An analytical solution for a system consisting of a pin-fin heat sink and a chimney is presented. The result is applied to problems in which the size of the overall system is constrained. For a given heat dissipation and total system size, optimal values of the pin-fin diameter and heat-sink porosity are observed. The optima occur for systems with and without chimneys. The optimization is used to show that the minimum thermal resistance from a pin-fin heat sink is about two times larger than that of an idealized model based on inviscid flow.
Issue Section:
Natural and Mixed Convection
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