Thermal Analysis and Optimum Fin Length of a Heat Sink

Abstract

Abstract A theoretical analysis of the cooling effect of a heat sink is presented in this study. With the input data of Biot number, Bi, and heat transfer coefficient ratios, H and H *, the optimum heat transfer equation can be utilized to obtain the optimum length of fins in a heat sink, which affects the overall thermal effectiveness of the heat sink. This optimum equation is in transcendental form, which involves three dimensionless parameters, $\sqrt{\hbox{Bi}}$ S opt. , $\sqrt{\hbox{Bi}}$ H , and $\sqrt{\hbox{Bi}}$ H *. Finally, the thermal resistance of a heat sink is derived and examples are provided to illustrate the effect on the cooling performance of a heat sink under various design conditions.