Optimum Arrays of Longitudinal, Rectangular Fins in Corrective Heat Transfer

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Abstract
The theoretical basis for the least material optimization of convectively cooled arrays of longitudinal, rectangular fins is presented. The aspect ratio (fin thickness divided by fin width J of the array-optimum fin is found to be only marginally thinner than implied by the. conventional single fin optimization. Using this result, it is possible to define the geometry and thermal performance of least material, air-cooled natural convection arrays and to identify the array geometry yielding the maximum heat dissipation capability. Alternately, the added mass of a forced convection-cooled fin array is shown to be inversely related to the available pumping power and, as a consequence, no single optimum geometry could be defined. This paper includes several illustrative examples that serve to demonstrate the optimization pro cedure and to quantify the theoretical thermal performance of specific natural and forced convection air-cooled fin arrays.