A numerical solution of the melting problem of a semitransparent gray, medium contained in a closed heated spherical shell is presented in this study. The influence of all the fundamental energy transfer mechanisms on the melting dynamics of the phase change medium (PCM) has been analyzed, in order to extend the convectional natural convection-dominated model and to expand the limited literature in the thermal energy storage (TES) area at high operating temperatures (>800°C). A two-dimensional, axisymmetric, transient model has been solved numerically. The discrete ordinate method was used to solve the equation of radiative transfer and the finite volume scheme was used to solve the equations for mass, momentum and energy conservation. The effect of the optical thickness of the medium on the melt fraction rate, total and radiative heat transfer rates at the inner surface of the shell has been analyzed and discussed. Also the influence of thermal radiation has been quantified by performing comparisons between the pure conduction and the simultaneous conduction and radiation models. The results showed that the presence of thermal radiation enhances the melting process, particularly during the solid phase sensible heating process in the multi-mode heat transfer model. Also, it was found that the contribution of the radiant energy exchange is one order of magnitude smaller than the convective transport process.
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