Practical significance of brinkman's extension of darcy's law: Coupled parallel flows within a channel and a bounding porous medium

Abstract

Abstract Problems involving fluid flow past permeable surfaces have customarily been solved by matching Darcy's Law with the Navier‐Stokes equation via an empirical slip‐flow boundary condition at these surfaces. The present analysis serves to place the semi‐empirical theory proposed by Beavers and Joseph (1967) on a more rigorous physical and mathematical basis. It is demonstrated that the predictions of these workers may be derived independently, without having to formulate empirical boundary conditions, by employing Brinkman's extension of Darcy's Law within the porous medium. These predictions are in satisfactory agreement with experimental data, thereby providing a quantitative verification of Brink‐man's equation to complement its theoretical verification presented recently by several authors.