A Modified Beavers and Joseph Condition for Gravity-Driven Flow over Porous Layers

Abstract

Gravity-driven flow through an inclined channel over a semi-infinite porous layer is considered in order to obtain a modification to the usual Beavers and Joseph slip condition that is suitable for this type of flow. Expressions for the velocity, shear stress, volumetric flow rates, and pressure distribution across the channel are obtained together with an expression for the interfacial velocity. In the absence of values for the slip parameter when the flow is over a Forchheimer porous layer, this work provides a relationship between the slip parameters of the Darcy and Forchheimer layers. Expressions for the interfacial velocities in both cases are obtained. This original work is intended to provide baseline analysis and a benchmark with which more sophisticated types of flow, over porous layers in an inclined domain can be compared.