ABSTRACT. Magnetohydrodynamics, heat and mass transfer, thermal radiation, heat source, chemical reaction, porous medium, vertical plate.

Transcription

1 Inenaional Reseach Jonal of Mahemaics Engineeing and I Vol. 3 Isse Ocobe 6 IF I: 39-3 Associaed Asia Reseach Fondaion AARF Websie: edio@aaf.asia edioaaf@gmail.com HYDROMAGEI FREE OVEIVE RADIAIG FLOW OF HEMIALLY REAIG FLUID HROUGH POROU MEDIUM OVER A VERIAL URFAE I HE PREEE OF HEAABORPIO G. Mni aala.v.. Vama and. havedi 3* Reseach hola Depamen of Mahemaics.V.Univesi ipai A.P. Pofesso Depamen of Mahemaics.V.Univesiipai. 3* enio Lece Depamen of MahemaicsUnivesi of Boswana Gaboone Boswana. ABRA his pape discsses he analsis of fis ode homogeneos chemical eacion and hea soce on MHD flow wih hea and mass ansfe chaaceisics of an incompessible viscos elecicall condcing and ewonian flid. An analsis was done ove a veical oscillaing poos plae embedded in a poos medim.he flid consideed hee is a ga absobing/emiing adiaion b a non-scaeing medim. A ime he plae sas oscillaing in is own plane wih a veloci cos. And a he same ime he plae empeae and concenaion levels nea he plae aised lineal wih ime. he dimensionless govening eqaions fo momenm eneg and concenaion have been solved b sing he Laplace ansfom echniqe. he veloci empeae concenaion skin-ficion he ae of hea ansfe and he ae of mass ansfe ae sdied hogh gaphs and ablesin ems of diffeen phsical paamees eneing ino he poblem. EY WORD Magneohdodnamics hea and mass ansfe hemal adiaion hea soce chemical eacion poos medim veical plae. OMELAURE A a A consan Absopion coefficien B P Exenal magneic field pecific hea a consan pesse A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI P a g e

2 w D Gm G g pecies concenaion pecies concenaion a he sface pecies concenaion in he fee seam hemical molecla diffsivi Mass Gashof nmbe hemal Gashof nmbe Acceleaion de o gavi H Hea soce paamee Dimensionless pemeabili paamee M P Q q R h w Pemeabili of he poos medim Dimensionless chemical eacion paamee hemical eacion paamee Magneic field paamee ssel nmbe Pandl nmbe Dimensional hea absopion coefficien Radiaive hea flx Radiaive paamee hmid nmbe hewood nmbe empeae Flid empeae a he plae Flid empeae in he fee seam ime paamee Veloci of he plae Dimensionless veloci v Veloci componens along x -diecions Geek smbols Volmeic coefficien of hemal ansion Volmeic coefficien of concenaion ansion hemal condcivi of he flid oefficien of viscosi inemaic viscosi Densi of he flid Elecic condcivi efan-bolzmann consan heaing sess Dimensionless flid empeae Dimensionless species concenaion Feqenc of he oscillaion bscips w ondiions on he wall Fee seam condiions. IRODUIO In man anspo pocesses in boh nae and indsial applicaions hea and mass ansfe is a conseqence of boanc effecs cased b diffsion of hea and chemical species. Hence Radiaive hea and mass ansfe pla an impoan ole in manfacing indsies fo he design of fins seel olling nclea powe plans gas bines and viscos poplsion device fo aicaf missiles saellies combsion and fnace design maeials pocessing empeae measemens emoe sensing fo asonom and space loaion eneg ilizaion cogenic engineeing food pocessing healh and milia applicaions as well as pollion of he envionmen fomaion and dispesion of fog and moise of agiclal fields. In nae he exisence of pe ai o wae is impossible and some foeign mass ma be pesen eihe naall o mixed wih hem. A lage nmbe of eseach woks concening ansfe pocesses wih chemical eacions have been epoed. In paicla he sd of A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI P a g e

3 chemical eacion and hea and mass ansfe is of consideable impoance in chemical and hdomeallgical indsies. hambe and Yong [3] analzed a fis-ode chemical eacion in he neighbohood of a hoizonal plae. A eacion is said o be fis-ode if he ae of eacion is diecl popoional o he concenaion iself. In man chemical pocesses a chemical eacion occs beween a foeign mass and a flid in which a plae is moving. onvecion in poos media has applicaions in geohemal eneg ecove oil exacion hemal eneg soage and flow hogh fileing devices. onvecive hea ansfe in poos media has eceived consideable aenion in ecen eas owing o is impoance in vaios echnological applicaions sch as fibe and ganla inslaion eleconic ssem cooling cool combsos and poos maeial egeneaive hea exchanges. In view of hese applicaions man eseaches have sdied MHD fee convecive hea and mass ansfe flowin a poos medim. Books b ield and Bejan[] Bejan and as[] and Ingham e al.[7] excellenl descibe he exen of he eseach infomaion in his aea. Magneohdodnamics has aaced he aenion of a lage nmbe of scholas de o is divese applicaions. In asophsics and geophsics i is applied o sd he sella and sola sces adio popagaion hogh he ionosphee ec. In engineeing we find is applicaions like in MHD pmps MHD beaings ec.he phenomenon of mass ansfe is also ve common in heo of sella sce and obsevable effecs ae deecable on he sola sface. he sd of effecs of magneic field on fee convecion flow is impoan in liqid-meals elecoles and ionized gases. he hemal phsics of hdomagneic poblems wih mass ansfe is of inees in powe engineeing and meallg. hemal adiaion in flid dnamics has become a significan banch of he engineeing sciences and is an essenial aspec of vaios scenaios in mechanical aeospace chemical envionmen sola powe and hazads engineeing. If he empeae of sonding flid is ahe high adiaion effecs pla an impoan ole and his siaion does exis in space echnolog. In sch cases one has o ake ino accon he combined effec of hemal adiaion and mass diffsion. MHD effecs on implsivel saed veical infinie plae wih vaiable empeae in he pesence of ansvese magneic field wee sdied b ondalgeka e al.[6].he effecs ansvesel applied magneic field on he flow of an elecicall condcing flid pas an implsivel saed infinie isohemal veical plae wee also sdied b ondalgeka e al.[7]. he dimensionless govening eqaions wee solved sing Laplace ansfom echniqe.ma and Vama [8] sdied he poblem of nsead flow pas an infinie veical pemeable plae wih consan scion and ansvese magneic field wih oscillaing plae empeae. Rajp and ma [] consideed he adiaion effecs on MHD flow pas an implsivel saed veical plae wih vaiable hea and mass ansfe b Laplace ansfom echniqe. In all sdies cied above he flow is diven eihe b a pescibed sface empeae o b a pescibed sface hea flx. Hee a elaivel diffeen diving mechanism fo nsead fee convecion along a veical sface is consideed whee i is assmed ha he flow is also se p b ewonian heaing fom he sface. Hea ansfe chaaceisics ae dependen on he hemal bonda condiions. In geneal hee ae fo common heaing pocesses specifing he wall-o-ambien empeae disibions namel pescibed wall empeae A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 3 P a g e

4 disibionspowe-law wall empeae disibion along he sface has been sall sed; pescibed sface hea flx disibions; conjgae condiions whee hea is spplied hogh a bonding sface of finie hickness and finie hea capaci. he ineface empeae is no known a pioi b depends on he ininsic popeies of he ssem namel he hemal condciviies of he flid and solid especivel; ewonian heaing whee he hea ansfe ae fom he bonding sface wih a finie hea capaci is popoional o he local sface empeae and which is sall emed conjgae convecive flow. his configaion occs in man impoan engineeing devices fo example: i in hea exchanges whee he condcion is solid be wall geal inflenced b he convecion in he flid flowing ove i; ii fo conjgae hea ansfe aond fins whee he condcion wihin he fin and he convecion in he flid sonding i ms be simlaneosl analsed in ode o obain vial design infomaion; and iii in convecive flows se p when he bonding sfaces absobs hea b sola adiaion. heefoe we conclde ha he convenional assmpion of no ineacion of condcionconvecion copled effecs is no alwas ealisic and i ms be consideed when evalaing he conjgae hea ansfe pocesses in man pacical engineeing applicaions. ewonian heaing condiion has been onl ecenl sed in convecive hea ansfe. Mekin [9] was he fis o conside he fee convecion bonda lae ove a veical fla plae immesed in a viscos flid. hamkha [] pesened an analical solion fo hea and mass ansfe b lamina flow of a ewonian viscos elecicall condcing flid and hea geneaion/absopion.aahai and aan[] consideed fee convecion flow pas an implsivel saed infinie veical plae wih ewonian heaing in he pesence of hemal adiaion and mass diffsion. he effecs of mass ansfe on flow pas an implsivel saed infinie veical plae wih ewonian heaing and chemical eacion was analsed b Rajesh[3].he fee convecion flow of a viscos incompessible flid pas an infinie veical oscillaing plae wih nifom hea flx in he pesence of hemal adiaion was sdied b handakala [5]. Rahod and Asha [5] examined magneic field effecs on wo-dimensional viscos incompessible ewonian flid wih he help of nmeical echniqe. An exac solion o he flow of a viscos incompessible nsead flow pas an infinie veical oscillaing plae wih vaiable empeae and mass diffsion b aking ino accon of he homogeneos chemical eacion of fis-ode was invesigaed b Mhcmaaswam e al. []. hadha e al. [6] invesigaed he MHD flow pas an infinie veical oscillaing plae hogh poos medim aking accon of he pesence of fee convecion and mass ansfe. Ahmed and alia[] sdied he MHD adiaing flow ove an infinie veical sface bonded b apoos medim in pesence of chemical eacion. he main objecive of his pape is o exend he wok of efeence [] in he diecion o conside he hea soce effec. Hence he pesen pape is aimed o sd he effecs of A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI P a g e

5 ansvese magneic field hemal adiaion and heasoce and fis-ode chemical eacion on nsead MHD flow hogh poos medimove an infinie veical oscillaing plae wih vaiable empeae and mass diffsion. he empeae and concenaion of he plae is oscillaing wih ime abo a consan non-zeo mean vale. he dimensionless govening eqaions involved in he pesen analsis ae solved b sing he Laplace ansfom echniqe.. MAHEMAIAL FORMULAIO hemal diffsion and adiaion effecs on nsead MHD flow of a viscos incompessible flid pas along a veical oscillaing plae wih vaiable empeae and also wih vaiable mass diffsion hogh poos medim in he pesence of ansvese applied magneic field hea soce and chemical eacion of fis ode ae sdied. he x -axis is aken along he plae in he veical pwad diecion and he -axis is aken nomal o he plae. Iniiall i is assmed ha he plae and flid a he same empeae in he saiona condiion wih concenaion level a all he poins. A ime he plae sas oscillaing in is own plane wih a veloci cos. And a he same ime he plae empeae and concenaion levels nea he plae aised lineal wih ime. A ansvese magneic field of nifom sengh B is assmed o be applied nomal o he diecion of flow. he viscos dissipaion and indced magneic field ae assmed o be negligible. he flid consideed hee is ga absobing/emiing adiaion b a non-scaeing medim. incehe plae is assmed o be infiniel long in he x -axisdiecion all he phsical vaiables ae fncions of and onl. Appling he Bossinesq s appoximaion he nsead flow is govened b he following eqaions. Fig. Phsical model and coodinae ssem A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 5 P a g e

6 A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 6 P a g e v B g g v Q q v p 3 D v he iniial and bonda condiions ae: : A A w w cos : a 5 : as Fo an opicall hin ga gas he adiaive hea flx q saisfies he following non-linea diffeenial eqaion. a q 6 whee a is he absopion coefficien and he efan-bolzmann consan.i is assmed ha he empeae diffeences wihin he flow ae sfficienl small sch ha ma be essed as a linea fncion of he flid empeae sing he alo s seies abo he fee seam empeae. Afe neglecing highe-ode ems gives Using Eqs.5 and 6 Eq. becomes 6 3 Q a p 8 he following non-dimensional qaniies ae inodced: P p w w D a R B M g Gm g G w w 9 Q H A In view of Eqs. 8 Eqs. 7 and 3 edces o he following non-dimensional fom especivel

7 A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 7 P a g e M Gm G P P H R wih he following iniial and bonda condiions: : cos : a 3 : as whee is phase angle 3. OLUIO OF HE PROBLEM he appeaed phsical paamees ae defined in he nomenclae. he dimensionless govening eqaions fom 9 o sbjec o he iniial and bonda condiions ae solved b he sal Laplace ansfom echniqe and he solions fo veloci empeae and concenaion fields ae essed in ems of onenial and complemena eo fncions. i efc i i efc i i i efc i i efc i i efc efc h efc efc g c efc c c efc c c l

8 A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 8 P a g e f efc f f efc f f m P P P P efc efc l P P P P P P efc efc c efc c c efc c c l P P P P P P efc efc m efc efc f efc f f efc f f m P P P P P P efc efc 5 efc efc 6 whee P P f Gm d c G b M H R Gm G P Gm m G l P Gm G h Gm G g I FRIIO: he bonda lae podces a dag foce on he plae de o he viscos sesses which ae developed a he wall. he viscos sess a he sface of he plae is given b 7

9 i i i i ef i i ef i i h ef g ef l c c ef c c m f f ef f f l P P l c ef cp ef P c P + m m f ef P P P c P f f ef f ef P ef P 8 UEL UMBER: Fom empeae field now we sd ssel nmbe ae of change of hea ansfe which is given in non-dimensional fom as P P P ef P 9 A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 9 P a g e

10 HERWOOD UMBER: Fom concenaion field now we sd hewood nmbe ae of change of mass ansfe which is given in non-dimensional fom as h h ef. REUL & DIUIO In ode o ge he phsical insigh in o he poblem nmeical compaions ae caied o o illsae he effecs of diffeen conol paamees pon he nae of he flow and anspo. he nmeical vales of he veloci empeae concenaion skin-ficion ssel nmbe and hewood nmbe ae comped fo diffeen phsical paamees M G Gm P R H and. A epesenaive se of nmeical esls is shown gaphicall in Figs. -5 and ables -3. he defal vales fo he conol paamees ae aken as: P. 7ai 7. wae. hdogen. 3 helim. 6 wae vapo.78 ammonia Phase angle. he ohe paamees ae abiail chosen.in ode o check he accac of nmeical esls he pesen sd when H is compaed wih he available heoeical solion of Ahmed and alia[]. Fig. epesens he veloci pofiles de o he vaiaions in. I is eviden fom fige ha he veloci nea he plae exceeds a he plae i.e. he veloci oveshoo occs. Fhemoe he magnide of he veloci deceases wih inceasing phase angle foai P.7. he effec of magneic field paamee M on he veloci is shown in Fig. 3. he veloci deceases wih an incease in he magneic paamee. I is becase ha he applicaion of ansvese magneic field will esl a esisive pe foce Loenz foce simila o dag foce which ends o esis he flid flow and hs edcing is veloci. Also he bonda lae hickness deceases wih an incease in he magneic paamee. I is also noiced ha he veloci is maximm fo ai nea he plae and deceases wih awa fom he plae and finall akes an asmpoic vale fo all vales of M. Fig. illsaes he inflences of hemal Gashof nmbe G and mass Gashof nmbe Gm on he veloci. I is obseved ha he veloci inceases wih inceasing vales of he hemal Gashof nmbe o mass Gashof nmbe. he hemal Gashof nmbe signifies he elaive effec of he hemal boanc foce o he viscos hdodnamic foce. he mass solal Gashof nmbe defines he aio of he species boanc foce o he viscos hdodnamic foce. he flow is acceleaed de o he enhancemen in boanc foce coesponding o an incease in he hemal Gashof nmbe i.e. fee convecion effecs. he posiive vales of A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI P a g e

11 G coespond o cooling of he plae b naal convecion. Hea is heefoe condced awa fom veical plae ino he flid which inceases he empeae and heeb enhances he boanc foce. I is also fond ha he veloci is maximm fo ai nea he plae and deceases wih awa fom he plae and finall akes an asmpoic vale fo all vales of G andgm. he veloci and concenaion pofiles ae ploed fo diffeen vales of he hmid nmbe in Figs. 5 and 6 especivel. he hmid nmbe embodies he aio of he momenm diffsivi o he mass species diffsivi. I phsicall elaes he elaive hickness of he hdodnamic bonda lae and mass ansfe concenaion bonda lae. As he hmid nmbe inceases he concenaion deceases. his cases he concenaion boanc effecs o decease ielding a edcion in he flid veloci. he edcions in he veloci and concenaion pofiles ae accompanied b simlaneos edcions in he veloci and concenaion bonda laes which is eviden fomfigs. 5 and 6. Fig. 7 illsaes he empeae pofiles fo diffeen vales of Pandl nmbe P. Fom his fige i is obseved ha an incease in he Pandl nmbe esls in a decease of he hemal bonda lae hickness and in geneal lowe aveage empeae wihin he bonda lae. his is de o he fac ha hemal condcivi of flid deceases wih inceasing P esling a decease in he hemal bonda lae hickness. he effecs of adiaion paamee R and he hea soce paamee H on empeae of he flow field ae shown in Fig. 8. I is seen ha as adiaion paamee R o hea soce paamee H inceases he empeae of he flow field deceases a all poins in flow egion. he inflence of chemical eacion paamee on veloci and concenaion pofiles is pesened in Figs. 9 and. As eced he pesence of he chemical eacion significanl affecs he concenaion pofiles as well as he veloci pofiles. Hee sdied case is fo descive chemical eacion. We noe fom Fig. 9 ha hee is decease in veloci pofiles wih incease in and pesence of he peak indicaes ha he maximm vale of he veloci occs in he bod of he flid nea he sface. Also i is obseved fom Fig. ha inceasing vale of he deceases he concenaion of species in he bonda lae his is de o he fac ha descive chemical edces he solal bonda lae hickness and inceases he mass ansfe. he veloci pofiles ae shown in Fig. fo diffeen vales of he pemeabili paamee. I is fond ha he veloci inceases wih inceasing vales of. his is de o he fac ha inceasing vales of edces he dag foce which assiss he flid consideabl o move fas. Also i is noiced ha he magnide of veloci fo ai is highe han ha of wae. he skin-ficion is sdied in Figs. and 3 agains ime. I is noiced ha as G ogm o inceases he skin-ficion deceases in Fig. whee as in Fig. 3 he skin-ficion A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI P a g e

12 inceases wih inceasing R o H o wih inceasing ime.. Also i is obsevedha he skin-ficion deceases Fig. illsaes he vaiaion of ssel nmbe agains ime.fom his fige i is obseved ha ssel nmbe inceases wih inceasing R o H fo wae and he evese effec is obseved wih he same vales of R and H fo ai.also i is fond ha he ssel nmbe inceases wih inceasing vales of P and. Finall fom Fig.5 i is seen ha as o inceases he hewood nmbe inceases... = = /6 = / = /3 = / Fig. : Veloci pofiles fo diffeen wih P.7.78 M.5 R H G 5 Gm M= M= 5 M= 7 M= M= Fig. 3: Veloci pofiles fo diffeen M wih P R H G 5 Gm 5 A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI P a g e

13 G= Gm= 5 G= 5Gm= 5 G= Gm= 5 G= Gm= G= 5Gm= G= Gm= Fig. : Veloci pofiles fo diffeen G and Gm wih P.7.78 M 5.5 R H.35.3 =. =.3 =.6 = Fig. 5: Veloci pofiles fo diffeen wih P.7 M 5.5 R H G Gm =. =.3 =.6 = A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 3 P a g e

14 Fig. 6: oncenaion pofiles fo diffeen wih P=.7 =. P= 7. =. P=.7 =. P= 7. = Fig. 7: empeae pofiles fo diffeen P and wih R 5 H R=H= R=5H= R=H= R=H= R=5H= R=H= Fig. 8: empeae pofiles fo diffeen R and H wih.p = = = 3 = A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI P a g e

15 Fig. 9: Veloci pofiles fo diffeen wih P.7.78 M.5 R H G 5 Gm = = 3 = 5 = Fig.: oncenaion pofiles fo diffeen wih =.P=.7 =.5P=.7 =.P=.7 =.;P= 7. =.5P= 7. =.;P= Fig. : Veloci pofiles fo diffeen and P wih. M 3 R H G 5 Gm 5 A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 5 P a g e

16 G=Gm=5=.5 G=5Gm=5=.5 G=Gm==.5 G=5Gm==.5 G=Gm=5=. G=5Gm== Fig : kin ficion fo diffeen G Gm and wih P 7.. M R H R=.5H=.5 = R=5H=.5 = R=.5H= = R=5H= = R=.5H=.5 =3 R=5H= = Fig 3: kin ficion fo diffeen R H and wih P.7.78 M.5 G 5 Gm R=.5H=.5P=7. R=5H=.5P=7. R=.5H=P=7. R=.5H=P=7. R=.5H=.5P=.7 R=5H=.5P= Fig: ssel nmbe fo diffeen R and H A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 6 P a g e

17 h =. = =.6 = =.78 = =. =3 =.6 =3 =.78 = Fig 5: hewood nmbe fo diffeen and he effecs of vaios govening paamees on he skin-ficion coefficien ssel nmbe and hewood nmbe ae shown in ables and 3. In all hese ables i is noed ha he compaison of each paamee is made wih fis ow in he coesponding able. Fom able i is obseved ha as M o R o H o o o P inceases he skin-ficion coefficien inceases wheeas he skin-ficion coefficien deceases as G o Gm o and inceases.able shows ha he ssel nmbe deceases wih inceasing R o H fo ai and he ssel nmbe inceases wih he same vales of R and H fo wae. Also i is fond ha he ssel nmbe inceases wih inceasing vales of P and. Finall fom able 3 i is seen ha as o o inceases he hewood nmbe inceases. P M G Gm R H A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 7 P a g e

18 able : meical vales of he skin-ficion coefficien P R H able : meical vales of ssel nmbe h able 3: meical vales of hewood nmbe h 5. OLUIO We analse he effecs of chemical eacion hemal adiaion and hea soce on nsead MHD flow of a viscos incompessible flid pas along an infinie veical oscillaing poos plae embedded in a poos medim. he eqaions of momenm eneg and diffsion which goven he flow field ae solved b he sal Laplace ansfom echniqe. he esls illsae he flow chaaceisics fo he veloci empeae concenaion skin-ficion ssel nmbe and hewood nmbe. A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 8 P a g e

19 he conclsions of he sd ae smmaized as follows: he veloci deceases wih an incease in he phase angle fo ai. he veloci deceases wih an incease in he magneic paamee. he veloci inceased wih inceased in eihe of he hemal Gashof nmbe o he mass Gashof nmbe. he veloci as well as concenaion deceased as he hmid nmbe inceased. An incease in he Pandl nmbe cased a decease in he empeae. empeae deceases wih an incease in he adiaion paamee o hea soce paamee. he veloci as well as concenaion deceases wih an incease in he chemical eacion paamee. he veloci inceases wih an incease in he pemeabili of he poos medim fo boh ai and wae. he skin-ficion deceases as G o Gm o inceaseswhee as he skin-ficion inceases wih inceasing R H and. he ae of hea ansfe inceases de o incease in he adiaion paamee o hea soce paamee. As hmid nmbe o chemical eacion paamee inceases he ae of mass ansfe inceases. REFEREE [] Ahmed. and alia. MHD adiaing flow ove an infinie veical sface bonded b a poos medim in pesence of chemical eacion Jonal of Applied Flid Mechanics Vol.6 o. pp [] Bejan A. and as A.D. Hea ansfe Handbook Wile ew Yok 3. [3] hambe P.L. and Yong J.D.On he diffsion of a chemicall eacive species in a lamina bonda lae flow Phs. Flids Vol. pp [] hamkha A.J. MHD Flow of nifoml seched veical pemeable sface in he pesence of hea geneaion/absopion and a chemical eacion In. omm. Hea Mass ansfe Vol.3 pp.3-3. [5] handakala P. Radiaion effecs on flow pas an implsivel saed veical oscillaing plae wih nifom hea flx Inenaional Jonal of Dnamics of flids Vol.6 o. pp.9-5. [6] hadha R.. and Apia Jain ombined hea and mass ansfe effecs on MHD fee convecion flow pas an oscillaing plae embedded in poos medim Rom. Jon. Phs.Vol.5 os.5-7 pp Bchaes 7. [7] Ingham D.B. Bejan A. Mam E. and Pop I. Emeging echnologies and echniqes in Poos Media lwe Dodech. [8] ma A.G.V. and Vama.V.. hemal adiaion and mass ansfe effecs on MHD flow pas an implsivel saed veical plae wih vaiable empeae effecs vaiable mass diffsion In. Jonal of Engineeing Vol.3 pp A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI 9 P a g e

20 [9] Mekin J.H. aal convecion bonda-lae flow on a veical sface wih ewonian heaing In. J. Hea flid flow Vol.5 o.5 pp [] Mhcmaaswam R. Meenakshisndaam. heoeical sd of chemical eacion effecs on veical oscillaing plae wih vaiable empeae heoe. Appl. Mech. Vol.33 o.3 pp.5-57 Belgade 6. [] aahai M. and aan M.Y. Fee convecion flow an implsivel saed infinie veical plae wih ewonian heaing in he pesence of hemal adiaion and mass diffsion kish J.Eng. Env. i Vol.35 pp [] ield D.A. and Bejan A. onvecion in Poos Media nd edn. pinge ew Yok 999. [3] Rajesh V. Effecs of mass ansfe on flow pas an implsivel saed infinie veical plae wih ewonian heaing and chemical eacion Jonal of Engineeing Phsics and hemophsics Vol.85 o. pp.-8. [] Rajp U.. and ma. Radiaion effecs on MHD flow pas an implsivel saed veical plae wih vaiable hea and mass ansfe In. J. of Appl. Mah. and Mech. Vol.8 o. pp [5] Rahod V.P. and Asha.. Magneic field effecs on wo-dimensional viscos incompessible ewonian flid Advances in Applied ience Reseach Vol. o. pp.-9. [6] ondalgeka V.M. Gpa.M. and Biajda.. Effecs of mass ansfe and fee convecion cens on MHD okes poblem fo a veical plae clea Engg. Des. Vol.53 pp [7] ondalgeka V.M.Pail M.R. and Jahagida M.D. MHD sokes poblem fo a veical plae wih vaiable empeae clea Engg. Des. Vol.6 pp A Monhl Doble-Blind Pee Reviewed Refeeed Open Access Inenaional e-jonal - Inclded in he Inenaional eial Diecoies. Inenaional Reseach Jonal of Mahemaics Engineeing and I IRJMEI P a g e