Multi-objective optimization of finned metal foam heat sinks: Tradeoff between heat transfer and pressure drop

In several research fields, e.g., the miniaturization of electronic components, new solutions for heat management are required and metal foam heat sinks can be a worthy solution. These latter provide the crucial challenge of heat transfer augmentation by limiting pressure drops, which presents a typical multi-objective optimization problem. In this background, the paper deals with both non-finned and finned metal foam heat sinks by numerically investigating thermo-fluid-dynamics to maximize heat rate and minimize pumping power. The governing equations of the problem are written by using the porous media theory under the assumptions of local thermal non-equilibrium. They are solved under appropriate boundary conditions with a finite element commercial code, i.e., COMSOL®. The closing coefficients for porous media equations are calibrated with reference to previous experimental studies, with discrepancies lower than 10% for both heat rate and pumping power. The numerical model is coupled with a MATLAB® multi-objective genetic algorithm by applying a Pareto approach that provides optimal tradeoff solutions for the two objective functions, i.e., heat rate to be maximized and pumping power to be minimized. Different morphological, geometrical and fluid-dynamic parameters are considered as design variables. It is shown that the finned metal foam heat sink can enhance dissipated heat rates of about 3.3–3.5 times the metal foam heat sink, at equal pumping power. By performing comparisons with experimental data, optimization process is shown to enhance heat rates at fixed pumping power of about 2.5–3 times and 5–6 times for metal foam and finned metal foam heat sinks, respectively. Finally, dimensionless correlations of the Pareto fronts are presented to drive the design of such optimized devices.