Received 14 November 2015; accepted 27 December 2015; published 30 December 2015

Transcription

1 Jonal of Applied Mateatis and Pysis, 15, 3, Pblised Online Deebe 15 in ires ttp://sipog/jonal/jap ttp://ddoiog/1436/jap eial oltion of MHD Convetion and Mass Tansfe Flo of Visos Inopessible Flid abot an Inlined Plate it Hall Cent and Constant Heat Fl Moaad Waidzzaan 1, Rn Bisas, Md Eaqb Ali 3, Md akaoat Kan 4, Ifsana Kai 4 1 Mateatis Disipline, Klna Univesity, Klna, Banglades Mateatis Open ool, Banglades Open Univesity, azip, Banglades 3 Depatent of Civil Engineeing, onagaon Univesity, Daka, Banglades 4 Disipline of Ceial Engineeing, Te Univesity of eastle, Callagan, Astalia Reeived 14 ovebe 15; aepted 7 Deebe 15; pblised 3 Deebe 15 Copyigt 15 by atos and ientifi Resea Pblising In Tis ok is liensed nde te Ceative Coons Attibtion Intenational Liense (CC BY) ttp://eativeoonsog/lienses/by/4/ Abstat Te pesent neially stdy investigates te inflene of te Hall ent and onstant eat fl on te Magneto ydodynai (MHD) natal onvetion bonday laye visos inopessible flid flo in te anifestation of tansvese agneti field nea an inlined vetial peeable flat plate It is assed tat te inded agneti field is negligible opaed it te iposed agneti field Te govening bonday laye eqations ave been tansfeed into non-siila odel by ipleenting siilaity appoaes Te pysial diensionless paaete as been set p into te odel as Pandtl nbe, Eket nbe, Magneti paaete, idt nbe, loal asof nbe and loal odified asof nbe Te neial etod of atsei- iget sooting iteation teniqe togete it Rnge-Ktta si ode iteation see as been sed to solve te syste of govening non-siila eqations Te pysial effets of te vaios paaetes on diensionless piay veloity pofile, seonday veloity pofile, and tepeate and onentation pofile ae disssed gapially Moeove, te loal skin fition oeffiient, te loal sselt nbe and eood nbe ae son in tabla fo fo vaios vales of te paaetes Keyods MHD, Heat and Mass Tansfe, Hall Cent, Inlined Plate, Constant Heat Fl Ho to ite tis pape: Waidzzaan, M, Bisas, R, Ali, MdE, Kan, Md and Kai, I (15) eial oltion of MHD Convetion and Mass Tansfe Flo of Visos Inopessible Flid abot an Inlined Plate it Hall Cent and Constant Heat Fl Jonal of Applied Mateatis and Pysis, 3, ttp://ddoiog/1436/jap

2 M Waidzzaan et al 1 Intodtion Hall ent as ipotant ontibtion in te stdy of MHD visos flos It as any appliations in pobles of te Hall aeleatos as ell as in te fligt MHD Te ent tend is on te appliation of MHD toads a stong agneti field and a lo density of gas Fo tis eason, te Hall ent and ion slip beoe ipotant Hydodynai flo of a visos liqid tog a staigt annel in pesene of Hall Effet is eained by ato [1], Yaanisi [], and ean and tton [3] Te Hall ent effets on te bonday laye flo past a sei-infinite plate ae stdied by Katagii [4] Fee onvetion flo of a ondting flid peeated by a tansvese agneti field in te pesene of te Hall effets and nifo agneti field is analyzed by Pop and Watanabe [5] Aboeldaab and Elbabay [6] stdied te effet of te Hall ent on te MHD fee onvetion flo in te pesene of foeign speies ove a vetial sfae, ee te flo is sbjeted to a stong etenal agneti field Eion [7] investigated te siilaity soltion by onsideing te poe-la vaiations in te plate tepeate and tanspiation veloity Vedanayaga et al [8] oked on te fee onvetion flo along a vetial plate it te abitay bloing and all tepeate Lin and Y [9] investigated te fee onvetion flo ove a oizontal plate Reently, Hossain et al [1] investigated te natal onvetion flo fo a vetial peeable flat plate it te vaiable sfae tepeate, onsideing te tepeate and tanspiation ates to follo te poe-la vaiation aa et al [11] stdied te effet of Hall ent on te steady laina natal onvetion bonday laye flo of MHD visos and inopessible flids Lately, aa et al [1] eained te effet of Hall ent on MHD natal onvetion flo fo vetial peeable flat plate it nifo sfae eat fl In eent yeas a nbe of stdies of MHD onvetive eat and ass tansfe bonday laye flo of visos inopessible flid ee epoted in te liteate [13]-[5] Hoeve, te effet of all ent and onstant eat fl is still not getting poising attation to te eseaes In tis stdy MHD Fee Convetion and Mass Tansfe Flo of Visos Inopessible Flid abot an inlined Plate it Hall Cent and Constant Heat Fl is investigated Mateatial Analysis teady natal onvetion bonday laye flo of an eletially ondting and visos inopessible flid fo a sei-infinite eated peeable inlined flat plate it a nifo sfae eat fl and tansvese agneti field it te effet of te Hall ent is onsideed Hee ais is taken along te vetially pad dietion and y ais is noal to it Te leading edge of te peeable sfae is taken along z ais Te nifo eat is spplied fo te sfae of te plate to te flid, i is aintained nifoly togot te flid flo Te tepeate and onentation at te all ae T and C espetively Te tepeate and onentation otside te bonday laye ae T and C espetively Unifo agneti field of agnitde B is iposed to pependila to te flo along te y ais Let te angle of inlination of te plate is γ and te plate is sei finite Te oponent oent eqation edes to te bonday laye eqation if and only if body foe is ade by gavity, ten te body foe pe nit ass is F os, = ρg γ ee g is te aele- p p ation de to gavity Fte no body foe eists in te dietion of y and z, ie =, =, and F y =, y z F z = Te oponent of pesse gadient at any point in te bonday laye st eqal to te pesse gadient in te egion otside te bonday laye, in tis egion =, v = Hene oponent of pesse ga- p dient beoe = ρ g os, γ ee ρ is te density of te sonding flid at tepeate T Te qantity ρ ρ is elated to te tepeate diffeene T T and onentation (o ass) diffeenes C C tog te teal vole epansion oeffiient β and onentation vole epansion oeffiient ρ ρ β by te elation, = β( T T ) β ( C C ), teefoe, ρ 1 p F = gβ( T T ) osγ + gβ ( C C ) os γ ρ We ave te genealized o s la in te absene of eleti field to te ase of sot iit poble is of te fo 1689

3 M Waidzzaan et al ( e ) ω + = σ + µ (1) B e e J J B E q B ee, µ e is te agneti peeability, e is te eleton ollision tie, σ is te eletial ondtivity, ω e is te yloton feqeny, B is te applied agneti field ine no applied o polaized voltage eist, so te effet of polaization of flid is negligible, ie E (,,) Teefoe Eqation (1) beoes ω e e J + J B = σµ e ( q B) () B If is assed tat inded agneti field geneated by flid otion is negligible in opaison to te applied one ie B (, B,) Tis assption is valid bease agneti Reynolds nbe is vey sall fo liqid etals and patially ionized flids ine te Hall oeffiient is = ω e e, so te Eqation () e an ite σµ eb J z = + 1+ ( ) σµ eb J = 1+ ( ) ee J y = Te fndaental eqations fo te steady inopessible MHD flo it te genealized O s la and Maell s eqations, nde te assptions tat te flid is qasi-netal, and te ion slip and teoeleti effets an be negleted ine te plate is sei-infinite and otion is steady, all pysial eqations ill be te fntions of and y Ts ateatially te poble edes to a to diensional poble given as follos: + = y σ B + ν = ν + g β( T T ) osγ + gβ ( C C ) osγ + y y ρ + bjeted to te bonday onditions σ B + ν = ν + y y ρ + ( ) ( ) 1 T T k T ν + ν = + y + ρ p y p y y C C + ν = D C y y ( ) ( ) 1 T Q =, v=, =, =, C = C at y = y k (1),, T T, C C as y ee v,, ae te veloity oponents in te yz,, dietion espetively, υ is te kineatis visosity, ρ is te density T, T and T ae te tepeate of te flid inside te teal bonday laye, te plate tepeate and te flid tepeate in te fee stea, espetively, ile C, C, C ae te oesponding onentations Also, σ is te eleti ondtivity of te edi, k is te teal ondtivity of te edi, D is te oeffiient of ass diffsivity, p is te speifi eat at onstant pesse, Q is te onstant eat fl pe nit aea and ote sybols ave tei sal eaning In ode to solve te above syste (Fige 1) of Eqations (6)-(9) it te bonday onditions (1), e (3) (4) (5) (6) (7) (8) (9) 169

4 M Waidzzaan et al Fige 1 Pysial onfigation and o-odinate syste adopt te ell-defined siilaity analysis to attain siilaity soltions Fo tis ppose, te folloing siilaity tansfoations ae no intoded; ( ) φη = C C η U υ = y, g ( ) U η =, θ( η), ψ = υu f ( η) = = U f ( η ) ( C C ) y ψ ( ) k T T U =, Q υ ψ Ts, Eqations (6)-(1) beoes; M f + ff + osγθ + os γϕ ( f + g ) = 1+ Te oesponding bonday onditions ae ee k P = ρc υ is te Pandtl nbe, p M g + fg + ( f + g ) = 1+ ( ) ( ) ( ) U ν and v = = η f ( η) f ( η) θ + PE f + g P f θ fθ = (14) ϕ + fϕ = (15) ( η) g( η) θ ( η) ( ) 1 at η ( η) g( η) θ( η) ( ) at η f =, =, = 1 ϕη = = f,, ϕη υ Magneti paaete, = is te idt nbe, D * β U ( ) 3 Uk E = is te Eket nbe, C Q υ U p g βq (11) (1) (13) (16) σ B M = is te ρu = is te loal asof nbe, ku νu g C C = is te loal odified asof nbe iilaity tansfoations epessions also satisfy te ontinity Eqation (5) 1691

5 M Waidzzaan et al 3 kin-fition Coeffiients, sselt be and eood be Te qantities of ief pysial inteest ae te skin fition oeffiients, te sselt nbe and te eood nbe Te eqation defining te all skin fitions ae = µ and z = µ i ae popotional to and Te sselt nbe denoted by y y y= y= f g T is popotional to, η η η= η = y y= C ene e ave θ ( ) Te eood nbe denoted by is popotional to, ene e y y= ave ϕ ( ) Te neial vales of te skin-fition oeffiients, te sselt nbe and te eood nbe ae soted in Tables Reslts and Disssions In tis stdy te MHD Fee Convetion and Mass Tansfe Flo of Visos Inopessible Flid abot an Table 1 eial vales of kin fition oeffiient, vales of f, taking γ = 6,, sselt nbe and eood fo diffeent = 4, =, M = 5, = 1, P = 71, E = 1, = 6 as fied f Table eial vales of kin fition oeffiient,, sselt nbe and eood fo diffeent vales of M, taking f = 5, γ = 6, = 4, =, = 1, P = 71, E = 1, = 6 as fied M

6 M Waidzzaan et al Table 3 eial vales of kin fition oeffiient, vales of E, taking f = 5, γ = 6,, sselt nbe and eood fo diffeent = 4, =, = 1, P = 71, M = 5, = 6 as fied Table 4 eial vales of kin fition oeffiient,, sselt nbe vales of P, taking f = 5, γ = 6, = 4, =, = 1, 6, and eood fo diffeent = M = 5, E = 1 as fied P Table 5 eial vales of kin fition oeffiient, vales of, taking f = 5, γ = 6,, sselt nbe and eood fo diffeent = 4, =, = 1, P = 71, M = 5, E = 1 as fied Table 6 eial vales of kin fition oeffiient,, sselt nbe vales of γ, taking f = 5, = 4, =, = 1, P = 71, 5, γ and eood E = 6 M = 1, fo diffeent = as fied

7 M Waidzzaan et al Table 7 eial vales of kin fition oeffiient, vales of, taking f = 5, γ = 6,, sselt nbe and eood fo diffeent P = 71, =, = 1, = 6, M = 5, E = 1 as fied Table 8 eial vales of kin fition oeffiient,, sselt nbe vales of, taking f = 5, γ = 6, and eood fo diffeent P = 71, = 4, = 1, = 6, M = 5, E = 1 as fied inlined Plate it Hall Cent and Constant Heat Fl ave been investigated sing te atsei-iget sooting iteation teniqe To stdy te pysial sitation of tis poble, e ave opted te neial vales of te veloity, tepeate, and onentation itin te bonday laye and also find te skin fition oeffiient, sseltnbe, eood nbe at te plate It an be seen tat te soltions ae affeted by te paaetes, naely stion paaete f, asof nbe, odified asof nbe, agneti paaete M, Pandtl nbe P, Eket nbe E, iidt nbe Te vales of M and ae taken to be lage fo ooling etonian flid keeping te plate at diffeent angle Te vales, 5, 73,, 3, 4, 5 ae onsideed fo P Te vales 1, 5, 6, 1,, 3, 4 also onsideed fo Te vales of ote paaetes ae oeve osen abitaily Figes -5, espetively, so te piay veloity, seonday veloity, tepeate and onentation pofiles fo diffeent vales of stion paaete f Hee f > oesponds to stion and f < oesponds to injetion at te plate o bloing Fo Fige -5, it an be seen tat te piay veloity, seonday veloity, tepeate and onentation pofiles deeases it te inease of stion paaete f Figes 6-9, espetively, so te piay veloity, seonday veloity pofiles deeased and tepeate and onentation pofiles ineases fo diffeent vales of M Fige 1 & Fige 11, espetively, so te oss-flo of piay veloity and seonday veloity, at fist ineases ten deeases it te inease of E Fige 1 & Fige 13 sos tat te tepeate pofile inease and onentation pofile deeases it te inease of E Figes so tat te piay veloity, seonday veloity pofile and onentation pofile deeases and tepeate pofile ineases it te inease of Fige 18 & Fige 19, espetively, sos te oss flo of te piay veloity and seonday veloity it te inease of P bot of te pofile is deease ten inease Fige & Fige 1 sos tat tepeate deease and onentation pofile inease it te inease of Fige & Fige 3, so te oss flo of te piay veloity and seonday veloity it te inease of γ bot of te pofile is deease ten inease Fige 4 & Fige 5, so tat tepeate and onentation pofile ineases it te inease of γ Fige 6 & Fige 7, so te oss flo of te piay veloity and seonday veloity it te inease of Fige 8 & Fige 9, sos tat te tepeate and onentation pofile deeases it te inease of Fige 3 & Fige 31, so te oss flo of te piay veloity and seonday veloity it te inease of Fige 3 & Fige 33, sos tat te tepeate and onentation pofile deeases 1694

8 M Waidzzaan et al Fige Piay veloity pofile fo f Fige 3 eonday veloity pofile fo f Fige 4 Tepeate pofile fo f 1695

9 M Waidzzaan et al Fige 5 Conentation pofile fo f Fige 6 Piay veloity pofile fo M Fige 7 eonday veloity pofile M 1696

10 M Waidzzaan et al Fige 8 Tepeate pofile fo M Fige 9 Conentation pofile fo M Fige 1 Piay veloity pofile fo E 1697

11 M Waidzzaan et al Fige 11 eonday veloity pofile E Fige 1 Tepeate pofile fo E Fige 13 Conentation pofile fo E 1698

12 M Waidzzaan et al Fige 14 Piay veloity pofile fo Fige 15 eonday veloity pofile fo Fige 16 Tepeate pofile fo 1699

13 M Waidzzaan et al Fige 17 Conentation pofile fo Fige 18 Piay veloity pofile P Fige 19 eonday veloity pofile P 17

14 M Waidzzaan et al Fige Tepeate pofile fo P Fige 1 Conentation pofile fo P Fige Piay veloity pofile fo γ 171

15 M Waidzzaan et al Fige 3 eonday veloity pofile fo γ Fige 4 Tepeate pofile fo γ Fige 5 Conentation pofile fo γ 17

16 M Waidzzaan et al Fige 6 Piay veloity pofile fo Fige 7 eonday veloity pofile fo Fige 8 Tepeate pofile fo 173

17 M Waidzzaan et al Fige 9 Conentation pofile fo Fige 3 Piay veloity pofile fo Fige 31 eonday veloity pofile fo 174

18 M Waidzzaan et al Fige 3 Tepeate pofile fo Fige 33 Conentation pofile fo it te inease of Fo Fige 34-37, so te veloity, seonday veloity, tepeate and onentation pofile field as a negligible effet fo diffeent vales of Finally te effet of vaios paaetes on te skin fition oeffiients (, ), sselt nbe ( ) and eood ( ) ae tablated in Tables 1-8 Table 1 sos tat te skin fition oeffiient (, ) deeases and sselt nbe ( ) and eood nbe ( ) inease it te inease of f Table sos tat te skin fition oeffiient deeases and ineases and sselt nbe ( ) and eood nbe ( ) deeases it te inease of M Table 3 sos tat te skin fition oeffiient (, ) and eood nbe ( ) ineases and sselt nbe ( ) deeases it te inease of E Table 4 sos tat te skin fition oeffiient (, ) and eood nbe ( ) deeases and sselt nbe ( ) ineases it te inease of P Table 5 sos tat te skin fition oeffiient (, ) and sselt nbe ( ) deeases and eood nbe ( ) ineases it te inease of Table 6 sos tat te skin fition oeffiients (, ), sselt nbe ( ) and eood nbe ( ) deeases it te inease of γ Table 7 & Table 8 sos tat te skin fition oeffiients (, ), sselt nbe ( ) and eood nbe ( ) ineases it te inease of and 175

19 M Waidzzaan et al Fige 34 Piay veloity pofile fo Fige 35 eonday veloity pofile fo Fige 36 Tepeate pofile fo 176

20 M Waidzzaan et al Fige 37 Conentation pofile fo 5 Conlsions Te effet of visos inopessible flid flo abot an inlined plate it all ent is analyzed in te pesent stdy fo onstant eat fl A ange of pysial paaete vales tested ove te bonday laye flos Te vaiation of diffeent pysial paaetes instigated diffeent flo patten as ineasing, deeasing and oss flo in te diensionless piay and seonday veloity, tepeate and onentation distibtion as ell as in te pofile of skin fition oeffiients, sseltand eood nbe Te findings of te pesent investigation ae biefly: As stion paaete ineases, te piay veloity, seonday veloity, tepeate and onentation pofiles deease gadally Hoeve fo te sae paaete effets, te skin fition oeffiient deeases and sselt and eood nbes inease Te piay veloity, seonday veloity pofiles as ell as te skin fition oeffiient, sselt and eood nbes deeased as agneti paaete ineased eeas te evese effets fond in te pofile of tepeate and onentation Te oss-flo of piay and seonday veloity obseved as Eket nbe ineases eeas tepeate pofile ineases and onentation pofile deeases fo te sae paaete effets Also fo te siila paaete effets skin fition oeffiient and eood nbe inease eeas sselt nbe deeases Te ineasing effet of idt nbe ases piay and seonday veloity pofile and onentation pofile as ell as te skin fition oeffiient and sselt nbe deease eeas te evese sitation obseved in te tepeate and eood nbe pofiles Te oss flo of te piay and seonday veloity it te inease of Pandlt nbe as been obseved, ee bot of te pofiles fist deease and nea te laye te pofiles inease Hoeve itin te sae paaete effets, te skin fition oeffiient and eood nbe deease and sselt nbe ineases As te paaete γ ises te oss flo patten obseved in piay and seonday veloity pofiles eeas tepeate and onentation pofile inease Hoeve fo te sae paaete effets te skin fition oeffiient, sselt nbe and eood nbe pofiles deease Te ineasing effet of asof and odified asof nbe ases te oss flo of te piay and seonday veloity eeas tepeate and onentation pofile deease fo te siila paaete effets Hoeve te skin fition oeffiient, sselt nbe and eood nbe inease Refeenes [1] ato, H (1961) Te Hall Effet in te Visos Flo of Ionized as beteen To Paallel Plates nde Tansvese Magneti Field Jonal of te Pysial oiety of Japan, 16, ttp://ddoiog/11143/jpj16147 [] Yaanisi, T (196) Hall Effet in te Visos Flo of Ionized as tog taigt Cannels 17t Annal Meeting, 177

21 M Waidzzaan et al Pysial oiety of Japan, 5, 9 [3] ean, A and tton, W (1961) Magnetoydodynais Evanston, [4] Katagii, M (1969) Te Effet of Hall Cents on te Visos Flo Magnetoydodynai Bonday Laye Flo Past a ei-infinite Flat Plate Jonal of te Pysial oiety of Japan, 7, ttp://ddoiog/11143/jpj7151 [5] Pop, I and Watanabe, T (1994) Hall Effet on Magnetoydodynai Fee Convetion abot a eiinfinite Vetial Flat Plate Intenational Jonal of Engineeing iene, 3, ttp://ddoiog/1116/-75(94)987-6 [6] Aboeldaab, ME and Elbabay, ME (1) Hall Cent Effet on Magnetoydodynai Fee Convetion Flo Past a ei-infinite Plate it Mass Tansfe Intenational Jonal of Engineeing iene, 39, ttp://ddoiog/1116/-75(1)-9 [7] Eion, R (196) Te Effet of Mass Tansfe on Fee Convetion Jonal of Heat Tansfe, 8, 6-63 ttp://ddoiog/11115/ [8] Vedanayaga, M, Altenki, RA and Eon, RA (198) A Tansfoation of te Bonday Laye Eqation fo Fee Convetion Flo Past a Vetial Flat Plate it Abitay Bloing and Wall Tepeate Vaiation Intenational Jonal of Heat and Mass Tansfe, 3, ttp://ddoiog/1116/17-931(8)959-9 [9] Lin, HT and Y, W (1988) Fee Convetion on Hoizontal Plate it Bloing and tion Jonal of Heat Tansfe, 11, ttp://ddoiog/11115/ [1] Hossain, MA, Ala, KCA and Rees, DA (1997) MHD Fee and Foed Convetion Bonday Laye Flo along a Vetial Poos Plate Applied Meanis and Engineeing,, [11] aa, LK, Hossain, MA and ola, RR (7) Effet of Hall Cent on te MHD Laina atal Convetion Flo fo a Vetial Peeable Flat Plate it Unifo fae Tepeate Intenational Jonal of Teal ienes, 46, ttp://ddoiog/1116/jijtealsi619 [1] aa, LK, iddiqa, and Hossain, MA (11) Effet of Hall Cent on MHD atal Convetion Flo fo Vetial Peeable Flat Plate it Unifo fae Heat Fl Applied Mateatis and Meanis, 3, ttp://ddoiog/117/s [13] Bég, OA, Kan, M, Kai, I, Ala, MM and Fedos, M (13) Epliit eial tdy of Unsteady Hydoagneti Mied Convetive anoflid Flo fo an Eponentially teting eet in Poos Media Applied anosiene, 4, ttp://ddoiog/117/s [14] Fedos, M, Kan, M, Ala, MM and n, (1) MHD Mied Convetive Bonday Laye Flo of a anoflid tog a Poos Medi De to an Eponentially teting eet Mateatial Pobles in Engineeing, 1, Atile ID: 4858 ttp://ddoiog/11155/1/4858 [15] Fedos, M, Kan, M, Bég, OA and Ala, MM (13) eial tdy of Tansient Magnetoydodynai Radiative Fee Convetion anoflid Flo fo a teting Peeable fae Jonal of Poess Meanial Engineeing, 8, ttp://ddoiog/11177/ [16] Kan, M, Kai, I, Isla, M and Waidzzaan, M (14) MHD Bonday Laye Radiative, Heat eneating and Ceial Reating Flo Past a Wedge Moving in a anoflid ano Convegene, 1, ttp://ddoiog/11186/s [17] Kan, M, Ala, MM and Fedos, M (13) Effets of Magneti Field on Radiative Flo of a anoflid Past a teting eet Poedia Engineeing, 56, ttp://ddoiog/1116/jpoeng13315 [18] Kan, M, Kai, I, Ali, LE and Isla, I (1) Unsteady MHD Fee Convetion Bonday-Laye Flo of a anoflid along a teting eet it Teal Radiation and Visos Dissipation Effets Intenational ano Lettes,, 4 ttp://ddoiog/11186/ [19] Kan, M, Kai, I and Bisas, HA (1) Heat eneation, Teal Radiation and Ceial Reation Effets on MHD Mied Convetion Flo ove an Unsteady teting Peeable fae Intenational Jonal of Basi and Applied iene, 1, [] Kan, M, Kai, I and Bisas, HA (1) on-etonian MHD Mied Convetive Poe-La Flid Flo ove a Vetial teting eet it Teal Radiation, Heat eneation and Ceial Reation Effets Aadei Resea Intenational, 3, 8-9 [1] Kan, M, Kai, I and Isla, M (14) MHD Boyany Flos of C, Al O 3 and Tio anoflid nea tagnation-point on a Vetial Plate it Heat eneation Pysial iene Intenational Jonal, 4, ttp://ddoiog/19734/pij/14/974 [] Kan, M, Kai, I and Isla, M (14) Possessions of Ceial Reation on MHD Heat and Mass Tansfe anoflid Flo on a Continosly Moving fae Aeian Ceial iene Jonal, 4,

22 M Waidzzaan et al ttp://ddoiog/19734/acj/14/54 [3] Kan, M, Waidzzaan, M, Kai, I, Isla, M and Ala, MM (14) Heat eneation Effets on Unsteady Mied Convetion Flo fo a Vetial Poos Plate it Inded Magneti Field Poedia Engineeing, 9, ttp://ddoiog/1116/jpoeng [4] Waidzzaan, M, Kan, M and Kai, I (15) MHD Convetive tagnation Flo of anoflid ove a inking fae it Teal Radiation, Heat eneation and Ceial Reation Poedia Engineeing, 15, ttp://ddoiog/1116/jpoeng1555 [5] Waidzzaan, M, Kan, M, Kai, I, Bisas, P and Uddin, M (15) MHD Flo of Flid ove a Rotating Inlined Peeable Plate it Vaiable Reative Inde Pysial iene Intenational Jonal, 6, oenlate ybol ae ybol ae yz,, Catesian oodinates P Pandtl nbe f Tanspiation paaete iidt nbe v,, Veloity oponents M Magneti paaete Q Constant eat fl pe nit aea D B Magneti field intensity p B Constant agneti field intensity Coeffiient of ass diffsivity peifi eat at onstant pesse sselt nbe k Teal ondtivity of te edi g avitational aeleation (, ) eood nbe kin-fition oeffiients z f on-diensional piay veloity v tion veloity g on-diensional seonday veloity µ Coeffiient of visosity U Unifo veloity η iilaity vaiable T Tepeate of te flo field υ Coeffiient of kineatis visosity T Tepeate at te plate θ Diensionless flid tepeate T Tepeate of te flid otside te bonday laye ϕ Diensionless flid onentation C peies onentation ρ Flid density C Conentation at te plate σ Eletial ondtivity C Conentation otside te bonday laye β Coeffiient of teal epansion asof nbe * β Coeffiient of onentation epansion Modified asof nbe 179