A Brinkman model for MHD viscous incompressible flow through a porous channel (Q1062884)

A steady flow of a viscous incompressible conducting fluid through a channel bounded by permeable media of different permeabilities is considered. A transverse magnetic field is applied perpendicular to the walls. The flow inside the lower porous medium is with high permeability (which is bounded below by a rigid wall) and it allows the consideration of Brinkman's model. The upper porous medium is of low permeability and the Darcy's law together with the Beavers-Joseph slip condition [\textit{G. S. Beavers} and \textit{D. D. Joseph}, J. Fluid Mech. 30, 197--207 (1967)] at the porous interface is used.