Characterization of compact heat sink models in natural convection

In this study, an approximate analytical-numerical procedure is used to model natural convection cooling of heat sinks using electronics cooling software. The analysis evolves in two stages: a numerical simulation of the detailed heat sink, and a simulation of a compact model that exhibits similar thermal and flow resistance characteristics to those of the actual heat sink. From the analysis, the thermal resistance of the heat sink is evaluated. Subsequently, the effective thermal conductivity that must be assigned to the compact heat sink is determined using the Nusselt number correlation for free convection over a vertical plate. Due to the algebraic form of the Nusselt number correlation, the effective thermal conductivity is determined in an iterative fashion. The purpose of a compact heat sink is to reduce computational effort while retaining a desired level of accuracy. In this article, the compact modeling scheme is first applied to either an extruded or a pin-fin heat sink in order to validate the procedure under laminar conditions. Subsequently, the same approach is applied to a multichip system consisting of a set of pin-fin heat sinks placed in series. At both individual and system-level models, it is found that the compact approach results in substantial savings in mesh size and computing time. These savings are accompanied by a small acceptable error that is less than 10% relative to the detailed model predictions.