Entropy Rates and Efficiency of Convecting-Radiating Fins

Claudio Giorgi,Federico Zullo

doi:10.3390/en14061643

Abstract

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.

Highlights

Longitudinal fins are widely adopted devices used to enhance heat dissipation from a given surface
We introduce a novel indicator for the efficiency of the fin by looking at the entropy produced by the fin in its steady state
We introduced a novel indicator of the performances of longitudinal fins of arbitrary profile

Summary

Introduction

Longitudinal fins are widely adopted devices used to enhance heat dissipation from a given surface (see e.g., [1,2] and the references therein). This model is widely adopted in literature (see, e.g., [1,2]) and simple enough to be manipulated analytically This gives the possibility to obtain, at least in simple cases, explicit fromulae for the efficiency and to make comparisons with the classical results. The pure convective case is analyzed first by showing how the entropy-based efficiency represents a concrete extension of the classical efficiency: if on the one hand it is possible within the limit of a small temperature gradient to obtain the classic results from our formulas, on the other hand, the temperature difference plays an explicit role and its effect can be evaluated directly. In the conclusions, we discuss our results and some potential generalizations

The Entropy Rate Due to Heat Exchange

An Entropy-Based Indicator for the Efficiency of the Fin in Its Steady State

The Pure Convective Case

The Convecting-Radiating Fin and Its Efficiency

Conclusions