Modeling of Pin Fin Heat Sinks Based on Volume Averaging Theory

Abstract

In this paper, a consistant model is developed to describe transport phenomena in a pin fin heat sink that take into account the scales and other characteristics of the medium morphology. The specific geometry of the heat sink is accounted for in such a way that the details of the original structure are replaced by their averaged counterparts. Equation sets allowing for turbulence and two-temperature or two-concentration diffusion are obtained for non-isotropic porous media with interface exchange. The equations differ from known equations and were developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in the space of every pore. The transport equations are shown to have additional integral and differential terms. These terms are closed experimentally from available data for pin fin morphology. The resulting equation set is relatively simple and is descretized using the finite difference method. Such computational algorithm is fast running, but still able to present a detailed picture of themperature fields in the airflow as well as in the solid structure of the heat sink. The calculated friction factor and thermal resistance are compared with experimental data to verify the porous model and validate the numerical code. The results calculated by the code agrees with the experimental data quite well, which offers possibility for multiple parameter optimization using Design of Experiment (DOE) to achieve high cooling capabilities.