Analysis for upper limit of air cooling by engineered porous metal heat sinks

We analyzed a new approach on porous metal heat sinks for highly integrated electronic applications aiming to address the exponential increase in the thermal management requirements of higher coefficient of performance (COP). Since the applications will be targeted to electronics cooling, we particularly look into air as the working fluid. The large area-to-volume ratio of porous structures could potentially provide high performance. The engineering challenge is to enhance lateral and vertical internal heat transport without substantial increasing the pressure drop. A Coefficient of Performance (COP) was introduced as a performance measure for evaluating this trade off as a function of the geometric design parameters (pore size and porosity). The pressure drop for porous structures has reported to be an order of magnitude larger than the conventional fin heat sinks in multiple articles. However even the effective heat transfer coefficient for porous metals is considerably larger (~600 W/m²K) owing to the large surface area in comparison. Relative lower density of porous medium is an additional advantage for light-weight heat sink designs. A study on the energy efficiency with respect to combined overall effect of parameters such as heat transfer, pressure drop and the mass of the material metal is done in this paper. A figure-of-merit (FOM) is defined to evaluate heat sink performance per unit mass. The optimum value for the structure is evaluated with respect to pore size and porosity in a comparison to conventional heat sinks. The analysis is done for aluminum foams targeted at a porosity of 0.85 up to near 1.0. The pore size considered for this analysis ranges from standard 1-2 mm to as small as 0.1 mm. We address a potential upper limit of air cooling for higher heat flux electronics applications. In our previous work, we showed existence of optimum porosity which results in better heat transfer. The analysis was restricted to a constant pore size mo- el. In this paper we present the combined impact of porosity and pore size for COP. A study is done on multiple models available in literature for estimating permeability and heat transfer coefficient. The ultimate aim is to have a generic model characterizing the performance of porous heat sinks to evaluate optimum design for a specific set of operating conditions as a function of porosity and pore size. A CFD simulation over the length of three unit cells is provided to study the general flow and temperature trends.