On the initial-boundary heat conduction problem for system with phase transfer

The paper is devoted to constructing of the mathematical model of aluminum alloy solidification process in a fettled steel mold with a centered thermosyphon. Thermal fields modeling is included boundary conditions of the second and third kind (radiative-convective heat exchange with the environment and the heat exchange with a thermosyphon), contact conditions of the fourth kind on the interface of dissimilar materials, as well as the construction of the phase transition boundary on the basis of the continuous calculation principles.