Convective heat transfer in a vertical anisotropic porous layer

Abstract

This paper summarizes an analytical and numerical study of natural convection in a fluid-saturated porous medium filled in a rectangular cavity. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. The principal directions of the permeability are oriented in a direction that is oblique to the gravity vector, while those of thermal conductivity coincide with the horizontal and vertical coordinate axes. The side walls of the cavity are, respectively, heated and cooled by a constant heat flux while the horizontal walls are adiabatic. An analytical solution, valid for stratified flow in slender enclosures, is presented. Scale analysis is applied to predict the order of magnitudes involved in the boundary layer regime. Comparisons between the fully numerical and analytical solutions are presented for A = 4, 0 ⩽ R ⩽ 600, 10 −3 ⩽ k∗ ⩽ 10 3, 10 −3 ⩽ K∗ ⩽ 10 3 and 0° ⩽ θ ⩽ 180° where A, R, k∗, K∗ and θ denote the enclosure aspect ratio, Rayleigh-Darcy number, anisotropic thermal conductivity ratio, anisotropic permeability ratio and the inclination angle of principal axes of the anisotropy in the permeability, respectively. It is found that the analytical solutions can faithfully predict the flow structure and heat transfer for a wide range of the governing parameters. The results indicate that a maximum (minimum) heat transfer rate can be obtained if the porous matrix is oriented with its the principal axis with higher permeability parallel (perpendicular) to the vertical direction. Also, it is found that a large thermal conductivity ratio causes a higher flow intensity but a lower heat transfer.