On the entropy production of fins.

Longitudinal fins are one of the most common tools used to enhance the heat transfer from a given device or surface. There is a broad amount of literature related to this subject. Nevertheless, the analysis and design of convecting and convecting-radiating fins are still a topic of great interest in the research community. In this work, we consider a longitudinal fin of arbitrary profile with convective and radiation losses. The properties of the entropy production in this type of fins are analyzed. By taking advantage of the explicit expression for the distribution of heat along the fin, we investigate the possibility to assess the efficiency of these devices through the amount of entropy produced in the heat transfer process. The steady state is described by a second order, non-linear, one dimensional differential equation describing the distribution of heat along the longitudinal fin. We introduce an auxiliary dependent variable, solving a first order differential equation and related to the thickness of the fin, realated to the distribution of the heat. The purely convecting case, corresponding to a linear equation, and the convecting-radiating case, corresponding to a non-linear equation, are treated separately. The analysis of the efficienvy is performed both for purely convecting fins and for convectingradiating fins. A comparison with standard definitions of efficiency is given.