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

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1 IOSR Jnal f Mamacs IOSR-JM -ISS: 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 ns llg f Scnc Osmana ns Hdabad 57 Anda Pads Inda. Absac: mcal slns f a and mass ansf b lamna fl f a nan scs lccall cndcng cmcall acng scs dssa fld n a cnnsl cal mabl sfac n snc f a a sc a fs d mgns cmcal acn and mass fl a d. la s assmd m a cnsan lc n dcn f fld fl. A nfm magnc fld acs ndcla s sfac c absbs fld a scn lc ang m. fld s cnsdd b a ga absbng mng b nn scang mdm and Rssland aman s sd dscb ada a fl n ng qan. blm s gnd b cld nn lna aal dffnal qans. Dmnsnlss qans f blm a bn sld nmcall b fn lmn md. ffcs f fl aams z. mal Gasf nmb slal Gasf nmb Hamann nmb Pmabl aam mal adan aam Pandl nmb Ha sc aam Scmd nmb and Ec nmb n lc ma and cncnan flds a nsgad g gas. Sn fcn Ra f a and mass ansf cffcns a dd dscssd nmcall and snd n abla fms. cmbnd a and mass ansf las an man l a dsgnng cmcal cssng qmn fman and dssn f fg dsbn f ma and ms agclal flds and gs f f s c damag d fzng and nnmnal lln. Kds: MHD F cncn scs dssan Ps mdm mal adan mcal acn and Fn lmn md. mncla: A A cnsan B Magnc fld cmnn alng ma f fld a nfn ncnan f fld as ncnan f fld na la Scfc a a cnsan ss ncnan f fld fa aa f G mal Gas f nmb fld fm la Gc slalgasf nmb g ncnan f fld a nfn Acclan f ga m n cdna ssm K mabl f mdm m n dmnsnlss c dnas K mabl aam M lc cmnn n dcn Hamann nmb Dmnsnlss lc cmnn n P Pandl nmb dcn Sc Scmd nmb ssl nmb Ec Ec nmb S Sd nmb S Ha sc aam R R mal adan aam Rnld s nmb Pla lc K mcal acn f fs d a cnsan mcal acn aam dna ssm D mcal mlcla dffs Dmnsn lsscdnas ma f fld na la Rfnc lc ma f fld fa aa f fld fm la Scn lc 89 Pag

2 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa G smbls: ffcn f lm ansn f a ansf ffcn f lm ansn f mass ansf mal cndc f fld Elccal cndc f fld Knmac scs n n dmnsnal ma Dns f fld Angl Pas angl A s cnsan Sn fcn I. Indcn: mbnd a and mass ansf blms cmcal acn a f manc n man csss and a f cd a cnsdabl amn f ann n cn as. In csss sc as dng aan a sfac f a a bd ng ansf n a clng and fl n a ds cl a and mass ansf cc smlansl. Pssbl alcans f s f fl can b fnd n man ndss. F aml n nds amng mds f gnang lcc s n n c lccal ng s acd dcl fm a mng cndcng fld. W a aclal nsd n cass n c dffsn and cmcal acn cc a gl sam sd. Wn dffsn s mc fas an cmcal acn n nl cmcal facs nflnc cmcal acn a; n dffsn s n mc fas an acn dffsn and ncs nac dc dffn ffcs. sd f a gnan absn ffcs n mng flds s man n f sal scal blms sc as flds ndgng mc ndmc cmcal acn. D fas g f lcnc cnlg ffc clng f lcnc qmn as bcm aand and clng f lcnc qmn angs fm nddal ansss man fam cms and fm ng sls ln sc bads and mal dffsn ffc as bn lzd f ss saan n m bn gass lg mlcla g dgn and lm and mdm mlcla g. Effcs f aabl s and Hall cn n sad MHD lamna cnc fld fl d a s ang ds as sdd b Abd Saa al. []. Anal D and Wlfd Saml Ra [] nsgad ffcs f m dffsn n nsad dmagnc f cncn fl f a scs ncmssbl lccall cndcng fld a and mass ansf as a mng s cal la f nfn lng m dndn scn n snc f a sc n a sl fl gm. Sl fl cndns f lc and m n ma a an n accn n bnda cndns. A nfm anss magnc fld s ald. f sam lc s cnsdd fll an nnall small ban la. gnng qans f blm sbc sl fl bnda cndns a sld analcall sng ban md.dlal Pal al. []sdd Pban analss f nsad magnddnamc cnc a and mass ansf n a bnda la sl fl as a cal mabl la mal adan and cmcal acn. Ibam al. [] sdd ffcs f cmcal acn and adan absn n ansn dmagnc naal cncn fl all ansan and a sc. Analcal slns f a and mass ansf b lamna fl f a nan scs lccall cndcng and a gnan/ absbng fld n a cnnsl cal mabl sfac n snc f a adan a fs d mgns cmcal acn and mass fl a d b Ksaaa al. [5]. la s assmd m a cnsan lc n dcn f fld fl. A nfm magnc fld acs ndcla s sfac c absbs fld a scn lc ang m. dmnsnlss gnng qans f s nsgan a sld analcall sng m amnc and nn amnc fncns. Fn dffnc sln f mgns fs d cmcal acn n nsad fl as an mlsl sad sm nfn cal la aabl ma and massdffsn n snc f mal adan a bn sdd b Lganaan al. [6]. fld cnsdd s a ga absbng mng adan b a nn scang mdm. dmnsnlss gnng qans a sld b an ffcn m acca and ncndnall sabl and fas cngng mlc scm. Mans al.[7] nsgas nflnc f cmcal acn and scs dssan n magnddnamc naal cncn fl. An ama nmcal sln f fl blm as bn band b slng gnng qans sng sng cnq a f d Rng Ka ngan scm. F dffn cass f fls a bn sdd naml an smal sfac a nfm a fl sfac a lan lm and fl gnad fm a znal ln ng sc a cal adabac sfac. Dbl Dffs ncn Radan nacn n nsad MHD fl a cal mng s la a gnan and S ffcs as sdd b Mamd [8]. F cncn fl f a scs ncmssbl fl as an scllang nfn cal la aabl ma and mass dffsn as bn sdd b Mcmaasam and aalasm [9]. In s sac a dmnsnlss gnng qans a acld sng Lalac ansfm cnq and ma and 9 Pag

3 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa scs cncnan na la a assmd b lnal ang sc m. Mcmaasam and Mnassndaam [] nsgad cal sd f cmcal acn ffcs n cal scllang la aabl ma and mass dffsn. as bn a nd ns n sdng magnddnamc MHD fl and a ansf n s and nn-s mda d ffc f magnc flds n bnda la fl cnl and n fmanc f man ssms sng lccall cndcng flds. Ma and Snas [] sdd fll dld MHD fl f a mcla and scs fld n a cal s sac sng HAM.nsad MHD f nc fl f a cmssbl fld as a mng cal la n snc f Rada a ansf as sdd b Ogl al. []. sd f a gnan absn ffcs n mng flds s man n f sal scal blms sc as flds ndgng mc ndmc cmcal acns. Pssbl a gnan ffcs ma al ma dsbn and cnsqnl acl dsn a n ncla acs lcc cs and smcndc afs. Pal and Klan [] sdd ffcs f cmcal acn n f cnc fl f a la fld g s mdm n snc f nnal a gnan. Radan ffcs n an nsad MHD cnc a and mass ansf fl as a sm nfn cal mabl mng la mbddd n a s mdm as sdd b Ramacanda Pasad al. []. Ramana Rdd al. [5] a sdd mass ansf and adan ffcs f nsad MHD f cnc fld fl mbddd n s mdm a gnan/absn. In s f all s sds nsad MHD f cncn a and mass ansf fl as a mng sm nfn ld s la aabl ma n snc f cmcal acn as cd a ll ann. MHD bnda la fl a ad scng s aabl scs as sdd b Samad al. [6]. Saanaaana and naaamana [7] sdd Hall cn ffc n magnddnamcs f cncn fl as a sm nfn cal s la mass ansf. Sdd [8] sdd ffcs f cmcal acn mss and aabl scs n sad dmagnc fl a and mass ansf a fla la n snc f a gnan/absn. Sama and Sng [9] nsgas fl f a scs ncmssbl lccall cndcng fld alng a s cal smal nn cndcng la aabl scn and nnall dcang a gnan n snc f anss magnc fld. gnng qans f mn and ng a ansfmd n dna dffnal qans sng m dndn smla aam. dna dffnal qans a n sld nmcall sng Rng Ka md alng sng cnq. Effcs f cmcal acn and adan absn n f cncn fl g s mdm aabl scn n snc f nfm magnc fld sdd b Sd Bab and Saanaaana []. In s f all s sds nsad MHD f cncn a and mass ansf f a a gnang fld adan absn as cd ll ann. nasal al. [] dal f cnnn fl alng a cal all n a s mdm magnc fld s cnsdd. znal alls a adabac. magnc fld ald ndcla cangla cannl. fl blm as dscbd b mans f aablc aal dffnal qans and slns a band b an mlc fn dffnc cnq. Zc [] cnsdd ansn magnddnamc naal cncn bnda la fl scn scs dssan and mal adan ffcs. ffc f adan n MHD fl and a ansf blm as bcm m man ndsall. A g ang ma adan ffc can b q sgnfcan. Man csss n ngnng aas cc a g ma and nldg f adan a ansf bcms man f dsgn f labl qmn ncla lans gas bns and as lsn dcs acaf mssls salls and sac cls. Basd n s alcans gl al. [] sd a n call n lm fld ds n absb s n md adan b fld ds absb adan md b bndas. Sa and Hamd [] nsgad nsad f cncn nacn mal adan n a bnda la fl as a cal s la. aal [5] sdd fl f a sad scs fld and a ansf caacsc n a s mdm b cnsdng dffn ang csss. Hssan and aa [6] a cnsdd adan ffc n md cncn bnda la fl f an call dns scs ncmssbl fld alng a cal la nfm sfac ma. Ras [7] nsga sad fl f a scs fld g a s mdm bndd b a s la sbcd a cnsan scn lc b snc f mal adan. Mand [8] amnd ansn f cncn nacn mal adan f an absbng mng fld alng mng cal mabl la. ffc f cmcal acn and adan absn n nsad MHD f cncn fl as a sm nfn cal mabl mng la a sc and scn as bn sdd b Ibam al. [9]. Rcnl Ba [] snd an analss n MHD f cncn and mass ansf adacn mng cal la f mcla fld n a ang fam f fnc n snc f a gnan/ absn and a cmcal acn. 9 Pag

4 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa Hnc man bc f sn nsgan s sd ffcs f adan absn mass dffsn cmcal acn and a sc aam f a gnang fld as a cal s la sbcd aabl scn. I s assmd a la s mbddd n a nfm s mdm and ms a cnsan lc n fl dcn n snc f a anss magnc fld. I s als assmd a ma c a smsd an nnall ang m. qans f cnn lna mmnm ng and dffsn c gn fl fld a sld nmcall b sng fn lmn md c s m cnmcal fm cmanal n and sls band a gd agmn sls f and sls band a gd agmn sls f Ksaaa al. [5] n sm scal cass. ba f lc ma cncnan sn fcn ssl nmb and Sd nmb as bn dscssd f aans n gnng aams. II. Mamacal fmlan: W cnsd nsaddmnsnal fl f a lamna scs lccall cndcng cmcall acng scs dssa and aabsbng fld as a smnfn cal mabl mng la mbddd n a nfm s mdm and sbcd a nfm anss magnc fld n snc f mal and cncnan banc ffcs. W mad fllng assmns.. In asan cdna ssm l as s an b alng la and as nmal la. Snc la s cnsdd nfn n dcn nc all scal qans ll b ndndn f dcn.. all s manand a cnsan ma and cncnan g an ambn ma and cncnan scl.. A nfm magnc fld f magnd B s ald nmal la. anss ald magnc fld and magnc Rnld s nmb a assmd b small s a ndcd magnc fld s nglgbl.. A nfm magnc fld acs ndcla s sfac c absbs fld a scn lc ang m. 5. la s assmd m a cnsan lc n dcn f fld fl. 6. fld s a assmd b cnsan c a nflnc f dns aan ma as bn cnsdd nl n bd fc m. 7. cmcal acns a ang lac n fl and all mscal s a assmd b cnsan f lna mmnm qan c s amad accdng Bssnsq s aman. 8. D sm nfn lan sfac assmn fl aabls a fncns f and m nl. 9. I s assmd a s n ald lag c mls absnc f an lcc fld. fld as cnsan nmac scs and cnsan mal cndc and Bssnsq s aman a bn add f fl. 9 Pag

5 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa 9 Pag Fg : Pscal mdl and cdna ssm f blm. fld s cnsdd b ga absbng mng adan b nn scang mdm and Rssland s aman s sd dscb ada a fl. I s cnsdd b nglgbl n dcn as cmad n dcn.. A m la s gn an mls mn n dcn f fl.. alng as agans ga cnsan lc.in addn s assmd a ma and cncnan a all as ll as scn lc a nnall ang m.. cncnan f dffsng scs s small n cmasn cmcal scs cncnan f scs fa fm all s nfnsmall small and nc S and Df ffcs a nglcd. nd s assmns qans a dscb scal san a gn b Eqan f nn: Mmnm Eqan: K B g g Eng Eqan: q S Scs Dffsn Eqan: K D. d and f ms n g and sd f qan dn mal and cncnan banc ffcs scl. Als las m n g and sd f ng qan sns ada a fl m. W fllng nal and bnda cndns: as a all f n n : : 5

6 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa 9 Pag Fm qan s cla a scn lc a la s a cnsan a fncn f m. Hnc scn lc nmal la s assmd n fm n A 6 W A s a al s cnsan and A s small als lss an n and s scal f scn lc c s nn z s cnsan. nga sgn ndcas a scn s ads la. ada a fl m s smlfd b mang s f Rssland aman [] as q 7 H s Sfan Blzmann cnsan and s man absn cffcn. I s assmd a ma dffncs n fl a sffcnl small s a can b ssd as a lna fncn f af sng al s ss and ab f sam ma and nglcng g d ms. s sls n fllng aman: 8 sng qans 7 and 8 n las m f qan ban: 6 q 9 Indcng 9 n qan ng qan bcms: 6 S In d gnng qans and bnda cndns n dmnsnlss fm fllng nn dmnsnal qans a ndcd. Ec R K K K Q S B M D Sc g Gc g G n P Sbsng ab nn dmnsnal qans n qans and n s qans a dcng fllng dmnsnal fm: Gc G K M A n P Ec S R A n Sc A n csndng nal and bnda cndns n dmnsnlss fm a: as a all f n n : : 5

7 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa 95 Pag All scal aams a dfnd n nmncla. I s n man calcla scal qans f ma ns c a lcal all sa sss lcal sfac a and mass fl. Gn lc fld n bnda la can n calcla lcal all sa sss.. sn fcn s gn b and n dmnsnlss fm ban nng ma fld s nsng sd ffc f f cncn and adan n a f a ansf. s s gn b c s n n dmnsnlss fm as 6 dmnsnlss lcal sfac a fl.. ssl nmb s band as n R 7 dfnn f lcal mass fl and lcal Sd nmb a scl gn b l f s qans n can S n R S S 8 W R s Rnld s nmb. III. Md f Sln: B alng Galn fn lmn md f qan lmn s: d P Y B 9 W n B A K M Y Gc G P Ingang fs m n qan 9 b as n bans d P Y B = glcng fs m n qan n gs: d P Y B L b lna cs aman sln lmn and a bass fncns. On bans: d B d d d P d Y Smlfng g

8 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa B Y P l 6 l 6 W m and d dns dffnan.. and m scl. Assmblng lmn qans f cnsc lmns and fllng s band: B Y P l 6 l 6 csndng nd z fm qan dffnc scms l s: B Y P 6 6 Alng azdal l fllng ssm f qans n an clsn md a band: n n n n n n A A A A A5 A6 P fm qans and fllng qans a band: n n n n n n B B B B B5 B6 Q n n n n n n D D D D D5 D6 5 W A Y B 6 A 8 Y A A Y B 6 Y B 6 A5 8 Y A6 Y B 6 P BP SP 6 B 8P SP Z P BP SP 6 B P BP SP 6Z 8P SP 6 B6 P BP SP 6Z Sc B Sc Sc 6 D 8 Sc Sc Sc B Sc Sc 6 D Sc B Sc Sc 6 8 Sc Sc D Sc B Sc Sc 6 B Z B Z B5 Z D D D 5 6 P P G Gc Q QP Ec Z R H and a ms szs alng dcn and m dcn scl. Ind fs sac and fs m. In qans and 5 ang n and sng bnda cndns 5 n fllng ssm f qans a band: A X B ; n 6 W A s a macs f d n and X B s a clmn macs ang n cmnns. slns f ab ssm f qans a band b sng mas algm f lc ma and cncnan. Als nmcal slns f s qans a band b gamm. In d cngnc and sabl f Galn fn lmn md sam gamm as n small als f and and n sgnfcan cang as bsd n als f and. Hnc Galn fn lmn md s sabl and cngn. 96 Pag

9 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa I. Rsls and Dscssn: fmlan f ffcs f cmcal acn a sc and mal adan n MHD cnc fl and mass ansf f an ncmssbl scs fld alng a sm nfn cal s mng la n a s mdm as bn fmd n cdng scns. s nabls s ca nmcal calclans f dsbn f lc ma and cncnan acss bnda la f as als f aams. In sn sd csn A.5. n..5. and l G Gc P Sc M K S Ec R and and n fg lgnds..75 a ad a ang c a lsd.5 G = Fg. lc fls f dffn als f mal Gasf nmb G F cas f dffnals f mal Gasf nmb G lc fls n bnda la a sn n fg. As cd s bsd a an ncas n G lads dcas n als flc d nancmn n banc fc. H s als f G csnd clng f sfac. In addn c s a a als f lcdcass adl na all f s la as Gasf nmb ncass and ndcas f sam lc. Fg sns cal lc fls n bnda la f as als f slal Gasf nmb Gc l all aams a a sm fd als. lc dsbn aans a dsnc mamm al n cn f la sfac and n dcas l aac f sam al. As cd fld lc ncass and a al m dsnc d ncas n cncnan banc ffcs snd bgc. s s dn n ncas n al f as ncassgc n fg..5 Gc =.... Fg. lc fls f dffn als f slal Gasf nmb Gc 97 Pag

10 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa.75.5 P = Fg. lc fls f dffn als f Pandl nmb P Fg and 5 llsa lc and ma fls f dffn als f Pandl nmb P. nmcal sls s a ffcf ncasng als f Pandl nmb sl n an dcasng lc. Fm fg 5 ascd nmcal sls s a an ncas n Pandl nmb sls a dcas f mal bnda la and n gnal l aag ma n bndala. asn s a small als f P a qaln ncas n malcndc f fld and f a s abl dffs aa fm ad sfacm adl f g als f P. Hnc n cas f small Pandl nmb malbnda la s c and a f a ansf s dcd. θ.5 P = Fg 5. ma fls f dffn als f P Sc = Fg 6. lc fls f dffn als f Scmd nmb Sc Fg 6 and 7 dsla ffcs f Scmd nmb Sc n lc and cncnan fls scl. As Scmd nmb ncass cncnan dcass. s cass cncnan banc ffcs dcass ldng a dcn n fld lc. dcns and lc and cncnan fls a accmand b smlans dcns n lc and cncnan bnda las. s bas a clal sn n fgs 6 and Pag

11 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa.5 Sc = Fg 7. ncnan fls f dffn als f Scmd nmb Sc M =.... Fg 8. lc fls f dffn als f Hamann nmb M ffc f Hamann nmb n lc fls n bnda la s dcd n fg 8. Fm s fg s sn a lc sas fm mnmm al a sfac and ncas ll aans a al and n sas dcasng nl acs mnmm al a nd f bnda la f all als f Hamann nmb. I s nsng n a ffc f magnc fld s dcas al f lc fls g bnda la. ffc f magnc fld s m mnn a n f a al.. a al dascall dcass ncass n al f magnc fld bcas snc f magnc fld n an lccall cndcng fld ndc a fc calld Lnz fc c acs agans fl f magnc fld s ald n nmal dcn as n sn blm. s f ssng fc sls dn fld lc as sn n s fg. Fg 9 Ss lc fls f dffn als f mabl aam K clal as K ncass a als f lc nds ncas. ffc f ncasng al f a sc aam S s dcas bnda la as sn n fg c s as cd d fac a n a s absbd banc fc dcass c ads fl a and b gng s dcas n lc fls K =.... Fg 9. lc fls f dffn als f Pmabl aam K 99 Pag

12 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa S =.... Fg. lc fls f dffn als f Ha sc aam S Fg as bn ld dc aan f ma fls agans f dffn als f a sc aam S b fng scal aams. Fm s ga bs a ma dcas ncas n a sc aam S bcas n a s absbd banc fc dcass ma fls. Fgs and dsla ffcs f cmcal acn aam n lc and cncnan fls scl. As cd snc f cmcal acn sgnfcanl affcs cncnan fls as ll as lc fls. I sld b mnnd a sdd cas s f a dsc cmcal acn. In fac as cmcal acn ncass cnsdabl dcn n lc fls s dcd and snc f a ndcas a mamm al f lc ccs n bd f fld cls sfac b n a sfac. Als an ncas n cmcal acn aam cncnan dcass. I s dn a ncas n cmcal acn sgnfcanl als cncnan bnda la cnss b ds n al mmnm bnda las. θ.5 S =.... Fg. ma fls f dffn als f Ha sc aam S Fg llsas aan f lc dsbn acss bnda la f sal als f la mng lc n dcn f fld fl. Alg a dffn nal la mng lcs lc dcas cnsan als f gn maal aams. nflnc f scs dssan aam.. Ec nmb Ec n lc and ma a sn n fgs 5 and 6 scl. Ec nmb Ec sss lans bn nc ng n fl and nal. I mbds cnsn f nc ng n nnal ng b dn agans scs fld ssss. Ga scs dssa a cass a s n ma as ll as lc. s ba s dn fm fgs 5 and 6. Pag

13 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa = Fg. lc fls f dffn als f mcal acn aam.5 = Fg. ncnan fls f dffn als f mcal acn aam Fgs 7 and 8 llsa aan f lc and ma f as als f adan absn aam R. I s mmdal aan a lc as ll as ma clal dcas as R ss fm. lc acs a mamm n cls m all and n falls gadall z a dg f bnda la. Inscn f fg 8 ss a f a small al f R R ma fl cnnsl dcass fm all l f g als f R ncass aanng a mamm na la bnda and n dcass. As sc s a ncabl ma s R snc cnsdabl mal ng s mad a snc f a mal adan sc fld casng an lan n mas na all = Fg. lc fls f dffn als f Pla lc Pag

14 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa.5 Ec =.... Fg 5. lc fls f dffn als f Ec nmb Ec θ.5 Ec =.... Fg 6. ma fls f dffn als f Ec nmb Ec R =.... Fg 7. lc fls f dffn als f mal adan aam R θ.5 R =.... Fg 8. ma fls f dffn als f mal adan aam R abl : Sn fcn sls f als f G Gc P Sc M K and G Gc P Sc M K S R Ec Pag

15 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa abl : Ra f a ansf als f dffn als f P and P S R Ec abl : Ra f mass ansf S als f dffn als f Sc and Sc S abl : masn f sn Sn fcn sls Sn fcn sls band b Ksaaa al. [5] f dffn als f G Gc P Sc M G Gc P Sc M K S K S and fls f sn fcn d lc nd ffcs f mal Gasf nmb slal Gasf nmb Pandl nmb Scmd nmb Hamann nmb Pmabl aamha sc aam mal adan aam and mcal acn aam a snd n abl scl. W bs fm s abl sn fcn ss nd ffcs f mal Gasf nmb slal Gasf nmb Ec nmb and Pmabl aam. And falls nd ffcs f Pandl nmb Scmd nmb Hamann nmb Ha sc aam mal adan aam and mcal acn aam. fls f ssl nmb d ma fl nd ffc f Pandl nmb Ec nmb mal adan aam and Ha sc aam a snd n abl. Fm s abl bs a ssl nmb d ma fls falls nd ffcs f Pandl nmb mal adan aam and Ha sc aam and ss nd ffc f Ec nmb. fls f Sd nmb S d cncnan fls nd ffc f Scmd nmb and mcal acn aam a snd n abl. W s fm s abl Sd nmb d cncnan fls dcass nd ffcs f Scmd nmb and mcal acn aam. In d ascan accac f nmcal sls sn sls a cmad Pag

16 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa s sls f Ksaaa al. [5] f G = Gc =. P =.7 Sc =. M =. K =. S =. and =. n abl. a fnd b n an clln agmn.. nclsns: gnng qans f a and mass ansf b lamna fl f a nan scs lccall cndcng cmcall acng scs dssa fld n a cnnsl cal mabl sfac n snc f a a sc a fs d mgns cmcal acn and mass fl a d. slng aal dffnal qans ansfmd n a s f aal dffnal qans sld b sng fn lmn md. mcal alans f nmcal sls fmd and gacal sls band llsa dals f fl and a and mass ansf caacscs and dndnc n sm scal aams.. An ncasng Hamann nmb Pandl nmb Scmd nmb Ha sc aam mal adan aam and mcal acn aam dcass lc f fl fld a all ns.. An ncasng mal Gasf nmb slal Gasf nmb Pmabl aam Ec nmb and Pla lc s ncas lc f fl fld a all ns.. A gng Pandl nmb mal adan aam and Ha absn aam dcass ma f fl fld a all ns.. Scmd nmb and mcal acn aam dcass cncnan f fl fld a all ns. 5. An ncasng Hamann nmb Pandl nmb Scmd nmb Ha sc aam mal adan aam and mcal acn aam dcass sn fcn cffcn. 6. An ncasng mal Gasf nmb slal Gasf nmb Pmabl aam Ec nmb and Pla lc s ncas sn fcn cffcn. 7. A gng Pandl nmb mal adan aam and Ha absn aam dcass ssl nmb f fl fld a all ns. 8. Scmd nmb and mcal acn aam dcass Sd nmb f fl fld a all ns. 9. On cmang sn fcn sls sn fcn sls f Ksaaa al. [5] can b sn a ag ll. Rfncs: [] Abd Saa Md. and K. Abdl Malq 5. Effcs f aabl s and Hall cn n sad MHD lamna cnc fld fl d a s ang ds In. Jnal f Ha and Mass ansf l [] Anal D S. P. and J. Wlfd Saml Ra. m dffsn ffcs n nsad dmagnc f cncn fl a and mass ansf as a mng cal la m dndn scn and a sc n a sl fl gmin. J. f Al. Ma. and Mc. l [] Dlal Pal and Bablal alda. Pban analss f nsad magnd dnamc cnc a and mass ansf n a bnda la sl fl as a cal mabl la mal adan and cmcal acn mmncans n nlna Scnc and mcal Smlan.8 8. [] Ibam F. S. A. M. Ela and A. A. Ba 8. Effc f cmcal acn and adan absn n nsad MHD f cncn fl as a sm nfn cal mabl mng la a sc and scn mmncans nlna Scnc mcal Smlan l [5] Ksaaa D.. P.. Saanaaana and S. naaamana. Effcs f cmcal acn and adan absn n an nsad MHD cnc a and mass ansf fl as a sm nfn cal mabl mng la mbddd n a s mdm a sc and scnin. J. f Al. Ma. and Mc. l [6] Lganaan P. Klandal and R. Mcmaasam 8. Fs d cmcal acn n mng sm nfn cal la n snc f call n ga gasin. J. f Al. Ma. and Mc. l [7] Mans M. A.. F. El Anssa and A. M. Al 8. Effc f cmcal acn and scs dssan n MHD naal cncn fls saad n s mda scn ncn In. J. f Al. Ma. and Mc. l [8] Mamad 9. Dbl dffs cncn adan nacn n nsad MHD fl a cal mng s la a gnan and S ffc as sdd Ald Mamacal Scncs l [9] Mcmaasam R. and A. aalasm 8. Effcs f a and mass ansf n fl as an Oscllang cal la aabl ma In. J. f Al. Ma. and Mc. l [] Mcmaasam R. and S. Mnassndaam 6. cal sd f cmcal acn ffcs n cal scllang la aabl ma. Al. Mc. l [] Ma R. and S. Snas. Fll dld MHD fl f a mcla and scs fld n a cal s sac sng HAM In. J. Al. Mamacs and Mcancs l [] Ogl A. A. R.. Ama. and I.. Mbldg 7. nsad MHD f cnc fl f a cmssbl fld as a mng cal la n snc f ada a ansf In. Jnal f Ha and Mass ansf l [] Pal P. M. and P. S. Klan 8. Effcs f cmcal acn n f cnc fl f a la fld g a s mdm n snc f nnal a gnan In. J. m. Sc.l.. 5. Pag

17 mal adan ffc n an nsad MHD f cnc cmcall acng scs dssa [] Ramacanda Pasad. and. Basa Rdd 8. Radan ffcs n an nsad MHD cnc a and mass ansf fl as a sm nfn cal mabl mng la mbddd n a s mdm Jnals f Eng Ha and mass ansfl [5] Ramana Rdd G.... Ramana M and. Basa Rdd. Mass ansf and adan ffcs f nsad MHD f cnc fld fl mbddd n s mdm a gnan/absn Jnal f Ald Mamacs and Fld Mcancs l [6] Samad S. A. G.. La and S. Madaa 5. MHD bnda la fl a ad scng s aabl scs In. Jnal f Ha and Mass ansf l [7] Saanaaana P.. and S. naaamana 7. Hall cn ffc n magnd dnamcs fcncn fl as a sm nfn cal s la mass ansf. S..ns P.D ss. [8] Sdd M. A. A. A. Das and M. S. Abdlmgd 7. Effcs f cmcal acn and aabl scs n dmagnc md cncn a and mass ansf f Hmnz fl g s mda adan mmncans n nlna Scnc and mcal Smlan l [9] Sama P. R. and G. Sng 8.nsad MHD f cnc fl and a ansf alng a cal s la aabl scn and nnal a gnanin. J. f Al. Ma. and Mc. l [] Sd Bab M. and P.. Saanaaana 9. Effcs f cmcal acn and adan absn n f cncn fl g s mdm aabl scn n snc f nfm magnc fld J. P. Jnal f Ha and mass ansf l.. 9. [] nasal S. K.. Sanaaana Ra and B. Rambal Rdd. Fn dffnc analss n cnc a ansf fl g a s mdm n a cal cannl magnc fldin. J. f Al. Ma. and Mc. l [] Zc J. 7. smlan md ald adan and scs dssanffcs n MHD nsad f cncn cal s laald Mamacal Mdllng l [] gl A.. ncn W. E. and Glls S. E Dffnal aman f adan n a nn-ga gas na qlbm A. I. A. A. J.l [] Abds Saa M. D. Kalm M. D. and Hamd 996. nsad f cncn nacn mal adan n a bnda la fl as a cal s la J. Ma. Ps. Sc. l [5] aal K. 99. Fl and a ansf n a saad s mdm ZAMM l [6] Hssan M. A. and aa H. S Radan ffc n md cncn alng a cal la nfm sfac ma Ha Mass ansf l.. 8. [7] Ras A Radan and f cncn fl g a s mdm In. mmn. Ha Mass ansfl [8] Mand O. D. 5. F cncn fl mal adan and mass ansf as a mng cal s la In. mmn. Ha Mass ansf l.. 9. [9] Ibam F. S. Ela A. M. and Ba A. A. 8. Effc f cmcal acn and adan absn n nsad MHD md cncn fl as a smnfn cal mabl mng la a sc and scn mmn. nlna Sc. m. Sml. l [] Ba A. A.. Effcs f cmcal acn n MHD f cncn and mass ansf fl f a mcla fld sclla la lc and cnsan a sc n a ang fam f fnc mmn. nlna Sc. m. Sml. l [] Bs M. Q. mal ada ansf & s Jn Wl & Sns Pag