Unsteady magnetohydrodynamic flow of a compressible liquid through a stainless steel plate of porous medium

Abstract The unsteady MHD flow of a compressible liquid through a stainless steel plate of porous medium described in terms of a non-linear partial differential equation for a liquid pressure or a linear differential equation for the density if gravitational effects are considered to be negligible. In gravitational flow fields the formulation yields a non-linear equation for both density and pressure. A transformation is given and it shows that in the absence of gravitational effects, the solution of the non-linear boundary value problem in terms of the pressure involves no complexity than the solution of the linear problem in terms of the density. More over this transformation gives in addition the solution to a problem in gravity flow.