Abstract
ABSTRACTThis paper deals with constant-area, longitudinal fins with rectangular and circular cross-sections for the condition of prescribed tip temperature. For these fin geometries, the optimum aspect ratios for maximum heat transfer per unit volume have been determined analytically in the literature for the cases of adiabatic tip and convective tip using a one-dimensional analysis. For the case of prescribed tip temperature, a numerical two-dimensional analysis was reported for rectangular fins. In the present study, the temperature distribution and rates of heat transfer at the base and tip of both fin cross-sections were determined using one– and two-dimensional analyses. The ranges of independent parameters within which the one-dimensional solution was within 1% from the two-dimensional solution were determined, and simple analytical formulae for the optimum aspect ratios were derived based on the one-dimensional solution. An example is given showing the application of the results in design.
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