Effects of Couple Stress and Porous Medium on Transient Magneto Peristaltic Flow under the Action of Heat Transfer

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1 IOSR Jonl of Meics IOSR-JM e-iss: ISS: 9-765X. Vole Isse Ve. V Jl. - Ag.6 PP Effecs of Cole Sess nd Poos Medi on nsien Mgneo Peislic Flow nde e Acion of He nsfe Aed M. Abdldi Al Wleed Sle Deen of Meics College of Science Uniesiy of Bgdd Bgdd Iq. Absc: Anlyicl nd coionl sdies on nsien eislic e flow og finie leng oos cnnel e esened in is e. e exession fo eee field xil elociy ole flow e esse diffeence locl wll se sess se fncion e obined nde e ssion of long weleng nd low Reynolds nbe. Effecs of diffeen ysicl ees eflecing cole-sess ee eebiliy ee Hn nbe consn e diion fco nd sof nbe s well s lide ion on ing cceisics nd ficionl foce se lines en nd ing of eislic flow en sdied wi icl esis.e effec of e nsfe on wo ineen enoen of eislic flow is discssed neiclly. is e inesiges e inflence of MHD on eislic flow of ewonin flid wi cole sess og oos edi wee e no-sli ssion beween wll nd e flid is no longe lid. Keywods: nsien eislic flow He nsfe Pesse gdien Locl wll se sess Cole sess Mgneic field Poos Medi. I. Inodcion Peislsis is nl ecnis of ing is obseed in e cse of os ysiologicl flids. is beio is slly ssocied wi ogessie we of e concion o exnsion long e leng of e bondy of flid-filled disensible be. is ecnis es lce in ny cicl linces inclding olle nd finge s e-lng cines blood cines dilysis cines nd lso nso of noxios flids in e ncle nd ceicl wse indsies.owing o e ionce of eislic flow soe significn inesigion on is sbjec e been eoed. Hisoiclly eislic flid dynics sdies wee iniied by Sio e l.969 wo eoeiclly exined e eislic flow of iscos flid indced by sinsoidl wll ogion. He nsfe ecniqes cnge e inenl enegy of bo syses inoled nd follow e fis lw of eodynics. He is genelly nsfeed fo objecs of ying eees i condcion nd conecion. Seel ocesses ely on e nsfe nd e coesonding el coefficiens. Seel os. Hy M.U. Qesi K.S. Meeie Y. Abd elbod 8 e eefoe eoed e inflence of e nsfe on eislic flow of ewonin nd non-ewonin flids Reine Rilin flid Jeffey-six consn flid second gde flid id ode flid fo gde flid Hescel Blley flid nd Jonson Segln flid wi o wio e effec of gneic field og nifo/nonnifo/syeic cnnels/eicl nnls syses nd lso oos edi. Fe ineesing sdies inclde e ecen es byabd elbod nd Meeie wic consideed el nso in nsien flow in eicl consiced nnls. A oos edi wic conins nbe of sll oles disibed ogo e e lys ey ole in e sdy of nso ocess in bio- flid ecnics indsil ecnics nd engineeing fields. A good exle of eislic in oos edi is focsed in inesinl flid dynics by Y. Miyoo e l.98&b.jeffey e l.. Soe os A.R. Ro M. Mis. Hy. Ali S. Asg7 sdied eislic flow of ewonin nd non- ewonin flids sc s owe lw flid gneo flid nd Mxwell flid og e oos edi. Hy M.U. Qesi Q. Hssin8inesiged e eislic flow wi e nsfe in oos sce.d. ii O.A. Beg eoed e inflence of e nsfe on nsedy ysiologicl gneo flid flow. D. ii. fe sdied e effec of e nsfe on eislic flow en og finie leng cnnel nd discssed e ic of ysicl ees on flow beio Wile e exended e eislic flow odel in D. ii.fo finie oos cnnel nd coe esls wi e esls of D. ii.in iew of e boe discssion in is e effec of e nsfe fo non- ewonin flid wi cole sess in MHD field og oos edi wi no sli bondy condiion nde e ssions of long we leng nd low Reynolds nbe. is nsien cole sess eislic flow of ewonin flid og finie leng cnnel wll og oos edi..in-bols esse disibion locl wll se sess nd elociy ofiles coed fo e effecs of e ey ydodynic ees.e inflence of ios einen ees on e flow cceisics Wee sdy e discssed og gs. DOI:.979/ Pge

2 DOI:.979/ Pge II. Meicl Folions Conside nsien eislic flow of iscos ewonin flid wi cole sess og oos edi in nifo cnnel wi e nsfe. Since we e consideing nifo cnnel eefoe e wll is inined eee nd de o syey e cene of e cnnel e cnge of e eee is en o be zeo wi consn seed c long e cnnel wlls. Fig : eoey of e oble e geoey of wll sfce see Fig. is descibed s : c cos Wee nd c eesen e nsese ibion of e wll e xil coodine ie e lf wid of e cnnel e lide of e we e weleng nd e we elociy eseciely. III.Bsic eqion e bsic eqions goening e non-ewonin flid flow nde e effec of nsese gneic field e gien by : e coniniy eqion : e oen eqions e : g B B c 5

3 DOI:.979/ Pge Wee is e flid densiy xil elociy nsese elociy nsese coodine esse iscosiy consn ssocied wi cole sess elecicl condciiy B nsese gneic field nd eebiliy ee g cceleion de o giy coefficien of line el exnsion of flid eee c secific e consn esse nd consn e ddiion / bsoion. eseciely. In ode o silify e goening eqions of e oion We inodcing e following diensionless ee : K c c c c P B M c c c g Re Wee is e we nbe Re Reynolds nbe is e cole sess ee M is e Hnn nbe K is e el condciiy sof nbe P Pndle nbe eee disibion nd consn e diion.sbsiing 6 ino eqions - 5 we obin e following non-diensionl eqions nd bondy condiions : cos 7. 8 M Re 9 c c c c c Re Re P e boe oble will be sole sbjec o e following bondy condiions : 6

4 DOI:.979/ Pge no sli condiion e egliy condiion e nising of cole sesses η = η = finie leng condiions l 5 e eee condiions 6 III. Solion of e oble e genel solion of e goening eqions 8 - in e genel cse sees o be iossible ; eefoe we sll confine e nlysis nde e ssion of sll diensionless we nbe. I follows δ. In oe wods we consideed e long - weleng oxiion. Along o is ssion eqions 8 - becoe : Wee K M e solion of Eq. sbjec o e ssocied bondy condiions 6 is fond of e fo.. Sbsied in Eq.8 nd e solion of Eq. 8 sbjec o e ssocied bondy condiion is fond of e fo cos cos cos cos Wee

5 DOI:.979/ Pge e locl wll se sess defined s w fe by sing Eq. n n w Vole flow e n ion ee in cnnel flows is defined s d Q wic on ineging Eq. yields : Q n n e following exession define e exising elion beween e eged flow e nd flow e in e we fe nd in e lbooy fe : Q q Q 5 A sile nilion of Eq. followed by licion of Eq. 5 yields e esse gdien s follows : f Q 6 f n n 7 Wic on inegion beween nd ξ genees e following exession fo esse diffeence : ds f Q 8 e esse diffeence l coss e one weleng wic on ilizing Eq.6 sses e fo : d l 9 Se fncion cn be obined by ineging eqion wi esec o η nd sing Eq. 6

6 6 f Q sin sin cos cos IV. eicl Resls nd Discssion In is secion e neicl nd coionl esls e discssed fo e oble of cole-sess ewonin flid in be wi oos edi og e gicl illsions. e nsien gneo - eislic flow of cole-sess flids og e oos edi wi effec of e nsfe e discssed og Figes -7. MAHEMAICA og is sed o find o neicl esls nd illsions. A. Bsed on Eq. 5 Figs.-5 illses e effecs of e ees ie sof nbe consn e diion nd eebiliy ee on e xil elociy disibion eseciely. Figes sow e elion beween xil elociy nd nsese dislceen. I is obseed e xil elociy ofile egion inceses wi incesing gnides of nd Wile elociy decese wen e oe ees incese finlly noiced e elociy e e og loced nd will be iniized e cnnel cene. B. Figs. 6-9 sows e inflence of e nsfe on locl wll se sess wi xil disnce long e leng of e cnnel ios insn.e elion beween locl se sess nd xil disnce is nonline wee e ces exibi bolic se. C. Figs. - illse e elion beween esse diffeence coss one weleng nd eged ole flow e exibis line elion beween e. fo e effec of nd. ole flow e incese wi incesing e gnide of sof nbe consn e diion. D. Figs.-6 illse e esse disibion long e leng of cnnel ios insns fo e inflence of nd ios ies wees l =.I is ysiclly ineeed if e nsfe is effecie en less esse is eqied fo e eislic flow of iscos flid og e cnnel. E. Figs.789dwn fo seline ens. e ics of sof ee consn e ee cole- sess ee Hn ee eebiliy ee nd ie e discssed og ese figes. I is ion o obsee e size of ing bols edces wen e gnide of sid ees M nd inceses. Fig. e xil elociy s. nsese dislceen fo diffeen les DOI:.979/ Pge

7 of wi M.6 5. Fig. e xil elociy s. nsese dislceen fo diffeen les of wi M.6 5. Fig. e xil elociy s. nsese dislceen fo diffeen les of wi M.6 5. Fig 5. e xil elociy s. nsese dislceen fo diffeen les DOI:.979/ Pge

8 of wi M.6. Fig 6. Locl wll se sess s. xil disnce fo diffeen les of wi M l.9 5. Fig 7. Locl wll se sess s. xil disnce fo diffeen les of wi. M l.9 5. Fig 8. Locl wll se sess s. xil disnce fo diffeen les of wi. M l.9 5. DOI:.979/ Pge

9 Fig 9. Locl wll se sess s. xil disnce fo diffeen les of wi M l.9.. Fig. e esse diffeence s. eged flow e fo diffeen les of wi l. M.. Fig. e esse diffeence s. eged flow e fo diffeen les of wi l. M.. DOI:.979/ Pge

10 Fig. e esse diffeence s. eged flow e fo diffeen les of wi l. M. Fig. e esse diffeence s. eged flow e fo diffeen les of wi l M.. Fig. e esse disibion s. xil disnce fo diffeen les of wi. M Q DOI:.979/ Pge

11 Fig 5. e esse disibion s. xil disnce fo diffeen les of wi. M Q Fig 6. e esse disibion s. xil disnce fo diffeen les of. M Q Fig 7. Seline in e we fe Q. 95 &. 5 Wen. M b.6 M DOI:.979/ Pge

12 c.9 M Fig 8. Seline in e we fe Q. 95 &. 5 Wen. M b 6. M c 9. M Fig 9. Seline in e we fe Q. 95 &. 5 Wen. M b. M c 8. M DOI:.979/ Pge

13 V. Conclding es we e discssed e inflence of e nsfe on nsien gneo eislic flow wi cole-sess flid og oos edi on ewonin flid in finie leng cnnel nde nsese gneic field. e esls e discssed og gs. We e conclded e following obseions:. e xil elociies incese wi e incese in nd decese wi e incese in.. e locl wll se sess decese wi incesing in nd. e incesing of sof nbe ie edces locl wll se sess ll disnces long e cnnel xis wi decese on i.. e esse diffeence decese wi incesing in nd φ wee s i incese wi incesing in nd. 5. A line elionsi is coed beween xil esse diffeence nd ole flow e e esse disibion deceses wi e incesing in nd wees i dislced fe long e cnnel xis wi incesing in. 7. e decesing in leng of e finie cnnel s jo effec on e esse disibion nd in soe cses on gnides. 8. Finlly i is conclded e ing ennces wi incesing e effec of oosiy wees i edces wi incesing e effec of e nsfe Refeences []. A.H. Sio M.Y. Jffin S.L. Weinbeg 969.Peislic ing wi long welengs low Reynolds nbe Jonl of Flid Mecnics []. A.R. Ro M. Mis Peislic nso of owe-lw flid in oos be. Jonl of on-ewonin Flid Mecnics6-7. []. B. Jeffey H.S. Udy K.S. Sclze.Flow fields geneed by eislic eflex in isoled gine ig ile: ic of concion de nd soldes Aeicn Jonl of Pysiology-soinesinl nd Lie Pysiology []. D. iio. A. Beg. A sdy of nsedy ysiologicl gneo-flid flow nd e nsfe og finie leng cnnel by eislic ing Poceedings of e Insiion of Mecnicl Enginees P H: Jonl of Engineeing in Medicine [5]. D. ii. A eicl odel fo swllowing of food bols og e oesogs nde e inflence of e nsfe Inenionl Jonl of el Science 5 9. [6]. D. ii.sdy of nsien eislic flow og finie oos cnnel Meicl nd Coe Modelling [7].. Rdisncy C. Sinisl 7. Inflence of wll oeies on eislic nso wi e nsfe Coes Rends Mecniqe [8]. K.S. Meeie Y. Abd elbod 8.e inflence of e nsfe nd gneic field on eislic nso of ewonin flid in eicl nnls: Alicion of endoscoe Pysics Lees A [9]. K.S. Meeie online eislic nso og oos edi in n inclined ln cnnel.jonl of Poos Medi []. K. Vjel. Rdisncy V.Rdisny7. Peislic nso nd e nsfe in eicl oos nnls wi long we oxiion Inenionl Jonl of on-line Mecnics []. M. Kondni S. Sinis 8. On e inflence of wll oeies in e MHD eislic nso wi e nsfe nd oos edi Pysics Lees A []..S. Ab S. dee.silion of e nd ceicl ecions on Reine Rilin flid odel fo blood flow og eed ey wi senosis He nd Mss nsfe []. S. dee.s. Ab M. Heed.Peislic nso nd e nsfe of MHD ewonin flid wi ible iscosiy Inenionl Jonl fo eicl Meods in Flids []. S. dee.s. Ab. Silion of second gde flid odel fo blood flow og eed ey wi senosis Cinise Pysics Lees [5]. S. dee.s. Ab.Inflence of e nd ss nsfe on e eislic flow of Jonson Segln flid in eicl syeic cnnel wi indced MHD Jonl of e iwn Insie of Ceicl Enginees [6]. S. Sinis M. Kondni 9.e inflence of e nd ss nsfe on MHD eislic flow og oos sce wi colin wlls Alied Meics nd Coion [7]. S. Sinis R.yi9. Peislic nso of ewonin flid in eicl syeic cnnel wi e nsfe nd oos edi Alied Meics nd Coion [8].. Hy S. oeen.peislic nso of fo gde flid wi e nsfe nd indced gneic field Coes Rends Mécniqe [9].. Hy. Ali S. Asg Hll effecs on eislic flow of Mxwell flid in oos edi 7.Pysics Lees A [].. Hy M.U. Qesi Effec of e nsfe on e eislic flow of n eleciclly flid in oos sce8.alied Meicl Modelling []. Y. Abd elbod K.S. Meeie. Unsedy lsile flow og eicl consiced nnls wi e nsfe Zeiscif fü foscng []. Y.Miyoo M. Hnno. Ig 98 Concenion ofile in e ines inl c nd dg bsoion odel:wo-diensionl lin flow in cicl oos be Jonl of eoeicl Biology DOI:.979/ Pge.