This work is devoted to the study of the convective radial fin’s 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, and the 2-D conduction models, or experimental. Perusing the pertinent literature, 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, which we shall briefly discuss in the following sections, which allows using the 1-D conduction model, and their effect on steady-state operation. In addition, the bulk of the previous works refer to longitudinal and pin fins, while very few studies treat radial fins. Therefore, a re-examination and revision of the radial fin analysis is needed. The authors are indeed indebted to the pioneering work by previous researchers on this topic who have opened new avenues in the field of extended surface heat transfer. In this work, we present a new method, developed recently, which employs a new spatial coordinate system. It is also our intention to offer a different point of view to this problem, from those presented in the literature. The solutions presented here, rest on the previously mentioned certain fundamental concepts developed recently. In the following sections we show step by step, how the existing pertinent equations and formulae of the circular fins’ transient response, are transformed to new simpler forms, expressed in terms of certain more appropriate dimensionless parameters, from those presented in previously published papers. We confine our analysis to the constant thickness radial fins subject to specific boundary conditions. For reasons of comparison, the solution of a previous example cited in literature is presented. We also give a logical explanation as to what is meant by “the time required for transient response to attain the steady-state condition”. In addition, roots of the transcendental equation for the transient solution, that were not reported before are presented.

This content is only available via PDF.
You do not currently have access to this content.