On the Transiant Response of Convective Extended Surface Heat Transfer: A New Approach

Abstract

This work is devoted to the study of the extended surfaces transient response. Although, the steady-state fin analysis has attracted considerable attention for a very long time, the interest in the transient response started in the last quarter of the past century. Several publications have appeared since, either analytical using the 1-D, conduction model, or experimental. Perusing the pertinent literature, however, we have observed that, in all previous published papers the authors treat the transient response of extended surfaces, or fins, like regular solids. However, fin endeavors rest on certain fundamental concepts, leading to some simplified assumptions, that we shall briefly discuss in the next section, which allows using the 1-D conduction model, and affect their steady-state operation. Therefore, the need for re-examining and revising the previously used methods becomes apparent. However, the authors are indebted to the pioneer workers on this topic that opened new avenues in the field of extended surface heat transfer. The aim of this work is to offer a different point of view to this problem, by introducing a new spatial coordinate system, and a new time scale. The solutions presented here, rest on the previously mentioned certain fundamental concepts developed recently. In the following we show step by step, how the existing pertinent equations and formulas of fins' transient response, are transformed to new simpler forms, expressed in terms of more appropriate dimensionless parameters, in accord with those appearing in recent publications. In the following, we confine to the analysis of constant thickness longitudinal and pin fins subject to specific1 boundary conditions. Each case is accompanied with an example that, for reasons of comparison are taken from the literature. We also discuss what is meant by "the time required for transient response to attain the steady-state condition."