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Laplace transforms and numerical quadrature are used to solve the problem of one-dimensional heat conduction in a double layered sandwich of two partially transparent materials, heated from above by EM radiation which is exponentially attenuated with depth. Criteria are given for simplifying these expressions where the upper medium is effectively opaque, and/or the lower medium is effectively infinitely thick. It is also shown that the general expressions reduce to commonly known results for limiting cases. The results are relevant to processing materials by means of radiant heating.
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Curzon et al. (1992) studied this question.
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