Fully developed flow through a porous channel bounded by flat plates

Plane, parallel and fully-developed flow through straight porous channels is considered in an attempt to study the effects of the porous matrix and the microscopic inertia on the velocity profiles, for different flow-driving mechanisms. By comparison, flows through free-space in the same configuration, as governed by the Navier-Stokes equations and subject to Poiseuille and Couette type entry profiles have become bench-mark problems in the study of flow equations that can be solved analytically by the method of reduction to ordinary differential equations. In this work, we therefore consider three types of Poiseuille-Couette combinations, together with the main models governing flow through porous media, and offer a comparison with the corresponding flow through free-space.