Extended surfaces, referred in the literature as fins, are usually metallic strips of different shapes and forms. These fins are attached to a primary surface of a structure, for the specific purpose of enhancing the heat transfer between the surface and the surrounding ambient fluid. For the last sixty three years, fins have attracted considerable attention and a vast literature exists on this subject. The aim of this study is to portray the analysis and optimization of rectangular longitudinal and pin fins of cylindrical cross sections. For this purpose a new method of analyzing fins is briefly discussed. Herein, specifically we examine the analysis and optimization of longitudinal fins with linear, exponential and other forms of space variable heat transfer coefficients taken from the existing literature. For pin fins, we examine the case where the heat transfer coefficient depends on the pin fin’s diameter. The results from the optimization process are presented in a concise fashion with practical examples.

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