Effects of nonuniformly heated wall(s) on a natural-convection flow in a square cavity filled with a porous medium

The influence of uniform and nonuniform heating of wall(s) on natural-convection flow in a square cavity filled with a porous matrix has been studied numerically by using the penalty finite-element method with biquadratic rectangular elements. In the present investigation, the left vertical wall and the bottom wall are uniformly and nonuniformly heated, while the right vertical wall is maintained at constant cold temperature and the top wall is well insulated. The Darcy-Forchheimer model is used to simulate the momentum transfer in the porous medium. The present numerical approach yields consistent performance over the range of parameters (Rayleigh number Ra, 10(3) <= Ra <= 10(6), Darcy number Da, 10(-5) <= Da <= 10(-3), and Prandtl number Pr, 0.71 <= Pr <= 10) in order to obtain the solutions in terms of stream functions, temperature profiles, and Nusselt numbers. Nonuniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than the uniform heating case for all Rayleigh numbers, but average Nusselt number shows overall lower heat transfer rate for the nonuniform heating case. Critical Rayleigh numbers for conduction-dominant heat transfer cases have been obtained. For convection-dominated regimes the power-law correlations between average Nusselt number and Rayleigh numbers are presented.