In this study, a mathematical model is introduced to simulate the coupled heat transfer equation and Stefan condition occurring in moving boundary problems such as the solidification process in the continuous casting machines. In the continuous casting process, there exists a two-phase Stefan problem with moving boundary. The control-volume finite difference approach together with the boundary ...

A model for species diffusion is presented, with evaporation at a moving free boundary. The resulting problem resembles a one-phase Stefan problem with superheating, but the usual Stefan condition at the moving boundary is replaced by a version which, in the classical setting, would violate conservation of energy. In the fast evaporation limit, however, the problem reduces to a classical nonlin...

Phase change materials are substances that absorb and release thermal energy during the process of melting and freezing. This characteristic makes phase change material (PCM)  a favourite choice to integrate it in buildings. Stephan problem including melting and solidification in PMC materials is an practical problem in many engineering processes. The position of the moving boundary, its veloci...

The one-phase reduction of the Stefan problem, where the phase change temperature is a variable, is analysed. It is shown that problems encountered in previous analyses may be traced back to an incorrectly formulated Stefan condition. Energy conserving reductions for Cartesian, cylindrically and spherically symmetric problems are presented and compared with solutions to the two-phase problem.

We argue that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics up to now, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii's ideas for numerical solution of the problem is developed. Mathematical modelling of energy relaxation of some processes useful in modern ion beam technologies i...

We claim that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii ideas for numerical solution of the problem is developed. Mathematical modelling of energy relaxation of some processes useful in modern ion beam technologies is fulfilled....

<p style='text-indent:20px;'>We consider the problem of recovering initial condition in one-dimensional one-phase Stefan for heat equation from knowledge position melting point. We first recall some properties free boundary solution. Then we study uniqueness and stability inversion. The principal contribution paper is a new logarithmic type estimate that shows inversion may be severely il...