œπ‘  πœŒπ‘”π‘π‘œπ‘  PROPN iajs-2987 49 32 οΏ½ οΏ½ PROPN iajs-2987 49 33 Μƒ Μƒ PROPN iajs-2987 49 34 οΏ½ οΏ½ PROPN iajs-2987 49 35 ( ( PUNCT iajs-2987 49 36 5 5 NUM iajs-2987 49 37 ) ) PUNCT iajs-2987 49 38 πœŒπΆπ‘ πœŒπΆπ‘ PRON iajs-2987 49 39 ( ( PUNCT iajs-2987 49 40 πœ•t πœ•t PROPN iajs-2987 49 41 πœ• πœ• PROPN iajs-2987 49 42 οΏ½ οΏ½ PROPN iajs-2987 49 43 Μƒ Μƒ PROPN iajs-2987 49 44 οΏ½ οΏ½ PROPN iajs-2987 49 45 + + SYM iajs-2987 49 46 uΜƒ uΜƒ PROPN iajs-2987 49 47 πœ•t πœ•t NOUN iajs-2987 49 48 πœ•xΜƒ πœ•xΜƒ ADP iajs-2987 49 49 + + PROPN iajs-2987 49 50 vΜƒ vΜƒ PROPN iajs-2987 49 51 πœ•t πœ•t PROPN iajs-2987 49 52 πœ• πœ• PROPN iajs-2987 49 53 οΏ½ οΏ½ PROPN iajs-2987 49 54 Μƒ Μƒ PROPN iajs-2987 49 55 οΏ½ οΏ½ PROPN iajs-2987 49 56 ) ) PUNCT iajs-2987 50 1 = = SYM iajs-2987 50 2 kΜƒ kΜƒ PROPN iajs-2987 50 3 ( ( PUNCT iajs-2987 50 4 βˆ‚2 βˆ‚2 PROPN iajs-2987 50 5 t t PROPN iajs-2987 50 6 βˆ‚ βˆ‚ NUM iajs-2987 50 7 οΏ½ οΏ½ PROPN iajs-2987 50 8 Μƒ Μƒ PROPN iajs-2987 50 9 οΏ½ οΏ½ NOUN iajs-2987 50 10 2 2 NUM iajs-2987 50 11 + + SYM iajs-2987 50 12 βˆ‚2 βˆ‚2 PROPN iajs-2987 50 13 t t PROPN iajs-2987 50 14 βˆ‚ βˆ‚ NUM iajs-2987 50 15 οΏ½ οΏ½ PROPN iajs-2987 50 16 Μƒ Μƒ PROPN iajs-2987 50 17 οΏ½ οΏ½ NOUN iajs-2987 50 18 2 2 NUM iajs-2987 50 19 ) ) PUNCT iajs-2987 50 20 + + X iajs-2987 50 21 πœ‡ πœ‡ X iajs-2987 50 22 [ [ X iajs-2987 50 23 2 2 NUM iajs-2987 50 24 { { PUNCT iajs-2987 50 25 ( ( PUNCT iajs-2987 50 26 βˆ‚uΜƒ βˆ‚uΜƒ PROPN iajs-2987 50 27 βˆ‚ βˆ‚ NUM iajs-2987 50 28 οΏ½ οΏ½ PROPN iajs-2987 50 29 Μƒ Μƒ PROPN iajs-2987 50 30 οΏ½ οΏ½ PROPN iajs-2987 50 31 ) ) PUNCT iajs-2987 50 32 2 2 NUM iajs-2987 50 33 + + CCONJ iajs-2987 50 34 ( ( PUNCT iajs-2987 50 35 βˆ‚vΜƒ βˆ‚vΜƒ ADJ iajs-2987 50 36 βˆ‚yΜƒ βˆ‚yΜƒ NUM iajs-2987 50 37 ) ) PUNCT iajs-2987 50 38 2 2 NUM iajs-2987 50 39 } } PUNCT iajs-2987 50 40 + + CCONJ iajs-2987 50 41 ( ( PUNCT iajs-2987 50 42 βˆ‚uΜƒ βˆ‚uΜƒ PROPN iajs-2987 50 43 βˆ‚ βˆ‚ NUM iajs-2987 50 44 οΏ½ οΏ½ PROPN iajs-2987 50 45 Μƒ Μƒ PROPN iajs-2987 50 46 οΏ½ οΏ½ NOUN iajs-2987 50 47 + + NUM iajs-2987 50 48 βˆ‚vΜƒ βˆ‚vΜƒ ADJ iajs-2987 50 49 βˆ‚xΜƒ βˆ‚xΜƒ ADV iajs-2987 50 50 ) ) PUNCT iajs-2987 50 51 2 2 NUM iajs-2987 50 52 ] ] PUNCT iajs-2987 51 1 + + PUNCT iajs-2987 51 2 πœ‚ πœ‚ X iajs-2987 51 3 [ [ X iajs-2987 51 4 ( ( PUNCT iajs-2987 51 5 βˆ‚2uΜƒ βˆ‚2uΜƒ PUNCT iajs-2987 51 6 βˆ‚xΜƒ2 βˆ‚xΜƒ2 PROPN iajs-2987 52 1 + + CCONJ iajs-2987 52 2 βˆ‚2uΜƒ βˆ‚2uΜƒ NOUN iajs-2987 52 3 βˆ‚ βˆ‚ NUM iajs-2987 52 4 οΏ½ οΏ½ PROPN iajs-2987 52 5 Μƒ Μƒ PROPN iajs-2987 52 6 οΏ½ οΏ½ NOUN iajs-2987 52 7 2 2 NUM iajs-2987 52 8 ) ) PUNCT iajs-2987 52 9 2 2 NUM iajs-2987 52 10 + + CCONJ iajs-2987 52 11 ( ( PUNCT iajs-2987 52 12 βˆ‚2vΜƒ βˆ‚2vΜƒ NOUN iajs-2987 52 13 βˆ‚ βˆ‚ NUM iajs-2987 52 14 οΏ½ οΏ½ PROPN iajs-2987 52 15 Μƒ Μƒ NOUN iajs-2987 52 16 οΏ½ οΏ½ NOUN iajs-2987 52 17 2 2 NUM iajs-2987 52 18 + + CCONJ iajs-2987 52 19 βˆ‚2vΜƒ βˆ‚2vΜƒ NOUN iajs-2987 52 20 βˆ‚ βˆ‚ NUM iajs-2987 52 21 οΏ½ οΏ½ PROPN iajs-2987 52 22 Μƒ Μƒ NOUN iajs-2987 52 23 οΏ½ οΏ½ NOUN iajs-2987 52 24 2 2 NUM iajs-2987 52 25 ) ) PUNCT iajs-2987 52 26 2 2 NUM iajs-2987 52 27 ] ] PUNCT iajs-2987 52 28 + + NUM iajs-2987 52 29 οΏ½ οΏ½ PROPN iajs-2987 52 30 Μƒ Μƒ PROPN iajs-2987 52 31 οΏ½ οΏ½ NOUN iajs-2987 52 32 π΅βˆ— π΅βˆ— NUM iajs-2987 52 33 2(uΜƒ 2(uΜƒ NOUN iajs-2987 52 34 π‘π‘œπ‘  π‘π‘œπ‘  PROPN iajs-2987 52 35 Ο† Ο† PROPN iajs-2987 53 1 βˆ’ βˆ’ PROPN iajs-2987 53 2 vΜƒ vΜƒ PROPN iajs-2987 53 3 𝑠𝑖𝑛φ 𝑠𝑖𝑛φ NOUN iajs-2987 53 4 ) ) PUNCT iajs-2987 53 5 2 2 NUM iajs-2987 53 6 ( ( PUNCT iajs-2987 53 7 6 6 NUM iajs-2987 53 8 ) ) PUNCT iajs-2987 53 9 ihjpas ihjpa NOUN iajs-2987 53 10 . . PUNCT iajs-2987 54 1 36(2)2023 36(2)2023 NUM iajs-2987 54 2 316 316 NUM iajs-2987 54 3 where where SCONJ iajs-2987 54 4 v′⃑⃑ v′⃑⃑ PROPN iajs-2987 54 5 ⃑=( ⃑=( PROPN iajs-2987 54 6 οΏ½ οΏ½ PROPN iajs-2987 54 7 Μƒ Μƒ PROPN iajs-2987 54 8 οΏ½ οΏ½ PROPN iajs-2987 54 9 , , PUNCT iajs-2987 54 10 vΜƒ vΜƒ PROPN iajs-2987 54 11 , , PUNCT iajs-2987 54 12 0 0 NUM iajs-2987 54 13 ) ) PUNCT iajs-2987 54 14 be be VERB iajs-2987 54 15 the the DET iajs-2987 54 16 velocity velocity NOUN iajs-2987 54 17 vector vector NOUN iajs-2987 54 18 , , PUNCT iajs-2987 54 19 Ο‰Μ€ Ο‰Μ€ PROPN iajs-2987 54 20 is be AUX iajs-2987 54 21 rotation rotation NOUN iajs-2987 54 22 , , PUNCT iajs-2987 54 23 οΏ½ οΏ½ PROPN iajs-2987 54 24 Μ‡ Μ‡ PROPN iajs-2987 54 25 οΏ½ οΏ½ PROPN iajs-2987 55 1 the the DET iajs-2987 55 2 coefficient coefficient NOUN iajs-2987 55 3 of of ADP iajs-2987 55 4 thermal thermal ADJ iajs-2987 55 5 expansion expansion NOUN iajs-2987 55 6 , , PUNCT iajs-2987 55 7 οΏ½ οΏ½ PROPN iajs-2987 55 8 Μƒ Μƒ PROPN iajs-2987 55 9 οΏ½ οΏ½ PROPN iajs-2987 55 10 is be AUX iajs-2987 55 11 the the DET iajs-2987 55 12 fluid fluid ADJ iajs-2987 55 13 pressure pressure NOUN iajs-2987 55 14 , , PUNCT iajs-2987 55 15 𝜌 𝜌 X iajs-2987 55 16 is be AUX iajs-2987 55 17 density density NOUN iajs-2987 55 18 of of ADP iajs-2987 55 19 fluid fluid NOUN iajs-2987 55 20 , , PUNCT iajs-2987 55 21 Ο† Ο† PROPN iajs-2987 55 22 is be AUX iajs-2987 55 23 the the DET iajs-2987 55 24 inclination inclination NOUN iajs-2987 55 25 of of ADP iajs-2987 55 26 the the DET iajs-2987 55 27 magnetic magnetic ADJ iajs-2987 55 28 field field NOUN iajs-2987 55 29 angle angle NOUN iajs-2987 55 30 , , PUNCT iajs-2987 55 31 ΞΌ ΞΌ PROPN iajs-2987 55 32 the the DET iajs-2987 55 33 dynamic dynamic ADJ iajs-2987 55 34 viscosity viscosity NOUN iajs-2987 55 35 , , PUNCT iajs-2987 55 36 Ξ· Ξ· PROPN iajs-2987 55 37 is be AUX iajs-2987 55 38 a a DET iajs-2987 55 39 constant constant ADJ iajs-2987 55 40 linked link VERB iajs-2987 55 41 to to ADP iajs-2987 55 42 the the DET iajs-2987 55 43 couple couple NOUN iajs-2987 55 44 stress stress NOUN iajs-2987 55 45 , , PUNCT iajs-2987 55 46 𝐢𝑝 𝐢𝑝 PROPN iajs-2987 55 47 is be AUX iajs-2987 55 48 the the DET iajs-2987 55 49 specific specific ADJ iajs-2987 55 50 heat heat NOUN iajs-2987 55 51 at at ADP iajs-2987 55 52 constant constant ADJ iajs-2987 55 53 pressure pressure NOUN iajs-2987 55 54 . . PUNCT iajs-2987 56 1 impact impact NOUN iajs-2987 56 2 bβˆ— bβˆ— ADJ iajs-2987 56 3 ⃑⃑⃑⃑ ⃑⃑⃑⃑ ADJ iajs-2987 56 4 =( =( PROPN iajs-2987 56 5 π΅βˆ— π΅βˆ— PROPN iajs-2987 56 6 𝑠𝑖𝑛φ 𝑠𝑖𝑛φ NOUN iajs-2987 56 7 , , PUNCT iajs-2987 56 8 π΅βˆ— π΅βˆ— PROPN iajs-2987 56 9 π‘π‘œπ‘  π‘π‘œπ‘  PROPN iajs-2987 56 10 Ο† Ο† PROPN iajs-2987 56 11 , , PUNCT iajs-2987 56 12 0 0 NUM iajs-2987 56 13 ) ) PUNCT iajs-2987 56 14 the the DET iajs-2987 56 15 magnetic magnetic ADJ iajs-2987 56 16 field field NOUN iajs-2987 56 17 vector vector NOUN iajs-2987 56 18 , , PUNCT iajs-2987 56 19 π‘˜ π‘˜ PROPN iajs-2987 56 20 Β° Β° PROPN iajs-2987 56 21 is be AUX iajs-2987 56 22 the the DET iajs-2987 56 23 permeability permeability NOUN iajs-2987 56 24 parameter parameter NOUN iajs-2987 56 25 , , PUNCT iajs-2987 56 26 t t PROPN iajs-2987 56 27 is be AUX iajs-2987 56 28 the the DET iajs-2987 56 29 temperature temperature NOUN iajs-2987 56 30 , , PUNCT iajs-2987 56 31 𝑔 𝑔 PROPN iajs-2987 56 32 is be AUX iajs-2987 56 33 the the DET iajs-2987 56 34 acceleration acceleration NOUN iajs-2987 56 35 by by ADP iajs-2987 56 36 gravity gravity NOUN iajs-2987 56 37 , , PUNCT iajs-2987 56 38 οΏ½ οΏ½ PROPN iajs-2987 56 39 Μƒ Μƒ PROPN iajs-2987 56 40 οΏ½ οΏ½ PROPN iajs-2987 56 41 is be AUX iajs-2987 56 42 the the DET iajs-2987 56 43 fluids fluid NOUN iajs-2987 56 44 electrical electrical ADJ iajs-2987 56 45 conductivity conductivity NOUN iajs-2987 56 46 , , PUNCT iajs-2987 56 47 kΜƒ kΜƒ PROPN iajs-2987 56 48 is be AUX iajs-2987 56 49 the the DET iajs-2987 56 50 thermal thermal ADJ iajs-2987 56 51 conductivity conductivity NOUN iajs-2987 56 52 . . PUNCT iajs-2987 57 1 the the DET iajs-2987 57 2 induced induce VERB iajs-2987 57 3 electric electric ADJ iajs-2987 57 4 field field NOUN iajs-2987 57 5 is be AUX iajs-2987 57 6 not not PART iajs-2987 57 7 taken take VERB iajs-2987 57 8 into into ADP iajs-2987 57 9 consideration consideration NOUN iajs-2987 57 10 at at ADV iajs-2987 57 11 all all ADV iajs-2987 57 12 , , PUNCT iajs-2987 57 13 because because SCONJ iajs-2987 57 14 assuming assume VERB iajs-2987 57 15 a a DET iajs-2987 57 16 low low ADJ iajs-2987 57 17 magnetic magnetic ADJ iajs-2987 57 18 reynolds reynold NOUN iajs-2987 57 19 number number NOUN iajs-2987 57 20 the the DET iajs-2987 57 21 fixed fix VERB iajs-2987 57 22 frame's( frame's( PROPN iajs-2987 57 23 οΏ½ οΏ½ PROPN iajs-2987 57 24 Μƒ Μƒ PROPN iajs-2987 57 25 οΏ½ οΏ½ PROPN iajs-2987 57 26 , , PUNCT iajs-2987 57 27 οΏ½ οΏ½ PROPN iajs-2987 57 28 Μƒ Μƒ PROPN iajs-2987 57 29 οΏ½ οΏ½ PROPN iajs-2987 57 30 ) ) PUNCT iajs-2987 57 31 flow flow NOUN iajs-2987 57 32 field field NOUN iajs-2987 57 33 and and CCONJ iajs-2987 57 34 the the DET iajs-2987 57 35 wave wave NOUN iajs-2987 57 36 frame's( frame's( PROPN iajs-2987 57 37 οΏ½ οΏ½ PROPN iajs-2987 57 38 Μ€ Μ€ ADJ iajs-2987 57 39 οΏ½ οΏ½ PROPN iajs-2987 57 40 , , PUNCT iajs-2987 57 41 yΜ€ yΜ€ NUM iajs-2987 57 42 ) ) PUNCT iajs-2987 57 43 wave wave NOUN iajs-2987 57 44 field field NOUN iajs-2987 57 45 are be AUX iajs-2987 57 46 also also ADV iajs-2987 57 47 considered consider VERB iajs-2987 57 48 the the DET iajs-2987 57 49 motions motion NOUN iajs-2987 57 50 of of ADP iajs-2987 57 51 an an DET iajs-2987 57 52 unsteady unsteady ADJ iajs-2987 57 53 and and CCONJ iajs-2987 57 54 steady steady ADJ iajs-2987 57 55 - - PUNCT iajs-2987 57 56 state state NOUN iajs-2987 57 57 . . PUNCT iajs-2987 58 1 it it PRON iajs-2987 58 2 's be AUX iajs-2987 58 3 important important ADJ iajs-2987 58 4 to to PART iajs-2987 58 5 think think VERB iajs-2987 58 6 about about ADP iajs-2987 58 7 the the DET iajs-2987 58 8 relationship relationship NOUN iajs-2987 58 9 between between ADP iajs-2987 58 10 the the DET iajs-2987 58 11 wave wave NOUN iajs-2987 58 12 ( ( PUNCT iajs-2987 58 13 οΏ½ οΏ½ PROPN iajs-2987 58 14 Μ€ Μ€ VERB iajs-2987 58 15 οΏ½ οΏ½ PROPN iajs-2987 58 16 , , PUNCT iajs-2987 58 17 yΜ€)and yΜ€)and CCONJ iajs-2987 58 18 the the DET iajs-2987 58 19 fixed fix VERB iajs-2987 58 20 frames frame NOUN iajs-2987 58 21 ( ( PUNCT iajs-2987 58 22 οΏ½ οΏ½ PROPN iajs-2987 58 23 Μƒ Μƒ PROPN iajs-2987 58 24 οΏ½ οΏ½ PROPN iajs-2987 58 25 , , PUNCT iajs-2987 58 26 οΏ½ οΏ½ PROPN iajs-2987 58 27 Μƒ Μƒ PROPN iajs-2987 58 28 οΏ½ οΏ½ PROPN iajs-2987 58 29 ) ) PUNCT iajs-2987 58 30 with with ADP iajs-2987 58 31 a a DET iajs-2987 58 32 velocity velocity NOUN iajs-2987 58 33 of of ADP iajs-2987 58 34 c c NOUN iajs-2987 58 35 as as SCONJ iajs-2987 58 36 they they PRON iajs-2987 58 37 move move VERB iajs-2987 58 38 apart apart ADV iajs-2987 58 39 from from ADP iajs-2987 58 40 one one NUM iajs-2987 58 41 another another DET iajs-2987 58 42 as as ADP iajs-2987 58 43 a a DET iajs-2987 58 44 result result NOUN iajs-2987 58 45 of of ADP iajs-2987 58 46 the the DET iajs-2987 58 47 transformations transformation NOUN iajs-2987 58 48 below below ADV iajs-2987 58 49 . . PUNCT iajs-2987 59 1 vΜ€ vΜ€ X iajs-2987 59 2 = = SYM iajs-2987 59 3 οΏ½ οΏ½ PROPN iajs-2987 59 4 Μƒ Μƒ PROPN iajs-2987 59 5 οΏ½ οΏ½ PROPN iajs-2987 59 6 , , PUNCT iajs-2987 59 7 yΜ€= yΜ€= PROPN iajs-2987 59 8 yΜƒ yΜƒ PROPN iajs-2987 59 9 , , PUNCT iajs-2987 59 10 t t PROPN iajs-2987 59 11 = = SYM iajs-2987 59 12 tΜƒ tΜƒ PROPN iajs-2987 59 13 , , PUNCT iajs-2987 59 14 xΜ€ xΜ€ PROPN iajs-2987 59 15 = = SYM iajs-2987 59 16 οΏ½ οΏ½ PROPN iajs-2987 59 17 Μƒ Μƒ PROPN iajs-2987 59 18 οΏ½ οΏ½ PROPN iajs-2987 59 19 βˆ’ βˆ’ ADP iajs-2987 59 20 𝑐 𝑐 PROPN iajs-2987 59 21 οΏ½ οΏ½ PROPN iajs-2987 59 22 Μƒ Μƒ PROPN iajs-2987 59 23 οΏ½ οΏ½ PROPN iajs-2987 59 24 , , PUNCT iajs-2987 59 25 uΜ€ uΜ€ PROPN iajs-2987 59 26 = = SYM iajs-2987 59 27 οΏ½ οΏ½ PROPN iajs-2987 59 28 Μƒ Μƒ PROPN iajs-2987 59 29 οΏ½ οΏ½ PROPN iajs-2987 59 30 βˆ’ βˆ’ PROPN iajs-2987 59 31 𝑐 𝑐 PROPN iajs-2987 59 32 , , PUNCT iajs-2987 59 33 οΏ½ οΏ½ PROPN iajs-2987 59 34 Μ€ Μ€ VERB iajs-2987 59 35 οΏ½ οΏ½ PROPN iajs-2987 59 36 = = SYM iajs-2987 59 37 οΏ½ οΏ½ PROPN iajs-2987 59 38 Μƒ Μƒ PROPN iajs-2987 59 39 οΏ½ οΏ½ PROPN iajs-2987 59 40 ( ( PUNCT iajs-2987 59 41 7 7 NUM iajs-2987 59 42 ) ) PUNCT iajs-2987 59 43 in in ADP iajs-2987 59 44 which which PRON iajs-2987 59 45 ( ( PUNCT iajs-2987 59 46 uΜ€ uΜ€ PROPN iajs-2987 59 47 , , PUNCT iajs-2987 59 48 vΜ€ vΜ€ PROPN iajs-2987 59 49 ) ) PUNCT iajs-2987 59 50 and and CCONJ iajs-2987 59 51 ( ( PUNCT iajs-2987 59 52 uΜƒ uΜƒ PROPN iajs-2987 59 53 , , PUNCT iajs-2987 59 54 vΜƒ)are vΜƒ)are VERB iajs-2987 59 55 the the DET iajs-2987 59 56 waves wave NOUN iajs-2987 59 57 ' ' PART iajs-2987 59 58 and and CCONJ iajs-2987 59 59 laboratories laboratory NOUN iajs-2987 59 60 ' ' PART iajs-2987 59 61 velocities velocity NOUN iajs-2987 59 62 , , PUNCT iajs-2987 59 63 respectively respectively ADV iajs-2987 59 64 . . PUNCT iajs-2987 60 1 the the DET iajs-2987 60 2 governing govern VERB iajs-2987 60 3 equations equation NOUN iajs-2987 60 4 ( ( PUNCT iajs-2987 60 5 3 3 NUM iajs-2987 60 6 ) ) PUNCT iajs-2987 60 7 , , PUNCT iajs-2987 60 8 ( ( PUNCT iajs-2987 60 9 4 4 NUM iajs-2987 60 10 ) ) PUNCT iajs-2987 60 11 , , PUNCT iajs-2987 60 12 ( ( PUNCT iajs-2987 60 13 5 5 NUM iajs-2987 60 14 ) ) PUNCT iajs-2987 60 15 , , PUNCT iajs-2987 60 16 and and CCONJ iajs-2987 60 17 ( ( PUNCT iajs-2987 60 18 6 6 X iajs-2987 60 19 ) ) PUNCT iajs-2987 60 20 be be AUX iajs-2987 60 21 expressed express VERB iajs-2987 60 22 in in ADP iajs-2987 60 23 wave wave NOUN iajs-2987 60 24 frame frame NOUN iajs-2987 60 25 as as ADP iajs-2987 60 26 using use VERB iajs-2987 60 27 the the DET iajs-2987 60 28 transformations transformation NOUN iajs-2987 60 29 mentioned mention VERB iajs-2987 60 30 above above ADV iajs-2987 60 31 . . PUNCT iajs-2987 61 1 βˆ‚uΜ€ βˆ‚uΜ€ PROPN iajs-2987 61 2 βˆ‚xΜ€ βˆ‚xΜ€ PROPN iajs-2987 62 1 + + CCONJ iajs-2987 62 2 πœ•vΜ€ πœ•vΜ€ ADJ iajs-2987 62 3 πœ•yΜ€ πœ•yΜ€ NOUN iajs-2987 62 4 = = SYM iajs-2987 62 5 0 0 PUNCT iajs-2987 62 6 ( ( PUNCT iajs-2987 62 7 8) 8) NUM iajs-2987 62 8 𝜌 𝜌 X iajs-2987 62 9 ( ( PUNCT iajs-2987 62 10 ( ( PUNCT iajs-2987 62 11 uΜ€ uΜ€ PROPN iajs-2987 62 12 + + CCONJ iajs-2987 62 13 𝑐 𝑐 X iajs-2987 62 14 ) ) PUNCT iajs-2987 62 15 βˆ‚uΜ€ βˆ‚uΜ€ PROPN iajs-2987 62 16 βˆ‚xΜ€ βˆ‚xΜ€ NOUN iajs-2987 62 17 + + CCONJ iajs-2987 62 18 vΜ€ vΜ€ X iajs-2987 62 19 πœ•uΜ€ πœ•uΜ€ ADJ iajs-2987 62 20 πœ•yΜ€ πœ•yΜ€ NOUN iajs-2987 62 21 ) ) PUNCT iajs-2987 62 22 βˆ’ βˆ’ ADP iajs-2987 62 23 𝜌 𝜌 ADP iajs-2987 62 24 οΏ½ οΏ½ PROPN iajs-2987 62 25 Μ€ Μ€ ADJ iajs-2987 62 26 οΏ½ οΏ½ PROPN iajs-2987 62 27 ( ( PUNCT iajs-2987 62 28 𝛺 𝛺 ADJ iajs-2987 62 29 Μ€ Μ€ PROPN iajs-2987 62 30 ( ( PUNCT iajs-2987 62 31 οΏ½ οΏ½ NOUN iajs-2987 62 32 Μ€ Μ€ VERB iajs-2987 62 33 οΏ½ οΏ½ PROPN iajs-2987 62 34 + + CCONJ iajs-2987 62 35 𝑐 𝑐 NOUN iajs-2987 62 36 ) ) PUNCT iajs-2987 62 37 + + CCONJ iajs-2987 62 38 2 2 NUM iajs-2987 62 39 πœ•vΜ€ πœ•vΜ€ PROPN iajs-2987 62 40 πœ• πœ• PROPN iajs-2987 62 41 οΏ½ οΏ½ PROPN iajs-2987 62 42 Μƒ Μƒ PROPN iajs-2987 62 43 οΏ½ οΏ½ PROPN iajs-2987 62 44 ) ) PUNCT iajs-2987 62 45 = = SYM iajs-2987 63 1 βˆ’ βˆ’ PROPN iajs-2987 63 2 πœ• πœ• NOUN iajs-2987 63 3 οΏ½ οΏ½ PROPN iajs-2987 63 4 Μ€ Μ€ NOUN iajs-2987 63 5 οΏ½ οΏ½ PROPN iajs-2987 63 6 πœ•xΜ€ πœ•xΜ€ VERB iajs-2987 63 7 + + CCONJ iajs-2987 63 8 πœ‡βˆ‡2uΜ€ πœ‡βˆ‡2uΜ€ NUM iajs-2987 63 9 βˆ’ βˆ’ NOUN iajs-2987 63 10 πœ‚βˆ‡4uΜ€ πœ‚βˆ‡4uΜ€ PUNCT iajs-2987 63 11 βˆ’ βˆ’ PROPN iajs-2987 63 12 οΏ½ οΏ½ PROPN iajs-2987 63 13 Μƒ Μƒ PROPN iajs-2987 63 14 οΏ½ οΏ½ NOUN iajs-2987 63 15 π΅βˆ— π΅βˆ— NUM iajs-2987 63 16 2 2 NUM iajs-2987 63 17 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 63 18 Ο† Ο† PROPN iajs-2987 63 19 ( ( PUNCT iajs-2987 63 20 ( ( PUNCT iajs-2987 63 21 uΜ€ uΜ€ PROPN iajs-2987 63 22 + + CCONJ iajs-2987 63 23 𝑐 𝑐 NOUN iajs-2987 63 24 ) ) PUNCT iajs-2987 63 25 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 63 26 Ο† Ο† PROPN iajs-2987 63 27 βˆ’ βˆ’ PROPN iajs-2987 63 28 vΜ€ vΜ€ PROPN iajs-2987 63 29 𝑠𝑖𝑛φ 𝑠𝑖𝑛φ NOUN iajs-2987 63 30 ) ) PUNCT iajs-2987 63 31 βˆ’ βˆ’ ADP iajs-2987 63 32 πœ‡ πœ‡ ADP iajs-2987 63 33 π‘˜ π‘˜ NOUN iajs-2987 63 34 Β° Β° PRON iajs-2987 63 35 ( ( PUNCT iajs-2987 63 36 uΜ€ uΜ€ PROPN iajs-2987 63 37 + + CCONJ iajs-2987 63 38 𝑐 𝑐 NOUN iajs-2987 63 39 ) ) PUNCT iajs-2987 63 40 + + CCONJ iajs-2987 63 41 πœŒπ‘” πœŒπ‘” PROPN iajs-2987 63 42 οΏ½ οΏ½ PROPN iajs-2987 63 43 Μ‡ Μ‡ PROPN iajs-2987 63 44 οΏ½ οΏ½ PROPN iajs-2987 63 45 ( ( PUNCT iajs-2987 63 46 tΜƒ tΜƒ PROPN iajs-2987 63 47 βˆ’ βˆ’ PROPN iajs-2987 63 48 t t PROPN iajs-2987 63 49 Β° Β° PROPN iajs-2987 63 50 )𝑠𝑖𝑛 )𝑠𝑖𝑛 PROPN iajs-2987 63 51 οΏ½ οΏ½ PROPN iajs-2987 63 52 Μƒ Μƒ PROPN iajs-2987 63 53 οΏ½ οΏ½ PROPN iajs-2987 63 54 + + CCONJ iajs-2987 63 55 πœŒπ‘”π‘ π‘–π‘› πœŒπ‘”π‘ π‘–π‘› PROPN iajs-2987 63 56 οΏ½ οΏ½ PROPN iajs-2987 63 57 Μƒ Μƒ PROPN iajs-2987 63 58 οΏ½ οΏ½ PROPN iajs-2987 63 59 ( ( PUNCT iajs-2987 63 60 9 9 NUM iajs-2987 63 61 ) ) PUNCT iajs-2987 63 62 𝜌 𝜌 X iajs-2987 63 63 ( ( PUNCT iajs-2987 63 64 ( ( PUNCT iajs-2987 63 65 uΜ€ uΜ€ PROPN iajs-2987 63 66 + + CCONJ iajs-2987 63 67 𝑐 𝑐 NOUN iajs-2987 63 68 ) ) PUNCT iajs-2987 63 69 πœ•vΜ€ πœ•vΜ€ NOUN iajs-2987 63 70 πœ•xΜ€ πœ•xΜ€ NOUN iajs-2987 63 71 + + CCONJ iajs-2987 63 72 vΜ€ vΜ€ X iajs-2987 63 73 πœ•vΜ€ πœ•vΜ€ NOUN iajs-2987 63 74 πœ•yΜ€ πœ•yΜ€ NOUN iajs-2987 63 75 ) ) PUNCT iajs-2987 63 76 βˆ’ βˆ’ ADP iajs-2987 63 77 𝜌 𝜌 ADP iajs-2987 63 78 οΏ½ οΏ½ PROPN iajs-2987 63 79 Μ€ Μ€ ADJ iajs-2987 63 80 οΏ½ οΏ½ PROPN iajs-2987 63 81 ( ( PUNCT iajs-2987 63 82 𝛺 𝛺 VERB iajs-2987 63 83 Μ€ Μ€ VERB iajs-2987 63 84 vΜ€ vΜ€ PRON iajs-2987 63 85 βˆ’ βˆ’ PROPN iajs-2987 63 86 2 2 NUM iajs-2987 63 87 πœ•uΜ€ πœ•uΜ€ PROPN iajs-2987 63 88 πœ• πœ• PROPN iajs-2987 63 89 οΏ½ οΏ½ PROPN iajs-2987 63 90 Μƒ Μƒ PROPN iajs-2987 63 91 οΏ½ οΏ½ PROPN iajs-2987 63 92 ) ) PUNCT iajs-2987 63 93 = = SYM iajs-2987 64 1 βˆ’ βˆ’ PROPN iajs-2987 64 2 πœ• πœ• NOUN iajs-2987 64 3 οΏ½ οΏ½ PROPN iajs-2987 64 4 Μ€ Μ€ ADJ iajs-2987 64 5 οΏ½ οΏ½ PROPN iajs-2987 64 6 πœ•yΜ€ πœ•yΜ€ ADJ iajs-2987 64 7 + + CCONJ iajs-2987 64 8 πœ‡βˆ‡2vΜ€ πœ‡βˆ‡2vΜ€ PRON iajs-2987 64 9 βˆ’ βˆ’ NUM iajs-2987 64 10 πœ‚βˆ‡4vΜ€ πœ‚βˆ‡4vΜ€ PUNCT iajs-2987 64 11 + + ADJ iajs-2987 64 12 οΏ½ οΏ½ PROPN iajs-2987 64 13 Μƒ Μƒ PROPN iajs-2987 64 14 οΏ½ οΏ½ NOUN iajs-2987 64 15 π΅βˆ— π΅βˆ— NUM iajs-2987 64 16 2 2 NUM iajs-2987 64 17 𝑠𝑖𝑛 𝑠𝑖𝑛 NOUN iajs-2987 64 18 Ο† Ο† PROPN iajs-2987 64 19 ( ( PUNCT iajs-2987 64 20 ( ( PUNCT iajs-2987 64 21 uΜ€ uΜ€ PROPN iajs-2987 64 22 + + CCONJ iajs-2987 64 23 𝑐 𝑐 NOUN iajs-2987 64 24 ) ) PUNCT iajs-2987 64 25 π‘π‘œπ‘ Ο† π‘π‘œπ‘ Ο† NOUN iajs-2987 64 26 βˆ’ βˆ’ PROPN iajs-2987 64 27 vΜ€ vΜ€ PROPN iajs-2987 64 28 𝑠𝑖𝑛 𝑠𝑖𝑛 PROPN iajs-2987 64 29 Ο† Ο† PROPN iajs-2987 64 30 ) ) PUNCT iajs-2987 64 31 βˆ’ βˆ’ PROPN iajs-2987 64 32 πœ‡ πœ‡ ADP iajs-2987 64 33 π‘˜ π‘˜ PROPN iajs-2987 64 34 Β° Β° ADP iajs-2987 64 35 vΜ€ vΜ€ X iajs-2987 64 36 βˆ’ βˆ’ PROPN iajs-2987 64 37 πœŒπ‘”π‘π‘œπ‘  πœŒπ‘”π‘π‘œπ‘  PROPN iajs-2987 64 38 οΏ½ οΏ½ PROPN iajs-2987 64 39 Μƒ Μƒ PROPN iajs-2987 64 40 οΏ½ οΏ½ PROPN iajs-2987 64 41 ( ( PUNCT iajs-2987 64 42 10 10 NUM iajs-2987 64 43 ) ) PUNCT iajs-2987 64 44 πœŒπΆπ‘ πœŒπΆπ‘ NOUN iajs-2987 64 45 ( ( PUNCT iajs-2987 64 46 ( ( PUNCT iajs-2987 64 47 uΜ€ uΜ€ PROPN iajs-2987 64 48 + + CCONJ iajs-2987 64 49 𝑐 𝑐 NOUN iajs-2987 64 50 ) ) PUNCT iajs-2987 64 51 βˆ‚tΜƒ βˆ‚tΜƒ NUM iajs-2987 64 52 βˆ‚xΜ€ βˆ‚xΜ€ NOUN iajs-2987 64 53 + + CCONJ iajs-2987 64 54 vΜ€ vΜ€ PROPN iajs-2987 64 55 βˆ‚tΜƒ βˆ‚tΜƒ NUM iajs-2987 64 56 βˆ‚yΜ€ βˆ‚yΜ€ PROPN iajs-2987 64 57 ) ) PUNCT iajs-2987 64 58 = = PUNCT iajs-2987 64 59 οΏ½ οΏ½ PROPN iajs-2987 64 60 Μƒ Μƒ PROPN iajs-2987 64 61 οΏ½ οΏ½ PROPN iajs-2987 64 62 ( ( PUNCT iajs-2987 64 63 βˆ‚2tΜƒ βˆ‚2tΜƒ PROPN iajs-2987 64 64 βˆ‚xΜ€2 βˆ‚xΜ€2 PART iajs-2987 64 65 + + NOUN iajs-2987 64 66 βˆ‚2tΜƒ βˆ‚2tΜƒ PROPN iajs-2987 64 67 βˆ‚yΜ€2 βˆ‚yΜ€2 NOUN iajs-2987 64 68 ) ) PUNCT iajs-2987 65 1 + + CCONJ iajs-2987 65 2 πœ‡ πœ‡ X iajs-2987 65 3 [ [ X iajs-2987 65 4 2 2 NUM iajs-2987 65 5 { { PUNCT iajs-2987 65 6 ( ( PUNCT iajs-2987 65 7 βˆ‚uΜ€ βˆ‚uΜ€ PROPN iajs-2987 65 8 βˆ‚xΜ€ βˆ‚xΜ€ PROPN iajs-2987 65 9 ) ) PUNCT iajs-2987 65 10 2 2 NUM iajs-2987 66 1 + + CCONJ iajs-2987 66 2 ( ( PUNCT iajs-2987 66 3 βˆ‚vΜ€ βˆ‚vΜ€ PROPN iajs-2987 66 4 βˆ‚yΜ€ βˆ‚yΜ€ PROPN iajs-2987 66 5 ) ) PUNCT iajs-2987 66 6 2 2 X iajs-2987 66 7 } } PUNCT iajs-2987 66 8 + + CCONJ iajs-2987 66 9 ( ( PUNCT iajs-2987 66 10 βˆ‚uΜ€ βˆ‚uΜ€ PROPN iajs-2987 66 11 βˆ‚yΜ€ βˆ‚yΜ€ PROPN iajs-2987 66 12 + + CCONJ iajs-2987 66 13 βˆ‚vΜ€ βˆ‚vΜ€ PROPN iajs-2987 66 14 βˆ‚xΜ€ βˆ‚xΜ€ PROPN iajs-2987 66 15 ) ) PUNCT iajs-2987 66 16 2 2 NUM iajs-2987 66 17 ] ] PUNCT iajs-2987 66 18 + + PUNCT iajs-2987 66 19 πœ‚ πœ‚ X iajs-2987 66 20 [ [ X iajs-2987 66 21 ( ( PUNCT iajs-2987 66 22 βˆ‚2uΜ€ βˆ‚2uΜ€ PROPN iajs-2987 66 23 βˆ‚xΜ€2 βˆ‚xΜ€2 PART iajs-2987 66 24 + + NUM iajs-2987 66 25 βˆ‚2uΜ€ βˆ‚2uΜ€ ADJ iajs-2987 66 26 βˆ‚y2 βˆ‚y2 NUM iajs-2987 66 27 ) ) PUNCT iajs-2987 66 28 2 2 NUM iajs-2987 66 29 + + CCONJ iajs-2987 66 30 ( ( PUNCT iajs-2987 66 31 βˆ‚2vΜ€ βˆ‚2vΜ€ ADJ iajs-2987 66 32 βˆ‚xΜ€2 βˆ‚xΜ€2 NOUN iajs-2987 66 33 + + CCONJ iajs-2987 66 34 βˆ‚2vΜ€ βˆ‚2vΜ€ ADJ iajs-2987 66 35 βˆ‚yΜ€2 βˆ‚yΜ€2 NOUN iajs-2987 66 36 ) ) PUNCT iajs-2987 66 37 2 2 NUM iajs-2987 66 38 ] ] PUNCT iajs-2987 66 39 + + NUM iajs-2987 66 40 οΏ½ οΏ½ PROPN iajs-2987 66 41 Μƒ Μƒ PROPN iajs-2987 66 42 οΏ½ οΏ½ NOUN iajs-2987 66 43 π΅βˆ— π΅βˆ— NOUN iajs-2987 66 44 2((uΜ€ 2((uΜ€ NUM iajs-2987 66 45 + + NUM iajs-2987 66 46 𝑐 𝑐 X iajs-2987 66 47 ) ) PUNCT iajs-2987 66 48 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 66 49 Ο† Ο† PROPN iajs-2987 66 50 βˆ’ βˆ’ PROPN iajs-2987 66 51 vΜ€ vΜ€ PROPN iajs-2987 66 52 𝑠𝑖𝑛 𝑠𝑖𝑛 PROPN iajs-2987 66 53 Ο† Ο† NUM iajs-2987 66 54 ) ) PUNCT iajs-2987 66 55 2 2 NUM iajs-2987 66 56 ( ( PUNCT iajs-2987 66 57 11 11 NUM iajs-2987 66 58 ) ) PUNCT iajs-2987 66 59 to to PART iajs-2987 66 60 reduce reduce VERB iajs-2987 66 61 the the DET iajs-2987 66 62 number number NOUN iajs-2987 66 63 of of ADP iajs-2987 66 64 additional additional ADJ iajs-2987 66 65 parameters parameter NOUN iajs-2987 66 66 , , PUNCT iajs-2987 66 67 we we PRON iajs-2987 66 68 shall shall AUX iajs-2987 66 69 define define VERB iajs-2987 66 70 the the DET iajs-2987 66 71 following follow VERB iajs-2987 66 72 nondimensional nondimensional ADJ iajs-2987 66 73 quantities quantity NOUN iajs-2987 66 74 : : PUNCT iajs-2987 66 75 π‘₯ π‘₯ X iajs-2987 66 76 = = PUNCT iajs-2987 66 77 xΜ€ xΜ€ PROPN iajs-2987 66 78 πœ† πœ† PROPN iajs-2987 66 79 , , PUNCT iajs-2987 66 80 𝑦 𝑦 NOUN iajs-2987 66 81 = = SYM iajs-2987 66 82 yΜ€ yΜ€ NUM iajs-2987 66 83 𝑑1 𝑑1 NOUN iajs-2987 66 84 , , PUNCT iajs-2987 66 85 β„Ž1 β„Ž1 PROPN iajs-2987 66 86 βˆ—(π‘₯ βˆ—(π‘₯ PROPN iajs-2987 66 87 ) ) PUNCT iajs-2987 67 1 = = SYM iajs-2987 67 2 β„Ž1Μƒ β„Ž1Μƒ X iajs-2987 67 3 ( ( PUNCT iajs-2987 67 4 οΏ½ οΏ½ NOUN iajs-2987 67 5 Μ… Μ… NOUN iajs-2987 67 6 οΏ½ οΏ½ PROPN iajs-2987 67 7 ) ) PUNCT iajs-2987 67 8 𝑑1 𝑑1 NOUN iajs-2987 67 9 , , PUNCT iajs-2987 67 10 β„Ž2 β„Ž2 ADJ iajs-2987 67 11 βˆ—(π‘₯ βˆ—(π‘₯ NOUN iajs-2987 67 12 ) ) PUNCT iajs-2987 67 13 = = SYM iajs-2987 67 14 β„Ž2Μƒ β„Ž2Μƒ PROPN iajs-2987 67 15 ( ( PUNCT iajs-2987 67 16 οΏ½ οΏ½ NOUN iajs-2987 67 17 Μ… Μ… NOUN iajs-2987 67 18 οΏ½ οΏ½ PROPN iajs-2987 67 19 ) ) PUNCT iajs-2987 67 20 𝑑1 𝑑1 NOUN iajs-2987 67 21 , , PUNCT iajs-2987 67 22 πœƒ πœƒ NOUN iajs-2987 67 23 Β° Β° NOUN iajs-2987 67 24 = = PUNCT iajs-2987 67 25 tΜƒβˆ’t0 tΜƒβˆ’t0 NOUN iajs-2987 67 26 t1βˆ’t0 t1βˆ’t0 NOUN iajs-2987 67 27 , , PUNCT iajs-2987 67 28 uβˆ— uβˆ— PROPN iajs-2987 67 29 = = SYM iajs-2987 67 30 uΜ€ uΜ€ PROPN iajs-2987 67 31 𝑐 𝑐 PROPN iajs-2987 67 32 , , PUNCT iajs-2987 67 33 vβˆ— vβˆ— PROPN iajs-2987 67 34 = = PUNCT iajs-2987 67 35 πœ†vΜ€ πœ†vΜ€ PROPN iajs-2987 67 36 𝑐𝑑1 𝑐𝑑1 PROPN iajs-2987 67 37 , , PUNCT iajs-2987 67 38 tβˆ— tβˆ— NOUN iajs-2987 67 39 = = SYM iajs-2987 67 40 𝑐 𝑐 NOUN iajs-2987 67 41 οΏ½ οΏ½ PROPN iajs-2987 67 42 Μƒ Μƒ PROPN iajs-2987 67 43 οΏ½ οΏ½ PROPN iajs-2987 67 44 πœ† πœ† ADP iajs-2987 67 45 , , PUNCT iajs-2987 67 46 𝑅𝑒 𝑅𝑒 PROPN iajs-2987 67 47 = = SYM iajs-2987 67 48 π‘πœŒπ‘‘1 π‘πœŒπ‘‘1 PROPN iajs-2987 67 49 πœ‡ πœ‡ ADP iajs-2987 67 50 , , PUNCT iajs-2987 67 51 𝛿 𝛿 PRON iajs-2987 67 52 = = NOUN iajs-2987 67 53 𝑑1 𝑑1 NOUN iajs-2987 67 54 πœ† πœ† SYM iajs-2987 67 55 , , PUNCT iajs-2987 67 56 β„‹=Ξ²βˆ—π‘‘1√ β„‹=Ξ²βˆ—π‘‘1√ PROPN iajs-2987 67 57 οΏ½ οΏ½ PROPN iajs-2987 67 58 Μƒ Μƒ PROPN iajs-2987 67 59 οΏ½ οΏ½ PROPN iajs-2987 67 60 πœ‡ πœ‡ ADP iajs-2987 67 61 , , PUNCT iajs-2987 67 62 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN iajs-2987 67 63 = = PUNCT iajs-2987 67 64 πœ‡ πœ‡ ADP iajs-2987 67 65 𝐢𝑝 𝐢𝑝 PROPN iajs-2987 67 66 οΏ½ οΏ½ PROPN iajs-2987 67 67 Μƒ Μƒ PROPN iajs-2987 67 68 οΏ½ οΏ½ PROPN iajs-2987 67 69 , , PUNCT iajs-2987 67 70 𝛾 𝛾 PROPN iajs-2987 67 71 = = PUNCT iajs-2987 67 72 𝑑1√ 𝑑1√ ADV iajs-2987 67 73 πœ‡ πœ‡ ADP iajs-2987 67 74 πœ‚ πœ‚ NOUN iajs-2987 67 75 , , PUNCT iajs-2987 67 76 π·π‘Ž π·π‘Ž PROPN iajs-2987 67 77 = = SYM iajs-2987 67 78 π‘˜πœŠ π‘˜πœŠ NUM iajs-2987 67 79 𝑑1 𝑑1 NOUN iajs-2987 67 80 2 2 NUM iajs-2987 67 81 , , PUNCT iajs-2987 67 82 πΉπ‘Ÿ πΉπ‘Ÿ PROPN iajs-2987 67 83 = = PUNCT iajs-2987 67 84 𝑐2 𝑐2 NOUN iajs-2987 67 85 𝑔𝑑1 𝑔𝑑1 NOUN iajs-2987 67 86 ( ( PUNCT iajs-2987 67 87 12 12 NUM iajs-2987 67 88 ) ) PUNCT iajs-2987 67 89 , , PUNCT iajs-2987 67 90 𝑑1 𝑑1 NOUN iajs-2987 67 91 2 2 NUM iajs-2987 67 92 οΏ½ οΏ½ NOUN iajs-2987 67 93 Μ€ Μ€ VERB iajs-2987 67 94 οΏ½ οΏ½ PROPN iajs-2987 67 95 ( ( PUNCT iajs-2987 67 96 οΏ½ οΏ½ PROPN iajs-2987 67 97 Μ€ Μ€ NOUN iajs-2987 67 98 οΏ½ οΏ½ NOUN iajs-2987 67 99 ) ) PUNCT iajs-2987 67 100 πœ†πœ‡π‘ πœ†πœ‡π‘ NOUN iajs-2987 67 101 = = SYM iajs-2987 67 102 𝑝 𝑝 NOUN iajs-2987 67 103 , , PUNCT iajs-2987 67 104 π΅π‘Ÿ=π‘ƒπ‘Ÿ π΅π‘Ÿ=π‘ƒπ‘Ÿ PROPN iajs-2987 67 105 . . PUNCT iajs-2987 68 1 𝐸𝑐 𝐸𝑐 INTJ iajs-2987 68 2 , , PUNCT iajs-2987 68 3 πΊπ‘Ÿ πΊπ‘Ÿ PROPN iajs-2987 68 4 = = PUNCT iajs-2987 68 5 𝜌 𝜌 PART iajs-2987 68 6 𝑔(t1βˆ’t0 𝑔(t1βˆ’t0 NOUN iajs-2987 68 7 ) ) PUNCT iajs-2987 68 8 οΏ½ οΏ½ PROPN iajs-2987 68 9 Μ‡ Μ‡ VERB iajs-2987 68 10 οΏ½ οΏ½ PROPN iajs-2987 68 11 𝑑1 𝑑1 NOUN iajs-2987 68 12 πœ‡ πœ‡ ADP iajs-2987 68 13 𝑐 𝑐 PROPN iajs-2987 68 14 , , PUNCT iajs-2987 68 15 𝐸𝑐 𝐸𝑐 PROPN iajs-2987 68 16 = = PUNCT iajs-2987 68 17 𝑐2 𝑐2 NOUN iajs-2987 68 18 ( ( PUNCT iajs-2987 68 19 t1βˆ’t0 t1βˆ’t0 NOUN iajs-2987 68 20 ) ) PUNCT iajs-2987 68 21 𝐢𝑝 𝐢𝑝 PROPN iajs-2987 68 22 . . PUNCT iajs-2987 69 1 where where SCONJ iajs-2987 69 2 β„‹ β„‹ PROPN iajs-2987 69 3 is be AUX iajs-2987 69 4 hartmann hartmann PROPN iajs-2987 69 5 number number NOUN iajs-2987 69 6 , , PUNCT iajs-2987 69 7 𝑅𝑒 𝑅𝑒 PROPN iajs-2987 69 8 is be AUX iajs-2987 69 9 reynolds reynolds PROPN iajs-2987 69 10 number number NOUN iajs-2987 69 11 , , PUNCT iajs-2987 69 12 𝛿 𝛿 PRON iajs-2987 69 13 is be AUX iajs-2987 69 14 wave wave NOUN iajs-2987 69 15 number number NOUN iajs-2987 69 16 , , PUNCT iajs-2987 69 17 𝛾 𝛾 PROPN iajs-2987 69 18 is be AUX iajs-2987 69 19 couple couple NOUN iajs-2987 69 20 stress stress NOUN iajs-2987 69 21 parameter parameter NOUN iajs-2987 69 22 , , PUNCT iajs-2987 69 23 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN iajs-2987 69 24 is be AUX iajs-2987 69 25 prandtl prandtl NOUN iajs-2987 69 26 number number NOUN iajs-2987 69 27 , , PUNCT iajs-2987 69 28 π·π‘Ž π·π‘Ž PROPN iajs-2987 69 29 is be AUX iajs-2987 69 30 darcy darcy NOUN iajs-2987 69 31 number number NOUN iajs-2987 69 32 , , PUNCT iajs-2987 69 33 πΉπ‘Ÿ πΉπ‘Ÿ PROPN iajs-2987 69 34 is be AUX iajs-2987 69 35 froude froude ADJ iajs-2987 69 36 number number NOUN iajs-2987 69 37 , , PUNCT iajs-2987 69 38 π΅π‘Ÿ π΅π‘Ÿ PROPN iajs-2987 69 39 is be AUX iajs-2987 69 40 brinkman brinkman NOUN iajs-2987 69 41 number number NOUN iajs-2987 69 42 , , PUNCT iajs-2987 69 43 𝐸𝑐 𝐸𝑐 PROPN iajs-2987 69 44 is be AUX iajs-2987 69 45 eckert eckert PROPN iajs-2987 69 46 number number NOUN iajs-2987 69 47 , , PUNCT iajs-2987 69 48 and and CCONJ iajs-2987 69 49 πΊπ‘Ÿ πΊπ‘Ÿ PROPN iajs-2987 69 50 is be AUX iajs-2987 69 51 grashof grashof ADJ iajs-2987 69 52 number number NOUN iajs-2987 69 53 . . PUNCT iajs-2987 70 1 ihjpas ihjpas PROPN iajs-2987 70 2 . . PUNCT iajs-2987 71 1 36(2)2023 36(2)2023 NUM iajs-2987 71 2 317 317 NUM iajs-2987 71 3 according accord VERB iajs-2987 71 4 to to ADP iajs-2987 71 5 equations equation NOUN iajs-2987 71 6 ( ( PUNCT iajs-2987 71 7 1 1 NUM iajs-2987 71 8 ) ) PUNCT iajs-2987 71 9 and and CCONJ iajs-2987 71 10 ( ( PUNCT iajs-2987 71 11 2 2 NUM iajs-2987 71 12 ) ) PUNCT iajs-2987 72 1 , , PUNCT iajs-2987 72 2 the the DET iajs-2987 72 3 dimensionless dimensionless NOUN iajs-2987 72 4 shape shape NOUN iajs-2987 72 5 of of ADP iajs-2987 72 6 the the DET iajs-2987 72 7 peristaltic peristaltic ADJ iajs-2987 72 8 channel channel NOUN iajs-2987 72 9 walls wall NOUN iajs-2987 72 10 may may AUX iajs-2987 72 11 be be AUX iajs-2987 72 12 shown show VERB iajs-2987 72 13 in in ADP iajs-2987 72 14 β„Ž1 β„Ž1 PROPN iajs-2987 72 15 βˆ—(π‘₯ βˆ—(π‘₯ PROPN iajs-2987 72 16 ) ) PUNCT iajs-2987 72 17 and and CCONJ iajs-2987 72 18 β„Ž2 β„Ž2 PROPN iajs-2987 72 19 βˆ—(π‘₯ βˆ—(π‘₯ NOUN iajs-2987 72 20 ) ) PUNCT iajs-2987 73 1 β„Ž1 β„Ž1 PROPN iajs-2987 73 2 βˆ—(π‘₯ βˆ—(π‘₯ PROPN iajs-2987 73 3 ) ) PUNCT iajs-2987 74 1 = = SYM iajs-2987 74 2 1 1 NUM iajs-2987 75 1 + + NUM iajs-2987 75 2 π‘˜π‘₯ π‘˜π‘₯ PRON iajs-2987 75 3 + + CCONJ iajs-2987 75 4 π‘Ž π‘Ž PROPN iajs-2987 75 5 cos(2πœ‹π‘₯ cos(2πœ‹π‘₯ NUM iajs-2987 75 6 ) ) PUNCT iajs-2987 75 7 ( ( PUNCT iajs-2987 75 8 13 13 NUM iajs-2987 75 9 ) ) PUNCT iajs-2987 75 10 β„Ž2 β„Ž2 ADJ iajs-2987 75 11 βˆ—(π‘₯ βˆ—(π‘₯ NOUN iajs-2987 75 12 ) ) PUNCT iajs-2987 75 13 = = PUNCT iajs-2987 76 1 βˆ’π‘‘ βˆ’π‘‘ VERB iajs-2987 76 2 βˆ’ βˆ’ PROPN iajs-2987 76 3 π‘˜π‘₯ π‘˜π‘₯ NOUN iajs-2987 76 4 βˆ’ βˆ’ NOUN iajs-2987 77 1 𝑏 𝑏 PROPN iajs-2987 78 1 cos(2πœ‹π‘₯ cos(2πœ‹π‘₯ PROPN iajs-2987 79 1 + + CCONJ iajs-2987 80 1 πœ™ πœ™ NOUN iajs-2987 80 2 Β° Β° NUM iajs-2987 80 3 ) ) PUNCT iajs-2987 80 4 ( ( PUNCT iajs-2987 80 5 14 14 NUM iajs-2987 80 6 ) ) PUNCT iajs-2987 80 7 where where SCONJ iajs-2987 80 8 π‘Ž π‘Ž X iajs-2987 80 9 = = SYM iajs-2987 80 10 π‘Ž1 π‘Ž1 NOUN iajs-2987 80 11 βˆ— βˆ— NOUN iajs-2987 80 12 𝑑1 𝑑1 NOUN iajs-2987 80 13 , , PUNCT iajs-2987 80 14 𝑏 𝑏 PROPN iajs-2987 80 15 = = SYM iajs-2987 80 16 π‘Ž2 π‘Ž2 PROPN iajs-2987 80 17 βˆ— βˆ— NOUN iajs-2987 80 18 𝑑1 𝑑1 NOUN iajs-2987 80 19 , , PUNCT iajs-2987 81 1 𝑑 𝑑 NOUN iajs-2987 81 2 = = PUNCT iajs-2987 81 3 𝑑2 𝑑2 NOUN iajs-2987 81 4 𝑑1 𝑑1 NOUN iajs-2987 81 5 , , PUNCT iajs-2987 81 6 π‘˜ π‘˜ PROPN iajs-2987 81 7 = = PUNCT iajs-2987 81 8 ( ( PUNCT iajs-2987 81 9 πœ† πœ† PROPN iajs-2987 81 10 tan tan PROPN iajs-2987 81 11 οΏ½ οΏ½ PROPN iajs-2987 81 12 Μƒ Μƒ PROPN iajs-2987 81 13 οΏ½ οΏ½ PROPN iajs-2987 81 14 𝑑1 𝑑1 NOUN iajs-2987 81 15 ) ) PUNCT iajs-2987 81 16 is be AUX iajs-2987 81 17 referred refer VERB iajs-2987 81 18 to to ADP iajs-2987 81 19 as as ADP iajs-2987 81 20 the the DET iajs-2987 81 21 channel channel NOUN iajs-2987 81 22 's 's PART iajs-2987 81 23 non non ADJ iajs-2987 81 24 - - ADJ iajs-2987 81 25 uniform uniform ADJ iajs-2987 81 26 parameter parameter NOUN iajs-2987 81 27 and and CCONJ iajs-2987 81 28 πœ™ πœ™ NOUN iajs-2987 81 29 Β° Β° NOUN iajs-2987 81 30 the the DET iajs-2987 81 31 relation relation NOUN iajs-2987 81 32 π‘Ž2 π‘Ž2 NOUN iajs-2987 81 33 + + CCONJ iajs-2987 81 34 𝑏2 𝑏2 PROPN iajs-2987 81 35 + + CCONJ iajs-2987 81 36 2π‘Žπ‘π‘π‘œπ‘ πœ™ 2π‘Žπ‘π‘π‘œπ‘ πœ™ PROPN iajs-2987 81 37 Β° Β° NOUN iajs-2987 81 38 ≀ ≀ NOUN iajs-2987 81 39 ( ( PUNCT iajs-2987 81 40 1 1 NUM iajs-2987 81 41 + + NUM iajs-2987 81 42 𝑑)2 𝑑)2 NOUN iajs-2987 81 43 where(πœ“ where(πœ“ NOUN iajs-2987 81 44 Β° Β° NOUN iajs-2987 81 45 ) ) PUNCT iajs-2987 81 46 stream stream NOUN iajs-2987 81 47 function function NOUN iajs-2987 81 48 of of ADP iajs-2987 81 49 velocity velocity NOUN iajs-2987 81 50 components component NOUN iajs-2987 81 51 uβˆ— uβˆ— VERB iajs-2987 81 52 and and CCONJ iajs-2987 81 53 vβˆ— vβˆ— PROPN iajs-2987 81 54 that that PRON iajs-2987 81 55 is be AUX iajs-2987 81 56 dimensionless dimensionless ADJ iajs-2987 81 57 uβˆ— uβˆ— NOUN iajs-2987 81 58 = = SYM iajs-2987 81 59 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 81 60 Β° Β° ADJ iajs-2987 81 61 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 81 62 and and CCONJ iajs-2987 81 63 vβˆ— vβˆ— PROPN iajs-2987 81 64 = = PUNCT iajs-2987 82 1 βˆ’ βˆ’ PROPN iajs-2987 82 2 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 82 3 Β° Β° NUM iajs-2987 82 4 πœ•π‘₯ πœ•π‘₯ NOUN iajs-2987 82 5 , , PUNCT iajs-2987 82 6 respectively respectively ADV iajs-2987 82 7 , , PUNCT iajs-2987 82 8 and and CCONJ iajs-2987 82 9 satisfy satisfy VERB iajs-2987 82 10 the the DET iajs-2987 82 11 continuity continuity NOUN iajs-2987 82 12 equation equation NOUN iajs-2987 82 13 ( ( PUNCT iajs-2987 82 14 8) 8) NUM iajs-2987 82 15 . . PUNCT iajs-2987 83 1 in in ADP iajs-2987 83 2 terms term NOUN iajs-2987 83 3 of of ADP iajs-2987 83 4 stream stream NOUN iajs-2987 83 5 function function NOUN iajs-2987 83 6 πœ“ πœ“ PROPN iajs-2987 83 7 Β° Β° NOUN iajs-2987 83 8 , , PUNCT iajs-2987 83 9 the the DET iajs-2987 83 10 dimensionless dimensionless NOUN iajs-2987 83 11 variables variable NOUN iajs-2987 83 12 are be AUX iajs-2987 83 13 specified specify VERB iajs-2987 83 14 in in ADP iajs-2987 83 15 equations equation NOUN iajs-2987 83 16 . . PUNCT iajs-2987 84 1 ( ( PUNCT iajs-2987 84 2 9 9 NUM iajs-2987 84 3 ) ) PUNCT iajs-2987 84 4 , , PUNCT iajs-2987 84 5 ( ( PUNCT iajs-2987 84 6 10 10 NUM iajs-2987 84 7 ) ) PUNCT iajs-2987 84 8 , , PUNCT iajs-2987 84 9 and and CCONJ iajs-2987 84 10 ( ( PUNCT iajs-2987 84 11 11 11 NUM iajs-2987 84 12 ) ) PUNCT iajs-2987 84 13 were be AUX iajs-2987 84 14 translated translate VERB iajs-2987 84 15 into into ADP iajs-2987 84 16 the the DET iajs-2987 84 17 following follow VERB iajs-2987 84 18 equations equation NOUN iajs-2987 84 19 . . PUNCT iajs-2987 85 1 𝑅𝑒 𝑅𝑒 VERB iajs-2987 85 2 . . PUNCT iajs-2987 86 1 𝛿 𝛿 PRON iajs-2987 86 2 [ [ X iajs-2987 86 3 ( ( PUNCT iajs-2987 86 4 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 86 5 Β° Β° ADJ iajs-2987 86 6 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 86 7 . . PUNCT iajs-2987 87 1 πœ• πœ• NOUN iajs-2987 87 2 πœ•π‘₯ πœ•π‘₯ X iajs-2987 87 3 βˆ’ βˆ’ PROPN iajs-2987 87 4 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 87 5 Β° Β° NUM iajs-2987 87 6 πœ•π‘₯ πœ•π‘₯ X iajs-2987 87 7 . . PUNCT iajs-2987 88 1 πœ• πœ• NOUN iajs-2987 88 2 πœ•π‘¦ πœ•π‘¦ PROPN iajs-2987 88 3 ) ) PUNCT iajs-2987 88 4 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 88 5 Β° Β° ADJ iajs-2987 88 6 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 88 7 + + NUM iajs-2987 88 8 πœ•2πœ“ πœ•2πœ“ NUM iajs-2987 88 9 Β° Β° NUM iajs-2987 88 10 πœ•π‘₯πœ•π‘¦ πœ•π‘₯πœ•π‘¦ NOUN iajs-2987 88 11 ] ] PUNCT iajs-2987 88 12 βˆ’ βˆ’ PROPN iajs-2987 88 13 πœŒΟ‰Μ€2𝑑1 πœŒΟ‰Μ€2𝑑1 PROPN iajs-2987 88 14 2 2 NUM iajs-2987 88 15 πœ‡ πœ‡ X iajs-2987 88 16 ( ( PUNCT iajs-2987 88 17 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 88 18 Β° Β° ADJ iajs-2987 88 19 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 88 20 + + X iajs-2987 88 21 1 1 X iajs-2987 88 22 ) ) PUNCT iajs-2987 88 23 + + CCONJ iajs-2987 89 1 2ὼ𝑅𝑒𝛿 2ὼ𝑅𝑒𝛿 NUM iajs-2987 89 2 2 2 NUM iajs-2987 89 3 πœ•2πœ“ πœ•2πœ“ NOUN iajs-2987 89 4 Β° Β° NOUN iajs-2987 89 5 πœ•π‘₯πœ• πœ•π‘₯πœ• X iajs-2987 89 6 π‘‘βˆ— π‘‘βˆ— NOUN iajs-2987 89 7 = = SYM iajs-2987 89 8 βˆ’ βˆ’ PROPN iajs-2987 89 9 πœ•π‘ πœ•π‘ NOUN iajs-2987 89 10 πœ•π‘₯ πœ•π‘₯ X iajs-2987 89 11 + + CCONJ iajs-2987 89 12 𝛿2 𝛿2 NOUN iajs-2987 89 13 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 89 14 Β° Β° NOUN iajs-2987 89 15 πœ•π‘₯2πœ•π‘¦ πœ•π‘₯2πœ•π‘¦ VERB iajs-2987 89 16 + + NUM iajs-2987 89 17 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 89 18 Β° Β° ADP iajs-2987 89 19 πœ•π‘¦3 πœ•π‘¦3 NOUN iajs-2987 89 20 βˆ’ βˆ’ NOUN iajs-2987 89 21 1 1 NUM iajs-2987 89 22 𝛾2 𝛾2 NOUN iajs-2987 89 23 ( ( PUNCT iajs-2987 89 24 𝛿4 𝛿4 NOUN iajs-2987 89 25 πœ•5πœ“ πœ•5πœ“ NOUN iajs-2987 89 26 Β° Β° ADP iajs-2987 89 27 πœ•π‘₯4πœ•π‘¦ πœ•π‘₯4πœ•π‘¦ NOUN iajs-2987 89 28 + + NOUN iajs-2987 89 29 2𝛿2 2𝛿2 NUM iajs-2987 89 30 πœ•5πœ“ πœ•5πœ“ ADJ iajs-2987 89 31 Β° Β° NOUN iajs-2987 89 32 πœ•π‘₯2πœ•π‘¦3 πœ•π‘₯2πœ•π‘¦3 NOUN iajs-2987 90 1 + + SYM iajs-2987 91 1 πœ•5πœ“ πœ•5πœ“ NOUN iajs-2987 91 2 Β° Β° ADP iajs-2987 91 3 πœ•π‘¦5 πœ•π‘¦5 PROPN iajs-2987 91 4 ) ) PUNCT iajs-2987 92 1 βˆ’ βˆ’ PROPN iajs-2987 93 1 β„‹2 β„‹2 INTJ iajs-2987 93 2 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 94 1 Ο† Ο† PROPN iajs-2987 95 1 [ [ X iajs-2987 95 2 ( ( PUNCT iajs-2987 95 3 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 95 4 Β° Β° ADJ iajs-2987 95 5 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 95 6 + + X iajs-2987 95 7 1 1 X iajs-2987 95 8 ) ) PUNCT iajs-2987 95 9 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 95 10 Ο† Ο† PROPN iajs-2987 95 11 + + PROPN iajs-2987 95 12 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 95 13 Β° Β° NOUN iajs-2987 95 14 πœ•π‘₯ πœ•π‘₯ NOUN iajs-2987 95 15 𝛿 𝛿 DET iajs-2987 95 16 𝑠𝑖𝑛 𝑠𝑖𝑛 ADJ iajs-2987 95 17 Ο† Ο† X iajs-2987 95 18 ] ] X iajs-2987 95 19 βˆ’ βˆ’ PROPN iajs-2987 95 20 1 1 NUM iajs-2987 95 21 π·π‘Ž π·π‘Ž PROPN iajs-2987 95 22 ( ( PUNCT iajs-2987 95 23 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 95 24 Β° Β° ADJ iajs-2987 95 25 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 95 26 + + X iajs-2987 95 27 1 1 X iajs-2987 95 28 ) ) PUNCT iajs-2987 95 29 + + CCONJ iajs-2987 96 1 𝑅𝑒 𝑅𝑒 VERB iajs-2987 96 2 πΉπ‘Ÿ πΉπ‘Ÿ PROPN iajs-2987 96 3 sin sin VERB iajs-2987 96 4 Ξ±Μƒ Ξ±Μƒ PROPN iajs-2987 96 5 + + CCONJ iajs-2987 96 6 gπ‘Ÿ gπ‘Ÿ ADJ iajs-2987 96 7 ΞΈ ΞΈ PROPN iajs-2987 96 8 sinΞ±Μƒ sinΞ±Μƒ X iajs-2987 96 9 ( ( PUNCT iajs-2987 96 10 15 15 NUM iajs-2987 96 11 ) ) PUNCT iajs-2987 96 12 𝑅𝑒 𝑅𝑒 VERB iajs-2987 96 13 . . PUNCT iajs-2987 97 1 𝛿 𝛿 DET iajs-2987 97 2 3 3 NUM iajs-2987 97 3 [ [ X iajs-2987 97 4 ( ( PUNCT iajs-2987 97 5 βˆ’ βˆ’ PROPN iajs-2987 97 6 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 97 7 Β° Β° ADJ iajs-2987 97 8 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 97 9 . . PUNCT iajs-2987 98 1 πœ• πœ• NOUN iajs-2987 98 2 πœ•π‘₯ πœ•π‘₯ X iajs-2987 98 3 + + CCONJ iajs-2987 98 4 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 98 5 Β° Β° ADJ iajs-2987 98 6 πœ•π‘₯ πœ•π‘₯ X iajs-2987 98 7 . . PUNCT iajs-2987 99 1 πœ• πœ• NOUN iajs-2987 99 2 πœ•π‘¦ πœ•π‘¦ PROPN iajs-2987 99 3 ) ) PUNCT iajs-2987 99 4 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 99 5 Β° Β° NOUN iajs-2987 99 6 πœ•π‘₯ πœ•π‘₯ X iajs-2987 99 7 βˆ’ βˆ’ NUM iajs-2987 99 8 πœ•2πœ“ πœ•2πœ“ NOUN iajs-2987 99 9 Β° Β° NOUN iajs-2987 99 10 πœ•π‘₯2 πœ•π‘₯2 NOUN iajs-2987 99 11 ] ] PUNCT iajs-2987 100 1 + + CCONJ iajs-2987 100 2 πœŒΟ‰Μ€2𝑑1 πœŒΟ‰Μ€2𝑑1 PROPN iajs-2987 100 3 2 2 NUM iajs-2987 100 4 πœ‡ πœ‡ ADP iajs-2987 100 5 𝛿2 𝛿2 PROPN iajs-2987 100 6 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 100 7 Β° Β° ADJ iajs-2987 100 8 πœ•π‘₯ πœ•π‘₯ X iajs-2987 100 9 + + CCONJ iajs-2987 100 10 2ὼ𝑅𝑒𝛿 2ὼ𝑅𝑒𝛿 NUM iajs-2987 100 11 2 2 NUM iajs-2987 100 12 πœ•2πœ“ πœ•2πœ“ NOUN iajs-2987 100 13 Β° Β° NOUN iajs-2987 100 14 πœ•π‘¦πœ• πœ•π‘¦πœ• ADP iajs-2987 100 15 π‘‘βˆ— π‘‘βˆ— NOUN iajs-2987 100 16 = = PUNCT iajs-2987 100 17 βˆ’ βˆ’ PROPN iajs-2987 100 18 πœ•π‘ πœ•π‘ NOUN iajs-2987 100 19 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 100 20 βˆ’ βˆ’ NOUN iajs-2987 100 21 𝛿2 𝛿2 NOUN iajs-2987 100 22 ( ( PUNCT iajs-2987 100 23 𝛿2 𝛿2 NOUN iajs-2987 100 24 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 100 25 Β° Β° NOUN iajs-2987 100 26 πœ•π‘₯3 πœ•π‘₯3 PROPN iajs-2987 100 27 + + NUM iajs-2987 100 28 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 100 29 Β° Β° NUM iajs-2987 100 30 πœ•π‘¦2πœ•π‘₯ πœ•π‘¦2πœ•π‘₯ X iajs-2987 100 31 ) ) PUNCT iajs-2987 100 32 + + CCONJ iajs-2987 100 33 𝛿2 𝛿2 NOUN iajs-2987 100 34 𝛾2 𝛾2 NOUN iajs-2987 100 35 ( ( PUNCT iajs-2987 100 36 𝛿4 𝛿4 NOUN iajs-2987 100 37 πœ•5πœ“ πœ•5πœ“ NOUN iajs-2987 100 38 Β° Β° ADP iajs-2987 100 39 πœ•π‘₯5 πœ•π‘₯5 PROPN iajs-2987 100 40 + + SYM iajs-2987 100 41 2𝛿2 2𝛿2 NUM iajs-2987 100 42 πœ•5πœ“ πœ•5πœ“ ADJ iajs-2987 100 43 Β° Β° NOUN iajs-2987 100 44 πœ•π‘₯3πœ•π‘¦2 πœ•π‘₯3πœ•π‘¦2 ADJ iajs-2987 100 45 + + NOUN iajs-2987 100 46 πœ•5πœ“ πœ•5πœ“ ADJ iajs-2987 100 47 Β° Β° ADP iajs-2987 100 48 πœ•π‘¦4πœ•π‘₯ πœ•π‘¦4πœ•π‘₯ PROPN iajs-2987 100 49 ) ) PUNCT iajs-2987 101 1 + + CCONJ iajs-2987 101 2 β„‹2 β„‹2 ADP iajs-2987 101 3 𝛿 𝛿 ADJ iajs-2987 101 4 𝑠𝑖𝑛 𝑠𝑖𝑛 ADJ iajs-2987 101 5 Ο† Ο† X iajs-2987 101 6 [ [ X iajs-2987 101 7 ( ( PUNCT iajs-2987 101 8 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 101 9 Β° Β° ADJ iajs-2987 101 10 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 101 11 + + X iajs-2987 101 12 1 1 X iajs-2987 101 13 ) ) PUNCT iajs-2987 101 14 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 101 15 Ο† Ο† PROPN iajs-2987 101 16 + + PROPN iajs-2987 101 17 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 101 18 Β° Β° NOUN iajs-2987 101 19 πœ•π‘₯ πœ•π‘₯ NOUN iajs-2987 101 20 𝛿 𝛿 DET iajs-2987 101 21 𝑠𝑖𝑛φ 𝑠𝑖𝑛φ NOUN iajs-2987 101 22 ] ] X iajs-2987 102 1 + + CCONJ iajs-2987 102 2 𝛿2 𝛿2 PROPN iajs-2987 102 3 π·π‘Ž π·π‘Ž PROPN iajs-2987 102 4 . . PUNCT iajs-2987 103 1 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 103 2 Β° Β° NOUN iajs-2987 103 3 πœ•π‘₯ πœ•π‘₯ NOUN iajs-2987 103 4 βˆ’ βˆ’ PUNCT iajs-2987 104 1 𝑅𝑒 𝑅𝑒 VERB iajs-2987 104 2 πΉπ‘Ÿ πΉπ‘Ÿ PROPN iajs-2987 104 3 𝛿 𝛿 ADJ iajs-2987 104 4 π‘π‘œπ‘  π‘π‘œπ‘  PROPN iajs-2987 104 5 οΏ½ οΏ½ PROPN iajs-2987 104 6 Μƒ Μƒ PROPN iajs-2987 104 7 οΏ½ οΏ½ PROPN iajs-2987 104 8 ( ( PUNCT iajs-2987 104 9 16 16 NUM iajs-2987 104 10 ) ) PUNCT iajs-2987 105 1 𝑅𝑒 𝑅𝑒 VERB iajs-2987 105 2 . . PUNCT iajs-2987 106 1 𝛿. 𝛿. ADJ iajs-2987 107 1 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN iajs-2987 107 2 ( ( PUNCT iajs-2987 107 3 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 107 4 Β° Β° NUM iajs-2987 107 5 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 107 6 . . PUNCT iajs-2987 108 1 πœ•πœƒ πœ•πœƒ NOUN iajs-2987 108 2 Β° Β° PRON iajs-2987 108 3 πœ•π‘₯ πœ•π‘₯ X iajs-2987 108 4 + + PUNCT iajs-2987 108 5 πœ•πœƒ πœ•πœƒ NOUN iajs-2987 108 6 Β° Β° PRON iajs-2987 108 7 πœ•π‘₯ πœ•π‘₯ X iajs-2987 109 1 βˆ’ βˆ’ PROPN iajs-2987 109 2 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 109 3 Β° Β° NUM iajs-2987 109 4 πœ•π‘₯ πœ•π‘₯ X iajs-2987 109 5 . . PUNCT iajs-2987 110 1 πœ•πœƒ πœ•πœƒ NOUN iajs-2987 110 2 Β° Β° NUM iajs-2987 110 3 πœ•π‘¦ πœ•π‘¦ PUNCT iajs-2987 110 4 ) ) PUNCT iajs-2987 111 1 = = SYM iajs-2987 111 2 ( ( PUNCT iajs-2987 111 3 𝛿2 𝛿2 NOUN iajs-2987 111 4 πœ•2πœƒ πœ•2πœƒ PROPN iajs-2987 111 5 Β° Β° NUM iajs-2987 111 6 πœ•π‘₯2 πœ•π‘₯2 NOUN iajs-2987 111 7 + + CCONJ iajs-2987 111 8 πœ•2πœƒ πœ•2πœƒ NUM iajs-2987 112 1 Β° Β° NOUN iajs-2987 112 2 πœ•π‘¦2 πœ•π‘¦2 NUM iajs-2987 112 3 ) ) PUNCT iajs-2987 113 1 + + NUM iajs-2987 113 2 π΅π‘Ÿ π΅π‘Ÿ PROPN iajs-2987 114 1 [ [ X iajs-2987 114 2 4𝛿2 4𝛿2 NUM iajs-2987 114 3 ( ( PUNCT iajs-2987 114 4 πœ•2πœ“ πœ•2πœ“ NOUN iajs-2987 114 5 Β° Β° NUM iajs-2987 114 6 πœ•π‘₯πœ•π‘¦ πœ•π‘₯πœ•π‘¦ NOUN iajs-2987 114 7 ) ) PUNCT iajs-2987 114 8 2 2 NUM iajs-2987 115 1 + + CCONJ iajs-2987 115 2 ( ( PUNCT iajs-2987 115 3 πœ•2πœ“ πœ•2πœ“ PROPN iajs-2987 115 4 Β° Β° NUM iajs-2987 115 5 πœ•π‘¦2 πœ•π‘¦2 NOUN iajs-2987 115 6 βˆ’ βˆ’ PROPN iajs-2987 115 7 𝛿 𝛿 ADJ iajs-2987 115 8 πœ•2πœ“ πœ•2πœ“ NOUN iajs-2987 115 9 Β° Β° NOUN iajs-2987 115 10 πœ•π‘₯2 πœ•π‘₯2 NOUN iajs-2987 115 11 ) ) PUNCT iajs-2987 116 1 2 2 NUM iajs-2987 116 2 + + SYM iajs-2987 116 3 1 1 NUM iajs-2987 116 4 𝛾2 𝛾2 NOUN iajs-2987 116 5 [ [ X iajs-2987 116 6 ( ( PUNCT iajs-2987 116 7 𝛿2 𝛿2 NOUN iajs-2987 116 8 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 116 9 Β° Β° NOUN iajs-2987 116 10 πœ•π‘₯2πœ•π‘¦ πœ•π‘₯2πœ•π‘¦ VERB iajs-2987 116 11 + + NUM iajs-2987 117 1 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 117 2 Β° Β° NUM iajs-2987 117 3 πœ•π‘¦3 πœ•π‘¦3 NOUN iajs-2987 117 4 ) ) PUNCT iajs-2987 117 5 2 2 NUM iajs-2987 118 1 + + CCONJ iajs-2987 118 2 ( ( PUNCT iajs-2987 118 3 𝛿2 𝛿2 NOUN iajs-2987 118 4 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 118 5 Β° Β° NOUN iajs-2987 118 6 πœ•π‘₯3 πœ•π‘₯3 PROPN iajs-2987 118 7 + + NUM iajs-2987 118 8 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 118 9 Β° Β° NUM iajs-2987 118 10 πœ•π‘₯πœ•π‘¦2 πœ•π‘₯πœ•π‘¦2 NOUN iajs-2987 118 11 ) ) PUNCT iajs-2987 118 12 2 2 NUM iajs-2987 118 13 ] ] PUNCT iajs-2987 118 14 ] ] PUNCT iajs-2987 119 1 + + CCONJ iajs-2987 119 2 π΅π‘Ÿ π΅π‘Ÿ PROPN iajs-2987 119 3 β„‹ β„‹ PROPN iajs-2987 119 4 2 2 NUM iajs-2987 119 5 [ [ X iajs-2987 119 6 ( ( PUNCT iajs-2987 119 7 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 119 8 Β° Β° ADJ iajs-2987 119 9 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 119 10 + + X iajs-2987 119 11 1 1 X iajs-2987 119 12 ) ) PUNCT iajs-2987 119 13 π‘π‘œπ‘  π‘π‘œπ‘  NOUN iajs-2987 119 14 Ο† Ο† PROPN iajs-2987 119 15 + + PROPN iajs-2987 119 16 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 119 17 Β° Β° NOUN iajs-2987 119 18 πœ•π‘₯ πœ•π‘₯ NOUN iajs-2987 119 19 𝛿 𝛿 DET iajs-2987 119 20 𝑠𝑖𝑛 𝑠𝑖𝑛 ADJ iajs-2987 119 21 Ο† Ο† X iajs-2987 119 22 ] ] X iajs-2987 119 23 2 2 NUM iajs-2987 119 24 ( ( PUNCT iajs-2987 119 25 17 17 NUM iajs-2987 119 26 ) ) PUNCT iajs-2987 119 27 cross cross NOUN iajs-2987 119 28 differentiation differentiation NOUN iajs-2987 119 29 from from ADP iajs-2987 119 30 dimensionless dimensionless ADJ iajs-2987 119 31 equations equation NOUN iajs-2987 119 32 is be AUX iajs-2987 119 33 used use VERB iajs-2987 119 34 to to PART iajs-2987 119 35 remove remove VERB iajs-2987 119 36 the the DET iajs-2987 119 37 pressure pressure NOUN iajs-2987 119 38 term term NOUN iajs-2987 119 39 . . PUNCT iajs-2987 120 1 ( ( PUNCT iajs-2987 120 2 17 17 NUM iajs-2987 120 3 ) ) PUNCT iajs-2987 120 4 , , PUNCT iajs-2987 120 5 ( ( PUNCT iajs-2987 120 6 18 18 NUM iajs-2987 120 7 ) ) PUNCT iajs-2987 120 8 , , PUNCT iajs-2987 120 9 and and CCONJ iajs-2987 120 10 ( ( PUNCT iajs-2987 120 11 19 19 NUM iajs-2987 120 12 ) ) PUNCT iajs-2987 120 13 may may AUX iajs-2987 120 14 be be AUX iajs-2987 120 15 formulated formulate VERB iajs-2987 120 16 in in ADP iajs-2987 120 17 the the DET iajs-2987 120 18 context context NOUN iajs-2987 120 19 of of ADP iajs-2987 120 20 stream stream NOUN iajs-2987 120 21 function function NOUN iajs-2987 120 22 differential differential NOUN iajs-2987 120 23 equation equation NOUN iajs-2987 120 24 and and CCONJ iajs-2987 120 25 temperature temperature NOUN iajs-2987 120 26 under under ADP iajs-2987 120 27 low low ADJ iajs-2987 120 28 reynolds reynold NOUN iajs-2987 120 29 approximations approximation NOUN iajs-2987 120 30 and and CCONJ iajs-2987 120 31 long long ADJ iajs-2987 120 32 - - PUNCT iajs-2987 120 33 wavelength wavelength NOUN iajs-2987 120 34 assumptions(Ξ΄ assumptions(Ξ΄ ADP iajs-2987 120 35 < < X iajs-2987 120 36 < < X iajs-2987 120 37 1 1 NUM iajs-2987 120 38 ) ) PUNCT iajs-2987 120 39 . . PUNCT iajs-2987 121 1 πœ•6πœ“ πœ•6πœ“ NOUN iajs-2987 121 2 Β° Β° NUM iajs-2987 121 3 πœ•π‘¦6 πœ•π‘¦6 NOUN iajs-2987 121 4 βˆ’ βˆ’ NOUN iajs-2987 121 5 𝛾2 𝛾2 PROPN iajs-2987 121 6 πœ•4πœ“ πœ•4πœ“ NOUN iajs-2987 121 7 Β° Β° PROPN iajs-2987 121 8 πœ•π‘¦4 πœ•π‘¦4 NOUN iajs-2987 122 1 + + CCONJ iajs-2987 122 2 𝛾2 𝛾2 VERB iajs-2987 122 3 πœ•2πœ“ πœ•2πœ“ NOUN iajs-2987 122 4 Β° Β° NOUN iajs-2987 122 5 πœ•π‘¦2 πœ•π‘¦2 PROPN iajs-2987 123 1 [ [ X iajs-2987 123 2 β„‹2 β„‹2 X iajs-2987 123 3 π‘π‘œπ‘ 2 π‘π‘œπ‘ 2 PROPN iajs-2987 123 4 Ο† Ο† PROPN iajs-2987 123 5 + + CCONJ iajs-2987 123 6 1 1 NUM iajs-2987 123 7 π·π‘Ž π·π‘Ž PROPN iajs-2987 123 8 βˆ’ βˆ’ NOUN iajs-2987 123 9 𝜌 𝜌 ADP iajs-2987 123 10 οΏ½ οΏ½ PROPN iajs-2987 123 11 Μ€ Μ€ ADJ iajs-2987 123 12 οΏ½ οΏ½ NOUN iajs-2987 123 13 2𝑑1 2𝑑1 NUM iajs-2987 123 14 2 2 NUM iajs-2987 123 15 πœ‡ πœ‡ X iajs-2987 123 16 ] ] X iajs-2987 123 17 = = SYM iajs-2987 123 18 0 0 NUM iajs-2987 123 19 ( ( PUNCT iajs-2987 123 20 18 18 NUM iajs-2987 123 21 ) ) PUNCT iajs-2987 123 22 πœ•2ΞΈ πœ•2ΞΈ NOUN iajs-2987 123 23 Β° Β° NOUN iajs-2987 123 24 πœ•π‘¦2 πœ•π‘¦2 PROPN iajs-2987 123 25 + + CCONJ iajs-2987 123 26 π΅π‘Ÿ π΅π‘Ÿ PROPN iajs-2987 123 27 [ [ X iajs-2987 123 28 ( ( PUNCT iajs-2987 123 29 πœ•2πœ“ πœ•2πœ“ NOUN iajs-2987 123 30 Β° Β° NUM iajs-2987 123 31 πœ•π‘¦2 πœ•π‘¦2 NUM iajs-2987 123 32 ) ) PUNCT iajs-2987 123 33 2 2 NUM iajs-2987 123 34 + + SYM iajs-2987 123 35 1 1 NUM iajs-2987 123 36 𝛾2 𝛾2 NOUN iajs-2987 123 37 ( ( PUNCT iajs-2987 123 38 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 123 39 Β° Β° NUM iajs-2987 123 40 πœ•π‘¦3 πœ•π‘¦3 NOUN iajs-2987 123 41 ) ) PUNCT iajs-2987 123 42 2 2 NUM iajs-2987 123 43 ] ] PUNCT iajs-2987 124 1 + + CCONJ iajs-2987 124 2 π΅π‘Ÿ π΅π‘Ÿ PROPN iajs-2987 124 3 β„‹ β„‹ PROPN iajs-2987 124 4 2 2 NUM iajs-2987 124 5 π‘π‘œπ‘ 2 π‘π‘œπ‘ 2 NOUN iajs-2987 124 6 Ο† Ο† PROPN iajs-2987 124 7 ( ( PUNCT iajs-2987 124 8 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 124 9 Β° Β° ADJ iajs-2987 124 10 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 124 11 ) ) PUNCT iajs-2987 125 1 2 2 NUM iajs-2987 125 2 = = SYM iajs-2987 125 3 0 0 NUM iajs-2987 126 1 ( ( PUNCT iajs-2987 126 2 19 19 NUM iajs-2987 126 3 ) ) PUNCT iajs-2987 126 4 ihjpas ihjpa NOUN iajs-2987 126 5 . . PUNCT iajs-2987 127 1 36(2)2023 36(2)2023 NUM iajs-2987 127 2 318 318 NUM iajs-2987 127 3 the the DET iajs-2987 127 4 dimensionless dimensionless NOUN iajs-2987 127 5 boundary boundary ADJ iajs-2987 127 6 conditions condition NOUN iajs-2987 127 7 in in ADP iajs-2987 127 8 the the DET iajs-2987 127 9 wave wave NOUN iajs-2987 127 10 frame frame NOUN iajs-2987 127 11 are be AUX iajs-2987 127 12 [ [ X iajs-2987 127 13 5 5 NUM iajs-2987 127 14 ] ] PUNCT iajs-2987 127 15 : : PUNCT iajs-2987 127 16 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 127 17 Β° Β° ADJ iajs-2987 127 18 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 128 1 + + CCONJ iajs-2987 128 2 𝛽 𝛽 NOUN iajs-2987 128 3 πœ•2πœ“ πœ•2πœ“ NOUN iajs-2987 128 4 Β° Β° NOUN iajs-2987 128 5 πœ•π‘¦2 πœ•π‘¦2 ADJ iajs-2987 128 6 = = SYM iajs-2987 128 7 βˆ’1 βˆ’1 NOUN iajs-2987 128 8 π‘œπ‘› π‘œπ‘› PROPN iajs-2987 128 9 𝑦 𝑦 NOUN iajs-2987 128 10 = = SYM iajs-2987 128 11 β„Ž1 β„Ž1 PROPN iajs-2987 128 12 βˆ— βˆ— PROPN iajs-2987 128 13 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 128 14 Β° Β° PROPN iajs-2987 128 15 πœ•π‘¦ πœ•π‘¦ PROPN iajs-2987 128 16 βˆ’ βˆ’ NOUN iajs-2987 128 17 𝛽 𝛽 NOUN iajs-2987 128 18 πœ•2πœ“ πœ•2πœ“ NOUN iajs-2987 128 19 Β° Β° NOUN iajs-2987 128 20 πœ•π‘¦2 πœ•π‘¦2 ADJ iajs-2987 128 21 = = SYM iajs-2987 128 22 βˆ’1 βˆ’1 NOUN iajs-2987 128 23 π‘œπ‘› π‘œπ‘› PROPN iajs-2987 128 24 𝑦 𝑦 NOUN iajs-2987 128 25 = = SYM iajs-2987 128 26 β„Ž2 β„Ž2 PROPN iajs-2987 128 27 βˆ— βˆ— NOUN iajs-2987 128 28 πœ“ πœ“ NOUN iajs-2987 128 29 Β° Β° NOUN iajs-2987 129 1 = = SYM iajs-2987 130 1 𝐹 𝐹 PROPN iajs-2987 130 2 2 2 NUM iajs-2987 130 3 , , PUNCT iajs-2987 130 4 πœƒ πœƒ NOUN iajs-2987 130 5 Β° Β° NOUN iajs-2987 130 6 = = SYM iajs-2987 130 7 0 0 PUNCT iajs-2987 130 8 π‘œπ‘› π‘œπ‘› PROPN iajs-2987 130 9 𝑦 𝑦 NOUN iajs-2987 130 10 = = SYM iajs-2987 130 11 β„Ž1 β„Ž1 PROPN iajs-2987 130 12 βˆ— βˆ— NOUN iajs-2987 130 13 ( ( PUNCT iajs-2987 130 14 20 20 NUM iajs-2987 130 15 ) ) PUNCT iajs-2987 130 16 πœ“ πœ“ NOUN iajs-2987 130 17 Β° Β° NOUN iajs-2987 130 18 = = PUNCT iajs-2987 131 1 βˆ’ βˆ’ PUNCT iajs-2987 131 2 𝐹 𝐹 PROPN iajs-2987 131 3 2 2 NUM iajs-2987 131 4 , , PUNCT iajs-2987 131 5 ΞΈ ΞΈ PROPN iajs-2987 131 6 Β° Β° NUM iajs-2987 131 7 = = SYM iajs-2987 131 8 1 1 NUM iajs-2987 131 9 π‘œπ‘› π‘œπ‘› PROPN iajs-2987 131 10 𝑦 𝑦 NOUN iajs-2987 131 11 = = SYM iajs-2987 131 12 β„Ž2 β„Ž2 ADJ iajs-2987 131 13 βˆ— βˆ— NOUN iajs-2987 131 14 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 131 15 Β° Β° PUNCT iajs-2987 131 16 πœ•π‘¦3 πœ•π‘¦3 NOUN iajs-2987 131 17 = = PUNCT iajs-2987 131 18 0 0 PUNCT iajs-2987 131 19 π‘œπ‘› π‘œπ‘› PROPN iajs-2987 131 20 𝑦 𝑦 NOUN iajs-2987 131 21 = = PUNCT iajs-2987 131 22 β„Ž1 β„Ž1 PROPN iajs-2987 131 23 βˆ—π‘Žπ‘›π‘‘ βˆ—π‘Žπ‘›π‘‘ X iajs-2987 131 24 𝑦 𝑦 NOUN iajs-2987 131 25 = = SYM iajs-2987 131 26 β„Ž2 β„Ž2 ADJ iajs-2987 131 27 βˆ— βˆ— NOUN iajs-2987 131 28 as as ADP iajs-2987 131 29 a a DET iajs-2987 131 30 result result NOUN iajs-2987 131 31 of of ADP iajs-2987 131 32 solving solve VERB iajs-2987 131 33 equations equation NOUN iajs-2987 131 34 ( ( PUNCT iajs-2987 131 35 18 18 NUM iajs-2987 131 36 ) ) PUNCT iajs-2987 131 37 and and CCONJ iajs-2987 131 38 ( ( PUNCT iajs-2987 131 39 19 19 NUM iajs-2987 131 40 ) ) PUNCT iajs-2987 131 41 , , PUNCT iajs-2987 131 42 the the DET iajs-2987 131 43 associated associated ADJ iajs-2987 131 44 boundary boundary ADJ iajs-2987 131 45 conditions condition NOUN iajs-2987 131 46 ( ( PUNCT iajs-2987 131 47 20 20 NUM iajs-2987 131 48 ) ) PUNCT iajs-2987 131 49 are be AUX iajs-2987 131 50 satisfied satisfied ADJ iajs-2987 131 51 . . PUNCT iajs-2987 132 1 πœ“ πœ“ NOUN iajs-2987 132 2 Β° Β° NOUN iajs-2987 132 3 = = SYM iajs-2987 132 4 2β…‡βˆ’π‘¦π‘Ž1𝑑1 2β…‡βˆ’π‘¦π‘Ž1𝑑1 NUM iajs-2987 132 5 π‘Ž3 π‘Ž3 NOUN iajs-2987 132 6 + + CCONJ iajs-2987 132 7 2β…‡π‘¦π‘Ž1𝑑2 2β…‡π‘¦π‘Ž1𝑑2 NUM iajs-2987 132 8 π‘Ž3 π‘Ž3 ADJ iajs-2987 132 9 + + CCONJ iajs-2987 132 10 2β…‡βˆ’π‘¦π‘Ž2𝑑3 2β…‡βˆ’π‘¦π‘Ž2𝑑3 NUM iajs-2987 132 11 π‘Ž4 π‘Ž4 PROPN iajs-2987 132 12 + + CCONJ iajs-2987 132 13 2β…‡π‘¦π‘Ž2𝑑4 2β…‡π‘¦π‘Ž2𝑑4 NUM iajs-2987 132 14 π‘Ž4 π‘Ž4 NOUN iajs-2987 132 15 + + CCONJ iajs-2987 132 16 𝑑5 𝑑5 PROPN iajs-2987 132 17 + + CCONJ iajs-2987 132 18 𝑦𝑑6 𝑦𝑑6 INTJ iajs-2987 132 19 ( ( PUNCT iajs-2987 132 20 21 21 NUM iajs-2987 132 21 ) ) PUNCT iajs-2987 132 22 ΞΈ ΞΈ NOUN iajs-2987 132 23 Β° Β° NOUN iajs-2987 132 24 = = SYM iajs-2987 132 25 π‘Ÿ1 π‘Ÿ1 NOUN iajs-2987 132 26 + + CCONJ iajs-2987 132 27 π‘¦π‘Ÿ2 π‘¦π‘Ÿ2 ADV iajs-2987 133 1 + + CCONJ iajs-2987 133 2 1 1 NUM iajs-2987 133 3 2𝛾2π‘Ž3 2𝛾2π‘Ž3 NUM iajs-2987 133 4 3π‘Ž4 3π‘Ž4 NUM iajs-2987 133 5 3 3 NUM iajs-2987 133 6 ( ( PUNCT iajs-2987 133 7 βˆ’ βˆ’ PROPN iajs-2987 133 8 1 1 NUM iajs-2987 133 9 2π‘Ž1 2π‘Ž1 NUM iajs-2987 133 10 β…‡βˆ’2π‘¦π‘Ž1 β…‡βˆ’2π‘¦π‘Ž1 NOUN iajs-2987 133 11 + + NOUN iajs-2987 133 12 3𝑦(π‘Ž1+π‘Ž2)βˆ’π‘¦(π‘Ž1 3𝑦(π‘Ž1+π‘Ž2)βˆ’π‘¦(π‘Ž1 NUM iajs-2987 133 13 + + ADJ iajs-2987 133 14 3π‘Ž2)(β„‹2 3π‘Ž2)(β„‹2 NUM iajs-2987 133 15 + + SYM iajs-2987 133 16 2β„‹2πΆπ‘œπ‘ [2𝛷 2β„‹2πΆπ‘œπ‘ [2𝛷 NUM iajs-2987 133 17 ] ] PUNCT iajs-2987 133 18 + + CCONJ iajs-2987 133 19 β„‹2πΆπ‘œπ‘ [4Ο† β„‹2πΆπ‘œπ‘ [4Ο† NUM iajs-2987 133 20 ] ] X iajs-2987 133 21 + + PUNCT iajs-2987 133 22 2𝑖ℋ2𝑆𝑖𝑛[2Ο† 2𝑖ℋ2𝑆𝑖𝑛[2Ο† NUM iajs-2987 133 23 ] ] X iajs-2987 133 24 + + NUM iajs-2987 133 25 𝑖ℋ2𝑆𝑖𝑛[4Ο† 𝑖ℋ2𝑆𝑖𝑛[4Ο† PROPN iajs-2987 133 26 ] ] X iajs-2987 134 1 + + CCONJ iajs-2987 134 2 4πΆπ‘œπ‘ [2Ο†]π‘Ž1 4πΆπ‘œπ‘ [2Ο†]π‘Ž1 NOUN iajs-2987 134 3 2 2 NUM iajs-2987 134 4 + + CCONJ iajs-2987 134 5 4𝑖𝑆𝑖𝑛[2Ο†]π‘Ž1 4𝑖𝑆𝑖𝑛[2Ο†]π‘Ž1 NUM iajs-2987 134 6 2 2 NUM iajs-2987 134 7 ) ) PUNCT iajs-2987 134 8 . . PUNCT iajs-2987 134 9 . . PUNCT iajs-2987 134 10 . . PUNCT iajs-2987 135 1 ( ( PUNCT iajs-2987 135 2 22 22 X iajs-2987 135 3 ) ) PUNCT iajs-2987 135 4 it it PRON iajs-2987 135 5 's be AUX iajs-2987 135 6 possible possible ADJ iajs-2987 135 7 to to PART iajs-2987 135 8 write write VERB iajs-2987 135 9 the the DET iajs-2987 135 10 velocity velocity NOUN iajs-2987 135 11 as as ADP iajs-2987 135 12 : : PUNCT iajs-2987 135 13 w w PROPN iajs-2987 135 14 = = SYM iajs-2987 135 15 βˆ’ βˆ’ PROPN iajs-2987 135 16 2π‘’βˆ’π‘¦π‘Ž1π‘Ž1𝑑1 2π‘’βˆ’π‘¦π‘Ž1π‘Ž1𝑑1 NUM iajs-2987 135 17 π‘Ž3 π‘Ž3 NOUN iajs-2987 135 18 + + CCONJ iajs-2987 135 19 2π‘’π‘¦π‘Ž1π‘Ž1𝑑2 2π‘’π‘¦π‘Ž1π‘Ž1𝑑2 NUM iajs-2987 135 20 π‘Ž3 π‘Ž3 NOUN iajs-2987 135 21 βˆ’ βˆ’ PROPN iajs-2987 135 22 2π‘’βˆ’π‘¦π‘Ž2π‘Ž2𝑑3 2π‘’βˆ’π‘¦π‘Ž2π‘Ž2𝑑3 NUM iajs-2987 135 23 π‘Ž4 π‘Ž4 PROPN iajs-2987 135 24 + + CCONJ iajs-2987 135 25 2π‘’π‘¦π‘Ž2π‘Ž2𝑑4 2π‘’π‘¦π‘Ž2π‘Ž2𝑑4 NUM iajs-2987 135 26 π‘Ž4 π‘Ž4 NOUN iajs-2987 135 27 + + CCONJ iajs-2987 135 28 𝑑6 𝑑6 PROPN iajs-2987 135 29 ( ( PUNCT iajs-2987 135 30 23 23 NUM iajs-2987 135 31 ) ) PUNCT iajs-2987 135 32 the the DET iajs-2987 135 33 axial axial ADJ iajs-2987 135 34 pressure pressure NOUN iajs-2987 135 35 gradient gradient NOUN iajs-2987 135 36 can can AUX iajs-2987 135 37 be be AUX iajs-2987 135 38 calculated calculate VERB iajs-2987 135 39 once once SCONJ iajs-2987 135 40 we we PRON iajs-2987 135 41 've have AUX iajs-2987 135 42 identified identify VERB iajs-2987 135 43 the the DET iajs-2987 135 44 stream stream NOUN iajs-2987 135 45 function function NOUN iajs-2987 135 46 . . PUNCT iajs-2987 136 1 πœ•π‘ πœ•π‘ NOUN iajs-2987 136 2 πœ•π‘₯ πœ•π‘₯ NOUN iajs-2987 136 3 = = PUNCT iajs-2987 136 4 πœ•3πœ“ πœ•3πœ“ NOUN iajs-2987 136 5 Β° Β° NUM iajs-2987 136 6 πœ•π‘¦3 πœ•π‘¦3 NOUN iajs-2987 136 7 βˆ’ βˆ’ NOUN iajs-2987 136 8 1 1 NUM iajs-2987 136 9 𝛾2 𝛾2 NOUN iajs-2987 136 10 . . PUNCT iajs-2987 137 1 πœ•5πœ“ πœ•5πœ“ ADJ iajs-2987 137 2 Β° Β° ADP iajs-2987 137 3 πœ•π‘¦5 πœ•π‘¦5 PROPN iajs-2987 137 4 βˆ’ βˆ’ PROPN iajs-2987 138 1 β„‹2 β„‹2 PROPN iajs-2987 138 2 π‘π‘œπ‘ 2 π‘π‘œπ‘ 2 PROPN iajs-2987 138 3 Ο† Ο† PROPN iajs-2987 138 4 [ [ X iajs-2987 138 5 ( ( PUNCT iajs-2987 138 6 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 138 7 Β° Β° ADJ iajs-2987 138 8 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 138 9 + + X iajs-2987 138 10 1 1 NUM iajs-2987 138 11 ) ) PUNCT iajs-2987 138 12 ] ] PUNCT iajs-2987 139 1 βˆ’ βˆ’ PROPN iajs-2987 139 2 1 1 NUM iajs-2987 139 3 π·π‘Ž π·π‘Ž PROPN iajs-2987 139 4 ( ( PUNCT iajs-2987 139 5 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 139 6 Β° Β° ADJ iajs-2987 139 7 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 139 8 + + X iajs-2987 139 9 1 1 X iajs-2987 139 10 ) ) PUNCT iajs-2987 139 11 + + CCONJ iajs-2987 140 1 𝑅𝑒 𝑅𝑒 VERB iajs-2987 140 2 πΉπ‘Ÿ πΉπ‘Ÿ PROPN iajs-2987 140 3 sin sin VERB iajs-2987 140 4 Ξ±Μƒ Ξ±Μƒ PROPN iajs-2987 140 5 + + CCONJ iajs-2987 140 6 gπ‘ŸΞΈ gπ‘ŸΞΈ PROPN iajs-2987 140 7 Β° Β° PROPN iajs-2987 140 8 sinΞ±Μƒ sinΞ±Μƒ NOUN iajs-2987 140 9 + + CCONJ iajs-2987 140 10 πœŒΟ‰Μ€2𝑑1 πœŒΟ‰Μ€2𝑑1 PROPN iajs-2987 140 11 2 2 NUM iajs-2987 140 12 πœ‡ πœ‡ X iajs-2987 140 13 ( ( PUNCT iajs-2987 140 14 πœ•πœ“ πœ•πœ“ NOUN iajs-2987 140 15 Β° Β° ADJ iajs-2987 140 16 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 140 17 + + X iajs-2987 140 18 1 1 X iajs-2987 140 19 ) ) PUNCT iajs-2987 140 20 ( ( PUNCT iajs-2987 140 21 24 24 NUM iajs-2987 140 22 ) ) PUNCT iajs-2987 140 23 πœ•π‘ πœ•π‘ NOUN iajs-2987 140 24 πœ•π‘¦ πœ•π‘¦ NOUN iajs-2987 140 25 = = SYM iajs-2987 140 26 0 0 PUNCT iajs-2987 140 27 ( ( PUNCT iajs-2987 140 28 25 25 NUM iajs-2987 140 29 ) ) PUNCT iajs-2987 140 30 in in ADP iajs-2987 140 31 non non ADJ iajs-2987 140 32 - - ADJ iajs-2987 140 33 dimensional dimensional ADJ iajs-2987 140 34 form form NOUN iajs-2987 140 35 , , PUNCT iajs-2987 140 36 the the DET iajs-2987 140 37 pressure pressure NOUN iajs-2987 140 38 rise rise NOUN iajs-2987 140 39 per per ADP iajs-2987 140 40 wavelength wavelength NOUN iajs-2987 140 41 Ξ΄π‘βˆ— Ξ΄π‘βˆ— NOUN iajs-2987 140 42 is be AUX iajs-2987 140 43 defined define VERB iajs-2987 140 44 as as ADP iajs-2987 140 45 Ξ΄π‘βˆ— Ξ΄π‘βˆ— ADJ iajs-2987 140 46 = = SYM iajs-2987 140 47 ∫ ∫ PROPN iajs-2987 140 48 πœ•π‘ πœ•π‘ NOUN iajs-2987 140 49 πœ•π‘₯ πœ•π‘₯ X iajs-2987 140 50 1 1 NUM iajs-2987 140 51 0 0 NUM iajs-2987 140 52 dx dx PROPN iajs-2987 140 53 ( ( PUNCT iajs-2987 140 54 26 26 NUM iajs-2987 140 55 ) ) PUNCT iajs-2987 140 56 3.volumetric 3.volumetric NUM iajs-2987 140 57 flow flow NOUN iajs-2987 140 58 rate rate NOUN iajs-2987 140 59 in in ADP iajs-2987 140 60 the the DET iajs-2987 140 61 laboratory laboratory NOUN iajs-2987 140 62 frame frame NOUN iajs-2987 140 63 , , PUNCT iajs-2987 140 64 the the DET iajs-2987 140 65 volumetric volumetric NOUN iajs-2987 140 66 flow flow NOUN iajs-2987 140 67 rate rate NOUN iajs-2987 140 68 is be AUX iajs-2987 140 69 equal equal ADJ iajs-2987 140 70 to to ADP iajs-2987 140 71 οΏ½ οΏ½ PROPN iajs-2987 140 72 Μƒ Μƒ PROPN iajs-2987 140 73 οΏ½ οΏ½ PROPN iajs-2987 140 74 = = SYM iajs-2987 140 75 ∫ ∫ PROPN iajs-2987 140 76 uΜƒ uΜƒ PROPN iajs-2987 140 77 β„Ž1Μƒ β„Ž1Μƒ X iajs-2987 140 78 β„Ž2Μƒ β„Ž2Μƒ PROPN iajs-2987 140 79 ( ( PUNCT iajs-2987 140 80 xΜƒ xΜƒ PROPN iajs-2987 140 81 , , PUNCT iajs-2987 140 82 yΜƒ yΜƒ PROPN iajs-2987 140 83 , , PUNCT iajs-2987 140 84 tΜƒ tΜƒ PROPN iajs-2987 140 85 ) ) PUNCT iajs-2987 140 86 d d SYM iajs-2987 140 87 yΜƒ yΜƒ PROPN iajs-2987 140 88 ( ( PUNCT iajs-2987 140 89 27 27 NUM iajs-2987 140 90 ) ) PUNCT iajs-2987 140 91 whereβ„Ž1Μƒ whereβ„Ž1Μƒ SCONJ iajs-2987 140 92 andβ„Ž2Μƒ andβ„Ž2Μƒ PROPN iajs-2987 140 93 are be AUX iajs-2987 140 94 functions function NOUN iajs-2987 140 95 of of ADP iajs-2987 140 96 οΏ½ οΏ½ PROPN iajs-2987 140 97 Μƒ Μƒ PROPN iajs-2987 140 98 οΏ½ οΏ½ PROPN iajs-2987 140 99 and and CCONJ iajs-2987 140 100 οΏ½ οΏ½ PROPN iajs-2987 140 101 Μƒ Μƒ PROPN iajs-2987 140 102 οΏ½ οΏ½ PROPN iajs-2987 140 103 . . PUNCT iajs-2987 141 1 in in ADP iajs-2987 141 2 the the DET iajs-2987 141 3 wave wave NOUN iajs-2987 141 4 frame frame NOUN iajs-2987 141 5 , , PUNCT iajs-2987 141 6 the the DET iajs-2987 141 7 volumetric volumetric NOUN iajs-2987 141 8 flow flow NOUN iajs-2987 141 9 rate rate NOUN iajs-2987 141 10 is be AUX iajs-2987 141 11 calculated calculate VERB iajs-2987 141 12 : : PUNCT iajs-2987 141 13 π‘ž π‘ž X iajs-2987 141 14 Β° Β° PROPN iajs-2987 141 15 = = SYM iajs-2987 141 16 ∫ ∫ PROPN iajs-2987 141 17 uΜ€ uΜ€ PROPN iajs-2987 141 18 β„Ž1Μƒ β„Ž1Μƒ PROPN iajs-2987 141 19 β„Ž2Μƒ β„Ž2Μƒ PROPN iajs-2987 141 20 ( ( PUNCT iajs-2987 141 21 xΜ€ xΜ€ PROPN iajs-2987 141 22 , , PUNCT iajs-2987 141 23 yΜ€)d yΜ€)d PROPN iajs-2987 141 24 οΏ½ οΏ½ PROPN iajs-2987 141 25 Μ€ Μ€ PROPN iajs-2987 141 26 οΏ½ οΏ½ PROPN iajs-2987 141 27 ( ( PUNCT iajs-2987 141 28 28 28 NUM iajs-2987 141 29 ) ) PUNCT iajs-2987 141 30 the the DET iajs-2987 141 31 relationship relationship NOUN iajs-2987 141 32 between between ADP iajs-2987 141 33 𝑄 𝑄 PROPN iajs-2987 141 34 and and CCONJ iajs-2987 141 35 π‘ž π‘ž X iajs-2987 141 36 can can AUX iajs-2987 141 37 is be AUX iajs-2987 141 38 calculated calculate VERB iajs-2987 141 39 as as SCONJ iajs-2987 141 40 follows follow VERB iajs-2987 141 41 : : PUNCT iajs-2987 141 42 οΏ½ οΏ½ PROPN iajs-2987 141 43 Μƒ Μƒ NOUN iajs-2987 141 44 οΏ½ οΏ½ NOUN iajs-2987 141 45 = = SYM iajs-2987 142 1 π‘ž π‘ž PROPN iajs-2987 142 2 Β° Β° NOUN iajs-2987 142 3 + + CCONJ iajs-2987 142 4 𝑐(β„Ž1Μƒ 𝑐(β„Ž1Μƒ PROPN iajs-2987 142 5 βˆ’ βˆ’ ADP iajs-2987 142 6 β„Ž2Μƒ β„Ž2Μƒ PROPN iajs-2987 142 7 ) ) PUNCT iajs-2987 142 8 ( ( PUNCT iajs-2987 142 9 29 29 NUM iajs-2987 142 10 ) ) PUNCT iajs-2987 142 11 the the DET iajs-2987 142 12 time time NOUN iajs-2987 142 13 - - PUNCT iajs-2987 142 14 mean mean NOUN iajs-2987 142 15 flow flow NOUN iajs-2987 142 16 over over ADP iajs-2987 142 17 a a DET iajs-2987 142 18 span span NOUN iajs-2987 142 19 of of ADP iajs-2987 142 20 time time NOUN iajs-2987 142 21 π‘‡βˆ— π‘‡βˆ— PROPN iajs-2987 142 22 fixed fix VERB iajs-2987 142 23 in in ADP iajs-2987 142 24 place place NOUN iajs-2987 142 25 οΏ½ οΏ½ NOUN iajs-2987 142 26 Μ… Μ… NOUN iajs-2987 142 27 οΏ½ οΏ½ NOUN iajs-2987 142 28 as as ADP iajs-2987 142 29 𝑄 𝑄 NOUN iajs-2987 142 30 Β° Β° NOUN iajs-2987 142 31 = = SYM iajs-2987 142 32 1 1 NUM iajs-2987 142 33 π‘‡βˆ— π‘‡βˆ— PROPN iajs-2987 142 34 ∫ ∫ PROPN iajs-2987 142 35 οΏ½ οΏ½ PROPN iajs-2987 142 36 Μƒ Μƒ PROPN iajs-2987 142 37 οΏ½ οΏ½ PROPN iajs-2987 142 38 𝑑𝑑 𝑑𝑑 ADP iajs-2987 142 39 ( ( PUNCT iajs-2987 142 40 30 30 NUM iajs-2987 142 41 ) ) PUNCT iajs-2987 142 42 π‘‡βˆ— π‘‡βˆ— NOUN iajs-2987 142 43 0 0 NUM iajs-2987 142 44 using use VERB iajs-2987 142 45 equation equation NOUN iajs-2987 142 46 ( ( PUNCT iajs-2987 142 47 29 29 NUM iajs-2987 142 48 ) ) PUNCT iajs-2987 142 49 in in ADP iajs-2987 142 50 equation equation NOUN iajs-2987 142 51 ( ( PUNCT iajs-2987 142 52 30 30 NUM iajs-2987 142 53 ) ) PUNCT iajs-2987 142 54 the the DET iajs-2987 142 55 flow flow NOUN iajs-2987 142 56 rate rate NOUN iajs-2987 142 57 𝑄 𝑄 PROPN iajs-2987 142 58 Β° Β° PROPN iajs-2987 142 59 has have VERB iajs-2987 142 60 the the PRON iajs-2987 142 61 from from ADP iajs-2987 142 62 𝑄 𝑄 PROPN iajs-2987 142 63 Β° Β° NOUN iajs-2987 142 64 = = SYM iajs-2987 143 1 1 1 NUM iajs-2987 143 2 π‘‡βˆ— π‘‡βˆ— NUM iajs-2987 143 3 ∫ ∫ PROPN iajs-2987 143 4 π‘ž π‘ž PROPN iajs-2987 143 5 Β° Β° PROPN iajs-2987 143 6 𝑑𝑑 𝑑𝑑 ADP iajs-2987 143 7 + + NUM iajs-2987 143 8 π‘‡βˆ— π‘‡βˆ— NOUN iajs-2987 143 9 0 0 SYM iajs-2987 143 10 𝑐(β„Ž1Μƒ 𝑐(β„Ž1Μƒ PUNCT iajs-2987 143 11 βˆ’ βˆ’ ADP iajs-2987 143 12 β„Ž2Μƒ β„Ž2Μƒ PROPN iajs-2987 143 13 ) ) PUNCT iajs-2987 143 14 ihjpas ihjpas PROPN iajs-2987 143 15 . . PUNCT iajs-2987 144 1 36(2)2023 36(2)2023 NUM iajs-2987 144 2 319 319 NUM iajs-2987 144 3 = = SYM iajs-2987 144 4 π‘ž π‘ž X iajs-2987 144 5 Β° Β° X iajs-2987 144 6 + + CCONJ iajs-2987 144 7 𝑐𝑑1 𝑐𝑑1 PROPN iajs-2987 144 8 + + NUM iajs-2987 144 9 𝑐𝑑2 𝑐𝑑2 NOUN iajs-2987 145 1 + + CCONJ iajs-2987 145 2 2𝑐π‘₯πœ† 2𝑐π‘₯πœ† PROPN iajs-2987 145 3 tan tan PROPN iajs-2987 145 4 οΏ½ οΏ½ PROPN iajs-2987 145 5 Μƒ Μƒ PROPN iajs-2987 145 6 οΏ½ οΏ½ PROPN iajs-2987 145 7 + + NUM iajs-2987 145 8 π‘π‘Ž1 π‘π‘Ž1 NOUN iajs-2987 145 9 cos(2πœ‹π‘₯ cos(2πœ‹π‘₯ NUM iajs-2987 145 10 ) ) PUNCT iajs-2987 146 1 + + NUM iajs-2987 146 2 π‘π‘Ž2 π‘π‘Ž2 NOUN iajs-2987 146 3 cos(2πœ‹π‘₯ cos(2πœ‹π‘₯ PROPN iajs-2987 146 4 + + CCONJ iajs-2987 146 5 πœ™ πœ™ NOUN iajs-2987 146 6 Β° Β° NUM iajs-2987 146 7 ) ) PUNCT iajs-2987 146 8 ( ( PUNCT iajs-2987 146 9 31 31 NUM iajs-2987 146 10 ) ) PUNCT iajs-2987 146 11 the the DET iajs-2987 146 12 non non ADJ iajs-2987 146 13 - - ADJ iajs-2987 146 14 dimensional dimensional ADJ iajs-2987 146 15 of of ADP iajs-2987 146 16 equation equation NOUN iajs-2987 146 17 ( ( PUNCT iajs-2987 146 18 28 28 NUM iajs-2987 146 19 ) ) PUNCT iajs-2987 146 20 is be AUX iajs-2987 146 21 provided provide VERB iajs-2987 146 22 by by ADP iajs-2987 146 23 πœ” πœ” NOUN iajs-2987 146 24 = = PUNCT iajs-2987 146 25 𝐹 𝐹 PROPN iajs-2987 146 26 + + NOUN iajs-2987 146 27 1 1 NUM iajs-2987 146 28 + + CCONJ iajs-2987 146 29 𝑑 𝑑 PROPN iajs-2987 146 30 + + X iajs-2987 146 31 2π‘˜π‘₯ 2π‘˜π‘₯ ADJ iajs-2987 146 32 + + CCONJ iajs-2987 146 33 π‘Ž π‘Ž X iajs-2987 146 34 cos(2πœ‹π‘₯ cos(2πœ‹π‘₯ NUM iajs-2987 146 35 ) ) PUNCT iajs-2987 146 36 + + NOUN iajs-2987 146 37 𝑏 𝑏 PROPN iajs-2987 146 38 cos(2πœ‹π‘₯ cos(2πœ‹π‘₯ PROPN iajs-2987 146 39 + + NUM iajs-2987 146 40 πœ™ πœ™ NOUN iajs-2987 146 41 Β° Β° NUM iajs-2987 146 42 ) ) PUNCT iajs-2987 146 43 ( ( PUNCT iajs-2987 146 44 32 32 NUM iajs-2987 146 45 ) ) PUNCT iajs-2987 146 46 where where SCONJ iajs-2987 146 47 πœ” πœ” VERB iajs-2987 146 48 = = SYM iajs-2987 146 49 𝑄 𝑄 PROPN iajs-2987 146 50 Β° Β° NOUN iajs-2987 146 51 cd1 cd1 NOUN iajs-2987 146 52 and and CCONJ iajs-2987 146 53 f f PROPN iajs-2987 146 54 = = SYM iajs-2987 146 55 π‘ž π‘ž PROPN iajs-2987 146 56 Β° Β° PROPN iajs-2987 146 57 cd1 cd1 PROPN iajs-2987 146 58 has have VERB iajs-2987 146 59 the the DET iajs-2987 146 60 expression expression NOUN iajs-2987 146 61 in in ADP iajs-2987 146 62 the the DET iajs-2987 146 63 form form NOUN iajs-2987 146 64 𝐹 𝐹 PROPN iajs-2987 146 65 = = SYM iajs-2987 146 66 ∫ ∫ PROPN iajs-2987 146 67 πœ•πœ“ πœ•πœ“ PROPN iajs-2987 146 68 Β° Β° PROPN iajs-2987 146 69 πœ•π‘¦ πœ•π‘¦ PROPN iajs-2987 147 1 β„Ž1 β„Ž1 PROPN iajs-2987 147 2 βˆ— βˆ— NOUN iajs-2987 147 3 β„Ž2 β„Ž2 NOUN iajs-2987 147 4 βˆ— βˆ— NOUN iajs-2987 147 5 dy dy X iajs-2987 147 6 = = SYM iajs-2987 147 7 πœ“ πœ“ PROPN iajs-2987 147 8 Β° Β° PROPN iajs-2987 147 9 (β„Ž1 (β„Ž1 NOUN iajs-2987 147 10 βˆ— βˆ— PROPN iajs-2987 147 11 ) ) PUNCT iajs-2987 148 1 βˆ’ βˆ’ ADP iajs-2987 148 2 πœ“ πœ“ PROPN iajs-2987 148 3 Β° Β° PROPN iajs-2987 148 4 (β„Ž2 (β„Ž2 PUNCT iajs-2987 148 5 βˆ— βˆ— NOUN iajs-2987 148 6 ) ) PUNCT iajs-2987 148 7 ( ( PUNCT iajs-2987 148 8 33 33 NUM iajs-2987 148 9 ) ) PUNCT iajs-2987 148 10 4 4 NUM iajs-2987 148 11 . . NOUN iajs-2987 148 12 results result NOUN iajs-2987 148 13 and and CCONJ iajs-2987 148 14 discussion discussion NOUN iajs-2987 148 15 this this DET iajs-2987 148 16 section section NOUN iajs-2987 148 17 focuses focus VERB iajs-2987 148 18 on on ADP iajs-2987 148 19 " " PUNCT iajs-2987 148 20 velocity"w velocity"w NOUN iajs-2987 148 21 , , PUNCT iajs-2987 148 22 " " PUNCT iajs-2987 148 23 temperature temperature NOUN iajs-2987 148 24 " " PUNCT iajs-2987 148 25 ΞΈ ΞΈ NOUN iajs-2987 148 26 Β° Β° PROPN iajs-2987 148 27 , , PUNCT iajs-2987 148 28 " " PUNCT iajs-2987 148 29 gradient gradient NOUN iajs-2987 148 30 of of ADP iajs-2987 148 31 pressure pressure NOUN iajs-2987 148 32 " " PUNCT iajs-2987 148 33 Ξ΄pβˆ— Ξ΄pβˆ— NOUN iajs-2987 148 34 , , PUNCT iajs-2987 148 35 " " PUNCT iajs-2987 148 36 pressure pressure NOUN iajs-2987 148 37 rise rise NOUN iajs-2987 148 38 " " PUNCT iajs-2987 148 39 Ξ΄π‘βˆ— Ξ΄π‘βˆ— NOUN iajs-2987 148 40 , , PUNCT iajs-2987 148 41 and and CCONJ iajs-2987 148 42 " " PUNCT iajs-2987 148 43 stream stream NOUN iajs-2987 148 44 function function NOUN iajs-2987 148 45 " " PUNCT iajs-2987 148 46 πœ“ πœ“ PROPN iajs-2987 148 47 Β° Β° NUM iajs-2987 148 48 . . PUNCT iajs-2987 149 1 to to PART iajs-2987 149 2 get get VERB iajs-2987 149 3 the the DET iajs-2987 149 4 numerical numerical ADJ iajs-2987 149 5 values value NOUN iajs-2987 149 6 corresponding correspond VERB iajs-2987 149 7 to to ADP iajs-2987 149 8 the the DET iajs-2987 149 9 abovementioned abovementioned ADJ iajs-2987 149 10 analytical analytical ADJ iajs-2987 149 11 formulas formula NOUN iajs-2987 149 12 , , PUNCT iajs-2987 149 13 we we PRON iajs-2987 149 14 utilized utilize VERB iajs-2987 149 15 " " PUNCT iajs-2987 149 16 mathematica mathematica PROPN iajs-2987 149 17 " " PUNCT iajs-2987 149 18 program program NOUN iajs-2987 149 19 . . PUNCT iajs-2987 150 1 4.1 4.1 NUM iajs-2987 150 2 . . PUNCT iajs-2987 151 1 the the DET iajs-2987 151 2 distribution distribution NOUN iajs-2987 151 3 of of ADP iajs-2987 151 4 velocity velocity NOUN iajs-2987 151 5 now now ADV iajs-2987 151 6 , , PUNCT iajs-2987 151 7 we we PRON iajs-2987 151 8 'll will AUX iajs-2987 151 9 look look VERB iajs-2987 151 10 at at ADP iajs-2987 151 11 the the DET iajs-2987 151 12 effect effect NOUN iajs-2987 151 13 of of ADP iajs-2987 151 14 axial axial ADJ iajs-2987 151 15 velocity velocity NOUN iajs-2987 151 16 ( ( PUNCT iajs-2987 151 17 w w NOUN iajs-2987 151 18 ) ) PUNCT iajs-2987 151 19 variation variation NOUN iajs-2987 151 20 across across ADP iajs-2987 151 21 the the DET iajs-2987 151 22 canal canal NOUN iajs-2987 151 23 on on ADP iajs-2987 151 24 several several ADJ iajs-2987 151 25 parameters parameter NOUN iajs-2987 151 26 . . PUNCT iajs-2987 152 1 note note VERB iajs-2987 152 2 that that SCONJ iajs-2987 152 3 the the DET iajs-2987 152 4 velocity velocity NOUN iajs-2987 152 5 is be AUX iajs-2987 152 6 parabolic parabolic ADJ iajs-2987 152 7 . . PUNCT iajs-2987 153 1 in in ADP iajs-2987 153 2 the the DET iajs-2987 153 3 center center NOUN iajs-2987 153 4 , , PUNCT iajs-2987 153 5 the the DET iajs-2987 153 6 axial axial ADJ iajs-2987 153 7 velocity velocity NOUN iajs-2987 153 8 rises rise VERB iajs-2987 153 9 with with ADP iajs-2987 153 10 increasing increase VERB iajs-2987 153 11 rotation rotation NOUN iajs-2987 153 12 parameter parameter NOUN iajs-2987 153 13 " " PUNCT iajs-2987 153 14 οΏ½ οΏ½ PROPN iajs-2987 153 15 Μ€ Μ€ NOUN iajs-2987 153 16 οΏ½ οΏ½ NOUN iajs-2987 153 17 " " PUNCT iajs-2987 153 18 , , PUNCT iajs-2987 153 19 density density NOUN iajs-2987 153 20 " " PUNCT iajs-2987 153 21 ρ ρ PROPN iajs-2987 153 22 " " PUNCT iajs-2987 153 23 , , PUNCT iajs-2987 153 24 the the DET iajs-2987 153 25 width width NOUN iajs-2987 153 26 of of ADP iajs-2987 153 27 the the DET iajs-2987 153 28 channel channel NOUN iajs-2987 153 29 " " PUNCT iajs-2987 153 30 𝑑1 𝑑1 NOUN iajs-2987 153 31 " " PUNCT iajs-2987 153 32 , , PUNCT iajs-2987 153 33 darcy darcy PROPN iajs-2987 153 34 number number NOUN iajs-2987 153 35 " " PUNCT iajs-2987 153 36 π·π‘Ž π·π‘Ž PROPN iajs-2987 153 37 " " PUNCT iajs-2987 153 38 and and CCONJ iajs-2987 153 39 the the DET iajs-2987 153 40 magnetic magnetic ADJ iajs-2987 153 41 field field NOUN iajs-2987 153 42 inclination inclination NOUN iajs-2987 153 43 angle angle NOUN iajs-2987 153 44 " " PUNCT iajs-2987 153 45 Ο† Ο† NOUN iajs-2987 153 46 " " PUNCT iajs-2987 153 47 , , PUNCT iajs-2987 153 48 whereas whereas SCONJ iajs-2987 153 49 the the DET iajs-2987 153 50 axial axial ADJ iajs-2987 153 51 velocity velocity NOUN iajs-2987 153 52 reduces reduce VERB iajs-2987 153 53 near near ADP iajs-2987 153 54 the the DET iajs-2987 153 55 channel channel NOUN iajs-2987 153 56 wall wall NOUN iajs-2987 153 57 's 's PART iajs-2987 153 58 edge edge NOUN iajs-2987 153 59 , , PUNCT iajs-2987 153 60 as as SCONJ iajs-2987 153 61 seen see VERB iajs-2987 153 62 in in ADP iajs-2987 153 63 figure figure NOUN iajs-2987 153 64 1 1 NUM iajs-2987 153 65 ( ( PUNCT iajs-2987 153 66 a a NOUN iajs-2987 153 67 - - PUNCT iajs-2987 153 68 e e NOUN iajs-2987 153 69 ) ) PUNCT iajs-2987 153 70 . . PUNCT iajs-2987 154 1 according accord VERB iajs-2987 154 2 to to PART iajs-2987 154 3 figure figure NOUN iajs-2987 154 4 1(f 1(f NUM iajs-2987 154 5 ) ) PUNCT iajs-2987 154 6 " " PUNCT iajs-2987 154 7 πœ™ πœ™ NOUN iajs-2987 154 8 Β° Β° NOUN iajs-2987 154 9 " " PUNCT iajs-2987 154 10 , , PUNCT iajs-2987 154 11 is be AUX iajs-2987 154 12 shown show VERB iajs-2987 154 13 to to PART iajs-2987 154 14 increase increase VERB iajs-2987 154 15 axial axial ADJ iajs-2987 154 16 velocity velocity NOUN iajs-2987 154 17 in in ADP iajs-2987 154 18 the the DET iajs-2987 154 19 middle middle NOUN iajs-2987 154 20 of of ADP iajs-2987 154 21 the the DET iajs-2987 154 22 canal canal NOUN iajs-2987 154 23 while while SCONJ iajs-2987 154 24 axial axial ADJ iajs-2987 154 25 velocity velocity NOUN iajs-2987 154 26 lowers lower VERB iajs-2987 154 27 at at ADP iajs-2987 154 28 one one NUM iajs-2987 154 29 wall wall NOUN iajs-2987 154 30 boundary boundary NOUN iajs-2987 154 31 and and CCONJ iajs-2987 154 32 rises rise VERB iajs-2987 154 33 at at ADP iajs-2987 154 34 the the DET iajs-2987 154 35 other other ADJ iajs-2987 154 36 . . PUNCT iajs-2987 155 1 as as SCONJ iajs-2987 155 2 can can AUX iajs-2987 155 3 be be AUX iajs-2987 155 4 seen see VERB iajs-2987 155 5 in in ADP iajs-2987 155 6 figures figure NOUN iajs-2987 155 7 1(g 1(g NUM iajs-2987 155 8 - - SYM iajs-2987 155 9 k k NOUN iajs-2987 155 10 ) ) PUNCT iajs-2987 155 11 , , PUNCT iajs-2987 155 12 as as SCONJ iajs-2987 155 13 " " PUNCT iajs-2987 155 14 β„‹ β„‹ PROPN iajs-2987 155 15 " " PUNCT iajs-2987 155 16 , , PUNCT iajs-2987 155 17 " " PUNCT iajs-2987 155 18 Ξ³ Ξ³ X iajs-2987 155 19 " " PUNCT iajs-2987 155 20 , , PUNCT iajs-2987 155 21 " " PUNCT iajs-2987 155 22 Ξ² Ξ² X iajs-2987 155 23 " " PUNCT iajs-2987 155 24 , , PUNCT iajs-2987 155 25 viscosity viscosity NOUN iajs-2987 155 26 " " PUNCT iajs-2987 155 27 ΞΌ ΞΌ PROPN iajs-2987 155 28 " " PUNCT iajs-2987 155 29 , , PUNCT iajs-2987 155 30 and and CCONJ iajs-2987 155 31 " " PUNCT iajs-2987 155 32 k k ADJ iajs-2987 155 33 " " PUNCT iajs-2987 155 34 increase increase NOUN iajs-2987 155 35 , , PUNCT iajs-2987 155 36 the the DET iajs-2987 155 37 axial axial ADJ iajs-2987 155 38 velocity velocity NOUN iajs-2987 155 39 decreases decrease VERB iajs-2987 155 40 in in ADP iajs-2987 155 41 the the DET iajs-2987 155 42 channel channel NOUN iajs-2987 155 43 's 's PART iajs-2987 155 44 middle middle NOUN iajs-2987 155 45 while while SCONJ iajs-2987 155 46 increasing increase VERB iajs-2987 155 47 near near ADP iajs-2987 155 48 the the DET iajs-2987 155 49 channel channel NOUN iajs-2987 155 50 's 's PART iajs-2987 155 51 wall wall NOUN iajs-2987 155 52 border border NOUN iajs-2987 155 53 . . PUNCT iajs-2987 156 1 ( ( PUNCT iajs-2987 156 2 a a X iajs-2987 156 3 ) ) PUNCT iajs-2987 156 4 ( ( PUNCT iajs-2987 156 5 b b X iajs-2987 156 6 ) ) PUNCT iajs-2987 156 7 ( ( PUNCT iajs-2987 156 8 c c NOUN iajs-2987 156 9 ) ) PUNCT iajs-2987 156 10 ( ( PUNCT iajs-2987 156 11 d d X iajs-2987 156 12 ) ) PUNCT iajs-2987 156 13 ( ( PUNCT iajs-2987 156 14 e e NOUN iajs-2987 156 15 ) ) PUNCT iajs-2987 156 16 ( ( PUNCT iajs-2987 156 17 f f X iajs-2987 156 18 ) ) PUNCT iajs-2987 156 19 ihjpas ihjpas PROPN iajs-2987 156 20 . . PUNCT iajs-2987 157 1 36(2)2023 36(2)2023 NUM iajs-2987 157 2 320 320 NUM iajs-2987 157 3 ( ( PUNCT iajs-2987 157 4 g g NOUN iajs-2987 157 5 ) ) PUNCT iajs-2987 157 6 ( ( PUNCT iajs-2987 157 7 h h NOUN iajs-2987 157 8 ) ) PUNCT iajs-2987 157 9 ( ( PUNCT iajs-2987 157 10 i i NOUN iajs-2987 157 11 ) ) PUNCT iajs-2987 157 12 ( ( PUNCT iajs-2987 157 13 j j NOUN iajs-2987 157 14 ) ) PUNCT iajs-2987 157 15 ( ( PUNCT iajs-2987 157 16 k k X iajs-2987 157 17 ) ) PUNCT iajs-2987 157 18 figure figure NOUN iajs-2987 157 19 1.variation 1.variation NUM iajs-2987 157 20 the the DET iajs-2987 157 21 axial axial ADJ iajs-2987 157 22 velocity velocity NOUN iajs-2987 157 23 " " PUNCT iajs-2987 157 24 w w NOUN iajs-2987 157 25 " " PUNCT iajs-2987 157 26 with with ADP iajs-2987 157 27 different different ADJ iajs-2987 157 28 parameters parameter NOUN iajs-2987 157 29 { { PUNCT iajs-2987 157 30 π·π‘Ž π·π‘Ž X iajs-2987 157 31 = = NOUN iajs-2987 157 32 0.5 0.5 NUM iajs-2987 157 33 , , PUNCT iajs-2987 157 34 β„‹ β„‹ NOUN iajs-2987 157 35 = = SYM iajs-2987 157 36 3 3 NUM iajs-2987 157 37 , , PUNCT iajs-2987 157 38 𝛾 𝛾 NOUN iajs-2987 157 39 = = SYM iajs-2987 157 40 2 2 NUM iajs-2987 157 41 , , PUNCT iajs-2987 157 42 π‘Ž π‘Ž NOUN iajs-2987 157 43 = = SYM iajs-2987 157 44 0.6 0.6 NUM iajs-2987 157 45 , , PUNCT iajs-2987 157 46 πœ‡ πœ‡ ADP iajs-2987 157 47 = = NOUN iajs-2987 157 48 0.1 0.1 NUM iajs-2987 157 49 , , PUNCT iajs-2987 157 50 οΏ½ οΏ½ PROPN iajs-2987 157 51 Μ€ Μ€ VERB iajs-2987 157 52 οΏ½ οΏ½ PROPN iajs-2987 157 53 = = SYM iajs-2987 157 54 1 1 NUM iajs-2987 157 55 , , PUNCT iajs-2987 157 56 𝑏 𝑏 PROPN iajs-2987 157 57 = = SYM iajs-2987 157 58 0.7 0.7 NUM iajs-2987 157 59 , , PUNCT iajs-2987 157 60 πœ™ πœ™ X iajs-2987 157 61 Β° Β° NOUN iajs-2987 157 62 = = SYM iajs-2987 158 1 πœ‹ πœ‹ PRON iajs-2987 158 2 6 6 NUM iajs-2987 158 3 , , PUNCT iajs-2987 158 4 𝑑 𝑑 NOUN iajs-2987 158 5 = = NOUN iajs-2987 158 6 1 1 NUM iajs-2987 158 7 , , PUNCT iajs-2987 158 8 𝛽 𝛽 NOUN iajs-2987 158 9 = = NOUN iajs-2987 158 10 0.1 0.1 NUM iajs-2987 158 11 , , PUNCT iajs-2987 158 12 Ο† Ο† NOUN iajs-2987 158 13 = = PUNCT iajs-2987 158 14 πœ‹ πœ‹ X iajs-2987 158 15 4 4 NUM iajs-2987 158 16 , , PUNCT iajs-2987 158 17 π‘˜ π‘˜ PRON iajs-2987 158 18 = = NOUN iajs-2987 158 19 0.2 0.2 NUM iajs-2987 158 20 , , PUNCT iajs-2987 158 21 π‘₯ π‘₯ NOUN iajs-2987 158 22 = = SYM iajs-2987 158 23 1 1 NUM iajs-2987 158 24 , , PUNCT iajs-2987 158 25 𝜌 𝜌 X iajs-2987 158 26 = = NOUN iajs-2987 158 27 0.5 0.5 NUM iajs-2987 158 28 , , PUNCT iajs-2987 158 29 𝐹 𝐹 PROPN iajs-2987 158 30 = = NOUN iajs-2987 158 31 1 1 NUM iajs-2987 158 32 , , PUNCT iajs-2987 158 33 𝑑1 𝑑1 NOUN iajs-2987 158 34 = = NOUN iajs-2987 158 35 0.2 0.2 NUM iajs-2987 158 36 } } SYM iajs-2987 158 37 4.2 4.2 NUM iajs-2987 158 38 . . PUNCT iajs-2987 159 1 pumping pump VERB iajs-2987 159 2 characteristics characteristic NOUN iajs-2987 159 3 in in ADP iajs-2987 159 4 this this DET iajs-2987 159 5 subsection subsection NOUN iajs-2987 159 6 , , PUNCT iajs-2987 159 7 we we PRON iajs-2987 159 8 will will AUX iajs-2987 159 9 analyze analyze VERB iajs-2987 159 10 the the DET iajs-2987 159 11 pressure pressure NOUN iajs-2987 159 12 through through ADP iajs-2987 159 13 the the DET iajs-2987 159 14 channel channel NOUN iajs-2987 159 15 . . PUNCT iajs-2987 160 1 4.2.1 4.2.1 NOUN iajs-2987 160 2 . . PUNCT iajs-2987 160 3 pressure pressure NOUN iajs-2987 160 4 gradient gradient NOUN iajs-2987 160 5 " " PUNCT iajs-2987 160 6 π›…πβˆ— π›…πβˆ— PROPN iajs-2987 160 7 " " PUNCT iajs-2987 160 8 each each PRON iajs-2987 160 9 of of ADP iajs-2987 160 10 the the DET iajs-2987 160 11 figures figure NOUN iajs-2987 160 12 in in ADP iajs-2987 160 13 this this DET iajs-2987 160 14 section section NOUN iajs-2987 160 15 illustrates illustrate VERB iajs-2987 160 16 the the DET iajs-2987 160 17 pressure pressure NOUN iajs-2987 160 18 gradient gradient NOUN iajs-2987 160 19 and and CCONJ iajs-2987 160 20 the the DET iajs-2987 160 21 axial axial ADJ iajs-2987 160 22 axis axis NOUN iajs-2987 160 23 of of ADP iajs-2987 160 24 fluctuation fluctuation NOUN iajs-2987 160 25 along along ADP iajs-2987 160 26 the the DET iajs-2987 160 27 canal canal NOUN iajs-2987 160 28 at at ADP iajs-2987 160 29 one one NUM iajs-2987 160 30 wavelength wavelength NOUN iajs-2987 160 31 π‘₯ π‘₯ NOUN iajs-2987 160 32 ∈[0,1 ∈[0,1 ADV iajs-2987 160 33 ] ] PUNCT iajs-2987 160 34 . . PUNCT iajs-2987 161 1 figures figure NOUN iajs-2987 161 2 like like ADP iajs-2987 161 3 this this DET iajs-2987 161 4 show show NOUN iajs-2987 161 5 that that SCONJ iajs-2987 161 6 flow flow NOUN iajs-2987 161 7 is be AUX iajs-2987 161 8 restricted restrict VERB iajs-2987 161 9 in in ADP iajs-2987 161 10 the the DET iajs-2987 161 11 narrowing narrow VERB iajs-2987 161 12 portion portion NOUN iajs-2987 161 13 of of ADP iajs-2987 161 14 channel channel NOUN iajs-2987 161 15 π‘₯ π‘₯ PROPN iajs-2987 161 16 ∈[0.2,0.6 ∈[0.2,0.6 PROPN iajs-2987 161 17 ] ] PUNCT iajs-2987 161 18 . . PUNCT iajs-2987 162 1 as as ADP iajs-2987 162 2 a a DET iajs-2987 162 3 result result NOUN iajs-2987 162 4 , , PUNCT iajs-2987 162 5 a a DET iajs-2987 162 6 larger large ADJ iajs-2987 162 7 pressure pressure NOUN iajs-2987 162 8 gradient gradient NOUN iajs-2987 162 9 is be AUX iajs-2987 162 10 needed need VERB iajs-2987 162 11 to to PART iajs-2987 162 12 achieve achieve VERB iajs-2987 162 13 a a DET iajs-2987 162 14 normal normal ADJ iajs-2987 162 15 flow flow NOUN iajs-2987 162 16 . . PUNCT iajs-2987 163 1 because because SCONJ iajs-2987 163 2 of of ADP iajs-2987 163 3 the the DET iajs-2987 163 4 smaller small ADJ iajs-2987 163 5 pressure pressure NOUN iajs-2987 163 6 gradient gradient NOUN iajs-2987 163 7 in in ADP iajs-2987 163 8 the the DET iajs-2987 163 9 larger large ADJ iajs-2987 163 10 area area NOUN iajs-2987 163 11 of of ADP iajs-2987 163 12 the the DET iajs-2987 163 13 channel channel NOUN iajs-2987 163 14 π‘₯ π‘₯ X iajs-2987 163 15 ∈ ∈ PROPN iajs-2987 163 16 [ [ X iajs-2987 163 17 0,0.2]βˆͺ 0,0.2]βˆͺ NOUN iajs-2987 164 1 [ [ X iajs-2987 164 2 0.6,1 0.6,1 X iajs-2987 164 3 ] ] X iajs-2987 164 4 fluid fluid NOUN iajs-2987 164 5 may may AUX iajs-2987 164 6 pass pass VERB iajs-2987 164 7 readily readily ADV iajs-2987 164 8 . . PUNCT iajs-2987 165 1 figure figure VERB iajs-2987 165 2 2(a 2(a NUM iajs-2987 165 3 - - PUNCT iajs-2987 165 4 b b NOUN iajs-2987 165 5 ) ) PUNCT iajs-2987 165 6 shows show VERB iajs-2987 165 7 that that SCONJ iajs-2987 165 8 when when SCONJ iajs-2987 165 9 viscosity viscosity NOUN iajs-2987 165 10 " " PUNCT iajs-2987 165 11 πœ‡ πœ‡ NOUN iajs-2987 165 12 " " PUNCT iajs-2987 165 13 and and CCONJ iajs-2987 165 14 the the DET iajs-2987 165 15 hartmann hartmann PROPN iajs-2987 165 16 number number NOUN iajs-2987 165 17 " " PUNCT iajs-2987 165 18 β„‹ β„‹ PROPN iajs-2987 165 19 " " PUNCT iajs-2987 165 20 raises raise VERB iajs-2987 165 21 , , PUNCT iajs-2987 165 22 the the DET iajs-2987 165 23 pressure pressure NOUN iajs-2987 165 24 gradient gradient NOUN iajs-2987 165 25 also also ADV iajs-2987 165 26 increases increase VERB iajs-2987 165 27 in in ADP iajs-2987 165 28 size size NOUN iajs-2987 165 29 . . PUNCT iajs-2987 166 1 this this DET iajs-2987 166 2 graphic graphic ADJ iajs-2987 166 3 shows show VERB iajs-2987 166 4 that that SCONJ iajs-2987 166 5 greater great ADJ iajs-2987 166 6 pressure pressure NOUN iajs-2987 166 7 is be AUX iajs-2987 166 8 required require VERB iajs-2987 166 9 to to PART iajs-2987 166 10 move move VERB iajs-2987 166 11 some some DET iajs-2987 166 12 volume volume NOUN iajs-2987 166 13 of of ADP iajs-2987 166 14 fluid fluid NOUN iajs-2987 166 15 through through ADP iajs-2987 166 16 the the DET iajs-2987 166 17 narrower narrow ADJ iajs-2987 166 18 region region NOUN iajs-2987 166 19 of of ADP iajs-2987 166 20 the the DET iajs-2987 166 21 channel channel NOUN iajs-2987 166 22 . . PUNCT iajs-2987 167 1 when when SCONJ iajs-2987 167 2 looking look VERB iajs-2987 167 3 at at ADP iajs-2987 167 4 channel channel NOUN iajs-2987 167 5 parameters parameter NOUN iajs-2987 167 6 such such ADJ iajs-2987 167 7 as as ADP iajs-2987 167 8 the the DET iajs-2987 167 9 magnetic magnetic ADJ iajs-2987 167 10 field field NOUN iajs-2987 167 11 inclination inclination NOUN iajs-2987 167 12 angle angle NOUN iajs-2987 167 13 " " PUNCT iajs-2987 167 14 Ο† Ο† NOUN iajs-2987 167 15 " " PUNCT iajs-2987 167 16 , , PUNCT iajs-2987 167 17 the the DET iajs-2987 167 18 inclination inclination NOUN iajs-2987 167 19 " " PUNCT iajs-2987 167 20 𝛼 𝛼 NOUN iajs-2987 167 21 Μƒ Μƒ PROPN iajs-2987 167 22 " " PUNCT iajs-2987 167 23 of of ADP iajs-2987 167 24 the the DET iajs-2987 167 25 channel channel NOUN iajs-2987 167 26 , , PUNCT iajs-2987 167 27 rotation rotation NOUN iajs-2987 167 28 parameter parameter NOUN iajs-2987 167 29 " " PUNCT iajs-2987 167 30 οΏ½ οΏ½ PROPN iajs-2987 167 31 Μ€ Μ€ NOUN iajs-2987 167 32 οΏ½ οΏ½ NOUN iajs-2987 167 33 " " PUNCT iajs-2987 167 34 , , PUNCT iajs-2987 167 35 density density NOUN iajs-2987 167 36 " " PUNCT iajs-2987 167 37 𝜌 𝜌 NOUN iajs-2987 167 38 " " PUNCT iajs-2987 167 39 , , PUNCT iajs-2987 167 40 width width NOUN iajs-2987 167 41 of of ADP iajs-2987 167 42 the the DET iajs-2987 167 43 channel channel NOUN iajs-2987 167 44 " " PUNCT iajs-2987 167 45 𝑑1 𝑑1 NOUN iajs-2987 167 46 " " PUNCT iajs-2987 167 47 , , PUNCT iajs-2987 167 48 grashof grashof NOUN iajs-2987 167 49 numbers number NOUN iajs-2987 167 50 " " PUNCT iajs-2987 167 51 gπ‘Ÿ gπ‘Ÿ INTJ iajs-2987 167 52 " " PUNCT iajs-2987 167 53 , , PUNCT iajs-2987 167 54 slip slip NOUN iajs-2987 167 55 parameter"𝛽 parameter"𝛽 NOUN iajs-2987 167 56 " " PUNCT iajs-2987 167 57 , , PUNCT iajs-2987 167 58 darcy darcy PROPN iajs-2987 167 59 number number NOUN iajs-2987 167 60 " " PUNCT iajs-2987 167 61 π·π‘Ž π·π‘Ž PROPN iajs-2987 167 62 " " PUNCT iajs-2987 167 63 , , PUNCT iajs-2987 168 1 reynolds reynolds PROPN iajs-2987 168 2 number"𝑅𝑒",couple number"𝑅𝑒",couple ADV iajs-2987 168 3 stress stress VERB iajs-2987 168 4 " " PUNCT iajs-2987 168 5 𝛾 𝛾 NOUN iajs-2987 168 6 " " PUNCT iajs-2987 168 7 , , PUNCT iajs-2987 168 8 temperature temperature NOUN iajs-2987 168 9 " " PUNCT iajs-2987 168 10 ΞΈ ΞΈ NOUN iajs-2987 168 11 Β° Β° NUM iajs-2987 168 12 " " PUNCT iajs-2987 168 13 , , PUNCT iajs-2987 168 14 the the DET iajs-2987 168 15 phase phase NOUN iajs-2987 168 16 difference difference NOUN iajs-2987 168 17 " " PUNCT iajs-2987 168 18 πœ™ πœ™ NOUN iajs-2987 168 19 Β° Β° NOUN iajs-2987 168 20 " " PUNCT iajs-2987 168 21 and and CCONJ iajs-2987 168 22 non non ADJ iajs-2987 168 23 - - ADJ iajs-2987 168 24 uniformity uniformity ADJ iajs-2987 168 25 " " PUNCT iajs-2987 168 26 π‘˜ π‘˜ NOUN iajs-2987 168 27 " " PUNCT iajs-2987 168 28 as as SCONJ iajs-2987 168 29 depicted depict VERB iajs-2987 168 30 in in ADP iajs-2987 168 31 figures figure NOUN iajs-2987 168 32 2 2 NUM iajs-2987 168 33 ( ( PUNCT iajs-2987 168 34 c c NOUN iajs-2987 168 35 – – PUNCT iajs-2987 168 36 o o NOUN iajs-2987 168 37 ) ) PUNCT iajs-2987 168 38 , , PUNCT iajs-2987 168 39 the the DET iajs-2987 168 40 pattern pattern NOUN iajs-2987 168 41 is be AUX iajs-2987 168 42 the the DET iajs-2987 168 43 opposite opposite NOUN iajs-2987 168 44 . . PUNCT iajs-2987 169 1 because because SCONJ iajs-2987 169 2 of of ADP iajs-2987 169 3 the the DET iajs-2987 169 4 inclination inclination NOUN iajs-2987 169 5 , , PUNCT iajs-2987 169 6 less less ADJ iajs-2987 169 7 pressure pressure NOUN iajs-2987 169 8 is be AUX iajs-2987 169 9 needed need VERB iajs-2987 169 10 to to PART iajs-2987 169 11 move move VERB iajs-2987 169 12 liquids liquid NOUN iajs-2987 169 13 . . PUNCT iajs-2987 170 1 ihjpas ihjpas PROPN iajs-2987 170 2 . . PUNCT iajs-2987 171 1 36(2)2023 36(2)2023 NUM iajs-2987 171 2 321 321 NUM iajs-2987 171 3 4.2.2 4.2.2 NUM iajs-2987 171 4 . . PUNCT iajs-2987 171 5 pressure pressure NOUN iajs-2987 171 6 rise rise NOUN iajs-2987 171 7 " " PUNCT iajs-2987 171 8 πš«π©βˆ— πš«π©βˆ— NOUN iajs-2987 171 9 " " PUNCT iajs-2987 171 10 figures figure NOUN iajs-2987 171 11 3(a 3(a NUM iajs-2987 171 12 - - SYM iajs-2987 171 13 o o NOUN iajs-2987 171 14 ) ) PUNCT iajs-2987 171 15 show show VERB iajs-2987 171 16 the the DET iajs-2987 171 17 relationship relationship NOUN iajs-2987 171 18 between between ADP iajs-2987 171 19 pressure pressure NOUN iajs-2987 171 20 rise rise NOUN iajs-2987 171 21 and and CCONJ iajs-2987 171 22 volumetric volumetric NOUN iajs-2987 171 23 flow flow NOUN iajs-2987 171 24 rate rate NOUN iajs-2987 171 25 . . PUNCT iajs-2987 172 1 the the DET iajs-2987 172 2 connection connection NOUN iajs-2987 172 3 between between ADP iajs-2987 172 4 pressure pressure NOUN iajs-2987 172 5 rise rise NOUN iajs-2987 172 6 and and CCONJ iajs-2987 172 7 the the DET iajs-2987 172 8 rate rate NOUN iajs-2987 172 9 of of ADP iajs-2987 172 10 volumetric volumetric NOUN iajs-2987 172 11 flow flow NOUN iajs-2987 172 12 for for ADP iajs-2987 172 13 each each DET iajs-2987 172 14 wavelength wavelength NOUN iajs-2987 172 15 is be AUX iajs-2987 172 16 seen see VERB iajs-2987 172 17 to to PART iajs-2987 172 18 be be AUX iajs-2987 172 19 linear linear ADJ iajs-2987 172 20 . . PUNCT iajs-2987 173 1 the the DET iajs-2987 173 2 whole whole ADJ iajs-2987 173 3 region region NOUN iajs-2987 173 4 is be AUX iajs-2987 173 5 considered consider VERB iajs-2987 173 6 into into ADP iajs-2987 173 7 five five NUM iajs-2987 173 8 parts part NOUN iajs-2987 173 9 ( ( PUNCT iajs-2987 173 10 1 1 NUM iajs-2987 173 11 ) ) PUNCT iajs-2987 173 12 the the DET iajs-2987 173 13 peristaltic peristaltic ADJ iajs-2987 173 14 pumping pumping NOUN iajs-2987 173 15 region region NOUN iajs-2987 173 16 where(βˆ†π‘βˆ— where(βˆ†π‘βˆ— X iajs-2987 173 17 > > X iajs-2987 173 18 0 0 PROPN iajs-2987 173 19 , , PUNCT iajs-2987 173 20 𝐹 𝐹 PROPN iajs-2987 173 21 > > X iajs-2987 173 22 0 0 NUM iajs-2987 173 23 ) ) PUNCT iajs-2987 173 24 ( ( PUNCT iajs-2987 173 25 2 2 X iajs-2987 173 26 ) ) PUNCT iajs-2987 173 27 when when SCONJ iajs-2987 173 28 ( ( PUNCT iajs-2987 173 29 βˆ†π‘βˆ— βˆ†π‘βˆ— NOUN iajs-2987 173 30 > > X iajs-2987 173 31 0 0 PUNCT iajs-2987 173 32 , , PUNCT iajs-2987 173 33 𝐹 𝐹 PROPN iajs-2987 173 34 < < X iajs-2987 173 35 0 0 NUM iajs-2987 173 36 ) ) PUNCT iajs-2987 173 37 , , PUNCT iajs-2987 173 38 then then ADV iajs-2987 173 39 it it PRON iajs-2987 173 40 is be AUX iajs-2987 173 41 a a DET iajs-2987 173 42 retrograde retrograde ADJ iajs-2987 173 43 pumping pump VERB iajs-2987 173 44 region region NOUN iajs-2987 173 45 ( ( PUNCT iajs-2987 173 46 3 3 NUM iajs-2987 173 47 ) ) PUNCT iajs-2987 173 48 augmented augment VERB iajs-2987 173 49 pumping pumping NOUN iajs-2987 173 50 ( ( PUNCT iajs-2987 173 51 co co ADJ iajs-2987 173 52 - - ADJ iajs-2987 173 53 pumping pumping ADJ iajs-2987 173 54 ) ) PUNCT iajs-2987 173 55 region region NOUN iajs-2987 173 56 where where SCONJ iajs-2987 173 57 ( ( PUNCT iajs-2987 173 58 βˆ†π‘βˆ— βˆ†π‘βˆ— NOUN iajs-2987 173 59 < < X iajs-2987 173 60 0 0 PROPN iajs-2987 173 61 , , PUNCT iajs-2987 173 62 𝐹 𝐹 PROPN iajs-2987 173 63 > > X iajs-2987 173 64 0 0 NUM iajs-2987 173 65 ) ) PUNCT iajs-2987 173 66 ( ( PUNCT iajs-2987 173 67 4 4 X iajs-2987 173 68 ) ) PUNCT iajs-2987 173 69 there there PRON iajs-2987 173 70 is be VERB iajs-2987 173 71 a a DET iajs-2987 173 72 co co ADJ iajs-2987 173 73 - - ADJ iajs-2987 173 74 pumping pumping ADJ iajs-2987 173 75 region region NOUN iajs-2987 173 76 where where SCONJ iajs-2987 173 77 ( ( PUNCT iajs-2987 173 78 βˆ†π‘βˆ— βˆ†π‘βˆ— NOUN iajs-2987 173 79 < < X iajs-2987 173 80 0 0 PROPN iajs-2987 173 81 , , PUNCT iajs-2987 173 82 𝐹 𝐹 PROPN iajs-2987 173 83 < < X iajs-2987 173 84 0 0 NUM iajs-2987 173 85 ) ) PUNCT iajs-2987 173 86 ( ( PUNCT iajs-2987 173 87 5 5 NUM iajs-2987 173 88 ) ) PUNCT iajs-2987 173 89 ( ( PUNCT iajs-2987 173 90 βˆ†π‘βˆ— βˆ†π‘βˆ— NOUN iajs-2987 173 91 = = PUNCT iajs-2987 173 92 0)corresponds 0)corresponds NUM iajs-2987 173 93 to to ADP iajs-2987 173 94 the the DET iajs-2987 173 95 free free ADJ iajs-2987 173 96 pumping pumping NOUN iajs-2987 173 97 region region NOUN iajs-2987 173 98 . . PUNCT iajs-2987 174 1 figure3 figure3 NOUN iajs-2987 175 1 ( ( PUNCT iajs-2987 175 2 a a DET iajs-2987 175 3 - - PUNCT iajs-2987 175 4 b b NOUN iajs-2987 175 5 ) ) PUNCT iajs-2987 175 6 shows show VERB iajs-2987 175 7 the the DET iajs-2987 175 8 impact impact NOUN iajs-2987 175 9 of of ADP iajs-2987 175 10 viscosity viscosity NOUN iajs-2987 175 11 " " PUNCT iajs-2987 175 12 πœ‡ πœ‡ X iajs-2987 175 13 " " PUNCT iajs-2987 175 14 and and CCONJ iajs-2987 175 15 hartmann hartmann PROPN iajs-2987 175 16 number number NOUN iajs-2987 175 17 " " PUNCT iajs-2987 175 18 β„‹ β„‹ PROPN iajs-2987 175 19 " " PUNCT iajs-2987 175 20 on on ADP iajs-2987 175 21 βˆ†π‘βˆ— βˆ†π‘βˆ— NOUN iajs-2987 175 22 on on ADP iajs-2987 175 23 it it PRON iajs-2987 175 24 has have AUX iajs-2987 175 25 been be AUX iajs-2987 175 26 noticed notice VERB iajs-2987 175 27 in in ADP iajs-2987 175 28 the the DET iajs-2987 175 29 retrograde retrograde ADJ iajs-2987 175 30 pumping pumping NOUN iajs-2987 175 31 region region NOUN iajs-2987 175 32 . . PUNCT iajs-2987 176 1 the the DET iajs-2987 176 2 pumping pump VERB iajs-2987 176 3 rate rate NOUN iajs-2987 176 4 increases increase NOUN iajs-2987 176 5 as as ADP iajs-2987 176 6 hartmann hartmann PROPN iajs-2987 176 7 number number NOUN iajs-2987 176 8 " " PUNCT iajs-2987 176 9 β„‹"increases β„‹"increase NOUN iajs-2987 176 10 . . PUNCT iajs-2987 177 1 co co VERB iajs-2987 177 2 - - ADJ iajs-2987 177 3 pumping pumping ADJ iajs-2987 177 4 reduces reduce NOUN iajs-2987 177 5 when when SCONJ iajs-2987 177 6 in in ADP iajs-2987 177 7 this this DET iajs-2987 177 8 region region NOUN iajs-2987 177 9 and and CCONJ iajs-2987 177 10 increases increase NOUN iajs-2987 177 11 in in ADP iajs-2987 177 12 " " PUNCT iajs-2987 177 13 β„‹ β„‹ PROPN iajs-2987 177 14 " " PUNCT iajs-2987 177 15 and and CCONJ iajs-2987 177 16 " " PUNCT iajs-2987 177 17 πœ‡ πœ‡ X iajs-2987 177 18 " " PUNCT iajs-2987 177 19 . . PUNCT iajs-2987 178 1 volumetric volumetric NOUN iajs-2987 178 2 flow flow NOUN iajs-2987 178 3 rate rate NOUN iajs-2987 178 4 and and CCONJ iajs-2987 178 5 pressure pressure NOUN iajs-2987 178 6 increase increase NOUN iajs-2987 178 7 βˆ†π‘βˆ— βˆ†π‘βˆ— NOUN iajs-2987 178 8 are be AUX iajs-2987 178 9 shown show VERB iajs-2987 178 10 to to PART iajs-2987 178 11 be be AUX iajs-2987 178 12 linearly linearly ADV iajs-2987 178 13 related relate VERB iajs-2987 178 14 in in ADP iajs-2987 178 15 figures figure NOUN iajs-2987 178 16 3 3 NUM iajs-2987 178 17 ( ( PUNCT iajs-2987 178 18 c c NOUN iajs-2987 178 19 f f PROPN iajs-2987 178 20 ) ) PUNCT iajs-2987 178 21 for for ADP iajs-2987 178 22 a a DET iajs-2987 178 23 variety variety NOUN iajs-2987 178 24 of of ADP iajs-2987 178 25 grashof grashof ADJ iajs-2987 178 26 numbers number NOUN iajs-2987 178 27 " " PUNCT iajs-2987 178 28 gπ‘Ÿ gπ‘Ÿ PROPN iajs-2987 178 29 " " PUNCT iajs-2987 178 30 , , PUNCT iajs-2987 178 31 " " PUNCT iajs-2987 178 32 𝑅𝑒 𝑅𝑒 PROPN iajs-2987 178 33 " " PUNCT iajs-2987 178 34 , , PUNCT iajs-2987 178 35 " " PUNCT iajs-2987 178 36 οΏ½ οΏ½ PROPN iajs-2987 178 37 Μƒ Μƒ NOUN iajs-2987 178 38 οΏ½ οΏ½ PROPN iajs-2987 178 39 " " PUNCT iajs-2987 178 40 and and CCONJ iajs-2987 178 41 " " PUNCT iajs-2987 178 42 ΞΈ ΞΈ NOUN iajs-2987 178 43 Β° Β° NUM iajs-2987 178 44 " " PUNCT iajs-2987 178 45 . . PUNCT iajs-2987 179 1 we we PRON iajs-2987 179 2 observed observe VERB iajs-2987 179 3 that that SCONJ iajs-2987 179 4 a a DET iajs-2987 179 5 rise rise NOUN iajs-2987 179 6 results result VERB iajs-2987 179 7 in in ADP iajs-2987 179 8 an an DET iajs-2987 179 9 increase increase NOUN iajs-2987 179 10 in in ADP iajs-2987 179 11 retrograde retrograde ADJ iajs-2987 179 12 pumping pumping NOUN iajs-2987 179 13 rate rate NOUN iajs-2987 179 14 and and CCONJ iajs-2987 179 15 augmented augment VERB iajs-2987 179 16 pumping pumping NOUN iajs-2987 179 17 ( ( PUNCT iajs-2987 179 18 co co ADJ iajs-2987 179 19 - - ADJ iajs-2987 179 20 pumping pumping ADJ iajs-2987 179 21 ) ) PUNCT iajs-2987 179 22 region region NOUN iajs-2987 179 23 an an DET iajs-2987 179 24 increase increase NOUN iajs-2987 179 25 in in ADP iajs-2987 179 26 the the DET iajs-2987 179 27 pressure pressure NOUN iajs-2987 179 28 rise rise NOUN iajs-2987 179 29 . . PUNCT iajs-2987 180 1 figures figure NOUN iajs-2987 180 2 3 3 NUM iajs-2987 180 3 ( ( PUNCT iajs-2987 180 4 g g NOUN iajs-2987 180 5 m m ADV iajs-2987 180 6 ) ) PUNCT iajs-2987 180 7 graph graph NOUN iajs-2987 180 8 shows show VERB iajs-2987 180 9 that that SCONJ iajs-2987 180 10 with with ADP iajs-2987 180 11 an an DET iajs-2987 180 12 increase increase NOUN iajs-2987 180 13 in in ADP iajs-2987 180 14 rotation rotation NOUN iajs-2987 180 15 parameter parameter NOUN iajs-2987 180 16 " " PUNCT iajs-2987 180 17 οΏ½ οΏ½ PROPN iajs-2987 180 18 Μ€ Μ€ NOUN iajs-2987 180 19 οΏ½ οΏ½ NOUN iajs-2987 180 20 " " PUNCT iajs-2987 180 21 , , PUNCT iajs-2987 180 22 density density NOUN iajs-2987 180 23 " " PUNCT iajs-2987 180 24 𝜌 𝜌 NOUN iajs-2987 180 25 " " PUNCT iajs-2987 180 26 , , PUNCT iajs-2987 180 27 width width NOUN iajs-2987 180 28 of of ADP iajs-2987 180 29 the the DET iajs-2987 180 30 channel channel NOUN iajs-2987 180 31 " " PUNCT iajs-2987 180 32 d1 d1 NOUN iajs-2987 180 33 " " PUNCT iajs-2987 180 34 , , PUNCT iajs-2987 180 35 " " PUNCT iajs-2987 180 36 π·π‘Ž π·π‘Ž NOUN iajs-2987 180 37 " " PUNCT iajs-2987 180 38 , , PUNCT iajs-2987 180 39 " " PUNCT iajs-2987 180 40 𝛽 𝛽 NOUN iajs-2987 180 41 " " PUNCT iajs-2987 180 42 , , PUNCT iajs-2987 180 43 " " PUNCT iajs-2987 180 44 𝛾 𝛾 NOUN iajs-2987 180 45 " " PUNCT iajs-2987 180 46 and and CCONJ iajs-2987 180 47 " " PUNCT iajs-2987 180 48 Ο† Ο† PROPN iajs-2987 180 49 " " PUNCT iajs-2987 180 50 . . PUNCT iajs-2987 181 1 the the DET iajs-2987 181 2 pumping pump VERB iajs-2987 181 3 rate rate NOUN iajs-2987 181 4 decreases decrease NOUN iajs-2987 181 5 in in ADP iajs-2987 181 6 the the DET iajs-2987 181 7 region region NOUN iajs-2987 181 8 of of ADP iajs-2987 181 9 retrograde retrograde ADJ iajs-2987 181 10 pumping pumping NOUN iajs-2987 181 11 while while NOUN iajs-2987 181 12 in in ADP iajs-2987 181 13 the the DET iajs-2987 181 14 augmented augment VERB iajs-2987 181 15 pumping pumping NOUN iajs-2987 181 16 region region NOUN iajs-2987 181 17 found find VERB iajs-2987 181 18 to to PART iajs-2987 181 19 increase increase VERB iajs-2987 181 20 . . PUNCT iajs-2987 182 1 figure figure NOUN iajs-2987 182 2 3 3 NUM iajs-2987 182 3 ( ( PUNCT iajs-2987 182 4 n)shows n)show VERB iajs-2987 182 5 an an DET iajs-2987 182 6 impact impact NOUN iajs-2987 182 7 of of ADP iajs-2987 182 8 channel channel NOUN iajs-2987 182 9 non non ADJ iajs-2987 182 10 - - ADJ iajs-2987 182 11 uniform uniform ADJ iajs-2987 182 12 parameter parameter NOUN iajs-2987 182 13 " " PUNCT iajs-2987 182 14 π‘˜"on π‘˜"on PROPN iajs-2987 183 1 βˆ†π‘βˆ—. βˆ†π‘βˆ—. NOUN iajs-2987 183 2 it it PRON iajs-2987 183 3 is be AUX iajs-2987 183 4 observed observe VERB iajs-2987 183 5 that that SCONJ iajs-2987 183 6 in in ADP iajs-2987 183 7 a a DET iajs-2987 183 8 retrograde retrograde ADJ iajs-2987 183 9 pumping pumping NOUN iajs-2987 183 10 region region NOUN iajs-2987 183 11 and and CCONJ iajs-2987 183 12 a a DET iajs-2987 183 13 free free ADJ iajs-2987 183 14 pumping pumping NOUN iajs-2987 183 15 region region NOUN iajs-2987 183 16 ( ( PUNCT iajs-2987 183 17 βˆ†π‘βˆ— βˆ†π‘βˆ— NOUN iajs-2987 183 18 = = NOUN iajs-2987 183 19 0 0 NUM iajs-2987 183 20 ) ) PUNCT iajs-2987 183 21 , , PUNCT iajs-2987 183 22 the the DET iajs-2987 183 23 pumping pump VERB iajs-2987 183 24 rate rate NOUN iajs-2987 183 25 decreases decrease VERB iajs-2987 183 26 with with ADP iajs-2987 183 27 an an DET iajs-2987 183 28 increase increase NOUN iajs-2987 183 29 in in ADP iajs-2987 183 30 " " PUNCT iajs-2987 183 31 π‘˜ π‘˜ PRON iajs-2987 183 32 " " PUNCT iajs-2987 183 33 . . PUNCT iajs-2987 184 1 figure figure VERB iajs-2987 184 2 3 3 NUM iajs-2987 184 3 ( ( PUNCT iajs-2987 184 4 o o NOUN iajs-2987 184 5 ) ) PUNCT iajs-2987 184 6 depicts depict VERB iajs-2987 184 7 the the DET iajs-2987 184 8 effect effect NOUN iajs-2987 184 9 of of ADP iajs-2987 184 10 " " PUNCT iajs-2987 184 11 πœ™ πœ™ NOUN iajs-2987 184 12 Β° Β° NOUN iajs-2987 184 13 " " PUNCT iajs-2987 184 14 on on ADP iajs-2987 184 15 βˆ†π‘βˆ—. βˆ†π‘βˆ—. PROPN iajs-2987 184 16 it it PRON iajs-2987 184 17 is be AUX iajs-2987 184 18 observed observe VERB iajs-2987 184 19 that that SCONJ iajs-2987 184 20 in in ADP iajs-2987 184 21 a a DET iajs-2987 184 22 retrograde retrograde ADJ iajs-2987 184 23 pumping pumping NOUN iajs-2987 184 24 region region NOUN iajs-2987 184 25 and and CCONJ iajs-2987 184 26 a a DET iajs-2987 184 27 free free ADJ iajs-2987 184 28 pumping pumping NOUN iajs-2987 184 29 region region NOUN iajs-2987 184 30 ( ( PUNCT iajs-2987 184 31 βˆ†π‘βˆ— βˆ†π‘βˆ— NOUN iajs-2987 184 32 = = NOUN iajs-2987 184 33 0 0 NUM iajs-2987 184 34 ) ) PUNCT iajs-2987 184 35 , , PUNCT iajs-2987 184 36 the the DET iajs-2987 184 37 pumping pump VERB iajs-2987 184 38 rate rate NOUN iajs-2987 184 39 increases increase NOUN iajs-2987 184 40 with with ADP iajs-2987 184 41 an an DET iajs-2987 184 42 increase increase NOUN iajs-2987 184 43 in"πœ™ in"πœ™ ADJ iajs-2987 184 44 Β° Β° PRON iajs-2987 184 45 " " PUNCT iajs-2987 184 46 . . PUNCT iajs-2987 185 1 ) ) PUNCT iajs-2987 186 1 a a X iajs-2987 186 2 ) ) PUNCT iajs-2987 186 3 ( ( PUNCT iajs-2987 186 4 b b NOUN iajs-2987 186 5 ( ( PUNCT iajs-2987 186 6 ) ) PUNCT iajs-2987 186 7 c c X iajs-2987 186 8 ) ) PUNCT iajs-2987 186 9 ( ( PUNCT iajs-2987 186 10 d d NOUN iajs-2987 186 11 ) ) PUNCT iajs-2987 186 12 ) ) PUNCT iajs-2987 187 1 e e X iajs-2987 187 2 ) ) PUNCT iajs-2987 187 3 ( ( PUNCT iajs-2987 187 4 f f X iajs-2987 187 5 ) ) PUNCT iajs-2987 187 6 ihjpas ihjpas PROPN iajs-2987 187 7 . . PUNCT iajs-2987 188 1 36(2)2023 36(2)2023 NUM iajs-2987 188 2 322 322 NUM iajs-2987 188 3 ( ( PUNCT iajs-2987 188 4 g g NOUN iajs-2987 188 5 ) ) PUNCT iajs-2987 188 6 ( ( PUNCT iajs-2987 188 7 h h NOUN iajs-2987 188 8 ( ( PUNCT iajs-2987 188 9 ( ( PUNCT iajs-2987 188 10 i i NOUN iajs-2987 188 11 ) ) PUNCT iajs-2987 188 12 ( ( PUNCT iajs-2987 188 13 j j NOUN iajs-2987 188 14 ) ) PUNCT iajs-2987 188 15 ( ( PUNCT iajs-2987 188 16 k k NOUN iajs-2987 188 17 ) ) PUNCT iajs-2987 188 18 ( ( PUNCT iajs-2987 188 19 l l NOUN iajs-2987 188 20 ) ) PUNCT iajs-2987 188 21 ( ( PUNCT iajs-2987 188 22 m m NOUN iajs-2987 188 23 ) ) PUNCT iajs-2987 188 24 ( ( PUNCT iajs-2987 188 25 n n CCONJ iajs-2987 188 26 ) ) PUNCT iajs-2987 188 27 ( ( PUNCT iajs-2987 188 28 o o NOUN iajs-2987 188 29 ) ) PUNCT iajs-2987 188 30 figure figure NOUN iajs-2987 188 31 2 2 NUM iajs-2987 188 32 . . 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PUNCT iajs-2987 193 1 temperature temperature NOUN iajs-2987 193 2 profile profile NOUN iajs-2987 193 3 " " PUNCT iajs-2987 193 4 𝛉 𝛉 PROPN iajs-2987 193 5 Β° Β° NOUN iajs-2987 193 6 " " PUNCT iajs-2987 193 7 an an DET iajs-2987 193 8 examination examination NOUN iajs-2987 193 9 of of ADP iajs-2987 193 10 the the DET iajs-2987 193 11 fluid fluid ADJ iajs-2987 193 12 temperature temperature NOUN iajs-2987 193 13 profile profile NOUN iajs-2987 193 14 for for ADP iajs-2987 193 15 a a DET iajs-2987 193 16 fixed fix VERB iajs-2987 193 17 value value NOUN iajs-2987 193 18 of of ADP iajs-2987 193 19 x x SYM iajs-2987 193 20 = = SYM iajs-2987 193 21 1 1 NUM iajs-2987 193 22 yields yield VERB iajs-2987 193 23 a a DET iajs-2987 193 24 parabolic parabolic ADJ iajs-2987 193 25 temperature temperature NOUN iajs-2987 193 26 profile profile NOUN iajs-2987 193 27 , , PUNCT iajs-2987 193 28 with with ADP iajs-2987 193 29 a a DET iajs-2987 193 30 higher high ADJ iajs-2987 193 31 graph graph NOUN iajs-2987 193 32 in in ADP iajs-2987 193 33 the the DET iajs-2987 193 34 middle middle NOUN iajs-2987 193 35 . . PUNCT iajs-2987 194 1 fluids fluid NOUN iajs-2987 194 2 that that PRON iajs-2987 194 3 have have VERB iajs-2987 194 4 a a DET iajs-2987 194 5 high high ADJ iajs-2987 194 6 viscosity viscosity NOUN iajs-2987 194 7 are be AUX iajs-2987 194 8 more more ADV iajs-2987 194 9 likely likely ADJ iajs-2987 194 10 to to PART iajs-2987 194 11 convert convert VERB iajs-2987 194 12 kinetic kinetic ADJ iajs-2987 194 13 energy energy NOUN iajs-2987 194 14 into into ADP iajs-2987 194 15 internal internal ADJ iajs-2987 194 16 energy energy NOUN iajs-2987 194 17 , , PUNCT iajs-2987 194 18 which which PRON iajs-2987 194 19 causes cause VERB iajs-2987 194 20 them they PRON iajs-2987 194 21 to to PART iajs-2987 194 22 get get VERB iajs-2987 194 23 hotter hot ADJ iajs-2987 194 24 . . PUNCT iajs-2987 195 1 there there PRON iajs-2987 195 2 is be VERB iajs-2987 195 3 no no DET iajs-2987 195 4 doubt doubt NOUN iajs-2987 195 5 about about ADP iajs-2987 195 6 that that PRON iajs-2987 195 7 . . 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PUNCT iajs-2987 202 36 variation variation VERB iajs-2987 202 37 the the DET iajs-2987 202 38 temperature temperature NOUN iajs-2987 202 39 " " PUNCT iajs-2987 202 40 ΞΈ ΞΈ NOUN iajs-2987 202 41 Β° Β° NOUN iajs-2987 202 42 " " PUNCT iajs-2987 202 43 with with ADP iajs-2987 202 44 different different ADJ iajs-2987 202 45 parameters parameter NOUN iajs-2987 202 46 { { PUNCT iajs-2987 202 47 π·π‘Ž π·π‘Ž X iajs-2987 202 48 = = NOUN iajs-2987 202 49 0.5 0.5 NUM iajs-2987 202 50 , , PUNCT iajs-2987 202 51 β„‹ β„‹ NOUN iajs-2987 202 52 = = SYM iajs-2987 202 53 3 3 NUM iajs-2987 202 54 , , PUNCT iajs-2987 202 55 𝛾 𝛾 NOUN iajs-2987 202 56 = = SYM iajs-2987 202 57 2 2 NUM iajs-2987 202 58 , , PUNCT iajs-2987 202 59 π‘Ž π‘Ž NOUN iajs-2987 202 60 = = SYM iajs-2987 202 61 0.6 0.6 NUM iajs-2987 202 62 , , PUNCT iajs-2987 202 63 πœ‡ πœ‡ ADP iajs-2987 202 64 = = NOUN iajs-2987 202 65 0.1 0.1 NUM iajs-2987 202 66 , , PUNCT iajs-2987 202 67 οΏ½ οΏ½ PROPN iajs-2987 202 68 Μ€ Μ€ VERB iajs-2987 202 69 οΏ½ οΏ½ PROPN iajs-2987 202 70 = = SYM iajs-2987 202 71 1 1 NUM iajs-2987 202 72 , , PUNCT iajs-2987 202 73 𝑏 𝑏 PROPN iajs-2987 202 74 = = SYM iajs-2987 202 75 0.7 0.7 NUM iajs-2987 202 76 , , PUNCT iajs-2987 202 77 πœ™ πœ™ X iajs-2987 202 78 Β° Β° NOUN iajs-2987 202 79 = = SYM iajs-2987 203 1 πœ‹ πœ‹ PRON iajs-2987 203 2 6 6 NUM iajs-2987 203 3 , , PUNCT iajs-2987 203 4 𝑑 𝑑 NOUN iajs-2987 203 5 = = NOUN iajs-2987 203 6 1 1 NUM iajs-2987 203 7 , , PUNCT iajs-2987 203 8 𝛽 𝛽 NOUN iajs-2987 203 9 = = NOUN iajs-2987 203 10 0.1 0.1 NUM iajs-2987 203 11 , , PUNCT iajs-2987 203 12 Ο† Ο† NOUN iajs-2987 203 13 = = PUNCT iajs-2987 203 14 πœ‹ πœ‹ X iajs-2987 203 15 4 4 NUM iajs-2987 203 16 , , PUNCT iajs-2987 203 17 π‘˜ π‘˜ PRON iajs-2987 203 18 = = NOUN iajs-2987 203 19 0.2 0.2 NUM iajs-2987 203 20 , , PUNCT iajs-2987 203 21 π‘₯ π‘₯ NOUN iajs-2987 203 22 = = SYM iajs-2987 203 23 1 1 NUM iajs-2987 203 24 , , PUNCT iajs-2987 203 25 𝜌 𝜌 X iajs-2987 203 26 = = NOUN iajs-2987 203 27 0.5 0.5 NUM iajs-2987 203 28 , , PUNCT iajs-2987 203 29 𝐹 𝐹 PROPN iajs-2987 203 30 = = NOUN iajs-2987 203 31 0.1 0.1 NUM iajs-2987 203 32 , , PUNCT iajs-2987 203 33 𝑑1 𝑑1 NOUN iajs-2987 203 34 = = NOUN iajs-2987 203 35 0.2 0.2 NUM iajs-2987 203 36 , , PUNCT iajs-2987 203 37 π΅π‘Ÿ π΅π‘Ÿ PROPN iajs-2987 203 38 = = VERB iajs-2987 203 39 1 1 NUM iajs-2987 203 40 } } PUNCT iajs-2987 203 41 4.4 4.4 NUM iajs-2987 203 42 . . PUNCT iajs-2987 204 1 the the DET iajs-2987 204 2 trapping trap VERB iajs-2987 204 3 phenomena phenomenon NOUN iajs-2987 204 4 in in ADP iajs-2987 204 5 order order NOUN iajs-2987 204 6 to to PART iajs-2987 204 7 explain explain VERB iajs-2987 204 8 the the DET iajs-2987 204 9 trapping trap VERB iajs-2987 204 10 phenomena phenomenon NOUN iajs-2987 204 11 , , PUNCT iajs-2987 204 12 the the DET iajs-2987 204 13 formation formation NOUN iajs-2987 204 14 of of ADP iajs-2987 204 15 a a DET iajs-2987 204 16 circulating circulate VERB iajs-2987 204 17 bolus bolus NOUN iajs-2987 204 18 of of ADP iajs-2987 204 19 fluid fluid NOUN iajs-2987 204 20 , , PUNCT iajs-2987 204 21 which which PRON iajs-2987 204 22 is be AUX iajs-2987 204 23 a a DET iajs-2987 204 24 closed closed ADJ iajs-2987 204 25 streamline streamline NOUN iajs-2987 204 26 region region NOUN iajs-2987 204 27 , , PUNCT iajs-2987 204 28 at at ADP iajs-2987 204 29 the the DET iajs-2987 204 30 speed speed NOUN iajs-2987 204 31 of of ADP iajs-2987 204 32 the the DET iajs-2987 204 33 wave wave NOUN iajs-2987 204 34 . . PUNCT iajs-2987 205 1 there there PRON iajs-2987 205 2 will will AUX iajs-2987 205 3 be be AUX iajs-2987 205 4 points point NOUN iajs-2987 205 5 in in ADP iajs-2987 205 6 the the DET iajs-2987 205 7 wave wave NOUN iajs-2987 205 8 frame frame NOUN iajs-2987 205 9 where where SCONJ iajs-2987 205 10 the the DET iajs-2987 205 11 fluid fluid NOUN iajs-2987 205 12 's 's PART iajs-2987 205 13 velocity velocity NOUN iajs-2987 205 14 is be AUX iajs-2987 205 15 zero zero NUM iajs-2987 205 16 due due ADP iajs-2987 205 17 to to ADP iajs-2987 205 18 the the DET iajs-2987 205 19 trapping trap VERB iajs-2987 205 20 phenomenon phenomenon NOUN iajs-2987 205 21 . . PUNCT iajs-2987 206 1 the the DET iajs-2987 206 2 volumetric volumetric NOUN iajs-2987 206 3 flow flow NOUN iajs-2987 206 4 rate rate NOUN iajs-2987 206 5 via via ADP iajs-2987 206 6 a a DET iajs-2987 206 7 line line NOUN iajs-2987 206 8 linking link VERB iajs-2987 206 9 any any DET iajs-2987 206 10 two two NUM iajs-2987 206 11 places place NOUN iajs-2987 206 12 is be AUX iajs-2987 206 13 computed compute VERB iajs-2987 206 14 by by ADP iajs-2987 206 15 taking take VERB iajs-2987 206 16 into into ADP iajs-2987 206 17 account account NOUN iajs-2987 206 18 the the DET iajs-2987 206 19 difference difference NOUN iajs-2987 206 20 in in ADP iajs-2987 206 21 stream stream NOUN iajs-2987 206 22 function function NOUN iajs-2987 206 23 values value NOUN iajs-2987 206 24 at at ADP iajs-2987 206 25 the the DET iajs-2987 206 26 two two NUM iajs-2987 206 27 sites site NOUN iajs-2987 206 28 in in ADP iajs-2987 206 29 question question NOUN iajs-2987 206 30 , , PUNCT iajs-2987 206 31 which which PRON iajs-2987 206 32 is be AUX iajs-2987 206 33 why why SCONJ iajs-2987 206 34 studying study VERB iajs-2987 206 35 streamline streamline VERB iajs-2987 206 36 patterns pattern NOUN iajs-2987 206 37 is be AUX iajs-2987 206 38 so so ADV iajs-2987 206 39 ihjpas ihjpas ADJ iajs-2987 206 40 . . PUNCT iajs-2987 207 1 36(2)2023 36(2)2023 NUM iajs-2987 207 2 326 326 NUM iajs-2987 207 3 important important ADJ iajs-2987 207 4 . . PUNCT iajs-2987 207 5 figures figure NOUN iajs-2987 207 6 5–15 5–15 PROPN iajs-2987 207 7 indicate indicate VERB iajs-2987 207 8 that that SCONJ iajs-2987 207 9 bolus bolus ADJ iajs-2987 207 10 formation formation NOUN iajs-2987 207 11 occurs occur VERB iajs-2987 207 12 from from ADP iajs-2987 207 13 both both DET iajs-2987 207 14 sides side NOUN iajs-2987 207 15 of of ADP iajs-2987 207 16 the the DET iajs-2987 207 17 center center ADJ iajs-2987 207 18 line line NOUN iajs-2987 207 19 in in ADP iajs-2987 207 20 the the DET iajs-2987 207 21 extended extended ADJ iajs-2987 207 22 region region NOUN iajs-2987 207 23 . . PUNCT iajs-2987 208 1 bigger big ADJ iajs-2987 208 2 and and CCONJ iajs-2987 208 3 larger large ADJ iajs-2987 208 4 volumes volume NOUN iajs-2987 208 5 of of ADP iajs-2987 208 6 the the DET iajs-2987 208 7 trapped trap VERB iajs-2987 208 8 bolus bolus NOUN iajs-2987 208 9 can can AUX iajs-2987 208 10 be be AUX iajs-2987 208 11 extracted extract VERB iajs-2987 208 12 from from ADP iajs-2987 208 13 the the DET iajs-2987 208 14 system system NOUN iajs-2987 208 15 by by ADP iajs-2987 208 16 raising raise VERB iajs-2987 208 17 the the DET iajs-2987 208 18 strength strength NOUN iajs-2987 208 19 of of ADP iajs-2987 208 20 the the DET iajs-2987 208 21 magnetic magnetic ADJ iajs-2987 208 22 field field NOUN iajs-2987 208 23 in in ADP iajs-2987 208 24 figures figure NOUN iajs-2987 208 25 ( ( PUNCT iajs-2987 208 26 5 5 NUM iajs-2987 208 27 - - SYM iajs-2987 208 28 9 9 NUM iajs-2987 208 29 ) ) PUNCT iajs-2987 208 30 ( ( PUNCT iajs-2987 208 31 a a DET iajs-2987 208 32 , , PUNCT iajs-2987 208 33 b b NOUN iajs-2987 208 34 , , PUNCT iajs-2987 208 35 and and CCONJ iajs-2987 208 36 c c X iajs-2987 208 37 ) ) PUNCT iajs-2987 208 38 , , PUNCT iajs-2987 208 39 as as ADP iajs-2987 208 40 " " PUNCT iajs-2987 208 41 Ο† Ο† X iajs-2987 208 42 " " PUNCT iajs-2987 208 43 , , PUNCT iajs-2987 208 44 " " PUNCT iajs-2987 208 45 οΏ½ οΏ½ PROPN iajs-2987 208 46 Μ€ Μ€ NOUN iajs-2987 208 47 οΏ½ οΏ½ NOUN iajs-2987 208 48 " " PUNCT iajs-2987 208 49 , , PUNCT iajs-2987 208 50 " " PUNCT iajs-2987 208 51 𝜌 𝜌 X iajs-2987 208 52 " " PUNCT iajs-2987 208 53 , , PUNCT iajs-2987 208 54 " " PUNCT iajs-2987 208 55 d1 d1 NOUN iajs-2987 208 56 " " PUNCT iajs-2987 208 57 and and CCONJ iajs-2987 208 58 " " PUNCT iajs-2987 208 59 π·π‘Ž π·π‘Ž NOUN iajs-2987 208 60 " " PUNCT iajs-2987 208 61 . . PUNCT iajs-2987 209 1 in in ADP iajs-2987 209 2 figures figure NOUN iajs-2987 209 3 ( ( PUNCT iajs-2987 209 4 10 10 NUM iajs-2987 209 5 and and CCONJ iajs-2987 209 6 11 11 NUM iajs-2987 209 7 ) ) PUNCT iajs-2987 209 8 ( ( PUNCT iajs-2987 209 9 a a DET iajs-2987 209 10 , , PUNCT iajs-2987 209 11 b b NOUN iajs-2987 209 12 and and CCONJ iajs-2987 209 13 c c NOUN iajs-2987 209 14 ) ) PUNCT iajs-2987 209 15 , , PUNCT iajs-2987 209 16 as as ADP iajs-2987 209 17 " " PUNCT iajs-2987 209 18 πœ™ πœ™ NOUN iajs-2987 209 19 Β° Β° NOUN iajs-2987 209 20 " " PUNCT iajs-2987 209 21 and and CCONJ iajs-2987 209 22 " " PUNCT iajs-2987 209 23 πœ‡ πœ‡ NOUN iajs-2987 209 24 " " PUNCT iajs-2987 209 25 changes change NOUN iajs-2987 209 26 , , PUNCT iajs-2987 209 27 so so ADV iajs-2987 209 28 does do VERB iajs-2987 209 29 the the DET iajs-2987 209 30 variation variation NOUN iajs-2987 209 31 in in ADP iajs-2987 209 32 streamlines streamline NOUN iajs-2987 209 33 . . 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PUNCT iajs-2987 211 1 the the DET iajs-2987 211 2 figure figure NOUN iajs-2987 211 3 12(a 12(a NUM iajs-2987 211 4 , , PUNCT iajs-2987 211 5 b b PROPN iajs-2987 211 6 and and CCONJ iajs-2987 211 7 c c X iajs-2987 211 8 ) ) PUNCT iajs-2987 211 9 shows show VERB iajs-2987 211 10 that that SCONJ iajs-2987 211 11 the the DET iajs-2987 211 12 wall wall NOUN iajs-2987 211 13 draws draw VERB iajs-2987 211 14 fluid fluid NOUN iajs-2987 211 15 in in ADP iajs-2987 211 16 the the DET iajs-2987 211 17 widest wide ADJ iajs-2987 211 18 section section NOUN iajs-2987 211 19 of of ADP iajs-2987 211 20 the the DET iajs-2987 211 21 duct duct NOUN iajs-2987 211 22 , , PUNCT iajs-2987 211 23 but but CCONJ iajs-2987 211 24 this this DET iajs-2987 211 25 fluid fluid NOUN iajs-2987 211 26 is be AUX iajs-2987 211 27 pushed push VERB iajs-2987 211 28 away away ADV iajs-2987 211 29 from from ADP iajs-2987 211 30 the the DET iajs-2987 211 31 wall wall NOUN iajs-2987 211 32 in in ADP iajs-2987 211 33 the the DET iajs-2987 211 34 narrower narrow ADJ iajs-2987 211 35 section section NOUN iajs-2987 211 36 and and CCONJ iajs-2987 211 37 the the DET iajs-2987 211 38 bolus bolus NOUN iajs-2987 211 39 disappears disappear VERB iajs-2987 211 40 in in ADP iajs-2987 211 41 the the DET iajs-2987 211 42 central central ADJ iajs-2987 211 43 part part NOUN iajs-2987 211 44 as as ADP iajs-2987 211 45 " " PUNCT iajs-2987 211 46 𝛽 𝛽 NOUN iajs-2987 211 47 " " PUNCT iajs-2987 211 48 increases increase NOUN iajs-2987 211 49 . . PUNCT iajs-2987 212 1 graphing graph VERB iajs-2987 212 2 the the DET iajs-2987 212 3 non non ADJ iajs-2987 212 4 - - ADJ iajs-2987 212 5 uniformity uniformity ADJ iajs-2987 212 6 parameter parameter NOUN iajs-2987 212 7 " " PUNCT iajs-2987 212 8 π‘˜"of π‘˜"of NUM iajs-2987 212 9 the the DET iajs-2987 212 10 asymmetric asymmetric ADJ iajs-2987 212 11 channel channel NOUN iajs-2987 212 12 as as SCONJ iajs-2987 212 13 shown show VERB iajs-2987 212 14 in in ADP iajs-2987 212 15 figure figure NOUN iajs-2987 212 16 13(a 13(a NUM iajs-2987 212 17 , , PUNCT iajs-2987 212 18 b b NOUN iajs-2987 212 19 , , PUNCT iajs-2987 212 20 and and CCONJ iajs-2987 212 21 c c X iajs-2987 212 22 ) ) PUNCT iajs-2987 212 23 , , PUNCT iajs-2987 212 24 when when SCONJ iajs-2987 212 25 it it PRON iajs-2987 212 26 is be AUX iajs-2987 212 27 raised raise VERB iajs-2987 212 28 , , PUNCT iajs-2987 212 29 the the DET iajs-2987 212 30 trapped trap VERB iajs-2987 212 31 bolus bolus ADJ iajs-2987 212 32 decreases decrease NOUN iajs-2987 212 33 in in ADP iajs-2987 212 34 size size NOUN iajs-2987 212 35 and and CCONJ iajs-2987 212 36 migrates migrate VERB iajs-2987 212 37 downstream downstream ADJ iajs-2987 212 38 . . 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PUNCT iajs-2987 214 1 ( ( PUNCT iajs-2987 214 2 a a X iajs-2987 214 3 ) ) PUNCT iajs-2987 214 4 ( ( PUNCT iajs-2987 214 5 b b X iajs-2987 214 6 ) ) PUNCT iajs-2987 214 7 ( ( PUNCT iajs-2987 214 8 c c X iajs-2987 214 9 ) ) PUNCT iajs-2987 214 10 figure figure NOUN iajs-2987 214 11 5 5 NUM iajs-2987 214 12 . . PUNCT iajs-2987 215 1 distribution distribution NOUN iajs-2987 215 2 of of ADP iajs-2987 215 3 streamlines streamline NOUN iajs-2987 215 4 " " PUNCT iajs-2987 215 5 πœ“ πœ“ PROPN iajs-2987 215 6 Β° Β° PROPN iajs-2987 215 7 " " PUNCT iajs-2987 215 8 for for ADP iajs-2987 215 9 ( ( PUNCT iajs-2987 215 10 a a NOUN iajs-2987 215 11 ) ) PUNCT iajs-2987 215 12 " " PUNCT iajs-2987 215 13 Ο† Ο† X iajs-2987 215 14 " " PUNCT iajs-2987 215 15 = = SYM iajs-2987 215 16 Ο€/4 Ο€/4 X iajs-2987 215 17 ( ( PUNCT iajs-2987 215 18 b b NOUN iajs-2987 215 19 ) ) PUNCT iajs-2987 215 20 " " PUNCT iajs-2987 215 21 Ο† Ο† X iajs-2987 215 22 " " PUNCT iajs-2987 215 23 = = NOUN iajs-2987 215 24 Ο€/3 Ο€/3 X iajs-2987 215 25 ( ( PUNCT iajs-2987 215 26 c c NOUN iajs-2987 215 27 ) ) PUNCT iajs-2987 215 28 " " PUNCT iajs-2987 215 29 Ο†"= Ο†"= X iajs-2987 215 30 2Ο€/5 2Ο€/5 NUM iajs-2987 215 31 ( ( PUNCT iajs-2987 215 32 a a NOUN iajs-2987 215 33 ) ) PUNCT iajs-2987 215 34 ( ( PUNCT iajs-2987 215 35 b b X iajs-2987 215 36 ) ) PUNCT iajs-2987 215 37 ( ( PUNCT iajs-2987 215 38 c c X iajs-2987 215 39 ) ) PUNCT iajs-2987 215 40 figure figure NOUN iajs-2987 215 41 6 6 NUM iajs-2987 215 42 . . PUNCT iajs-2987 216 1 distribution distribution NOUN iajs-2987 216 2 of of ADP iajs-2987 216 3 streamlines streamline NOUN iajs-2987 216 4 " " PUNCT iajs-2987 216 5 πœ“ πœ“ PROPN iajs-2987 216 6 Β° Β° PROPN iajs-2987 216 7 " " PUNCT iajs-2987 216 8 for for ADP iajs-2987 216 9 ( ( PUNCT iajs-2987 216 10 a a NOUN iajs-2987 216 11 ) ) PUNCT iajs-2987 216 12 " " PUNCT iajs-2987 216 13 οΏ½ οΏ½ PROPN iajs-2987 216 14 Μ€ Μ€ NOUN iajs-2987 216 15 οΏ½ οΏ½ NOUN iajs-2987 216 16 " " PUNCT iajs-2987 216 17 = = NOUN iajs-2987 216 18 1 1 NUM iajs-2987 216 19 ( ( PUNCT iajs-2987 216 20 b b NOUN iajs-2987 216 21 ) ) PUNCT iajs-2987 216 22 " " PUNCT iajs-2987 216 23 οΏ½ οΏ½ PROPN iajs-2987 216 24 Μ€ Μ€ NOUN iajs-2987 216 25 οΏ½ οΏ½ NOUN iajs-2987 216 26 " " PUNCT iajs-2987 216 27 = = NOUN iajs-2987 216 28 2 2 NUM iajs-2987 216 29 ( ( PUNCT iajs-2987 216 30 c c NOUN iajs-2987 216 31 ) ) PUNCT iajs-2987 216 32 " " PUNCT iajs-2987 216 33 οΏ½ οΏ½ PROPN iajs-2987 216 34 Μ€ Μ€ NOUN iajs-2987 216 35 οΏ½ οΏ½ NOUN iajs-2987 216 36 " " PUNCT iajs-2987 216 37 = = NOUN iajs-2987 216 38 4 4 NUM iajs-2987 216 39 ( ( PUNCT iajs-2987 216 40 a a NOUN iajs-2987 216 41 ) ) PUNCT iajs-2987 216 42 ( ( PUNCT iajs-2987 216 43 b b X iajs-2987 216 44 ) ) PUNCT iajs-2987 216 45 ( ( PUNCT iajs-2987 216 46 c c X iajs-2987 216 47 ) ) PUNCT iajs-2987 216 48 figure figure NOUN iajs-2987 216 49 7.distribution 7.distribution NUM iajs-2987 216 50 of of ADP iajs-2987 216 51 streamlines streamline NOUN iajs-2987 216 52 " " PUNCT iajs-2987 216 53 πœ“ πœ“ PROPN iajs-2987 216 54 Β° Β° PROPN iajs-2987 216 55 " " PUNCT iajs-2987 216 56 for for ADP iajs-2987 216 57 ( ( PUNCT iajs-2987 216 58 a a NOUN iajs-2987 216 59 ) ) PUNCT iajs-2987 216 60 " " PUNCT iajs-2987 216 61 𝜌 𝜌 X iajs-2987 216 62 " " PUNCT iajs-2987 216 63 = = SYM iajs-2987 216 64 0.5 0.5 NUM iajs-2987 216 65 ( ( PUNCT iajs-2987 216 66 b b NOUN iajs-2987 216 67 ) ) PUNCT iajs-2987 216 68 " " PUNCT iajs-2987 216 69 𝜌 𝜌 X iajs-2987 216 70 " " PUNCT iajs-2987 216 71 = = SYM iajs-2987 216 72 2 2 NUM iajs-2987 216 73 ( ( PUNCT iajs-2987 216 74 c c NOUN iajs-2987 216 75 ) ) PUNCT iajs-2987 216 76 " " PUNCT iajs-2987 216 77 𝜌 𝜌 X iajs-2987 216 78 " " PUNCT iajs-2987 216 79 = = SYM iajs-2987 216 80 6 6 NUM iajs-2987 216 81 ihjpas ihjpa NOUN iajs-2987 216 82 . . PUNCT iajs-2987 217 1 36(2)2023 36(2)2023 NUM iajs-2987 217 2 327 327 NUM iajs-2987 217 3 ( ( PUNCT iajs-2987 217 4 a a NOUN iajs-2987 217 5 ) ) PUNCT iajs-2987 217 6 ( ( PUNCT iajs-2987 217 7 b b X iajs-2987 217 8 ) ) PUNCT iajs-2987 217 9 ( ( PUNCT iajs-2987 217 10 c c X iajs-2987 217 11 ) ) PUNCT iajs-2987 217 12 figure figure NOUN iajs-2987 217 13 8 8 NUM iajs-2987 217 14 . . PUNCT iajs-2987 218 1 distribution distribution NOUN iajs-2987 218 2 of of ADP iajs-2987 218 3 streamlines streamline NOUN iajs-2987 218 4 " " PUNCT iajs-2987 218 5 πœ“ πœ“ PROPN iajs-2987 218 6 Β° Β° PROPN iajs-2987 218 7 " " PUNCT iajs-2987 218 8 for for ADP iajs-2987 218 9 ( ( PUNCT iajs-2987 218 10 a a NOUN iajs-2987 218 11 ) ) PUNCT iajs-2987 218 12 " " PUNCT iajs-2987 218 13 𝑑1 𝑑1 NOUN iajs-2987 218 14 " " PUNCT iajs-2987 218 15 = = NOUN iajs-2987 218 16 0.2 0.2 NUM iajs-2987 218 17 ( ( PUNCT iajs-2987 218 18 b b NOUN iajs-2987 218 19 ) ) PUNCT iajs-2987 218 20 " " PUNCT iajs-2987 218 21 𝑑1 𝑑1 NOUN iajs-2987 218 22 " " PUNCT iajs-2987 218 23 = = NOUN iajs-2987 218 24 0.8 0.8 NUM iajs-2987 218 25 ( ( PUNCT iajs-2987 218 26 c c NOUN iajs-2987 218 27 ) ) PUNCT iajs-2987 218 28 " " PUNCT iajs-2987 218 29 𝑑1 𝑑1 NOUN iajs-2987 218 30 " " PUNCT iajs-2987 218 31 = = NOUN iajs-2987 218 32 1 1 NUM iajs-2987 218 33 ( ( PUNCT iajs-2987 218 34 a a NOUN iajs-2987 218 35 ) ) PUNCT iajs-2987 218 36 ( ( PUNCT iajs-2987 218 37 b b X iajs-2987 218 38 ) ) PUNCT iajs-2987 218 39 ( ( PUNCT iajs-2987 218 40 c c X iajs-2987 218 41 ) ) PUNCT iajs-2987 218 42 figure figure NOUN iajs-2987 218 43 9 9 NUM iajs-2987 218 44 . . PUNCT iajs-2987 218 45 distribution distribution NOUN iajs-2987 218 46 of of ADP iajs-2987 218 47 streamlines streamline NOUN iajs-2987 218 48 " " PUNCT iajs-2987 218 49 πœ“ πœ“ PROPN iajs-2987 218 50 Β° Β° PROPN iajs-2987 218 51 " " PUNCT iajs-2987 218 52 for for ADP iajs-2987 218 53 ( ( PUNCT iajs-2987 218 54 a a NOUN iajs-2987 218 55 ) ) PUNCT iajs-2987 218 56 " " PUNCT iajs-2987 218 57 π·π‘Ž π·π‘Ž NOUN iajs-2987 218 58 " " PUNCT iajs-2987 218 59 = = NOUN iajs-2987 218 60 0.5 0.5 NUM iajs-2987 218 61 ( ( PUNCT iajs-2987 218 62 b b NOUN iajs-2987 218 63 ) ) PUNCT iajs-2987 218 64 " " PUNCT iajs-2987 218 65 π·π‘Ž π·π‘Ž NOUN iajs-2987 218 66 " " PUNCT iajs-2987 218 67 = = NOUN iajs-2987 218 68 2 2 NUM iajs-2987 218 69 ( ( PUNCT iajs-2987 218 70 c c NOUN iajs-2987 218 71 ) ) PUNCT iajs-2987 218 72 " " PUNCT iajs-2987 218 73 π·π‘Ž π·π‘Ž NOUN iajs-2987 218 74 " " PUNCT iajs-2987 218 75 = = NOUN iajs-2987 218 76 6 6 NUM iajs-2987 218 77 ( ( PUNCT iajs-2987 218 78 a a NOUN iajs-2987 218 79 ) ) PUNCT iajs-2987 218 80 ( ( PUNCT iajs-2987 218 81 b b X iajs-2987 218 82 ) ) PUNCT iajs-2987 218 83 ( ( PUNCT iajs-2987 218 84 c c X iajs-2987 218 85 ) ) PUNCT iajs-2987 218 86 figure figure NOUN iajs-2987 218 87 10 10 NUM iajs-2987 218 88 . . PUNCT iajs-2987 219 1 distribution distribution NOUN iajs-2987 219 2 of of ADP iajs-2987 219 3 streamlines streamline NOUN iajs-2987 219 4 " " PUNCT iajs-2987 219 5 πœ“ πœ“ PROPN iajs-2987 219 6 Β° Β° PROPN iajs-2987 219 7 " " PUNCT iajs-2987 219 8 for for ADP iajs-2987 219 9 ( ( PUNCT iajs-2987 219 10 a a NOUN iajs-2987 219 11 ) ) PUNCT iajs-2987 219 12 " " PUNCT iajs-2987 219 13 πœ‡ πœ‡ ADP iajs-2987 219 14 " " PUNCT iajs-2987 219 15 = = NOUN iajs-2987 219 16 0.1 0.1 NUM iajs-2987 219 17 ( ( PUNCT iajs-2987 219 18 b)"πœ‡ b)"πœ‡ PUNCT iajs-2987 219 19 " " PUNCT iajs-2987 219 20 = = NOUN iajs-2987 219 21 0.4 0.4 NUM iajs-2987 219 22 ( ( PUNCT iajs-2987 219 23 c c NOUN iajs-2987 219 24 ) ) PUNCT iajs-2987 219 25 " " PUNCT iajs-2987 219 26 πœ‡ πœ‡ ADP iajs-2987 219 27 " " PUNCT iajs-2987 219 28 = = ADJ iajs-2987 219 29 1 1 NUM iajs-2987 219 30 ( ( PUNCT iajs-2987 219 31 a a NOUN iajs-2987 219 32 ) ) PUNCT iajs-2987 219 33 ( ( PUNCT iajs-2987 219 34 b b X iajs-2987 219 35 ) ) PUNCT iajs-2987 219 36 ( ( PUNCT iajs-2987 219 37 c c X iajs-2987 219 38 ) ) PUNCT iajs-2987 219 39 figure figure NOUN iajs-2987 219 40 11 11 NUM iajs-2987 219 41 . . PUNCT iajs-2987 220 1 distribution distribution NOUN iajs-2987 220 2 of of ADP iajs-2987 220 3 streamlines streamline NOUN iajs-2987 220 4 " " PUNCT iajs-2987 220 5 πœ“ πœ“ PROPN iajs-2987 220 6 Β° Β° PROPN iajs-2987 220 7 " " PUNCT iajs-2987 220 8 for for ADP iajs-2987 220 9 ( ( PUNCT iajs-2987 220 10 a a NOUN iajs-2987 220 11 ) ) PUNCT iajs-2987 220 12 " " PUNCT iajs-2987 220 13 πœ™ πœ™ NOUN iajs-2987 220 14 Β° Β° NOUN iajs-2987 220 15 " " PUNCT iajs-2987 220 16 = = VERB iajs-2987 220 17 πœ‹ πœ‹ NOUN iajs-2987 220 18 6 6 NUM iajs-2987 220 19 ( ( PUNCT iajs-2987 220 20 b b NOUN iajs-2987 220 21 ) ) PUNCT iajs-2987 220 22 " " PUNCT iajs-2987 220 23 πœ™ πœ™ NOUN iajs-2987 220 24 Β° Β° NOUN iajs-2987 220 25 " " PUNCT iajs-2987 220 26 = = VERB iajs-2987 220 27 πœ‹ πœ‹ NOUN iajs-2987 220 28 3 3 NUM iajs-2987 220 29 ( ( PUNCT iajs-2987 220 30 c c NOUN iajs-2987 220 31 ) ) PUNCT iajs-2987 220 32 " " PUNCT iajs-2987 220 33 πœ™ πœ™ NOUN iajs-2987 220 34 Β° Β° NOUN iajs-2987 220 35 " " PUNCT iajs-2987 220 36 = = SYM iajs-2987 220 37 πœ‹ πœ‹ PRON iajs-2987 220 38 2 2 NUM iajs-2987 220 39 ihjpas ihjpa NOUN iajs-2987 220 40 . . PUNCT iajs-2987 221 1 36(2)2023 36(2)2023 NUM iajs-2987 221 2 328 328 NUM iajs-2987 221 3 ( ( PUNCT iajs-2987 221 4 a a NOUN iajs-2987 221 5 ) ) PUNCT iajs-2987 221 6 ( ( PUNCT iajs-2987 221 7 b b X iajs-2987 221 8 ) ) PUNCT iajs-2987 221 9 ( ( PUNCT iajs-2987 221 10 c c X iajs-2987 221 11 ) ) PUNCT iajs-2987 221 12 figure figure NOUN iajs-2987 221 13 12 12 NUM iajs-2987 221 14 . . PUNCT iajs-2987 222 1 distribution distribution NOUN iajs-2987 222 2 of of ADP iajs-2987 222 3 streamlines streamline NOUN iajs-2987 222 4 " " PUNCT iajs-2987 222 5 πœ“ πœ“ PROPN iajs-2987 222 6 Β° Β° PROPN iajs-2987 222 7 " " PUNCT iajs-2987 222 8 for for ADP iajs-2987 222 9 ( ( PUNCT iajs-2987 222 10 a a NOUN iajs-2987 222 11 ) ) PUNCT iajs-2987 222 12 " " PUNCT iajs-2987 222 13 𝛽 𝛽 NOUN iajs-2987 222 14 " " PUNCT iajs-2987 222 15 = = NOUN iajs-2987 222 16 0.1 0.1 NUM iajs-2987 222 17 ( ( PUNCT iajs-2987 222 18 b b NOUN iajs-2987 222 19 ) ) PUNCT iajs-2987 222 20 " " PUNCT iajs-2987 222 21 𝛽 𝛽 NOUN iajs-2987 222 22 " " PUNCT iajs-2987 222 23 = = NOUN iajs-2987 222 24 0.5 0.5 NUM iajs-2987 222 25 ( ( PUNCT iajs-2987 222 26 c c NOUN iajs-2987 222 27 ) ) PUNCT iajs-2987 222 28 " " PUNCT iajs-2987 222 29 𝛽 𝛽 NOUN iajs-2987 222 30 " " PUNCT iajs-2987 222 31 = = NOUN iajs-2987 222 32 1 1 NUM iajs-2987 222 33 ( ( PUNCT iajs-2987 222 34 a a NOUN iajs-2987 222 35 ) ) PUNCT iajs-2987 222 36 ( ( PUNCT iajs-2987 222 37 b b X iajs-2987 222 38 ) ) PUNCT iajs-2987 222 39 ( ( PUNCT iajs-2987 222 40 c c X iajs-2987 222 41 ) ) PUNCT iajs-2987 222 42 figure figure NOUN iajs-2987 222 43 13 13 NUM iajs-2987 222 44 . . PUNCT iajs-2987 223 1 distribution distribution NOUN iajs-2987 223 2 of of ADP iajs-2987 223 3 streamlines streamline NOUN iajs-2987 223 4 " " PUNCT iajs-2987 223 5 πœ“ πœ“ PROPN iajs-2987 223 6 Β° Β° PROPN iajs-2987 223 7 " " PUNCT iajs-2987 223 8 for for ADP iajs-2987 223 9 ( ( PUNCT iajs-2987 223 10 a a NOUN iajs-2987 223 11 ) ) PUNCT iajs-2987 223 12 " " PUNCT iajs-2987 223 13 k k NOUN iajs-2987 223 14 " " PUNCT iajs-2987 223 15 = = NOUN iajs-2987 223 16 0.2 0.2 NUM iajs-2987 223 17 ( ( PUNCT iajs-2987 223 18 b b NOUN iajs-2987 223 19 ) ) PUNCT iajs-2987 223 20 " " PUNCT iajs-2987 223 21 π‘˜ π‘˜ X iajs-2987 223 22 " " PUNCT iajs-2987 223 23 = = SYM iajs-2987 223 24 0.4 0.4 NUM iajs-2987 223 25 ( ( PUNCT iajs-2987 223 26 c c NOUN iajs-2987 223 27 ) ) PUNCT iajs-2987 223 28 " " PUNCT iajs-2987 223 29 π‘˜"=0.6 π‘˜"=0.6 NOUN iajs-2987 223 30 ( ( PUNCT iajs-2987 223 31 a a NOUN iajs-2987 223 32 ) ) PUNCT iajs-2987 223 33 ( ( PUNCT iajs-2987 223 34 b b X iajs-2987 223 35 ) ) PUNCT iajs-2987 223 36 ( ( PUNCT iajs-2987 223 37 c c X iajs-2987 223 38 ) ) PUNCT iajs-2987 223 39 figure figure NOUN iajs-2987 223 40 14 14 NUM iajs-2987 223 41 . . PUNCT iajs-2987 224 1 distribution distribution NOUN iajs-2987 224 2 of of ADP iajs-2987 224 3 streamlines streamline NOUN iajs-2987 224 4 " " PUNCT iajs-2987 224 5 πœ“ πœ“ PROPN iajs-2987 224 6 Β° Β° PROPN iajs-2987 224 7 " " PUNCT iajs-2987 224 8 for for ADP iajs-2987 224 9 ( ( PUNCT iajs-2987 224 10 a a NOUN iajs-2987 224 11 ) ) PUNCT iajs-2987 224 12 " " PUNCT iajs-2987 224 13 β„‹ β„‹ PROPN iajs-2987 224 14 " " PUNCT iajs-2987 224 15 =3 =3 PROPN iajs-2987 224 16 ( ( PUNCT iajs-2987 224 17 b b NOUN iajs-2987 224 18 ) ) PUNCT iajs-2987 224 19 " " PUNCT iajs-2987 224 20 β„‹ β„‹ PROPN iajs-2987 224 21 " " PUNCT iajs-2987 224 22 = = NOUN iajs-2987 224 23 4 4 NUM iajs-2987 224 24 ( ( PUNCT iajs-2987 224 25 c c NOUN iajs-2987 224 26 ) ) PUNCT iajs-2987 224 27 " " PUNCT iajs-2987 224 28 β„‹ β„‹ PROPN iajs-2987 224 29 " " PUNCT iajs-2987 224 30 = = NOUN iajs-2987 224 31 8 8 NUM iajs-2987 224 32 ( ( PUNCT iajs-2987 224 33 a a NOUN iajs-2987 224 34 ) ) PUNCT iajs-2987 224 35 ( ( PUNCT iajs-2987 224 36 b b X iajs-2987 224 37 ) ) PUNCT iajs-2987 224 38 ( ( PUNCT iajs-2987 224 39 c c X iajs-2987 224 40 ) ) PUNCT iajs-2987 224 41 figure figure NOUN iajs-2987 224 42 15 15 NUM iajs-2987 224 43 . . PUNCT iajs-2987 225 1 distribution distribution NOUN iajs-2987 225 2 of of ADP iajs-2987 225 3 streamlines streamline NOUN iajs-2987 225 4 " " PUNCT iajs-2987 225 5 πœ“ πœ“ PROPN iajs-2987 225 6 Β° Β° PROPN iajs-2987 225 7 " " PUNCT iajs-2987 225 8 for for ADP iajs-2987 225 9 ( ( PUNCT iajs-2987 225 10 a a NOUN iajs-2987 225 11 ) ) PUNCT iajs-2987 225 12 " " PUNCT iajs-2987 225 13 𝛾 𝛾 NOUN iajs-2987 225 14 " " PUNCT iajs-2987 225 15 = = NOUN iajs-2987 225 16 2 2 NUM iajs-2987 225 17 ( ( PUNCT iajs-2987 225 18 b b NOUN iajs-2987 225 19 ) ) PUNCT iajs-2987 225 20 " " PUNCT iajs-2987 225 21 𝛾 𝛾 ADP iajs-2987 225 22 " " PUNCT iajs-2987 225 23 =3 =3 NOUN iajs-2987 225 24 ( ( PUNCT iajs-2987 225 25 c c NOUN iajs-2987 225 26 ) ) PUNCT iajs-2987 225 27 " " PUNCT iajs-2987 225 28 𝛾 𝛾 NOUN iajs-2987 225 29 " " PUNCT iajs-2987 225 30 = = NOUN iajs-2987 225 31 4 4 NUM iajs-2987 225 32 5 5 NUM iajs-2987 225 33 . . PUNCT iajs-2987 226 1 conclusions conclusion NOUN iajs-2987 226 2 in in ADP iajs-2987 226 3 this this DET iajs-2987 226 4 research research NOUN iajs-2987 226 5 , , PUNCT iajs-2987 226 6 we we PRON iajs-2987 226 7 studied study VERB iajs-2987 226 8 the the DET iajs-2987 226 9 effects effect NOUN iajs-2987 226 10 of of ADP iajs-2987 226 11 rotation rotation NOUN iajs-2987 226 12 and and CCONJ iajs-2987 226 13 incline incline VERB iajs-2987 226 14 magnetohydrodynamics magnetohydrodynamic NOUN iajs-2987 226 15 to to PART iajs-2987 226 16 investigate investigate VERB iajs-2987 226 17 the the DET iajs-2987 226 18 effects effect NOUN iajs-2987 226 19 of of ADP iajs-2987 226 20 heat heat NOUN iajs-2987 226 21 transfer transfer NOUN iajs-2987 226 22 and and CCONJ iajs-2987 226 23 couple couple NOUN iajs-2987 226 24 stress stress NOUN iajs-2987 226 25 fluid fluid NOUN iajs-2987 226 26 as as SCONJ iajs-2987 226 27 they they PRON iajs-2987 226 28 move move VERB iajs-2987 226 29 via via ADP iajs-2987 226 30 an an DET iajs-2987 226 31 inclined inclined ADJ iajs-2987 226 32 asymmetric asymmetric ADJ iajs-2987 226 33 channel channel NOUN iajs-2987 226 34 and and CCONJ iajs-2987 226 35 porous porous ADJ iajs-2987 226 36 medium medium NOUN iajs-2987 226 37 under under ADP iajs-2987 226 38 low low ADJ iajs-2987 226 39 reynolds reynold NOUN iajs-2987 226 40 approximations approximation NOUN iajs-2987 226 41 and and CCONJ iajs-2987 226 42 longwavelength longwavelength NOUN iajs-2987 226 43 assumptions assumption NOUN iajs-2987 226 44 in in ADP iajs-2987 226 45 the the DET iajs-2987 226 46 transport transport NOUN iajs-2987 226 47 of of ADP iajs-2987 226 48 bodily bodily ADJ iajs-2987 226 49 fluids fluid NOUN iajs-2987 226 50 by by ADP iajs-2987 226 51 the the DET iajs-2987 226 52 use use NOUN iajs-2987 226 53 of of ADP iajs-2987 226 54 non non ADJ iajs-2987 226 55 - - ADJ iajs-2987 226 56 newtonian newtonian ADJ iajs-2987 226 57 fluid fluid ADJ iajs-2987 226 58 models model NOUN iajs-2987 226 59 . . 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PUNCT iajs-2987 228 1 this this DET iajs-2987 228 2 investigation investigation NOUN iajs-2987 228 3 focused focus VERB iajs-2987 228 4 on on ADP iajs-2987 228 5 studying study VERB iajs-2987 228 6 the the DET iajs-2987 228 7 distribution distribution NOUN iajs-2987 228 8 of of ADP iajs-2987 228 9 velocity velocity NOUN iajs-2987 228 10 , , PUNCT iajs-2987 228 11 the the DET iajs-2987 228 12 pumping pumping NOUN iajs-2987 228 13 characteristics characteristic NOUN iajs-2987 228 14 , , PUNCT iajs-2987 228 15 the the DET iajs-2987 228 16 distribution distribution NOUN iajs-2987 228 17 of of ADP iajs-2987 228 18 temperature temperature NOUN iajs-2987 228 19 , , PUNCT iajs-2987 228 20 and and CCONJ iajs-2987 228 21 the the DET iajs-2987 228 22 trapping trap VERB iajs-2987 228 23 phenomena phenomenon NOUN iajs-2987 228 24 . . PUNCT iajs-2987 229 1 ihjpas ihjpas PROPN iajs-2987 229 2 . . PUNCT iajs-2987 230 1 36(2)2023 36(2)2023 NUM iajs-2987 230 2 329 329 NUM iajs-2987 230 3 1 1 NUM iajs-2987 230 4 . . PUNCT iajs-2987 231 1 it it PRON iajs-2987 231 2 notes note VERB iajs-2987 231 3 that that SCONJ iajs-2987 231 4 the the DET iajs-2987 231 5 temperature temperature NOUN iajs-2987 231 6 and and CCONJ iajs-2987 231 7 profile profile NOUN iajs-2987 231 8 of of ADP iajs-2987 231 9 velocity velocity NOUN iajs-2987 231 10 are be AUX iajs-2987 231 11 parabolic parabolic ADJ iajs-2987 231 12 . . PUNCT iajs-2987 232 1 2 2 X iajs-2987 232 2 . . X iajs-2987 232 3 there there PRON iajs-2987 232 4 is be VERB iajs-2987 232 5 a a DET iajs-2987 232 6 decrease decrease NOUN iajs-2987 232 7 in in ADP iajs-2987 232 8 axial axial ADJ iajs-2987 232 9 velocity velocity NOUN iajs-2987 232 10 " " PUNCT iajs-2987 232 11 w w NOUN iajs-2987 232 12 " " PUNCT iajs-2987 232 13 in in ADP iajs-2987 232 14 the the DET iajs-2987 232 15 central central ADJ iajs-2987 232 16 region region NOUN iajs-2987 232 17 when when SCONJ iajs-2987 232 18 increasing increase VERB iajs-2987 232 19 the the DET iajs-2987 232 20 viscosity viscosity NOUN iajs-2987 232 21 " " PUNCT iajs-2987 232 22 πœ‡ πœ‡ X iajs-2987 232 23 " " PUNCT iajs-2987 232 24 , , PUNCT iajs-2987 232 25 " " PUNCT iajs-2987 232 26 𝛾 𝛾 NOUN iajs-2987 232 27 " " PUNCT iajs-2987 232 28 , , PUNCT iajs-2987 232 29 " " PUNCT iajs-2987 232 30 β„‹ β„‹ PROPN iajs-2987 232 31 " " PUNCT iajs-2987 232 32 , , PUNCT iajs-2987 232 33 " " PUNCT iajs-2987 232 34 𝛽 𝛽 NOUN iajs-2987 232 35 " " PUNCT iajs-2987 232 36 , , PUNCT iajs-2987 232 37 and and CCONJ iajs-2987 232 38 " " PUNCT iajs-2987 232 39 π‘˜ π‘˜ X iajs-2987 232 40 " " PUNCT iajs-2987 232 41 " " PUNCT iajs-2987 232 42 , , PUNCT iajs-2987 232 43 but but CCONJ iajs-2987 232 44 there there PRON iajs-2987 232 45 is be VERB iajs-2987 232 46 a a DET iajs-2987 232 47 rise rise NOUN iajs-2987 232 48 in in ADP iajs-2987 232 49 velocity velocity NOUN iajs-2987 232 50 at at ADP iajs-2987 232 51 the the DET iajs-2987 232 52 boundary boundary NOUN iajs-2987 232 53 of of ADP iajs-2987 232 54 the the DET iajs-2987 232 55 channel channel NOUN iajs-2987 232 56 wall wall NOUN iajs-2987 232 57 . . PUNCT iajs-2987 233 1 3 3 X iajs-2987 233 2 . . X iajs-2987 233 3 there there PRON iajs-2987 233 4 is be VERB iajs-2987 233 5 an an DET iajs-2987 233 6 increase increase NOUN iajs-2987 233 7 in in ADP iajs-2987 233 8 axial axial ADJ iajs-2987 233 9 velocity velocity NOUN iajs-2987 233 10 " " PUNCT iajs-2987 233 11 w w NOUN iajs-2987 233 12 " " PUNCT iajs-2987 233 13 in in ADP iajs-2987 233 14 the the DET iajs-2987 233 15 central central ADJ iajs-2987 233 16 region region NOUN iajs-2987 233 17 when when SCONJ iajs-2987 233 18 increasing increase VERB iajs-2987 233 19 the the DET iajs-2987 233 20 rotation rotation NOUN iajs-2987 233 21 parameter parameter NOUN iajs-2987 233 22 " " PUNCT iajs-2987 233 23 οΏ½ οΏ½ PROPN iajs-2987 233 24 Μ€ Μ€ NOUN iajs-2987 233 25 οΏ½ οΏ½ NOUN iajs-2987 233 26 " " PUNCT iajs-2987 233 27 , , PUNCT iajs-2987 233 28 " " PUNCT iajs-2987 233 29 πœ™ πœ™ NOUN iajs-2987 233 30 Β° Β° NOUN iajs-2987 233 31 " " PUNCT iajs-2987 233 32 , , PUNCT iajs-2987 233 33 density density NOUN iajs-2987 233 34 " " PUNCT iajs-2987 233 35 𝜌 𝜌 NOUN iajs-2987 233 36 " " PUNCT iajs-2987 233 37 , , PUNCT iajs-2987 233 38 " " PUNCT iajs-2987 233 39 Ο† Ο† PROPN iajs-2987 233 40 " " PUNCT iajs-2987 233 41 , , PUNCT iajs-2987 233 42 " " PUNCT iajs-2987 233 43 d1 d1 NOUN iajs-2987 233 44 " " PUNCT iajs-2987 233 45 and and CCONJ iajs-2987 233 46 " " PUNCT iajs-2987 233 47 π·π‘Ž π·π‘Ž NOUN iajs-2987 233 48 " " PUNCT iajs-2987 233 49 , , PUNCT iajs-2987 233 50 but but CCONJ iajs-2987 233 51 there there PRON iajs-2987 233 52 is be VERB iajs-2987 233 53 a a DET iajs-2987 233 54 decrease decrease NOUN iajs-2987 233 55 in in ADP iajs-2987 233 56 velocity velocity NOUN iajs-2987 233 57 at at ADP iajs-2987 233 58 the the DET iajs-2987 233 59 boundary boundary NOUN iajs-2987 233 60 of of ADP iajs-2987 233 61 the the DET iajs-2987 233 62 channel channel NOUN iajs-2987 233 63 wall wall NOUN iajs-2987 233 64 . . PUNCT iajs-2987 234 1 4 4 NUM iajs-2987 234 2 . . X iajs-2987 234 3 when when SCONJ iajs-2987 234 4 the the DET iajs-2987 234 5 viscosity viscosity NOUN iajs-2987 234 6 " " PUNCT iajs-2987 234 7 πœ‡ πœ‡ X iajs-2987 234 8 " " PUNCT iajs-2987 234 9 , , PUNCT iajs-2987 234 10 and and CCONJ iajs-2987 234 11 hartmann hartmann PROPN iajs-2987 234 12 number number NOUN iajs-2987 234 13 " " PUNCT iajs-2987 234 14 β„‹ β„‹ PROPN iajs-2987 234 15 " " PUNCT iajs-2987 234 16 are be AUX iajs-2987 234 17 increased increase VERB iajs-2987 234 18 , , PUNCT iajs-2987 234 19 the the DET iajs-2987 234 20 pressure pressure NOUN iajs-2987 234 21 gradient gradient NOUN iajs-2987 234 22 " " PUNCT iajs-2987 234 23 Ξ΄pβˆ— Ξ΄pβˆ— PRON iajs-2987 234 24 " " PUNCT iajs-2987 234 25 increases increase NOUN iajs-2987 234 26 , , PUNCT iajs-2987 234 27 while while SCONJ iajs-2987 234 28 " " PUNCT iajs-2987 234 29 οΏ½ οΏ½ PROPN iajs-2987 234 30 Μ€ Μ€ NOUN iajs-2987 234 31 οΏ½ οΏ½ NOUN iajs-2987 234 32 " " PUNCT iajs-2987 234 33 , , PUNCT iajs-2987 234 34 " " PUNCT iajs-2987 234 35 Ο† Ο† X iajs-2987 234 36 " " PUNCT iajs-2987 234 37 , , PUNCT iajs-2987 234 38 " " PUNCT iajs-2987 234 39 Ξ² Ξ² X iajs-2987 234 40 " " PUNCT iajs-2987 234 41 , , PUNCT iajs-2987 234 42 " " PUNCT iajs-2987 234 43 𝛼 𝛼 X iajs-2987 234 44 Μƒ Μƒ PROPN iajs-2987 234 45 " " PUNCT iajs-2987 234 46 , , PUNCT iajs-2987 234 47 " " PUNCT iajs-2987 234 48 gπ‘Ÿ gπ‘Ÿ ADJ iajs-2987 234 49 " " PUNCT iajs-2987 234 50 , , PUNCT iajs-2987 234 51 " " PUNCT iajs-2987 234 52 π·π‘Ž π·π‘Ž NOUN iajs-2987 234 53 " " PUNCT iajs-2987 234 54 , , PUNCT iajs-2987 234 55 " " PUNCT iajs-2987 234 56 𝛾 𝛾 NOUN iajs-2987 234 57 " " PUNCT iajs-2987 234 58 , , PUNCT iajs-2987 234 59 " " PUNCT iajs-2987 234 60 πœ™ πœ™ NOUN iajs-2987 234 61 Β° Β° NOUN iajs-2987 234 62 " " PUNCT iajs-2987 234 63 , , PUNCT iajs-2987 234 64 " " PUNCT iajs-2987 234 65 𝜌 𝜌 X iajs-2987 234 66 " " PUNCT iajs-2987 234 67 , , PUNCT iajs-2987 234 68 " " PUNCT iajs-2987 234 69 π‘˜ π‘˜ X iajs-2987 234 70 " " PUNCT iajs-2987 234 71 , , PUNCT iajs-2987 234 72 " " PUNCT iajs-2987 234 73 d1 d1 NOUN iajs-2987 234 74 " " PUNCT iajs-2987 234 75 , , PUNCT iajs-2987 234 76 " " PUNCT iajs-2987 234 77 𝑅𝑒 𝑅𝑒 PROPN iajs-2987 234 78 " " PUNCT iajs-2987 234 79 , , PUNCT iajs-2987 234 80 and and CCONJ iajs-2987 234 81 " " PUNCT iajs-2987 234 82 ΞΈ ΞΈ NOUN iajs-2987 234 83 Β° Β° PRON iajs-2987 234 84 " " PUNCT iajs-2987 234 85 decrease decrease NOUN iajs-2987 234 86 . . PUNCT iajs-2987 235 1 5 5 X iajs-2987 235 2 . . X iajs-2987 235 3 the the DET iajs-2987 235 4 connection connection NOUN iajs-2987 235 5 between between ADP iajs-2987 235 6 pressure pressure NOUN iajs-2987 235 7 rise rise NOUN iajs-2987 235 8 " " PUNCT iajs-2987 235 9 Ξ΄π‘βˆ— Ξ΄π‘βˆ— NOUN iajs-2987 235 10 " " PUNCT iajs-2987 235 11 and and CCONJ iajs-2987 235 12 volumetric volumetric NOUN iajs-2987 235 13 flow flow NOUN iajs-2987 235 14 rate rate NOUN iajs-2987 235 15 for for ADP iajs-2987 235 16 each each DET iajs-2987 235 17 wavelength wavelength NOUN iajs-2987 235 18 is be AUX iajs-2987 235 19 seen see VERB iajs-2987 235 20 to to PART iajs-2987 235 21 be be AUX iajs-2987 235 22 linear linear ADJ iajs-2987 235 23 . . PUNCT iajs-2987 236 1 6 6 X iajs-2987 236 2 . . X iajs-2987 236 3 in in ADP iajs-2987 236 4 retrograde retrograde ADJ iajs-2987 236 5 pumping pumping NOUN iajs-2987 236 6 , , PUNCT iajs-2987 236 7 increases increase VERB iajs-2987 236 8 " " PUNCT iajs-2987 236 9 Ξ΄π‘βˆ— Ξ΄π‘βˆ— ADJ iajs-2987 236 10 " " PUNCT iajs-2987 236 11 pressure pressure NOUN iajs-2987 236 12 rise rise NOUN iajs-2987 236 13 with with ADP iajs-2987 236 14 the the DET iajs-2987 236 15 increasing increase VERB iajs-2987 236 16 values value NOUN iajs-2987 236 17 the the DET iajs-2987 236 18 viscosity viscosity NOUN iajs-2987 236 19 " " PUNCT iajs-2987 236 20 πœ‡ πœ‡ X iajs-2987 236 21 " " PUNCT iajs-2987 236 22 , , PUNCT iajs-2987 236 23 " " PUNCT iajs-2987 236 24 gπ‘Ÿ","𝑅𝑒 gπ‘Ÿ","𝑅𝑒 NOUN iajs-2987 236 25 " " PUNCT iajs-2987 236 26 , , PUNCT iajs-2987 236 27 " " PUNCT iajs-2987 236 28 h h NOUN iajs-2987 236 29 " " PUNCT iajs-2987 236 30 , , PUNCT iajs-2987 236 31 " " PUNCT iajs-2987 236 32 ΞΈ ΞΈ NOUN iajs-2987 236 33 Β° Β° NUM iajs-2987 236 34 " " PUNCT iajs-2987 236 35 , , PUNCT iajs-2987 236 36 " " PUNCT iajs-2987 236 37 𝛼 𝛼 PRON iajs-2987 236 38 Μƒ Μƒ PROPN iajs-2987 236 39 " " PUNCT iajs-2987 236 40 and and CCONJ iajs-2987 236 41 " " PUNCT iajs-2987 236 42 πœ™ πœ™ NOUN iajs-2987 236 43 Β° Β° NOUN iajs-2987 236 44 " " PUNCT iajs-2987 236 45 , , PUNCT iajs-2987 236 46 whereas whereas SCONJ iajs-2987 236 47 it it PRON iajs-2987 236 48 decreases decrease VERB iajs-2987 236 49 with with ADP iajs-2987 236 50 the the DET iajs-2987 236 51 rising rise VERB iajs-2987 236 52 values value NOUN iajs-2987 236 53 the the DET iajs-2987 236 54 rotation rotation NOUN iajs-2987 236 55 parameter parameter NOUN iajs-2987 236 56 " " PUNCT iajs-2987 236 57 οΏ½ οΏ½ PROPN iajs-2987 236 58 Μ€ Μ€ NOUN iajs-2987 236 59 οΏ½ οΏ½ NOUN iajs-2987 236 60 " " PUNCT iajs-2987 236 61 , , PUNCT iajs-2987 236 62 " " PUNCT iajs-2987 236 63 Ο† Ο† X iajs-2987 236 64 " " PUNCT iajs-2987 236 65 , , PUNCT iajs-2987 236 66 " " PUNCT iajs-2987 236 67 π·π‘Ž π·π‘Ž NOUN iajs-2987 236 68 " " PUNCT iajs-2987 236 69 , , PUNCT iajs-2987 236 70 " " PUNCT iajs-2987 236 71 𝛾 𝛾 NOUN iajs-2987 236 72 " " PUNCT iajs-2987 236 73 , , PUNCT iajs-2987 236 74 " " PUNCT iajs-2987 236 75 𝛽 𝛽 NOUN iajs-2987 236 76 " " PUNCT iajs-2987 236 77 , , PUNCT iajs-2987 236 78 density density NOUN iajs-2987 236 79 " " PUNCT iajs-2987 236 80 𝜌 𝜌 NOUN iajs-2987 236 81 " " PUNCT iajs-2987 236 82 , , PUNCT iajs-2987 236 83 " " PUNCT iajs-2987 236 84 d1 d1 NOUN iajs-2987 236 85 " " PUNCT iajs-2987 236 86 , , PUNCT iajs-2987 236 87 and and CCONJ iajs-2987 236 88 " " PUNCT iajs-2987 236 89 k k NOUN iajs-2987 236 90 " " PUNCT iajs-2987 236 91 . . PUNCT iajs-2987 237 1 7 7 X iajs-2987 237 2 . . X iajs-2987 237 3 the the DET iajs-2987 237 4 temperature temperature NOUN iajs-2987 237 5 " " PUNCT iajs-2987 237 6 ΞΈ ΞΈ NOUN iajs-2987 237 7 Β° Β° PRON iajs-2987 237 8 " " PUNCT iajs-2987 237 9 rises rise VERB iajs-2987 237 10 when when SCONJ iajs-2987 237 11 the the DET iajs-2987 237 12 rotation rotation NOUN iajs-2987 237 13 parameter parameter NOUN iajs-2987 237 14 " " PUNCT iajs-2987 237 15 οΏ½ οΏ½ PROPN iajs-2987 237 16 Μ€ Μ€ NOUN iajs-2987 237 17 οΏ½ οΏ½ NOUN iajs-2987 237 18 " " PUNCT iajs-2987 237 19 , , PUNCT iajs-2987 237 20 density density NOUN iajs-2987 237 21 " " PUNCT iajs-2987 237 22 𝜌 𝜌 NOUN iajs-2987 237 23 " " PUNCT iajs-2987 237 24 , , PUNCT iajs-2987 237 25 " " PUNCT iajs-2987 237 26 d1 d1 NOUN iajs-2987 237 27 " " PUNCT iajs-2987 237 28 , , PUNCT iajs-2987 237 29 " " PUNCT iajs-2987 237 30 π‘˜ π‘˜ NOUN iajs-2987 237 31 " " PUNCT iajs-2987 237 32 , , PUNCT iajs-2987 237 33 " " PUNCT iajs-2987 237 34 π·π‘Ž π·π‘Ž NOUN iajs-2987 237 35 " " PUNCT iajs-2987 237 36 , , PUNCT iajs-2987 237 37 " " PUNCT iajs-2987 237 38 β„‹ β„‹ PROPN iajs-2987 237 39 " " PUNCT iajs-2987 237 40 and and CCONJ iajs-2987 237 41 brinkman brinkman PROPN iajs-2987 237 42 number"π΅π‘Ÿ number"π΅π‘Ÿ PROPN iajs-2987 237 43 " " PUNCT iajs-2987 237 44 all all PRON iajs-2987 237 45 go go VERB iajs-2987 237 46 up up ADP iajs-2987 237 47 . . PUNCT iajs-2987 238 1 it it PRON iajs-2987 238 2 goes go VERB iajs-2987 238 3 decrease decrease NOUN iajs-2987 238 4 when when SCONJ iajs-2987 238 5 the the DET iajs-2987 238 6 inclination inclination NOUN iajs-2987 238 7 magnetic magnetic ADJ iajs-2987 238 8 field field NOUN iajs-2987 238 9 angle angle NOUN iajs-2987 238 10 " " PUNCT iajs-2987 238 11 Ο† Ο† PROPN iajs-2987 238 12 " " PUNCT iajs-2987 238 13 , , PUNCT iajs-2987 238 14 the the DET iajs-2987 238 15 slip slip NOUN iajs-2987 238 16 parameter parameter NOUN iajs-2987 238 17 " " PUNCT iajs-2987 238 18 𝛽 𝛽 NOUN iajs-2987 238 19 " " PUNCT iajs-2987 238 20 , , PUNCT iajs-2987 238 21 couple couple NOUN iajs-2987 238 22 - - PUNCT iajs-2987 238 23 stress stress NOUN iajs-2987 238 24 parameter"𝛾 parameter"𝛾 NOUN iajs-2987 238 25 " " PUNCT iajs-2987 238 26 , , PUNCT iajs-2987 238 27 phase phase NOUN iajs-2987 238 28 difference difference NOUN iajs-2987 238 29 " " PUNCT iajs-2987 238 30 πœ™ πœ™ NOUN iajs-2987 238 31 Β° Β° NOUN iajs-2987 238 32 " " PUNCT iajs-2987 238 33 , , PUNCT iajs-2987 238 34 and and CCONJ iajs-2987 238 35 the the DET iajs-2987 238 36 viscosity viscosity NOUN iajs-2987 238 37 " " PUNCT iajs-2987 238 38 πœ‡ πœ‡ AUX iajs-2987 238 39 " " PUNCT iajs-2987 238 40 all all PRON iajs-2987 238 41 go go VERB iajs-2987 238 42 up up ADV iajs-2987 238 43 . . PUNCT iajs-2987 239 1 8 8 X iajs-2987 239 2 . . X iajs-2987 240 1 when when SCONJ iajs-2987 240 2 the the DET iajs-2987 240 3 values value NOUN iajs-2987 240 4 of of ADP iajs-2987 240 5 " " PUNCT iajs-2987 240 6 β„‹"and β„‹"and NOUN iajs-2987 240 7 " " PUNCT iajs-2987 240 8 Ξ³ Ξ³ X iajs-2987 240 9 " " PUNCT iajs-2987 240 10 are be AUX iajs-2987 240 11 increased increase VERB iajs-2987 240 12 , , PUNCT iajs-2987 240 13 the the DET iajs-2987 240 14 trapped trap VERB iajs-2987 240 15 boluses bolus NOUN iajs-2987 240 16 are be AUX iajs-2987 240 17 eliminated eliminate VERB iajs-2987 240 18 . . PUNCT iajs-2987 241 1 the the DET iajs-2987 241 2 inclination inclination NOUN iajs-2987 241 3 magnetic magnetic ADJ iajs-2987 241 4 field field NOUN iajs-2987 241 5 angle angle NOUN iajs-2987 241 6 " " PUNCT iajs-2987 241 7 Ο† Ο† PROPN iajs-2987 241 8 " " PUNCT iajs-2987 241 9 , , PUNCT iajs-2987 241 10 " " PUNCT iajs-2987 241 11 οΏ½ οΏ½ PROPN iajs-2987 241 12 Μ€ Μ€ NOUN iajs-2987 241 13 οΏ½ οΏ½ NOUN iajs-2987 241 14 " " PUNCT iajs-2987 241 15 , , PUNCT iajs-2987 241 16 " " PUNCT iajs-2987 241 17 𝜌 𝜌 X iajs-2987 241 18 " " PUNCT iajs-2987 241 19 , , PUNCT iajs-2987 241 20 " " PUNCT iajs-2987 241 21 d1 d1 NOUN iajs-2987 241 22 " " PUNCT iajs-2987 241 23 and and CCONJ iajs-2987 241 24 " " PUNCT iajs-2987 241 25 π·π‘Ž π·π‘Ž NOUN iajs-2987 241 26 " " PUNCT iajs-2987 241 27 have have VERB iajs-2987 241 28 a a DET iajs-2987 241 29 increasing increase VERB iajs-2987 241 30 impact impact NOUN iajs-2987 241 31 on on ADP iajs-2987 241 32 the the DET iajs-2987 241 33 bolus bolus ADJ iajs-2987 241 34 size size NOUN iajs-2987 241 35 . . PUNCT iajs-2987 242 1 references reference NOUN iajs-2987 242 2 1 1 NUM iajs-2987 242 3 . . PUNCT iajs-2987 243 1 mekheimer mekheimer PROPN iajs-2987 243 2 , , PUNCT iajs-2987 243 3 kh kh PROPN iajs-2987 243 4 . . PUNCT iajs-2987 244 1 s. s. PROPN iajs-2987 244 2 effect effect PROPN iajs-2987 244 3 of of ADP iajs-2987 244 4 induced induced ADJ iajs-2987 244 5 magnetic magnetic ADJ iajs-2987 244 6 field field NOUN iajs-2987 244 7 on on ADP iajs-2987 244 8 peristaltic peristaltic ADJ iajs-2987 244 9 flow flow NOUN iajs-2987 244 10 of of ADP iajs-2987 244 11 a a DET iajs-2987 244 12 couple couple NOUN iajs-2987 244 13 stress stress NOUN iajs-2987 244 14 fluid fluid NOUN iajs-2987 244 15 . . PUNCT iajs-2987 245 1 physics physics NOUN iajs-2987 245 2 letters letter NOUN iajs-2987 245 3 a a DET iajs-2987 245 4 2008 2008 NUM iajs-2987 245 5 , , PUNCT iajs-2987 245 6 372 372 NUM iajs-2987 245 7 , , PUNCT iajs-2987 245 8 4271 4271 NUM iajs-2987 245 9 - - SYM iajs-2987 245 10 4278 4278 NUM iajs-2987 245 11 . . PUNCT iajs-2987 246 1 2 2 X iajs-2987 246 2 . . X iajs-2987 246 3 kumar kumar PROPN iajs-2987 246 4 , , PUNCT iajs-2987 246 5 p. p. PROPN iajs-2987 246 6 magnetorotatory magnetorotatory PROPN iajs-2987 246 7 thermal thermal ADJ iajs-2987 246 8 converction converction NOUN iajs-2987 246 9 in in ADP iajs-2987 246 10 couple couple NOUN iajs-2987 246 11 – – PUNCT iajs-2987 246 12 stress stress NOUN iajs-2987 246 13 fluid fluid NOUN iajs-2987 246 14 . . 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