Optimal Thermal Design of Forced Convection Heat Sinks-Analytical

Abstract

For fully developed flow in closed finned channels used to augment heat transfer, there exists an optimal geometrical design of the size and number of cooling channels. In this paper, the problem is generalized with a statement of dimensionless thermal resistance in terms of • the number of channels • a fin to channel thickness ratio • the length to width (planar dimensions) ratio of the heat source, and • a specified fin efficiency or fin length • a fluid to fin thermal conductivity ratio • the Prandtl Number of the coolant • a dimensionless pressure term, which incorporates the maximum allowable pressure drop through the cooling channels or alternatively, • a dimensionless work rate term, which incorporates the maximum allowable coolant pumping power required, An optimization scheme is described and used for comparison with two previously published cases wherein both designs were restricted to a fixed fin to channel thickness ratio and laminar flow; one by Goldberg (1984) using air and copper and a second one only by Tuckerman and Pease (1981) for water-cooled Silicon wafers. Results from the present optimization scheme show that upon reexamination of the first study by Goldberg, significant reduction of thermal resistance can be obtained by using fin/channel dimensions other than unity. A similar reduction is found in the second instance (Tuckerman and Pease) with the relaxation of the laminar limitation.