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Mixed Convection in a Two-Sided and Four-Sided Lid-Driven Square Porous Cavity

The present paper investigates the mixed convection in a two-sided and four-sided lid-driven square cavity in porous media. In the two-sided porous cavity, the left and right walls of the enclosure are maintained at constant but different temperatures, while the top and bottom walls are adiabatic. The top and the bottom walls of the enclosure move with a constant speed from left to right. In the four-sided porous cavity, the top and the bottom walls of the enclosure move from left to right and right to left, respectively, while the left and the right walls move from top to bottom and bottom to top, respectively, with a constant speed. The left and right walls of the enclosure are maintained at different heat fluxes, while the top and bottom walls are maintained at hot and cold temperatures, respectively. The governing equations are discretized by the fully implicit finite difference method, namely, Alternating-Direction-Implicit (ADI) method. The numerical results are analyzed for the effect of Darcy number (Da = 0.001, 0.01), Prandtl number (Pr = 7), Grashof number (Gr = 50,000), porosity (ε = 0.2) and viscosity ratio (Λ = 1, 3). The stability and convergence of the considered problem have been proved using the Matrix method.