Heat transfer through longitudinal fins

The performance of fins possessing longitudinal shapes is investigated by providing exact analytical solutions as previously performed for the exponential-type fins. Explicit closed-form formulae are provided for the fin tip temperature, the fin efficiency, and the fin base heat transfer, which are very important in practical situations. It is found here that the rectangular fins used in most industrial applications are not efficient and should be substituted by the longitudinal types, such as by the longitudinal profiles of hyperbolic shapes as worked out here since the efficiency and base heat transfer rate are higher than those corresponding to the other longitudinal profiles.