An integral approach is extended to determine the optimum dimensions for rectangular longitudinal fins and cylindrical pin fins by incorporating transverse heat conduction. The effects of variable heat transfer coefficient and heat transfer from the fin tip are also taken into account. The mathematical expression for optimum dimension ration thus obtained is found to be as simple as that of the classical one-dimensional approach, but the accuracy of numerical results is improved significantly. The same approach is then utilized for solving for the optimum dimensions of a cylindrical pin fin. To facilitate thermal designers, numerous design charts are presented according to the nature of the flow, the boundary condition at the fin tip, and the types of heat transfer under consideration.
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