Research has been undertaken here to determine a new fundamental parameter to judge the performance of optimally-shaped fins. Much research has been published on optimal shapes, but the gains have not been quantified explicitly versus even the constant cross-sectional area fin. Implicitly, optimum fins use less material to achieve the same or similar performance to that of the standard pin fin. But what performance is comparative? Thermal energy dissipation, fin effectiveness and fin efficiency are a few examples. As will be shown in this paper, a material utilization factor will be defined and the performance of an optimally shaped fin will be quantified with that of the standard pin fin for a variety of design conditions.

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