Darcy–Brinkman flow past a two-dimensional screen

Abstract

The flow past a screen composed of periodic slats in a plane is studied. The method of eigenfunction expansions and point match is used to solve the Darcy–Brinkman equations. The velocities, pressures and resistances are determined for the flow in three orthogonal directions. Aside from screen geometry, the flow is governed by a porous media parameter k which is zero for pure viscous flow. The fundamental case for the flow over a single slat is then extrapolated. It is found that for k = 0 the Stokes paradox occurs and the drag rises singularly as k is increased from zero.