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Fins or extended surfaces are frequently employed in heat exchangers for effectively improving the overall heat transfer performance. The simple design of fins and their stability in different surface conditions have created them a popular augmentation device. The different fin shapes are available in the literature. The geometry of the fin may be dependent upon the primary surface also. For circular primary surface, the attachment of circumferential fins is a common choice. The longitudinal and pin fins are generally used to the flat primary surface. However, due to attachment of fins with the primary surface, the heat transfer augments but the volume, weight, and cost of the heat exchanger equipments increase as well. Hence, it is a challenge to the designer to minimize the cost for the attachment of fins. This can be done by determining the optimum shape of a fin satisfying the maximization of heat transfer rate for a given fin volume. In general, two different approaches are considered for the optimization of any fin design problem. Through a rigorous technique, the profile of a fin for a particular geometry (flat or curved primary surface) may be obtained such that the criteria of the maximum heat transfer for a given fin volume or equivalently minimum fin volume for a given heat transfer duty is satisfied. In a parallel activity, the optimum dimensions of a fin of given profile (rectangular, triangular etc.) are determined from the solution of the optimality criteria. The resulting profile obtained from the first case of optimum design is superior in respect to heat transfer rate per unit volume and thus it is very much important in fin design problems. However, it may be limited to use in actual practice because the resulting profile shape would be slightly difficult to manufacture and fabricate. Alternatively, such theoretical shape would first be calculated and then a triangular profile approximating the base two thirds of the fin would be used. Such a triangular fin transfers heat per unit weight, which is closer to that of the analytical optimum value. Under a convective environmental condition, Schmidt (1926) was the first researcher to forward a systematic approach for the optimum design of fins. He proposed heuristically that for an optimum shape of a cooling fin, the fin temperature must be a linear function

Optimum Fin Profile under Dry and Wet Surface Conditions