The influence of heat release on the dynamics of a porous material saturation in the course of gaseous silicon condensation

Abstract

The results of a direct numerical simulation are presented which describe the specific process of a porous medium high-temperature siliconizing. The calculations were performed taking into account the diffusion, the weak pressure gradient across a workpiece and the heat release during the condensation of gaseous silicon in pores. Phenomenological formulas for the evaporation and condensation coefficients in dependence on temperature are offered. An evolutionary equation for the temperature distribution in a sample is derived, which takes into account these processes. Mathematical statement of the problem is based on the modified MIM-model with addition Darcy’s law. Numerical modeling has been fulfilled by the finite difference method using an explicit scheme. It is shown that the heating release in the sample slows down the process of particle settling. The results of numerical simulation are consistent qualitatively with known experimental data.