Optimization of Thermally and Geometrically Asymmetric Trapezoidal Fins

Abstract

Presented is an analysis of thermally and geometrically asymmetric trapezoidal fins using a two-dimensional analytical method. Some isothermal lines within this thermally and geometrically asymmetric fin are shown. The optimum heat loss is chosen to be 98% of the maximum heat loss by comparison of the increasing rate of dimensionless fin length and that of heat loss from the fin. The optimum heat loss, the corresponding dimensionless fin length, and fin volume are presented as a function of the ratio of the fin bottom-surface to top-surface Biot numbers, the ratio of the fin tip-surface to top-surface Biot numbers, and a fin shape factor