Abstract
This paper deals with an unsteady heat-conduction problem in a plate of regular polygonal shape using conformal mapping techniques. The classical approach to an exact solution of the Fourier heat equation is the separation of variables technique. For more complicated boundaries, e.g. a hexagonal plate, it is convenient to transform the given shape onto a unit circle where the boundary conditions can be identically satisfied. However, the transformed partial differential equation can only be satisfied approximately. Two “weighted-residuals” techniques are used to solve it, and solutions are obtained for several polygonal shapes. The method can be extended easily in the case of some doubly connected regions of technical importance, e.g. the graphite brick of a gas cooled nuclear reactor.
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