Unsteady MHD flow of a radiating fluid over a moving heated porous plate with time-dependent suction

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Shavonne McKenzie
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1 AMERICAN JOURNAL OF SCIENIFIC AND INDUSRIAL RESEARC Scnc β h://.schb.g/ajsir ISSN: 5-69X Unsady MD fl f a adang fld v a vng had s la h -dndn scn C. Isal-Cy * C. Nag Dan f Mahacs Rvs Sa Unvsy f Scnc and chnlgy ac 5 Nga ABSRAC hs sdy sns h fl f an lccally cndcng and adang fld v a vng had s la n h snc f an ndcd agnc fld. By ang h adav ha fl n h dffnal f f h cally hnnss and sng a dndn snsdal ban h cld nn-lna aal dffnal qans gvnng h bl a slvd f a vlcy and agnc fld. h ffcs f adan aa R la vlcy scn aa A Gashf nb G and agnc aa M n h fl a snd and dscssd. S f h an sls a as flls: ncas n adan aa dcass h a ncas n agnc aa dcass h vlcy ncas hang G< csnds hang f h a ncass h vlcy.vscn has ffc n h fld vlcy and agnc fld b has lss ffc n h a. yds Unsady MD fl adang fld dndn scn had s la cal hnnss. INRODUCION s d. h sls shd ha ncasd scn dcs h fld s vlcy. h sdy f h fl f an lccally cndcng and adang fld v s da has bn nsvly sdd d s ns alcans. Sch alcans ncld MD s ndcn s MD gnas l lan ncla lans Gas bns acafs and sac vhcls ang any hs. Sndagla 97 a b cnsdd h f-cnvcn ffcs n h Oscllay fl as an nfn vcal s la h cnsan scn. Bsan 988 nvsgad h nsady hyd agnc f cnvcn fl h adav ha ansf n a ang fld. Bsan al 99 als ld a h ffc f adav ha ansf a hydagnc fl f a slghly afd bnay gas n a vcal channl. h sls shd ha ncas n adan aa dcs h a. aha al. 996 sdd h bl f MD f cnvcn fl f a adang gas as a s-nfn la sng slay vaabls. Rcnly sdd h nsady MD cnvcv ha ansf as a s-nfn vcal s vng la h vaabl scn hn h ndcd agnc fld and vscs dssan a n an n accn. fnd ha ncas agnc aa dcass h vlcy. Ms cnly Asf and Ah 6 sdd h hy analyss f nsady bnday lay fl adjacn a abl schng sfac n a Alaga 997 sdd h ansn fl f agnd lasa d hal bans. shd ha cndcn aas and vscsy lagly gvn h lasa fls nad by a ban h nnal dcay ds. Isal-Cy and ay ndd h al f Alaga 997 by h nclsn f adav ha ansf hch s sgnfcan n hgh ang as sch as n l cvy and ncla as anagn. h sls shd ha a sall s adan aas nflncd h vlcy f h ansn fl f h lasa fld n hch a sddn a dsbn s ndcd n h snc f cnsan agnc fld. v h slans ffcs f adan and -dndn scn n h snc f ndcd agnc fld hav n bn sdd. hf h sn s ad a clnng h al s f Isal-Cy and ay by h nclsn f -dndn scn as hs ll dn h aa f alcably f bls f hs na. Mahacal flan: W cnsd h dnsnal f cnvnn fl f an ncssbl and adang hyd agnc fld as an nfn s had vng vcal la n an cally hn nvnn. h as s an

2 A. J. Sc. Ind. Rs. : alng h la n h ad dcn and h as nal h la. Fg : hyscal dl A h la has a hch s hgh ngh na adav ha ansf. A cnsan agnc fld ο s anand n h - dcn and h la vs h a vlcy. Assng ha h la s lccally nncndcng b absbng. L and b h vlcy and agnc fld cnns n h - dcn scvly. Und h Bssnsq aan and ang n accn h ndcd agnc fld and cnvcv s h fl s gvnd by h fllng qans: du µ ν gβ d ρ h κ q ρc ρc σ c a h vlcy cnns ν µ ρ h nac vscsy σ c h lccal cndcvy κ hal cndcvy µ h vscsy C h scfc ha caacy a cnsan ss and ρ s a cnsan dnsy. Als g β µ U and q h cnsan agnc fld gavanal acclan cffcn f vl ansn h agnc ably fld a f sa vlcy and ha fl scvly. h bnday cndns a: n 5a U U as 5b h all a U h an f sa vlcy h fqncy f scllan f h fld and << s a sall sv aa. N assng ha h d s ansan.. d f lavly l dnsy f hch h cally hn gay gas s. Wh hs assn h adav ha fl n ngy qan n h s f Vncn and gg 965 s an as q σα 6 If h fnc a s n s ch dffn f any h a hn h fl hn a ψ 7 h ψ s a nn cnsan sall a ccn aa hs s can b nglcd. Usng h ayl ss ansn n 7 and sbsng n 6 qan hav 89

3 A. J. Sc. Ind. Rs. : q σα 8 Fllng Alaga al. 999 and Isal-Cy al. a h scn vlcy as - A 9 h s a cnsan and A << h h ngav sgn ndcas ha h scn s ads h la. Usng qans 7 8 and 9 h slng dnsnlss qans snng h fl a: M G d du A R A M A sbjc n as U In qans - and bnday cndns hav sd h fllng nn dnsnal vaabls: ν ν U U U ν ρ µ M ρ µ R 6 C ρ ν σα. g G C β κ ρν σ cν Magnc andl nb. h G M and R a aan nb Gashf nb agnc aa andl nb agnc andl nb and Radan aa scvly. h ahacal san f h bl s n cl and bds h slns f qans - sbjc cndn. Mhd f sln: Eqans - a hghly cld aal dffnal qans n h fl vaabls and snc << ass h fllng gla ban ansns: Sbsng qans 5 n qans and nglcng s n and hgh s ban h fllng sqnc f aans: O Eqans. G M 6 7 R sbjc as n 9 O Eqans G M A M A A R as n sbjc By slvng qan 8 fs and ng h sl n qans 6 7 and hn slvng h slng syss f lna qans ban h fllng slns f h fl vaabls: s

4 A. J. Sc. Ind. Rs. : [ ] 6 h h cnsans a b c d α α β β - and - a gvn n And. RESULS AND DISCUSSION W hav flad and slvd h bl f h MD fl f a adang lccally cndcng fld v a had abl d by ang faly alsc asyc aans. Usng h sfa Mahaca Wlfa 99 h ncally cd and gahcal sls a als snd h h bnday cndn s aad by a 6 hch s sffcnly lag f h a vlcy and agnc fld aach h f sa vals. Fg. shs ha an ncas n adan aa R dcs h a. hs sl s n cnsnanc h h sls f Bsan al 99 and Ras 999. Fg. vals ha h vlcy dcass as adan aa ncass. hs sls ag h h al sls f Alaga al. 998 Isal-Cy and ay and Isal- Cy al.. I s als bsvd n Fg. ha ncass n la vlcy ld ncas n h fld vlcy hch adly Cnvg a cnsan val a f sa. hs sl s n agn h ha f. a G 5 M A. 5 and dffn vals f Fg. : a fls f. adan aa R. R.5..5 Vlcy Fg.: Vlcy fls f.. 7. G 5 M. 5 f adan aa R. Vlcy A and dffn vals Fg.: Vlcy fls f.. 7. G 5 R M A. 5 and dffn vals f la vlcy. R.5..5 Fg.5 shs ha agnc fld dcass h ncasng adan aa. hs sl qally ags h h sl f Isal-Cy and ay. Fg 6 vals ha ncasd hang G< ans clng ncass h fld vlcy. hs sl als csnds hs f Sndalga 97 and Raj 998 hch vald ha hn h Gashf nb s ngavly dcasd hang h vlcy abslly ncass. Fnally Fg. 7 shs ha ncasd agnc aa dcass h fld vlcy hs als n accdanc h h sls f Sndalga 97a and b and Isal-Cy al.. 9

5 A. J. Sc. Ind. Rs. : Magnc Fld..5 R Fg. 5: Magnc fld fls f.. 7. G 5 M A. 5 and dffn vals f adan aa R. Vlcy.5 G Fg. 6: Vlcy fls f.. 7. R M A. 5 and dffn vals f Gashf nb. Vlcy.5 M Magnc Fld G Fg.8: Magnc fld fls f.. 7. R M A. 5 and dffn vals f Gashf nb. abl vald ha a. hn h scn vlcy aa A s ncasd f 5 h as an ncas f.7% n a hch dcays ads f sa. hs sl ags h h sl f Isal-Cy and ay. abl shs qanavly h vaans f vlcy h sc scn. I can b sn ha a. hn A as ncasd f 5 5% h as an ncas f.5% n h vlcy. nc ncasng scn vlcy aa ncass h vlcy. hs s n agn h h sl Asf and Ah 6. F abl ncd ha ncas n scn vlcy aa casd dcas n agnc fld na h la and ncas n agnc fld aay f h la. F abl s bsvd ha hn h scn vlcy aa ncasd f 5 h agnc fld dcasd by.6%; hl h agnc fld ncasd by.7% hn h scn vlcy aa ncasd by h sa agn. CONCLUSION W hf cncld ha h la vlcy has lss ffc n h fl hl h adan scn agnc and f-cnvcn aas affc h fl. Fh h scn vlcy aa has ffc n h vlcy and agnc fld han h a. Fg7: Vlcy fls f.. 7. G 5 R A. 5 and dffn vals f agnc aa M. 9

6 A. J. Sc. Ind. Rs. : abl : Vals f a f.. 7. G 5 M R and dffn vals f scn aa A. A5 A abl : Vals f fld Vlcy f.. 7. G 5 M R and dffn vals f scn aa A. Z A A

7 A. J. Sc. Ind. Rs. : abl : Vals f fld Magnc Fld f.. 7. G 5 M R and dffn vals f scn aa A. A A ACNOWLEDGMEN h ahs a hghly ndbd Ms. G. Isal Cy f ysng f h ansc. AENDIX a b M c R d 6 b α d ac β a β a a b λ λ R M R β β A bd ac b α db a c 7 d β G M 6 7 A R 5 a b [ ][ A G ] M b c d G a b c d G α λ α c d A M A A G 9 a b c d A A a b c d G a 9 b c d REFERENCES Alaga. D 997. ansn fl f a agnd lasa d hal ban Ashyscs and Sac Scnc 5:59-7. Alaga.D. ay G. and Abby.M 999. Radav and f cnvcv ffcs f a MD fl hgh a s d bn nfn 9

8 A. J. Sc. Ind. Rs. : aalll las h dndn scn Ashyscs and Sac Scnc 6: Al A. Mhd A. 6 y analyss f nsady bnday lay fl adjacn abl schng sfac n a s d Cncans n nnlna scnc and Ncal Slan - 6. Bsan A.R. and Adjng S. 988 Unsady hydagnc f-cnvcn fl h adav ha ansf n a ang fld Ashyscs and Sac Scnc :7 8. Bsan A. R. Alababa M. A. Ogl A 99 Radav ha ansf ydagnc fl f a slghly afld bnay gas n a vcal channl Ashyscs and Sac Scnc 89:-8. Isal-Cy C. ay G ansn fl f a adang hydagnc fld as an nfn vcal la AMSE Mdllng Masn and Slan B 7 :. Isal-Cy C. Ogl A and Ob-l V. B Inflnc f vscs dssan and adan n nsady MD f-cnvcn fl as an nfn had vcal la n a s d h -dndn scn Innanal Jnal f a and Mass ansf 6: 5-. Y.J Unsady MD Cnvcv ha ansf as a s-nfn vcal s vng la h vaabl scn Innanal Jnal f Engnng Scnc 8: Raj Chnch V. C 998 Oscllay fl as an nfn vcal s la an fl Bsana Jnal f chnlgy: Sndalga V.M 97 F Cnvcn ffcs n h scllay fl as an nfn vcal s la h cnsan scn I c. Ryal sc. Lndn A : 5 6. Sndalga V.M 97 F Cnvcn ffcs n h scllay fl as an nfn vcal s la h cnsan scn II c. Ryal sc. Lndn A :7 5. aha.s. Gla R.S.R. Sndalga V.M 996 Radan ffcs n MD f cnvcn fl f a adang gas as a s-nfn vcal la Innanal Jnal f Ncal Mhds n a Fld fl 6: Vcn W.G. gg G. 965 Indcn hyscal Gasdynacs N Y. Wlfa S 99 Mahaca: A Sys f Dng Mahacs by Cs Addsn Wsly blshng. 95

IOSR Journal of Mathematics (IOSR-JM) e-issn: , p-issn: x. Volume 10, Issue 3 Ver. I (May-Jun. 2014), PP

IOSR Journal of Mathematics (IOSR-JM) e-issn: , p-issn: x. Volume 10, Issue 3 Ver. I (May-Jun. 2014), PP IOSR Jnal f Mamacs IOSR-JM -ISS: 78-578 -ISS:9-765X. lm Iss. I Ma-Jn. PP 89-5 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa fld fl as an nfn cal mng s la Ha sc Mama a & M. naa Ksna Damn f Mamacs