Unsteady MHD flow through an inclined closed rectangular channel with upper and lower surfaces of varying permeability

In this problem, unsteady laminar flow of a viscous incompressible conducting fluid down an inclined closed rectangular channel with upper and lower surfaces of varying permeability in presence of transverse magnetic field has been studied. The boundary condition at the interface of free flow region and fluid in the porous medium due to Beavers and Joseph (1987) has been applied. It is assumed that both the surfaces upper and lower, follow the exponential law. The velocity distribution is obtained using finite Fourier sine transform and Laplace transform technique. Four more results have been deduced as particular cases of the problem. The effect of magnetic field and pressure gradient on the velocity distribution field and pressure gradient on the velocity distribution under different permeability conditions has been discussed with the help of graphs. (author). 8 refs., 2 figs