Analysis of Steady Heat Conduction in Regions with Circular Holes by a Special Boundary-integral Method

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Abstract
Special boundary-integral equations developed in an earlier paper are used here to analyse problems of steady heat conduction in regions with circular holes. In this approach, the solution on the boundary of each hole is expanded in circular harmonics and the unknown coefficients are determined by a special system of boundary-integral equations. Approximate equations, which retain only the first harmonic of the solution expansion on each hole, are solved analytically for three problems involving symmetric arrangements of holes inside a circle. These results compare extremely well with an available exact solution in one case and with numerical solutions of an exact integral equation in several others.

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