MHD Three Dimensional Free Convection Couette Flow with Transpiration Cooling

A theoretical analysis of three dimensional free convection couette flow of a viscous incompressible fluid between two vertical parallel plates with transpiration cooling in the presence of a stationary magnetic field applied perpendicular to the planes of the insulating plates is presented. The stationary plate and the plate in uniform motion are, respectively, subjected to transverse sinusoidal injection and uniform suction of the fluid. The flow becomes three dimensional due to this type of injection velocity distribution. The series expansion method is used to obtain the expressions for the velocity and temperature fields. A comprehensive study of the problem is made for various parameters.