A New Optimum Pin Fin Beyond the “Length-of-Arc” Assumption

Abstract

The problem of determining the shape of a minimum volume pin fin that dissipates a given heat flow is solved without imposing the “length-of-arc” assumption. Based on the one-dimensional approximation to the temperature distribution and Schmidt's optimality principle, the profile of the optimum pin fin is found to be a circular arc and geometric parameters of the latter are determined. The volume of the optimum circular pin fin is at least 5.26 times smaller than the volume of the corresponding Schmidt's parabolic pin fin, the best known to date. Equivalently, the optimum circular pin fin dissipates at least 2.71 times larger heat flow than Schmidt's pin fin. The optimum circular pin fin tends to be shorter and have a larger radius at the base than the corresponding Schmidt's fin.