Modelling and simulation of radiative heat transfer in non-grey absorbing and emitting media under phase change

Abstract

A class of mathematical models are proposed for modelling and numerical simulation of coupled radiative and conductive heat transfer in non-grey absorbing and emitting media under phase change. Progress in this area of mathematical modelling would contribute to a sustainable future manufacturing involving high temperature and phase change. Accurately predicting phase-change interface is the crucial step for these applications in non-grey semi-transparent media. In the present study, the conduction and radiation effects are analyzed by a set of nonlinear partial differential equations and a linear integral equation, respectively. The proposed model forms a system of nonlinear integro-differential equations and it accounts for both thermal radiation and phase change in the design. For non-grey media, the spectrum is divided into a sequence of finite intervals of frequency bands with averaged absorption coefficients resulting in coupled systems to be solved for each frequency band. The coupled equations are approximated using a second-order method in both time and space. Using discrete ordinates for the angular discretization of the integral equation for the radiation effects, a Newton-type algorithm is used to deal with the nonlinear systems. Numerical results are presented for several test problems in both grey and non-grey media, and comparisons to simulations without radiation are also shown in this study. The findings here could be used to understand effects of thermal radiation in non-grey absorbing and emitting media under phase change.