Thermal optimization of radial plate fin heat sinks under an L-shaped flow

Abstract

Correlations for predicting optimum geometries of radial plate fin heat sinks under an L-shaped flow are suggested based on numerical and experimental results. A radial plate fin heat sink has plate fins radially attached to a cylindrical rod, and the heat source with the same diameter of the rod is located at the bottom of the cylindrical rod. The air flow is an L-shaped flow. Air is blown into the top of the heat sink and exits through the side of the heat sink because the bottom surface of the heat sink is blocked by an insulating plate. To find the optimum geometries of radial plate fin heat sinks, the thermal resistance is selected as the objective function of optimization under the constraints of given pumping power and box size. In order to conduct the optimization, new correlations of the pressure drop, the average Nusselt number, and the heat sink efficiency are proposed. The correlations of the pressure drop and the average Nusselt number are obtained based on numerical results, while the correlation of the heat sink efficiency is developed from an analytic model. To validate the newly proposed correlations, experiments are conducted for radial plate fin heat sinks with various geometries, and the results from the correlations are in close agreement with those from the experiments. Using these three correlations, the optimum number of fins and the optimum fin thickness are obtained under various pumping power and box size conditions. Finally, design guidelines for radial plate fin heat sinks are presented in the following closed-form equations: n(opt) = 1.24(r(r)/H)(0.3)(L/H)P-0.3(pump)*(0.2) and t(opt)/L = 0.0878(r(r)/H)(0.3)(L/H)(-0.45)(k*)(-0.4).