One way of increasing the energy efficiency in thermal processing of materials is to reduce exergy losses due to irreversibilities, measured as "entropy generation". In this study, an analysis of entropy generation during natural convection in rhombic enclosures with various inclination angles (phi = 30 degrees, 45 degrees, and 75 degrees) has been carried out for the efficient thermal processing of various fluids (Prandtl numbers of Pr = 0.015, 0.7, 7.2, and 1000) in a range of Rayleigh numbers (Ra = 10(3)-10(5)). The enclosure is bounded by an adiabatic top wall, cold side walls, and an isothermally (case 1) and nonisothermally (case 2) heated bottom wall. Isotherms (theta), streamlines (psi), and entropy generation contours due to heat transfer (S-theta) and fluid friction irreversibility (S-psi) are analyzed for both cases. At low Rayleigh number (Ra = 10(3)), the entropy generation in the cavity is dominated by S-theta for all phi, irrespective of Pr. As Ra increases to 10(5), the fluid flow intensifies and S-psi also increases for all phi, irrespective of Pr. The total entropy generation (S-total), average Bejan number (Be-av), and average heat-transfer rate ((Nu(b)) over bar) are plotted for Rayleigh number ranges of 10(3) <= Ra <= 10(5). The total entropy generation (S-total) is found to be low for phi = 30 degrees and high for phi = 75 degrees for all Pr values at Ra = 10(5). Analysis of variations of Be-av with Ra for high-Pr fluids indicates that S-psi contributes significantly for increase in S-total. It is also found that the largest heat-transfer rate ((Nu(b)) over bar) corresponds to minimum entropy generation (S-total) for phi = 30 degrees cavities at Ra = 10(5) with all Pr in case 1, The nonisothermal heating strategy (case 2) is energy efficient, because of its lower S-total value, corresponding to low (Nu(b)) over bar, which is due to a lesser heating effect than case 1 for all phi. Overall, rhombic cavities with phi = 30 degrees may be the optimal geometrical design for thermal processing of all types of fluids (Pr = 0.015, 0.7, 7.2, and 1000), irrespective of the heating strategy.