Analysis of 'entropy generation' is an important strategy to optimize the natural convection process in order to achieve efficient heat transfer within the system. Rhombic enclosures of various inclination angles (phi = 30 degrees, 45 degrees and 75 degrees) filled with porous media and bounded by adiabatic top wall, cold side walls, isothermally (case 1) and non-isothermally (case 2) heated bottom wall have been considered for the analysis of thermal processing of various fluids (Pr=0.015, 0.7, 7.2 and 1000) in the range of Darcy number (Da=10(-5) - 10(-3)). At Da=10(-5), the total entropy generation, S-total is found to be significantly high for phi = 30 degrees and low for phi = 75 degrees and is dominated by heat transfer irreversibility (S-theta) for all Pr in case 1 whereas the distributions of S-total for phi = 45 degrees, 75 degrees and 90 degrees closely follow the distributions of phi = 30 degrees for all Pr in case 2. Cup mixing temperature (Theta(cup)) is higher for phi = 75 degrees and 90 degrees whereas overall heat transfer rate, (Nu) over bar, is higher for phi = 30 compared to other cps in both heating cases except at high Pr (0.7-1000) fluids at Da=10(-5). On increase of Da to 10(-3), fluid friction irreversibility, S-psi, also increases for all cps irrespective of Pr in both cases. Increase in S-total with Da is small for lower phi (phi = 30 degrees) due to insignificant S-psi, of S-total and large for higher phi (phi = 75 degrees) due to significant S-psi, of S-total at Da >= 10(-4) irrespective of Pr in both cases. Also, Theta(cup) slightly decreases at Da >= 10(-4) and further, that reaches a constant value at higher Da as well as S-total in both cases irrespective of phi for all Pr except Pr=0.015. Maximum (Nu) over bar occurs for phi = 30 degrees cavities at Da=10(-3) for all Pr in case 1 due to less available energy loss corresponding to less S-psi. Current work attempts to analyze energy efficient thermal convection strategies within porous rhombic enclosures based on entropy generation minimization vs enhanced thermal mixing or heat transfer rates for various fluids in porous media. (C) 2012 Elsevier Ltd. All rights reserved.