Semi-analytical study of impingement cooling of metal foam heat sinks of CPUs with air and hydrogen jets under LTNE condition

Abstract

In this paper, a mathematical model for heat transfer in a heat sink covered by an open-cell metal foam under impinging jet flow is presented. Hydrogen and air were considered as the cooling fluids. The Darcy–Brinkman–Forchheimer relationship for the momentum equation was employed, while the two-equation energy model under the local thermal non-equilibrium (LTNE) condition for the energy equation was used. The mathematical model of similarity solution was first validated with analytical and experimental data from literature, and numerical data from Ansys-Fluent®. Then, the differences between numerical predictions under the local thermal equilibrium (LTE) and LTNE on flow and temperature distributions were presented and analyzed. It was shown that when the effective thermal conductivity of solid is very low, the difference of temperature of solid and gas cannot be neglected and LTNE should be considered. In other words, when effective thermal conductivity ratio, β, declines, the deviation between the LTNE and LTE models increases considerably. Finally, the effects of critical dimensionless parameters on the flow and heat transfer characteristics were investigated. The results indicate that cooling performance of the metal foam can be improved by increasing the Reynolds and Darcy numbers while decreasing the aspect ratio of the heat sink. Besides, the properties of metal foam and gas were studied. Hydrogen, as a cooling gas, has better thermal performance than air.