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

Abstract

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.