Viscous flow in a channel partially filled with a porous medium and with wall suction

Abstract

In this paper, we consider a coupled two-dimensional flow of a Newtonian fluid, both above and through a porous medium. In the fluid-only region, the two-dimensional flow field is governed by the Navier–Stokes equation. We consider the Brinkman-extended Darcy law relationship in the porous medium. Inertial terms are retained in the formulation and the interface conditions between the two domains are those as outlined by Ochoa-Tapia and Whitaker (Int. J. Heat Mass Transfer 38 (1995) 2635). It should be noted that these interface conditions are formulated with an empirical constant β that is unknown a priori. The model equations were solved using two independent methods. In the first method, we pose a similarity variable and reduce the governing equations to two, coupled, non-linear ordinary differential equations. In the second approach, the governing equations were re-posed as a one-domain problem, using the procedure outlined by Basu and Khalili (Phys. Fluids 11 (1999) 1031), so that the conditions at the interface need not be considered. The resulting equation was solved directly, in primitive variable form, using a finite volume formulation. This enabled us to determine β by comparing the resulting solutions.