Influence of magnetic field on the Poiseuille flow of immiscible Newtonian fluids through highly porous medium

This paper concerns with the flow of viscous, steady, incompressible and immiscible fluids of different viscosities in the channel formed by two infinite parallel plates. The flow is driven by the constant pressure gradient in the presence of the transverse magnetic field of uniform strength. Both the regions of the channel are filled with the highly porous media and having different permeabilities. The flow through the channel is governed by the Brinkman equation with the inclusion of inertia term. No-slip conditions at the end of plates, continuity of velocity and continuity of shearing stress at the interface have been used as boundary conditions to get the solution of the considered problem. The effect of various fluid parameters like permeability and porosity of porous regions, magnetic number, etc., on the flow velocity profile, the flow rate has been discussed graphically. Also, comparative study of the problem has been done.