Numerical simulation of stefan's problem in a plane layer with selective optical properties of a semitransparent medium

Abstract

Numerical investigation of melting of a plane layer with transparent and semitransparent boundaries has been carried out. The mathematical phase change model is a formulation of the One-Phase Stefan problem. The correct statement of radiative-conductive heat transfer (RCHT) problem requires accounting of optical properties as functions of radiation wavelength. To account the selectivity of optical properties the model of rectangular bands was applied. In this model some rectangular bands are taken in the spectrum with constant values of optical coefficients. The algorithm on the basis of modified mean fluxes method has been used for the numerical calculation of the radiation transfer equation. The energy equations are solved by a finite-difference method. The subject of this paper is to study the effect of the radiation on the temperature distribution and the velocity of the phase change front during melting of semitransparent medium. The first stage of the problem solving is to study RCHT in a solid plane layer by radiation and convection heating. The second stage is to consider Stefan’s problem. It is assumed that liquid phase sublimates and it is removed by convection. Numerical results of the temperature distribution, radiation fluxes and the position of the phase change front are presented in this paper. The numerical results are obtained first for the material with selective absorption of radiation with using One-Phase Stefan problem.