Boundary layer regime in a vertical porous layer with anisotropic permeability and boundary effects

In this paper, natural convection heat transfer in a vertical porous layer is studied both analytically and numerically. A constant heat flux is applied for heating and cooling the long side walls of the rectangular cavity, while the other two walls are insulated. The porous medium is assumed to be hydrodynamically anisotropic with its principal axes oriented in a direction that is oblique to the gravity vector. In the formulation of the problem, use is made of the Brinkman-extended Darcy model which allows the no-slip boundary condition on a solid wall, to be satisfied. The governing equations are solved analytically, under the boundary-layer approximations, using the modified Oseen technique. The effects of varying the Rayleigh and Darcy numbers, the anisotropic permeability ratio, and the orientation angle of the principle axes on the flow and heat transfer are investigated. A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is also conducted. Results are reported in the range 500 less than or equal to R less than or equal to 1000, 10(-7) less than or equal to Da less than or equal to 10(3), 0.25 less than or equal to K* less than or equal to 4, 0 degrees less than or equal to theta less than or equal to 90 degrees, and A = 1 and 4. Good agreement is found between the analytical prediction and the numerical solution. (C) 1997 by Elsevier Science Inc.