Role of entropy generation on thermal management during natural convection in porous square cavities with distributed heat sources

Abstract

Material processing by thermal convection may be carried out in an energy efficient way based on the second law of thermodynamics. In the current work, the entropy generation in porous square cavities with distributed heat sources during laminar natural convection has been studied. Four different configurations of discretely heated cavities are considered for the study based on the location of the heat sources on the walls of the cavities. The governing equations are solved using Galerkin finite element method. The entropy generation terms are evaluated using finite element basis sets and the derivatives at particular nodes are estimated based on the functions within adjacent elements. Simulations are performed for the range of Darcy number, Da = 10 − 6 – 10 − 3 and Rayleigh number, Ra = 10 3 – 10 6 for various fluids (Prandtl number, Pr = 0.015 , 0.7 , 10 and 1000). A detailed analysis on the effect of Da on entropy generation due to heat transfer ( S θ ) and fluid friction ( S ψ ) based on their local distribution in various cases is presented. The maximum values of S θ are found to occur near the hot–cold junctions while the maximum values of S ψ are found at various locations on the walls of the cavity depending on the circulation cells in various configurations. Significant S ψ is also observed in the interior regions due to the friction between counter rotating circulation cells. The dominance of S ψ is found to be high for higher Pr fluids. The total entropy generation rate ( S total ) is found to increase with Da and the average Bejan number ( Be av ) is found to be less than 0.5, indicating the dominance of fluid friction irreversibility at higher Da in all cases for various fluids. Finally, the thermal mixing, temperature uniformity has been correlated with S total and Be av for all distributed heating cases and the thermal management via enhanced thermal mixing vs optimal entropy production for efficient thermal processing of various fluids in porous media are proposed.