Entropy generation plays a significant role in the overall efficiency of a given system, and a judicious choice of optimal boundary conditions can be made based on a knowledge of entropy generation. Five different boundary conditions are considered and their effect of the permeability of the porous medium, heat transfer regime (conduction and convection) on entropy generation due to heat transfer, and fluid friction irreversibilities are investigated in detail for molten metals (Pr = 0.026) and aqueous solutions (Pr = 10), with Darcy numbers (Da) between 10⁻⁵–10⁻³ and at a representative high Rayleigh number, Ra = 5 × 10⁵. It is observed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating (case 1), with a penalty on thermal mixing. Finally, the analysis of total entropy generation due to variation in Da and thermal mixing and temperature uniformity indicates that, there exists an intermediate Da for optimal values of entropy generation, thermal mixing, and temperature uniformity.