Effect of the Hartmann number on MHD Stokes flow in a lid-driven cavity

A two-dimensional steady, incompressible and electrically conducting Stokes flow in a lid-driven rectangularly confined region is considered. A boundary value problem is formulated for a cavity with the upper lid moving with a constant velocity (u = 1) and the lower lid moving with an S velocity. The finite difference method is applied to generate solutions for the governing equations of the flow in the region. Moreover, streamline bifurcation under a magnetic field of different strengths applied in the x-or y-direction and the effect of the Hartmann number on the eddy formation are investigated.