An Efficient Algorithm for Evaluating Arrays of Extended Surface

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Abstract
In the consideration of single longitudinal fins of rectangular, trapezoidal, and triangular profile and in arrays of extended surface composed of these fins, it is shown that conditions of heat flow and temperature excess at the fin or array tip induce conditions of heat flow and temperature excess at the fin or array base. In particular, there is a linear transformation between the aforementioned data at the fin tip and the fin base. The conventional fin efficiency is abandoned and single fins or arrays of extended surface are instead characterized by a single important parameter, the heat flow to temperature excess ratio, which is a function only of fin geometry and heat transfer parameters. Algorithms are provided for combining the effects of individual fins in arrays of extended surface. A modification of the procedures developed leads to an exact solution for the double stack with unequal heat distribution at opposite ends, a problem which has heretofore required iterative solution procedures.

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