Coupled radiation and solidification heat transfer inside a graded index medium by finite element method

Effects of thermal radiation on solidification heat transfer must be considered inside semitransparent media. This paper investigates coupled heat transfer of solidification and radiation within a two-dimensional rectangular semitransparent medium having gradient index. Solidification process is supposed to happen at some temperature range, and accordingly three zones including liquid-, solid- and mushy-zones exist in phase-change media. In different phase field, parameters of thermophysical property are assumed different and those of radiative property are assumed same. Governing equation includes conduction, radiation and phase-change terms, and radiation and phase-change are treated as source terms in the equation, respectively. A Galerkin finite element method is used to solve energy equation of coupled radiation and phase-change heat transfer. This paper analyzes effect of thermal radiation on phase-change heat transfer and those of refractive index distributions on temperature fields and liquid fraction distributions during radiation-solidification coupled heat transfer. From the results, we can find that refractive index gradient has a major influence on phase-change process and compared with the case of smaller index gradient, bigger gradient can speed up phase-change heat transfer in semitransparent media.