Compact Modeling of Fluid Flow and Heat Transfer in Pin Fin Heat Sinks

In this work, a novel compact modeling method based on the volume-averaging technique is presented. Its application to the analysis of fluid flow and heat transfer in pin fin heat sinks are further analyzed. The pin fin heat sink is modeled as a porous medium. The volume-averaged momentum and energy equations for fluid flow and heat transfer in pin fin heat sinks are obtained by using the local volume-averaging method. The permeability, the Ergun constant, and the interstitial heat transfer coefficient required to solve these equations are determined experimentally and correlations for them are presented. To validate the compact model proposed in this paper, 20 aluminum pin fin heat sinks having a 101.43 mm×101.43 mm base size are tested with an inlet velocity ranging from 1 m/s to 5 m/s. In the experimental investigation, the heat sink is heated uniformly at the bottom. Pressure drop and heat transfer characteristics of pin fin heat sinks obtained from the porous medium approach are compared with experimental results. Upon comparison, the porous medium approach is shown to predict accurately the pressure drop and heat transfer characteristics of pin fin heat sinks. Finally, for minimal thermal resistance, the optimum surface porosities of the pin fin heat sink are obtained under constraints on pumping power and heat sink size. The optimized pin fin heat sinks are shown to be superior to the optimized straight fin heat sinks in thermal performance by about 50% under the same constraints on pumping power and heat sink size.