Entropy Rates and Efficiency of Convecting-Radiating Fins

We present a novel indicator for the effectiveness of longitudinal, convecting-radiating fins to dissipate heat. Starting from an analysis of the properties of the entropy rate of the steady state, we show how it is possible to assess the efficiency of such devices by looking at the amount of entropy produced in the heat transfer process. Our study concerns both purely convective fins and convection-radiant fins and takes advantage of explicit expressions for the distribution of heat along the fin. It is shown that, in a suitable limit, the standard definition of efficiency and the entropic definition coincide. The role of the fluid temperature is explicit in the new definition and in the purely convective case. An application to an aluminium fin is given. Analytical and numerical results are discussed.