The Effect of Slip Condition, Radiation and Chemical Reaction on Unsteady MHD Periodic Flow of a Viscous Fluid through Saturated Porous Medium in a Planer Channel

Tavva Sudhakar Reddy*, M. C. Raju**, S. Vijaya Kumar Varma***
* Department of Mathematics, Shree Rama Educational Society Group of institutions, Tirupathi,Chittor District, Andhra Pradesh, India.
** Department of Mathematics, Annamacharya Institute of Technology and Sciences Rajampet, Kadapa District, Andhra Pradesh, India.
*** Department of Mathematics, Sri Venkateswara University, Tirupati, Andhra Pradesh, India.
Periodicity:January - March'2012
DOI : https://doi.org/10.26634/jmat.1.1.1665

Abstract

In this paper the effect of slip condition, Chemical reaction, radiation and unsteady periodic flow of a viscous incompressible fluid through a porous medium in the presence of magnetic field is studied. The governing equations have been solved by general perturbation technique. The analytical solutions for velocity, temperature, concentration are presented and the effects of various physical parameters like Hartmann number M, Reynolds number Re,, Grashof number Gr, modified Grashof number Gm, permeability parameter k , the chemical reaction parameter kc, and Schmidt number on velocity, temperature and concentration are studied though graphs. The expression for skin friction is also derived and the effects of various physical parameters mentioned above are discussed. It is observed that the velocity of a fluid increases with an increase in slip parameter h, and it shows reverse effect in the case magnetic parameter M and concentration decreases with an increase in chemical reaction parameter kc.

Keywords

Chemical reaction, MHD, Radiation, Porous medium and Heat and Mass transfer.

How to Cite this Article?

Reddy, T.S., Raju, M.C., and Varma, S.V.K. (2012). The Effect of Slip Condition, Radiation and Chemical Reaction on Unsteady MHD Periodic Flow of a Viscous Fluid Through Saturated Porous Medium in a Planer Channel. i-manager’s Journal on Mathematics, 1(1), 18-28. https://doi.org/10.26634/jmat.1.1.1665

References

[1]. Derek, C., Tretheway, D.C., Meinhart, C.D. (2002). Apparent fluid slip at hydrophobic micro channels walls, Physics of Fluid, 14,pp- L9-L12.
[2]. F. Soltani, and U. Yilmazer, Slip velocity and slip layer thickness in flow of concentrated suspensions, J. Appl. Polym. Sci. 70 (1998) 515–522.
[3]. W. Marques Jr., G.M. Kremer, and F.M. Shapiro, Coutte flow with slip and jump boundary conditions, Continumm Mech. Thermodynam. 12 (2000) 379–386.
[4]. Khaled, A.R.A., and Vafai, K. (2004) The effect of the slip condition on Stokes and Couette flows due to an oscillatory wall: exact solutions, International Journal of Nonlinear Mechanics, 39, pp. 795-809.
[5]. Makinde, O.D., and Osalusi, E. (2006) MHD steady flow in a channel with slip at the permeable boundaries , Romanian Journal of Physics 51, pp. 319-328.
[6]. Anil Kumar, C.L. Varshney and Sajjanlal. (2010) perturbation technique to unsteady periodic Flow of viscous fluid through a planer channel, Journal of Enng. and Technology, Vol.2(4),pp.73-81,April 2010 .
[7]. Soundalgekar, V.M., and Takhar, H.S. “Radioactive convective flow past a semi-infinite vertical plate'', Modeling Measure and Cont., 51, 31-40, 1992.
[8]. Tahkar, H.S., Gorla, S.R., Soundalgekar, V.M. “Radiation effects on MHD free convection flow of a radiating gas past a semi-infinite vertical plate”, Int. J. Numerical Methods heat fluid flow, 6, 77-83, 1996.
[9]. Hossain, A.M., Alim, M.A., and Rees, D.A.S. “Effect of radiation on free convection from a porous a vertical plate”, Int.J.Heat Mass Transfer,42, 181-191, 1999.
[10]. Muthucumarswamy, R., and Kumar, G.S. “Heat and Mass Transfer effects on moving vertical plate in the presence of thermal radiation, Theoret. Appl. Mach., 31(1), 35-46,2004.
[11]. Magyari E, Pop I and Keller B. “ Analytical solutions for unsteady free convection flow through a porous media”., J.Eng. math., 48, 93-104, 2004.
[12]. Chamaka A.J. Hydro magnetic combined heat and mass transfer by natural convection from a permeable surface embedded in a fluid saturated porous medium”., Int. J. Num. Methods for heat and fluid flow, 10(5), 455-476,2000.
[13]. Mzumdar, M.K., and Deka, R.K. “MHD flow past an impulsively started infinite vertical plate in presence of thermal radiation”., Rom. Journ. Phys., Vol. 52, Nos. 5-7. p. 565-573, 2007.
[14]. Cussler, E.L. “Diffusion Mass transfer in Fluid systems, Cambridge University press, London, 1988.
[15]. Takhar, H.S., Chamkha, A.J., and Nath, G. “ Flow and Mass Transfer on a stretching sheet with a magnetic field and chemically reactive species, Int.J.Eng.Sci., 38, No.12, 1303-1314, 2000.
[16]. Muthucumarswamy, R.,and Ganesan, P. “Effect of chemical reaction and injection on flow characteristics in an unsteady upward motion of an isothermal plate”, J.Appl.mech.Tech. Phys., 42, No.4, 665-671, 2001.
[17]. Chamkha A.J., “MHD flow of a uniformly stretched vertical permeable surface in the presence of heat generation/absorption and a chemical reaction, Int.Commun.Heat mass transfer”,30,N0.3, 413-422,2003.
[18]. Ram, P.C. Effects of Hall and ion-slips currents on free convective heat generating flow ina rotating fluid, Int. J . of energy research 19,371-376,1995.
[19]. Mohamed A. Seddeek and Emad M. AboelDahab., “Radiation effects on unsteady MHD free convection with hall current near an infinite vertical porous plate”, IJMMS 26:4, 249-255 ,2001.
[20]. R.C. Chaudhary and Preeti Jain, “Hall effect on MHD mixed convection flow of a viscoelastic fluid past an infinite vertical porous plate with mass transfer and radiation” ,Theoret. Appl. Mech., Vol.33, No.4, pp. 281-309, 2006.
[21]. Ahmed, N., Kalita, H., and. Barua, D.P. “Unsteady MHD free convective flow past a vertical porous plate immersed in a porous medium with Hall current, thermal diffusion and heat source”, International Journal of Engineering, Science and Technology Vol. 2, No. 6, 2010, pp. 59-74.
[22]. Chaudhary, R.C., Jain, P. “Hall effect on mhd mixed convection flow of a viscoelastic fluid past an infinite vertical porous plate with mass transfer and radiation”, Ukr. J. Phys. 2007. V. 52, N 10.pp. 1001-1010.
[23]. Abdulla, I.A. “Analytic solution of heat and mass transfer over a permeable stretching plate affected by chemical reaction, internal heating, Dufour-Soret effect and Hall effect”, Thermal Science, Vol.13, No.2, pp. 183-197, 2009.
[24]. Raju, M.C., Reddy, N.A., and Varma, S.V.K. “Hall current effects on unsteady MHD flow between stretching sheet and an oscillating porous upper parallel plate with constant suction”, Thermal science, Vol. 15, No.2 , pp. 527-536, 2011.
[25]. Muthucumarswamy, R. “Effects of chemical reaction on a moving isothermal vertical surface with suction”, Acta Mech.155, 65-70,2002.
[26]. Manivannan, K., Muthucumarswamy, R., Thangaraj, V. “Radiation and chemical reaction effects on isothermal vertical oscillating plate with variable mass diffusion”, Thermal science, Vol.13, No.2, pp.155-162, 2009.
[27]. Sharma P.R, Kumar N, Sharma P., “Influence of chemical reaction and radiation on unsteady MHD free convection flow and mass transfer through viscous incompressible fluid past a heated vertical plate immersed in porous medium in the presence of heat source”, Appl. Math. Sciences, Vol.5, No.46, 2249-2260, 2011.
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