The current literature contains many studies of microchannel and micro-pin-fin heat exchangers, but none of them consider the size effect on the thermal conductivity of channel and fin walls. The present study analyzes the effect of size (i.e., the microscale effect) on the microfin performance, particularly in the cryogenic regime where the microscale effect is often appreciable. The size effect reduces the thermal conductivity of microchannel and microfin walls and thus reduces the heat transfer rate. For this reason, heat transfer enhancement by microfins becomes even more important than for macroscale fins. The need for better understanding of heat transfer enhancement by microfins motivates the current study, which resolves three basic issues. First, it is found that the heat, flow choking can occur even in the case of simple plate fins or pin fins in the microscale regime, although choking is usually caused by the accommodation of a cluster of fins at the fin tip. Second, this paper shows that the use of micro-plate-fin arrays yields a higher heat transfer enhancement ratio than the use of the micro-pin-fin arrays due to the stronger reduction of thermal conductivity in micro-pin-fins. The third issue is how the size effect influences the fin thickness optimization. For convenience in design applications, an equation for the optimum fin thickness is established which generalizes the case without the size effect as first reported by Tuckerman and Pease.
Thermal conductivity and specific heat of hollow nanowires: Theoretical modeling and size effect analysis