NATURAL-CONVECTION HEAT-TRANSFER IN AN INCLINED POROUS LAYER BOARDED BY A FINITE-THICKNESS WALL

In this paper, natural-convection heat transfer in an inclined porous layer boarded by a wall with finite thickness and conductivity is studied both analytically and numerically. A constant heat flux is applied for heating and cooling the long side walls of the rectangular enclosure while the other two walls are insulated. Several different flow models for porous media are considered, such as Brinkman-extended Darcy and Forschheimer-Brinkman-extended Darcy models. The governing equations, derived from the Brinkman-extended Darcy formulation, are solved analytically, in the limit of a thin system, using the parallel flow approximation. Results are obtained in terms of an overall Nusselt number as a function of Rayleigh and Darcy numbers, angle of inclination of the system, and thickness and conductivity of the bordering wall. The analytical solution is compared with the numerical results obtained by solving the complete system of governing equations. An analysis is made on the proper choice of parameters that can describe the criteria for the range of validity of Brinkman-extended Darcy's law in this type of configuration.