Abstract
A theoretical series solution for the one-dimensional temperature distribution along a straight rectangular profile fin with variable surface heat transfer coefficient is presented. The method of solution is by direct integration of the basic differential equation and avoids the need for tables of functions which is a feature of previous methods for this case. It is shown that the result corresponds with the familiar closed-form solution when the heat transfer coefficient is uniform. The results of calculations for the maximum temperature variation for a range of typical distribution of heat transfer coefficient are also included.
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