Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 5 (2010), 215 -- 228## MAGNETIC FIELD AND THERMAL RADIATION EFFECTS ON STEADY HYDROMAGNETIC COUETTE FLOW THROUGH A POROUS CHANNEL

## Ismail Gboyega Baoku, Chigozie Israel-Cookey and Bakai Ishola Olajuwon

Abstract. This paper investigates effects of thermal radiation and magnetic field on hydromagnetic Couette flow of a highly viscous fluid with temperature-dependent viscosity and thermal conductivity at constant pressure through a porous channel. The influence of the channel permeability is also assessed. The relevant governing partial differential equations have been transformed to non-linear coupled ordinary differential equations by virtue of the steady nature of the flow and are solved numerically using a marching finite difference scheme to give approximate solutions for the velocity and temperature profiles. We highlight the effects of Nahme numbers, magnetic field, radiation and permeability parameters on both profiles. The results obtained are used to give graphical illustrations of the distribution of the flow variables and are discussed.2010 Mathematics Subject Classification:35B15; 35B30; 76M20; 76S05.

Keywords:Magnetic field; Thermal Radiation; Hydromagnetic Couette Flow; Thermal conductivity; Porous Channel.

## References

Alagoa, K. D., Tay, G. and Abbey, T. M.,

Radiation and free convection effects on a MHD flow through a porous medium between infinite parallel plates with time-dependent suction, Astrophysics Space Science,260(1999), 455--468.Bestman, A. R.,

Free convection heat and mass to steady flow in a semi- infinite vertical plate, Int'l Journal of Energy Research,13(1989), 311--316.Chen, C.K. and Chang, M.H.,

Stability of hydromagnetic dissipative Couette flow with non- axis symmetry disturbance, J. Fluid Mech.,366(1998) 135--158.Daskalaski, J.,

Couette flow through a porous medium of a high Prandtl number fluid with temperature dependent viscosity, Int'l Journal of Energy Research,14(1990), 21--26.Eckert, E.R.G. and Faghri, M.,

Viscous heating of high Prandtl number fluids with temperature-dependent viscosity, Int'l Journal of Heat and Mass Transfer29(1986), 1177--1183.Elbashbeshy, E. M. A.,

The mixed convection along a vertical plate embedded in non-Darcian porous medium with suction and injection., Applied Mathematics and Computation,136(2003), 139--149. MR1935604(2003h:76119). Zbl1135.76341.Gbadeyan, J. A., Daniel, S. and Kefas, E. G.,

The radiation effect on electro-hydrodynamic froth flow in vertical channel, Journal of Mathematical Association of Nigeria,32No. 2B (2005), 388--396.Gbolagade, W. A. and Makinde, O. D.,

Effect of Biot number on thermal critically in a Couette flow, Journal of Nigerian Association of Mathematics Physics,9(2005),579--584.Guo, Z. Z. and Zhao, T. S.,

Lattice Boltzmann model for convection heat transfer in Porous media, www. linkinghub.elsevier.com (2006), 13th December, 2006.Hazeem, A.A.,

Influence of temperature dependent viscosity on the MHD Couette flow of dusty fluid with heat transfer, Differential Equations and Non-linear Mechanics,2006(2006), Article ID. 75290.Kafoussias, N. G.,

Flow through a porous medium in the presence of heat transfer, Int'l Journal of Engineering Fluid Mechanics2(4) (1989), 343--346.Kim, Y. J.,

Unsteady MHD convective heat transfer past a semi-infinite porous moving plate with variable suction, Int'l Journal of Engineering sciences,38(2000), 833--845.Kurzweg, U.H.,

The stability of Couette flow in the presence of an axial magnetic field, Journal of Fluid Mechanics,17(1963), 52--60.Makinde, O.D. and Sibanda, E.,

MHD steady flow in a channel with slip at the permeable boundaries, Romania Journal of Physics,51(2006), 319--328.Palm, E., Weber, J. E. and Kvernvold, O.,

On steady convection in a Porous medium, Journal of Fluid Mechanics,54(1972), 153--181.Paravassiliou, D. V. and Lyons, S. L.,

Non-Darcy flow through porous media in a turbulent plane Couette flow, Int'l J. Heat and fluid flow,18(1997), 55--69.Phone, C. and Hsu, C. T.,

A singular perturbation solution for Couette flow over a semi-infinite porous bed, Journal of Fluid Engineering,113(1991).Raptis, A. A. And Perdikis, C.P.,

Heat transfer inflow through a porous medium bounded by on an infinite vertical plate under the action of a magnetic field, Int'l Journal of Energy Research,12(1988), 557--560.Salomatov, W. and Puzyrev, E. M.,

Effect of thermal radiation on laminar Couette flow - the theory of non-Newtonian fluid filtration the porous media, Journal of Eng. Physics and Thermophysics,20(1971), 405--421.Takhar, H.S., Gorla, R.S.R. and Soundalgekar, V.M.,

Effect of Biot number on thermal critically in a Couette flow, Int'l J. Num. Heat Fluid Flow,2No. 2 (1996), 77--83.

Ismail Gboyega Baoku,Chigozie Israel-Cookey, Department of Mathematical Sciences, Department of Mathematics and Computer Science, Crescent University, Rivers State University of Science and Technology, Abeokuta, Nigeria. Port Harcourt, Nigeria. e-mail: baolastmail@yahoo.com e-mail: ci_cookey@yahoo.com http://www.crescentvarsity.edu.ng

Bakai Ishola Olajuwon,Department of Mathematics, University of Agriculture, Abeokuta, Nigeria. e-mail: olajuwonishola@yahoo.com http://www.unaab.edu.ng