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1 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved THE EFFECTS OF CHEMICAL REACTION AND RADIATION ON UNSTEAD MHD FREE CONVECTIVE FLUID FLOW EMBEDDED IN A POROUS MEDIUM WITH TIME-DEPENDENT SUCTION WITH TEMPERATURE GRADIENT HEAT SOURCE B. Seshaiah * S.V.K.Vama * M.C.Raju ** * Depatment of Mathematics, S.V.Univesit Tiupati, A.P, India. ** Depatment of Mathematics, Annamachaa Institute of technolog and Sciences, Rajampet (autonomous), A.P, India. Coesponding autho seshu.maths@gmail.com, mcmaths@ahoo.co.in ABSTRACT: The objective of the pesent stud is to investigate the effects of chemical eaction and adiation on unstead MHD fee convection fluid flow embedded in a poous medium with time dependant suction with tempeatue gadient heat souce ae studied. A vaiable time-dependent suction velocit nt v V Ae is consideed nomal to the flow. The plate is taken along x - axis in vetical upwad diection against the gavitational field. - axis is taken nomal to the flow in the diection of applied tansvese magnetic field. Futhe, due to semi-infinite plane suface assumption the flow vaiables ae the functions of and t onl. Emploing a Petubation technique, the solutions ae obtained fo Velocit, Tempeatue, Concentation, Skin-fiction, Nusselt numbe and Shewood numbe in tems of the paametes, like, Pandtl numbe(p), Schmidt paamete(s c ), magnetic field paamete(m), heat souce paamete(q), chemical eaction paamete( k ), mass Gashof numbe(g m ) and themal Gashof numbe(g ) espectivel, and ae discussed though gaphs and tables. Kewods: Chemical eaction, adiation, MHD, fee convection, poous medium and heat souce.. INTRODUCTION: The stud of adiative heat and mass tansfe in convective flow is found to be most impotant in industial and technologies. The applications ae often found in situations such as fibe and ganules insulations, geothemal sstems in heating and cooling of chambes. Futhe the magneto convection plas an impotant ole in the magnetic sepaation of molecula semi conducting mateials. MHD flows assumes geate significance in seveal biological and engineeing sstems when the flow is consideed ove a pemeable bounda. When mass tansfe takes place in a fluid at est, the mass is tansfeed puel b molecula diffusion esulting fom the concentation gadient. A numbe of investigations have been caied out with combined heat and mass tansfe unde the assumption of diffeent phsical eal life situations. Due to the pime impotance of heat and mass tansfe involving in chemical eaction, industial pocess, and the poblem eceived consideable attention in ecent eas. In the last few eas, man investigations [- ], have been caied out in egad to the pesent wok. Chamkha [] studied, themal adiation and buoanc effects on Hdomagnetic flow ove an acceleating pemeable suface with heat souce o sink. Radiation and mass tansfe effects on unstead MHD fee convective fluid flow embedded in poous medium with heat geneation / absoption was studied b Shanke et al. []. Unstead MHD fee convection oscillato couette flow though a poous medium with peiodic wall tempeatue was

2 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved consideed b Raju and Vama []. Radiation and mass tansfe effects on a fee convection flow though a poous medium bounded b a vetical suface wee studied b Raju et al. [5-6]. Ravikuma et al. [7] investigated magnetic field effect on tansient fee convection flow though poous medium past an impulsivel stated vetical plate with fluctuating tempeatue and mass diffusion. Chemical eaction and adiation effects on MHD fee convection flow though a poous medium bounded b a vetical suface with constant heat and mass flux was studied b Redd et al. [8]. This pape deals with the effects of themal adiation, time-dependant suction and chemical eaction on two dimensional MHD fee convective Boussinesq fluid flow, ove a semi-infinite vetical plate, moving exponentiall with time, in the pesence of tempeatue gadient heat souce unde the influence of applied tansvese magnetic field nomal to the flow. The Poblem is govened b the sstem of coupled patial diffeential equations, and emploing a petubation technique the solutions ae obtained.. NOMENCLATURE: A : Suction paamete C : Specific heat at constant pessue p D : Mola diffusivit g : Acceleation due to gavit G : Mass Gashof numbe m G : Themal Gashof numbe K : Pemeabilit of poous medium k : Chemical eaction ate constant M : Magnetic paamete n : Constant exponential index N : Themal adiation paamete N : Nusselt numbe P u : Pandtl numbe q : Radiative flux vecto Q : Heat souce paamete S c : Schmidt paamete t : Time T : Dimensionless tempeatue u, v : Velocit components U : Mean velocit x, : Catesian coodinates Geek smbols: : Coefficient of volume expansion due to tempeatue * : Coefficient of volume expansion due to concentation v : Kinematic viscosit : Themal conductivit : Densit Sub scipts: w : Condition at the wall : Fee steam conditions, Pimes denote dimensional quantities. MATHEMATICAL FORMULATION: Let us conside a poblem of unstead two-dimensional, lamina, bounda lae flow of a viscous, incompessible, electicall conducting fluid along a semi-infinite vetical plate in the pesence of themal and concentation buoanc effects. A vaiable time-dependent suction velocit v V Ae nt is consideed nomal to the flow. The plate is taken along x - axis in vetical upwad diection against the gavitational field. - axis is taken nomal to the flow in the diection of applied tansvese magnetic field. Futhe, due to semi-infinite plane suface assumption the flow vaiables ae the functions of and t onl. Figue-: Phsical configuation and coodinate sstem The following assumptions ae made in obtaining the govening equations. i. The viscous dissipation is neglected ii. The Joule dissipation is neglected. iii. The induced magnetic field is assumed to be negligible as the magnetic

3 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved Renolds numbe of the flow is taken to be ve small. iv. The plate is taken along x - axis in vetical upwad diection against to the gavitational field. - axis is taken nomal to the flow in the diection of applied tansvese magnetic field. v. Due to semi-infinite plane suface assumption the flow vaiables ae the functions of and t onl. Then unde above assumptions and b usual Boussinesq s appoximation, the unstead flow is govened b the following set of equations. v u u u v g T T t * B g C C u u k q T T T v t cp Q c p T T C C C v k C t () ( () () B using Rosselant appoximation as in Raptis, Ogulu and Makinde, we can wite the adiative flux q as: q * * k T (5) It is assumed that the tempeatue diffeences within the flow ae sufficientl small so that T can be expanded in a Talo seies about the fee steam tempeatue T so that afte ejecting highe ode tems: T T (6) T T The equation of eneg afte submission of equations (5) & (6) can now be witten as T T k v t c Fom equation (), p T 6 T c * * pk T (7) v we have v f ( t). Hee, we can see that the suction velocit is a function of time t onl. So, it is assumed in the fom Cooke et al. []. v f ( t) V Ae (8) Whee, A is the suction paamete and A. Hee the minus sign indicates that the suction is towads the plate. The following non-dimensional paametes ae intoduced in the equations (), () & (7) to get dimensionless fom. U Ut cv p v, t, P, Sc, v v k D T T C C u,, u, T T C C U w w (9) On intoducing equation (9) into equations (), () & (7), we obtain the following govening equations in dimensionless fom: Ae t * gv T T g v C C G, G, U m U vn ku B v k v n, K, M, k, U v U U N 6 k k _ * T Q, Q * CpU nt u u Ae G G M u u m t k n t nt N P () Q 5

4 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved The coesponding initial and bounda conditions ae: () () u e nt, e nt, e nt on. METHOD OF SOLUTION: () The equations () to () ae coupled non-linea patial diffeential equations whose solutions in closed-fom ae difficult to obtain, to solve these coupled non-linea patial diffeential equations, we assume that following Soundalgeka (975), the unstead flow is supeimposed on the mean stud flow, so that in the neighbohood of the plate, we have: u u e u o nt ( ) ( ) ( ) nt ( ) e ( ) o( ) nt ( ) e ( ) o( ) () We now substitute equation () in equations () to () and equating hamonic and nonhamonic tems, neglecting highe ode tems in, we obtain: u u Mu G Gm (5) u u ( M n) u G Gm Au (6) ( h hq) (7) ( Qh h) nh Ah (8) S c k Sc (9) S S n k AS c c c () nt Ae k t Sc u,, on P and pimes whee, M M, h k N indicate diffeentiation with espect to. The bounda conditions ae: u u ( () m5 m m ) B6e Be B5e () u ( ) B e B e B e m 6 m m 7 8 B e B e B e m m 9 m 5 () () (5) (6) (7) Such that the velocit, tempeatue and concentation distibutions can be expessed as: (, u,,,, on u, u,,,, as ( ) e ( ) ( ) (8) m m nt ( B e B e e m, t) e SKIN-FRICTION: u(, t) B e B e B e Skin-fiction coefficient ( ) at the plate is given b du m B m B m B d ) (9) () m B m B m B m B nt e mb m5b NUSSELT NUMBER: m5 m m 6 5 m 6 m m B e B7e B8e e m m m55 B9e B e Be (, ) m B e B e ( ) e m m ( ) B e B e m m m t e B e B e e m m m nt nt () 6

5 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved The ate of heat tansfe coefficient (Nu) at the plate is given b d Nu d () SHERWOOD NUMBER: The ate of mass tansfe coefficient (Sh) at the plate is given b 5. RESULTS AND DISCUSSION: () In ode to get a phsical insight of the poblem, numeical computations ae caied out fo the non-dimensional velocit ( u ), tempeatue ( ), Concentation ( ), Skin fiction, Nusselt numbe and Shewood numbe ae in tems of the paametes P S M,, c,, Q, k, N, k, A Gm and G espectivel. The values of Pandtl numbe ae chosen such that fo Ai ( P.7), Electoltic solution ( P.), wate ( P 7.) and wate at C ( P.). The values of Schmidt numbe ae chosen so that fo hdogen S c., wate-vapo S c.6, Ammonia S c.78, methanol S. and popl benzene S c.6 m ( B ) m B e d Sh d c m. Figues () to () displa the effects of Pandtl numbe ( P ), Themal adiation paamete ( N ) and Heat souce paamete ( Q ) on tempeatue distibution espectivel. An incease in the pandtl numbe ( P ) is obseved to decease in tempeatue bounda lae and an incease in suction paamete (A) shows a negligible effect on the tempeatue field. An incease in the themal adiation paamete ( N ) esults to incease in the themal bounda lae, while an incease in heat souce paamete ( Q ) esults to decease in the themal bounda lae. nt m m B m B e nt Tempeatue Tempeatue Figue : Tempeatue pofiles fo diffeent P Figue : Tempeatue pofiles fo diffeent N Figues () & (5) depict the effect of the chemical eaction ate constant k ) and Schmidt numbe ( S c ( ) on the species concentation. It is obseved that an incease in Schmidt numbe S ) o chemical eaction ( c P=.7, A=. P=., A=. P=., A=. P=.7, A=. N=. N=. N=. N= ate constant ( k ) esults in decease of concentation and concentation bounda lae. Again, fom figue () & () we obseve that suction paamete (A) has negligible effect on tempeatue and concentation fields. 7

6 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved Q=. Q=.5 Q=. Q=.5 velocit field, in the pesence of incease in chemical eaction constant... Sc=. Sc=.6 Sc=.78 Sc=. Sc=.6 Tempeatue.8.6. Concentation Figue : Effect of Q on Tempeatue field when P=.7, A=., N=.... K=., A=. K=., A=. K=., A=. K=., A= Figue 5: Concentation pofiles P=.7 P=. P=7. P=. Concentation Figue : Concentation pofiles Figues (6) to (9) shows the effects of mateial paametes such as P,, Sc, M, Q, k, N, k, A G and G m when the plate is cooled b fee convection cuents ( G >). It is obseved that an incease in Pandtl numbe o Schmidt numbe leads to eduction in the velocit field, also an incease in themal adiation paamete ( N ) esults to incease in the velocit field, while incease in ate of chemical eaction constant leads to decease in velocit and thee is a negligible effect of suction paamete (A) on Figue 5: Effect of P on velocit field fo cooling of the plate when G=, Gm=5, Sc=., Q=., N=., K=.5, M=.5, k=., A=. and t=. Figue () depicts the effects of Magnetic field paamete (M) and pemeabilit of poous medium (K) on the velocit field. An incease in Magnetic field paamete(m) fo fixed pemeabilit of poous medium(k) leads to decease in the velocit field, while an incease in pemeabilit of poous medium (K) fo fixed Magnetic field paamete(m) esults to incease in the velocit fo cooling of the 8

7 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved plate. Fom figue (9) it is also obseved that with an incease in suction paamete (A) leads to decease in the velocit fo cooling of the plate..5.5 Sc=. Sc=.6 Sc=.78 Sc=. Sc= N=. N=. N=. N= Figue 6: Effect of Sc on velocit field fo cooling of the plate G=, Gm=5, P=.7, Q=., N=., K=.5, M=.5, k=., A=. and t=. Figues () & () displa the effects of themal Gashoff numbe and mass Gashoff numbe on velocit field. An incease in themal Gashoff numbe o in mass Gashoff numbe esults in incease in the velocit field fo cooling of the plate. Figue () shows, an incease in heat souce paamete (Q) esults to decease in the velocit. Figues () to () descibes the effects of mateial paametes and P S M A, G, c,, Q, k, N, k, G G when the plate is heated b fee- m, convection cuents ( ). It is obseved that with an incease in heat souce paamete o Pandtl numbe o Schmidt numbe o Magnetic field paamete the velocit inceases, wheeas it deceases with inceasing values of themal adiation paamete o themal Gashoff numbe Figue 8: Effect of N on velocit field fo cooling of the plate G=, Gm=5, P=.7, Sc=.,Q=., N=., K=.5, M=.5, k=., A=. and t= K=., A=. K=., A=. K=., A=. K=., A= Figue 9: Effect of k on velocit field fo cooling of the plate G=, Gm=5, P=.7, Sc=.,Q=., N=., M=.5, k=., A=. and t=.. Nusselt numbe (Nu), which measues the ate of heat tansfe at the plate =, is shown in Table () fo diffeent values of Pandtl numbe ( P, Heat souce paamete (Q) and ) themal adiation ( N ) espectivel. It is found that an incease in the Pandtl numbe ( 9

8 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved P ) leads to decease in the ate of heat tansfe, while it deceases as heat souce paamete (Q) inceases and themal adiation ( N ) deceases. 6 5 G=5 G= G=5 G=.5.5 M=.,k=. M=.5,K=. M=.,K=. M=.5,K=. M=.,K= Figue : Effect of G on velocit field fo cooling of the plate Q=., Gm=5, P=.7, Sc=., N=., K=.5, e=., n=.5, A=., M=.5, k=. and t= Figue : Effect of M and k on velocit field fo cooling of the plate G=, Gm=5, P=.7, Sc=.,Q=., N=., K=.5, e=., n=.5, A=. and t= Gm=5 Gm= Gm=5 Gm= Shewood numbe (Sh), which measues the ate of mass tansfe at the plate =, is shown in Table () fo diffeent values of Schmidt numbe and chemical eaction ate constant espectivel. It is obseved that Shewood numbe deceases with an inceasing values of Schmidt numbe (Sc) o chemical eaction ate constant ( k. The numeical values of Skin ) fiction ae pesented in Table () & () fo the both cases cooling ( G > ) and heating ( G < ) of the plate espectivel. It is obseved that, an incease in M, P,Sc and k leads to decease in the value of skin-fiction, while it inceases with inceasing values of, k, and G fo G > Q, N G m (cooling of the plate). Fo G < (heating of the plate), Skin fiction inceases with an inceasing values of P, M, G and G, it deceases as S, Q, N, k & K inceases. c m Figue : Effect of Gm on velocit field fo cooling of the plate G=, P=.7, Sc=.,Q=., N=., K=.5, e=., n=.5, A=., M=.5,k=. and t=.

9 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved Q=. Q=.5 Q=. Q= P=.7 P=. P=7. P= Figue : Effect of Q on velocit field fo cooling of the plate G=, Gm=5, P=.7, Sc=., N=., K=.5, e=., n=.5, A=., M=.5, k=. and t= Figue 5: Effect of P on velocit field fo cooling of the plate when G=, Gm=-5, Sc=., Q=., N=., K=.5, M=.5, k=., A=. and t=. Q=. Q=. Q=. Q=..5.5 Sc=. Sc=.6 Sc=.78 Sc=. Sc= Figue : Effect of Q on velocit field fo cooling of the plate G=-, Gm=-5, P=.7, Sc=., N=., K=.5, e=., n=.5, A=., M=.5, k=. and t= Figue 6: Effect of Sc on velocit field fo cooling of the plate G=-, Gm=-5, P=.7, Q=., N=., K=.5, M=.5, k=., A=. and t=.

10 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved N=.,A=. N=.,A=. N=.,A=. N=.,A=. N=.,A=..5.5 M=.,K=. M=.,K=. M=.,K=. M=.,K=. M=.,K Figue 7: Effect of N on velocit field fo cooling of the plate G=-, Gm=-5, P=.7, Q=., N=., K=.5, M=.5, k=., A=. and t= Figue 9: Effect of M and k on velocit field fo cooling of the plate G=-, Gm=-5, P=.7, Sc=.,Q=., N=., K=.5, e=., n=.5, A=. and t=. K=.,A=. K=.,A=. K=.,A=. K=.,A=..5.5 G=- G=-5 G=- G= Figue 8: Effect of k on velocit field fo cooling of the plate G=-, Gm=-5, P=.7, Sc=.,Q=., N=., M=.5, k=., A=. and t= Figue : Effect of G on velocit field fo cooling of the plate G=-, Gm=5, P=.7, Sc=.,Q=., N=., K=.5, e=., n=.5, A=. and t=. Table.: Nusselt numbe P Q N Nusselt Numbe

11 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved Table.: Shewood numbe Sc K Shewood numbe Table.: Skin-fiction fo cooling of the plate (G > ) P Sc Q N K M k G Gm Skin-fiction Table. : Skin-fiction fo heating of the plate (G < ) P Sc Q N K M K G Gm Skin-fiction P ) is 6. CONCLUSIONS: The effects of chemical eaction and adiation on unstead MHD fee convection fluid flow embedded in a poous medium with time dependant suction with tempeatue gadient heat souce ae studied. Emploing a Petubation technique, the solutions ae obtained fo Velocit, Tempeatue, Concentation, Skin-fiction, Nusselt numbe and Shewood numbe in tems of the paametes, like, Pandtl numbe(p), Schmidt paamete(s c ), magnetic field paamete(m), heat souce paamete(q), chemical eaction paamete( k ), mass Gashof numbe(g m ) and themal Gashof numbe(g ) espectivel, and ae discussed though gaphs and tables. An incease in the Pandtl numbe ( obseved to decease in tempeatue bounda lae and suction paamete (A) has negligible effect on the tempeatue field. An incease in the themal adiation paamete ( N ) esults in incease in the themal bounda lae, while an incease in heat souce paamete( Q ) esults in decease in the themal bounda lae. An incease in Pandtl numbe(p ) o Schmidt numbe(s c ) leads to eduction in the velocit field, also incease in themal adiation paamete( N ) esults an incease in the velocit, while incease in the ate of chemical eaction constant( ) leads to decease in the velocit field and thee is a negligible effect of suction paamete(a) on the velocit field. An incease in magnetic k

12 June. Vol., No. ISSN 5-9 Intenational Jounal of Scientific Knowledge Computing and Infomation Technolog IJSK & K.A.J. All ights eseved field paamete (M) fo fixed pemeabilit of poous medium ( K ) leads to eduction in the velocit field, while an incease in pemeabilit of poous medium ( K ) fo fixed magnetic field paamete(m) esults to incease in velocit fo cooling of the plate. It is obseved that with an incease in heat souce paamete(q) o pandtl numbe(p ) o Schmidt numbe(s c ) o Magnetic field paamete(m) the velocit inceases, wheeas it deceases with an inceasing values of adiation paamete(r) o themal Gashof numbe(g ) fo heating of the plate. It is found that an incease in the pandtl numbe( P ) leads to decease in the ate of heat tansfe,while it deceases as heat souce paamete(q) inceases and themal adiation paamete( N ) deceases. 7. REFERENCES: [] Chambe,P.L and oung,j.d, (99)., On the diffusion of chemical eactive species in a lamina bounda flow; The phsics of fluids, Vol-, pp:8-5. [] Chamkha, A.J, ()., Themal adiation and buoanc effects on hdo-magnetic flow ove an acceleating pemeable suface with heat souce/sink; Int.J. Heat and mass tansfe, Vol- 8, pp: [] Chen, ()., Heat and mass tansfe effects with vaiable wall tempeatue and concentation, Acta Mathematica, Vol-7. [] Cooke.C.I, Ogulu.A & Omubu-pepple.V. B ()., Intenational. Jounal of Heat Mass Tansfe,Vol-6. [5] Came,K.R and Pai,S.L, (975)., Magneto- Hdodnamics fo Enginees ans Phsicists, Mc Gaw-Hill, New ok. [6] Das,U.N, Dekha,R.K and Soundalgeka,V.M, (999)., Effects of mass tansfe on flow past an impulsivel stated infinite vetical plate with constant heat flux and chemical eaction, The Bulletin, GUMA, vol-5, pp:-. [7] Had,F.M and Hossaine, J.A, (986)., Heat and mass tansfe fo powe-law fluids, Indian.J.Pue.Appl.Maths, Vol-7(), pp:8-. [8] Ogulu.A, Amikii.A.R & Mbeledogu.I.U, (7)., Unstead MHD fee convective flow past a Moving vetical plate, Intenational Jounal of Heat Mass Tansfe, Vol-5. [9] Ogulu, A. and Mbeledogu.I. U, (7)., Heat and mass tansfe of unstead natual convection flow of a otating fluid past a vetical poous plate, Intenational Jounal Heat Mass Tansfe, Vol-5. [ Pakash, J. and Ogulu. A, (6)., Unstead two-dimensional flow of a adiating and chemicall eacting MHD fluid with timedependent suction, Indian Jounal of Pue Applied Phsics, Vol-, pp:85-8. [] Raptis,A. A, (998)., Intenational Jounal of Heat Mass Tansfe, Vol-. [] Sunitha. S. Bhaske Redd, N.and Rama Chanda Pasad.V, (9)., Radiation and mass tansfe effects on MHD fee convective flow past an impulsivel stated isothemal vetical plate with dissipation, Themal Science, (in pess). [] Shanke, B. Pabhaka Redd, B. and Ananda Rao J, ()., Radiation and mass tansfe effects on unstead MHD fee convective fluid flow embedded in poous medium with heat geneation / absobtion, Indian Jounal of Pue Applied Phsics, Vol-, pp: [] Raju M.C, Vama S.V.K, (), Unstead MHD fee convection oscillato Couette flow though a poous medium with peiodic wall tempeatue, Jounal on Futue Engineeing and Technolog, Vol.6, No.. Pp.7-. [5] Raju M.C, Vama S.V.K, Ananda Redd, N., (), Radiation and mass tansfe effects on a fee convection flow though a poous medium bounded b a vetical suface, Jounal of Futue Engineeing and Technolog, Vol. 7, No:, pp. 7-. [6] Raju M.C, Vama S.V.K, Rao R.R.K, (), Unstead MHD fee convection and chemicall eactive flow past an infinite vetical poous plate, i-manage Jounal of Futue Engineeing and Technolog, Vol.8 (), 5-. [7] Ravikuma V, Raju M.C, Raju G.S.S, Vama S.V.K, (), Magnetic field effect on tansient fee convection flow though poous medium past an impulsivel stated vetical plate with fluctuating tempeatue and mass diffusion, Intenational Jounal of Mathematical Achive, Vol.(6), [8] Redd T.S, Raju M.C, Vama S.V.K, (), Chemical eaction and adiation effects on MHD fee convection flow though a poous medium bounded b a vetical suface with constant heat and mass flux, Jounal of computational and Applied eseach in Mechanical Engineeing, Vol. (),.