One approach to the analytical solution of a two-dimensional nonstationary problem of heat conduction in regions with moving boundaries on the model of a half-space


With the use of the solution of the Dirichlet nonstationary problem with discontinuous unmixed boundary conditions on the surface of an isotropic half-space a two-dimensional model of the problem with a moving phase boundary is considered. The problem models, for example, the processes of freezing of moist ground or the processes of formation of ice in stagnant water if a temperature lower than the freezing temperature is prescribed on the boundary surface in a circular region of finite radius. The classical one-dimensional result follows as a particular case from solution of this problem for an infinite radius of the circle

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