Effects of Heat Absorption and Porosity of the Medium on MHD Flow past a Vertical Plate

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1 ailable online.ejae.o Eopean Jonal of danes in Engineeing and ehnology 7 4 4: Reseah ile ISSN: X Effes of Hea bsopion and Poosiy of he Medi on MHD Flo pas a Veial Plae US Rajp and aa a Depaen of Maheais and sonoy Uniesiy of Lkno UP India ajpgaal@gail.o BSR Effes of hea absopion and poosiy of he edi on nseady MHD flo pas a oing eial plae ih aiable all epeae and ass diffsion in he pesene of Hall en is sdied hee. Ealie e [5] hae sdied heial eaion effe on nseady MHD flo pas an iplsiely saed osillaing inlined plae ih aiable epeae and ass diffsion in he pesene of Hall en. We obained he esls hih ee in ageeen ih he desied flo phenoenon. o sdy fhe e ae hanging he odel by onsideing hea absobing flid and hanging he geoey of he odel. Hee in his pape e ae aking he plae posiioned eially pad. Fhe edi of he flo is aken as poos. he goening eqaions inoled in he flo odel ae soled by he Laplae-ansfo ehniqe. he esls obained hae been analyed ih he help of gaphs dan fo diffeen paaees. he neial ales obained fo he dag a bonday hae been ablaed. Hee oo he esls ae fond o be in ageeen ih he aal flo. ey ods: MHD flo hea absobing flid ass diffsion Hall en INRODUION he nseady flo nde he aion of song agnei field plays a deisie ole in diffeen aeas of siene and ehnology. MHD effe on hea ansfe oe sehing shee ebedded in poos edi ih aiable isosiy isos dissipaion and hea soe o sink as analyed by Dessie and Naikoi []. hey soled flo odel by sing Rnge-a foh ode neial ehod and obseed ha if hea sink paaee is ineased hen he heal bonday laye ineases heeas he heal bonday laye deeases ih hea soe. Hall effe on nseady MHD naal oneion flo of a hea absobing flid pas an aeleaed oing eial plae ih aped all epeae as inesigaed by Seh e al [7]. he odel onsideed by Seh e al [7] as soled by Laplae ansfo ehniqe. In hei sdy hey obseed ha eloiy and epeae of flid nea he eial plae deeases hen hea absopion paaee ineases. Reddy e al [6] hae pesened adiaion and ass ansfe effes on nonlinea MHD bonday laye flo of liqid eal oe a poos sehing sfae ebedded in poos edi ih hea geneaion. Hossain e al [] hae deeloped MHD fee oneion and ass ansfe flo hogh a eial osillaoy poos plae ih Hall ion-slip ens and hea soe in a oaing syse. Hossain e al [] hae sed explii finie diffeene ehod o sole he opled non-linea paial diffeenial eqaions. hey exained ha he shea sess and Sheood nbes ae deeased ih he inease in hea soe paaee and Nssel nbe is ineased ih inease in hea soe. Myheye e al [3] hae poposed heial eaion on nseady MHD oneie hea and ass ansfe pas a sei-infinie eial peeable oing plae ih hea absopion. hey soled he goening eqaions by sing pebaion ehniqe and explained he pesene of hea absopion effe ased edions in he flid epeae hih esled in deease in he flid eloiy. Siila sdy as done by Seh e al [8] Shehad e al [9] and Ibahi and Sneeha []. heial eaion effe on nseady MHD flo pas an iplsiely saed osillaing inlined plae ih aiable epeae and ass diffsion in he pesene of Hall en as inesigaed by s [5]. Fhe e [4] hae oked on effes of Hall en and heial eaion on MHD flo hogh poos edi pas an osillaing inlined plae ih aiable epeae and ass diffsion. he ain ppose of he pesen inesigaion is o sdy he effes of hea absopion and poosiy of he edi on nseady MHD flo pas a oing eial plae ih aiable all epeae and ass 87

2 88 diffsion in he pesene of Hall en. he odels hae been soled sing he Laplae ansfos ehniqe. he esls ae shon ih he help of gaphs and able. MHEMIL NLYSIS he nseady flo of an eleially onding inopessible isos flid pas hogh poos edi in a eial plae has been onsideed. he x axis is aken in he dieion of he oion and noal o i. ansese agnei field B of nifo sengh is applied on he flo. he agnei Reynolds nbe is onsideed o be sall so ha he inded agnei field is negleed. Iniially i has been onsideed ha he plae as ell as he flid is a he sae epeae. he speies onenaion in he flid is aken as. ie > he plae sas oing ih a eloiy in is on plane and epeae of he plae is aised o. he onenaion nea he plae is aised linealy ih espe o ie. he goening eqaions ae as nde: B g g * B D 3 Q k p 4 he iniial and bonday ondiions ae : fo eey. : a =. 5 as hee. he folloing non-diensional qaniies ae inoded o ansfo eqaions 3 and 4 ino diensionless fo:. gβ ρ σb M g ρ Q H k μ P ρ μ D S θ 3 * p p 3 6 he diension less flo odel beoes M 7 M 8 S 9 H P he oesponding bonday ondiions beoe θ : fo eey. θ : a =. θ as. Dopping bas in he aboe eqaions e ge M

3 M S P H he bonday ondiions ae : θ fo eey. : θ a =. 6 θ as. obining eqaions and 3 he odel beoes q q θ qa S H P M i Hee q=+i and a Finally he bonday ondiions beoe: : q θ fo all. : q θ a =. q θ as. he diensionless goening eqaions 7 o sbje o he bonday ondiions ae soled by he sal Laplae - ansfo ehniqe. he solion obained is as nde: S S 4 S ef[ ] e S i HP i HP i HP e i H e P e 4Hi a a HP i a HP q e 33 [ a P HP e 3 e e 4 a 4 a HP a HP i os a 4 P 5 e P HP a] [6e a i H 4a S a 4 e a 8 9 S 5 7 S ] [a S 6 e a S a a S S ] 3 5 he sybols inoled in he aboe eqaions ae enioned in he appendix. Skin Fiion he diensionless skin fiion a he plae = is obained by dq x i. y d he neial ales of τ x and τ y fo diffeen paaees ae gien in able-. 89

4 RESUL ND DISUSSIONS In his pesen pape e hae sdied he effes of hea absopion and peeabiliy of poos edi on he flo. he behaio of ohe paaees like agnei field Hall en and heal boyany is alos siila he ealie odel sdied by s [5]. he analyial esls ae shon gaphially in Figs o7. he neial ales of skinfiion τ x and τ y ae pesened in able-. Fo Figs and i is obseed ha piay and seonday eloiies inease ih peeabiliy paaee. his esl is de o he fa ha ineases in he ale of esls in eding he dag foe and hene ineasing he flid eloiy... M =. = P =.7 S =. = = H=5 = = Fig. s fo diffeen ales of.5 = M =. = P =.7S =. = = H=5 = Fig. s fo diffeen ales of.8.6 H= M =. = P =.7S =. = = =. = Fig. 3 s fo diffeen ales of H 9

5 ..8.6 H= 5.4. M =. = P =.7S =. = = =. = Fig. 4 s fo diffeen ales of H.3 H= 5 P=.7 = Fig. 5 θ s fo diffeen ales of H.3 P=.7 4. H= 5 = Fig. 6 θs fo diffeen ales of P Effe of hea absopion flid flo behaio is shon by Figs3 and 4. I is seen hee ha hen hea absopion paaee H ineases piay eloiy ineases hogho he bonday laye egion; b seonday eloiy deeases nea he sfae of he plae. his iplies ha hea absopion ends o aeleae piay eloiy heeas i eads seonday eloiy in he bonday laye egion. Fhe i is obseed ha he epeae deeases hen Pandl nbe and hea absopion paaee ae ineased Figs5 and 6. Hoee fo Fig. 7 i is obseed ha he epeae ineases ih ie. his is de he eason hea is anspoed o he syse oninosly. 9

6 .5.4 = P=.7H= Fig. 7 θs fo diffeen ales of able - Skin Fiion fo Diffeen Paaee M M P S H τ x τ y he ales of skin fiion ae gien in able. he ale ofτ x ineases ih he inease in and. B τ x deeases ih M P S H and. Siila effes ae obseed ih τ y. ONLUSION In his pape a heoeial analysis has been done o sdy effes of hea absopion and poosiy of he edi on nseady MHD flo pas a oing eial plae ih aiable all epeae and ass diffsion in he pesene of Hall en. I is obseed ha he piay eloiy ineases ih ineasing he ales of hea absopion and peeabiliy of he poos edi. he effe is siila on he seonday eloiy exep he ase of hea absopion. ha is he seonday eloiy deeases hen hea absopion paaee is ineased. Noenlae D Mass diffsion μ he oeffiien of isosiy Volei oeffiien of heal β ρ he flid densiy Mass ashof nbe expansion σ Eleial ondiiy heal ashof nbe Volei oeffiien of onenaion expansion β* μ he agnei peeabiliy k he heal ondiiy epeae of he flid he epeae of he flid Veloiy of he flid in x & y- dieion he peeabiliy paaee epeae of he plae M he agnei Field paaee he Hall en paaee he diensionless onenaion dieion Speies onenaion in he flid Diensionless eloiy in x & y- P Pandl nbe P Speifi hea a onsan pesse θ he diensionless epeae ie Speies onenaion a he plae g aiy aeleaion S Shid nbe he onenaion in he flid H hea absopion paaee he kineai isosiy 9

7 ppendix Hi ef P a 4 7 e 8 Hi ef P a 3 7 e 8 a H P 9 exp P 5 as 6 exp a 7 3 exp 4 S exp a exp a 8 9 exphi P exphi P a H P as 7 exp exp 3 P S a a H P HP a as 4 exp 5 exp P P P S S 6 S ef 7 ef a 8 ef a a H P a H P 9 ef ef P P 4 7 as a a S ef ef 3 ef as S P P ef 5 ef Hi 6 ef Hi a H P a H P ef 8 ef a ef P P 9 S S a 3 a a ef S S [ ] 3 ef 3 ef [ ] REFERENES [] H Dessie and Naikoi MHD Effes on Hea ansfe Oe Sehing Shee Ebedded in Poos Medi ih Vaiable Visosiy in Shas Engineeing Jonal Elseie [] SM Ibahi and Sneeha Hea Soe and heial Effes on MHD oneion Flo Ebedded in a Poos Medi ih Soe Visos and Joles Dissipaion in Shas Engineeing JonalElseie [3] Myheye JP Paoda and S Balagan heial Reaion on Unseady MHD oneie Hea and Mass ansfe Pas a Sei-Infinie Veial Peeable Moing Plae ih Hea bsopion Poedia Engineeing Elseie [4] US Rajp and aa a Effes of Hall en and heial Reaion on MHD Flo hogh Poos Medi Pas an Osillaing Inlined Plae ih Vaiable epeae and Mass Diffsion Eopean Jonal of danes in Engineeing and ehnology [5] US Rajp and aa a heial Reaion Effe on Unseady MHD Flo Pas an Iplsiely Saed Osillaing Inlined Plae ih Vaiable epeae and Mass Diffsion in he Pesene of Hall en pplied Reseah Jonal [6] VR Reddy J Reddy and R Lakshi Radiaion and Mass ansfe Effes on Nonlinea MHD Bonday Laye Flo of Liqid Meal Oe a Poos Sehing Sfae Ebedded in Poos Medi ih Hea eneaion WSES ansaions on Flid Mehanis

8 [7] S Seh R Shaa and SM Hssain Hall Effes on Unseady MHD Naal oneion Flo of a Hea bsobing Flid Pas an eleaed Moing Veial Plae ih Raped epeae Eiaes Jonal fo Engineeing Reseah [8] S Seh B bhaka and R Shaa Unseady Hydoagnei Naal oneion Flo of a Hea bsobing Flid Wihin a Roaing Veial hannel in Poos Medi ih Hall effes Jonal of pplied Flid Mehanis [9] S Shehad Haya and lsaedi hee-diensional MHD flo of asson Flid in Poos Medi ih Hea eneaion Jonal of pplied Flid Mehanis [] M Saad MD Hossain and MM la MHD Fee oneion and Mass ansfe Flo hogh a Veial Osillaoy Poos Plae ih Hall Ion-Slip ens and Hea Soe in a Roaing Syse Poedia Engineeing Elseie

Scholars Journal of Physics, Mathematics and Statistics

Scholars Journal of Physics, Mathematics and Statistics DOI:.76/sjps holas Jonal of Physis aheais and aisis h. J. Phys. ah. a. 7; :5- holas adei and ienifi Pblishes Pblishes n Inenaional Pblishe fo adei and ienifi Resoes IN 9-856 Pin IN 9-86 Online Effes of