A thermal model of periodic crystallization

A model of periodic crystallization is constructed on the basis of the wave equation of heat transfer with two energy sources exponentially dependent on temperature. In the problem of metal crystallization in a mold, these sources are competing. In the problem of explosive crystallization of amorphous films, the sources have the same sign. Both problems are analytically solved using the generalized separation of variables and the construction of finite-mode Galerkin approximations. The amplitude and period of oscillations of the phase boundary velocity are analyzed. Spatially periodic structures of the one-and two-dimensional thermal fields are constructed. It is found that the isotherm chains are arranged in a staggered manner. Other important regularities are revealed.