An analytical solution for the static temperature distribution on the surface of a heat-sinked integrated chip with one isothermal heat source is derived. The mathematical technique applied to solve the Laplace equation is a double Schwarz-Christoffel conformal transformation. Perturbations in the temperature distribution due to the heat source and the chip finite length are evaluated as well as the temperature losses in the vicinity of the heat source. Explicit expressions of the normalized temperature and thermal input conductance are given and analyzed as a function of the source and chip relative dimensions.
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A.A. Bilotti (1974) studied this question.
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