Free convection in a cavity filled with a fluid-saturated porous medium is from prime importance in many technological applications. Transient free convection in a rectangular cavity filled with a porous medium is numerically studied in this paper. Uniformly and non-uniformly sinusoidal heated bottom wall and adiabatic side walls maintaining constant temperature of cold top wall has been performed. Investigation of problems with this boundary condition is very complicated, as there are a limited number of studies available in the literature dealing with this problem. The finite volume numerical method is used to solve the non-dimensional governing equations. The numerical procedure has been done over a range of Rayleigh number, Ra, 10 ≤ Ra ≤ 103 and Prandtl number, Pr, 0.71 and Aspect ratio, AR, 0.25≤ AR ≤8 and effect of them is investigated on heat transfer and entropy generation. For uniform heating of the bottom wall, the heat transfer rate or Nub is high at the edges of the bottom wall due to the discontinuities present in the temperature boundary conditions at the edges and reduces towards the center of the bottom wall with the minimum value at the center. Effect of streamline loop numbers on heat transfer is shown for various aspect ratios in this study. The present paper analyzes entropy generation induced by free convection and effect of different parameters on entropy generation is studied. Relation of Nusselt number and Bejan number with aspect ratio is given that is due to effect of stream loops number. In lower Ra, because of weak stream, entropy generation is more due to heat transfer irreversibility (HHI).

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