Heat distribution in an infinite medium in the presence of a flat interface
Abstract
Let us consider the following problem in the theory of heat conduction. An initial temperature distribution is given in a space consisting of two media separated by a flat interface. It is required to find the temperature at any point in the space, at any moment of time. The thermal characteristics of each of the two media are assumed to be constant. The formulated problem has been considered by a number of authors for the one-dimensional case. The possibility of solving the multidimensional case using integral equations was pointed out by Münz [4]. In [5], a two-dimensional problem was solved by the method of successive approximations. In the present paper, a closed-form solution of the problem under consideration is given for the two- and three-dimensional case. The solution method can be applied to a number of similar problems.
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References
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- Carslow H.S. Theory of Heat Conduction. Gostekhteoretizdat, 1947. (in Russian)
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- Munz G. Integral equations. V. 1, 1934. (in Russian)
- Kim E.I. Heat propagation in an infinite inhomogeneous body in two dimensions. PMM Prikladnaya matematika i mekhanika, 1953, vol. 17, vol. 5. (in Russian)