Effects of quadratic drag on natural convection in a tilted porous layer with uniform heat flux from the side

Abstract

This paper reports a numerical study of natural convection in an inclined enclosure filled with a fluid-saturated porous medium. The Darcy-Dupuit model, which includes effects of flow form drag, is used to describe the flow in the porous layer. Thermal boundary conditions of the Neumann type are applied on the long side walls of the enclosure while the short ones are assumed adiabatic. The governing parameters for the problem are the Rayleigh number R, inclination angle φ, form drag parameter G and aspect ratio of the cavity A. A semi-analytical solution, valid for an infinite layer (A≫1), is derived on the basis of the parallel flow approximation. It is demonstrated that both the inclination of the layer and the form drag parameter, have a strong influence on the strength of the natural convection heat transfer within the enclosure. The effect of form drag parameter on the existence of multiple steady state solutions, that are possible for an enclosure slightly inclined around the horizontal position, is investigated. For boundary layer flows in a vertical cavity it is demonstrated that, in the limit of Dupuit regime, the Nusselt number is given by Nu=0.556(R/G)1/4 . A good agreement is found between the predictions of the parallel flow approximation and the numerical results obtained by solving the full governing equations.