Hydromagnetic Three Dimensional Couette Flow and Heat Transfer

Abstract

This paper is concerned with the theoretical analysis of three dimensional couette flow of a viscous incompressible electrically conducting fluid 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 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 heat flux in terms of Nusselt number are obtained. The effects of the flow parameters on the velocity, temperature, skin friction and heat flux have been studied and analyzed with the help of figures and tables. It is observed that the magnetic parameter (M) has a retarding effect on the main velocity (u) and an accelerating effect on the cross velocity (w₁) of the flow field. The suction parameter (R_e) has a retarding effect on the main velocity as well as on the temperature field. The Prandtl number (P_r) reduces the temperature of the flow field and increases the rate of heat transfer at the wall (N_u). The effect of suction parameter is to reduce the x-component of skin friction and to enhance the magnitude of z-component of the skin friction at the wall. This problem is very much significant in view of its several engineering, geophysical and industrial applications.

Keywords: Hydromagnetic, couette flow, heat transfer, three dimensions

doi:10.3329/jname.v5i1.1784

Journal of Naval Architecture and Marine Engineering Vol. 5, No. 1 (June, 2008) 1-10.