Unsteady Stokes flow induced by a point source of electric current in a non-Darcy hemispherical porous medium

The time development of the magneto-hydrodynamic Stokes flow in a hemispherical porous medium induced by the symmetric discharge of an electric current from a point source at the center of the planar end of the hemisphere is investigated. Assuming the validity of the Brinkman model, a semi-analytical method is proposed for the determination of the flow field. The streamlines drawn in an axial cross section are found to be in the form of expanding vortices, one on either side of the axis of symmetry. Irrespective of the changes in the evolution of the flow field with time, the polar axis on which the stagnation points of the fluid motion lie from time to time remains stationary without any deviation from the initial position. A comparison of the porous and non-porous media solutions shows that in respect of pure fluids, the steady-state is established much earlier than that in a porous medium. The present analysis plays a significant role in the understanding of the welding processes.