Fundamental Concepts and an Innovating Approach for Extended Surface Heat Transfer

Abstract

In this work we re-examine the main fin equation qf = ηfAfΔT, proposed by Gardner [1] that has been used for the last sixty years to determine the performance of fins. The fundamental concepts of extended surface heat transfer are introduced, and their mathematical expressions are derived. The vital role of fin effectiveness, a term also introduced by Gardner [1] is established. It is shown that the effectiveness is inextricably linked in proving the validity of the simplifying assumptions that most of the fins’ endeavors are based on. It is also shown that the common practice of using the efficiency to predict the fin’s performance leads to serious errors. A novel approach to fin analysis, based on a proposed transformation of coordinates, is presented, which can be employed to considerably simplify the pertinent differential equations and obtain more friendly expressions describing the fin’s performance. The heat dissipation is expressed in a non-dimensional form and for several practical cases polynomial expressions have developed, that will help students to engage in rudimentary fin designs. It is also shown that, the one-dimensional approach can be used to obtain solutions involving extended surfaces made from anisotropic material. Three examples serve to illustrate the usefulness of our method.