Multi-mode heat transfer analysis during freezing of an encapsulated storage medium

Simultaneous conduction, convection and thermal radiation have been analyzed during the freezing of a non-opaque, non-gray phase change material (PCM) encapsulated in a closed spherical container and heated at relatively high temperatures (250 ⩽ T ⩽ 325 °C). In contrast to the well-known conduction-dominated model of the single phase Stefan problem, in the present study the influence of the participating thermal radiation and the buoyancy induced natural convection within the melt layer is highlighted and analyzed. 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 additional parameters like the shell size and the external heat transfer coefficient imposed on the outer shell surface as a boundary condition have also been analyzed. It was found that the contribution of thermal radiation on the solidification process of NaNO3NaNO3 is to reduce the solidification time by 17% as compared with the limiting case where thermal radiation is neglected.