Effect of constant suction and injection on MHD three dimensional couette flow and heat transfer through a porous medium

Abstract

The objective of this paper is to analyzethe effect of constant suction and sinusoidal injection on three dimensional couette flow of a viscous incompressible electrically conducting fluid through a porous medium between two infinite horizontal parallel porous flat plates in presence of a transverse magnetic field. The stationary plate and the plate in uniform motion are, respectively, subjected to a transverse sinusoidal injection and uniform suction of the fluid .The flow becomes three dimensional due to this type of injection velocity distribution. The governing equations of the flow field are solved by using series expansion method and the expressions for the velocity field, the temperature field, skin friction and the rate of heat transfer in terms of Nusselt number are obtained. The effects of the flow parameters on the velocity field, temperature field, skin friction and the Nusselt number have been studied and analyzed with the help of figures and tables. It is observed that a growing magnetic parameter (M) retards the main velocity (u) and accelerates the cross flow velocity (w₁) of the flow field and a growing permeability parameter (K_p) or suction / injection parameter (R_e) reverses the effect. Both Prandtl number (P_r) and the suction / injection parameter have retarding effect on the temperature field. Further, a growing suction / injection parameter diminishes both the components of skin friction at the wall while the permeability parameter enhances the x-component and reduces the z-component of the skin friction at the wall. The effect of increasing permeability parameter is to enhance the magnitude of rate of heat transfer at the wall while a growing Prandtl number (P_r) reverses the effect.

Keywords: MHD; couette flow; heat transfer; suction; sinusoidal injection; porous medium

DOI: 10.3329/jname.v5i2.2570

Journal of Naval Architecture and Marine Engineering 6(1)(2009) 41-51