Laminar Forced Convection MHD Couette-Poiseuille Flow with Viscous and Joule Dissipations

The laminar forced convection MHD Couette-Poiseuille flow of a viscous incompressible fluid with the viscous and Joule dissipations has been studied.  Two different orientations of the wall thermal boundary-conditions have been considered, namely: the constant heat-flux at the upper moving plate with the adiabatic stationary lower plate and the constant heat flux at the stationary lower plate with an adiabatic moving upper plate. The governing equations are solved analytically. It is observed that the fluid velocity increases near the stationary plate and it decreases near the moving plate with an increase in magnetic parameter. The temperature field is significantly affected by the modified Brinkman number. The fluid temperature increases when the lower plate is adiabatic and the upper plate is at positive constant heat flux while it decreases in case the lower plate is at negative constant heat flux and the upper plate is adiabatic with an increase in modified Brinkman number for the combined effects of viscous and Joule dissipations. Further, the fluid temperature decreases for positive heat flux case while it increases for negative heat flux case with an increase in either magnetic parameter or velocity parameter when the combined effects of viscous and Joule dissipations are taken into account.