The melting process of storage materials with relatively high phase change temperatures in partially filled spherical shells

A two dimensional axisymmetric model of the heat transfer and fluid flow during the melting process inside a spherical latent heat thermal storage capsule is analyzed. A void space was provided within the capsule to take into account the volumetric expansion of the PCM. The mathematical model was solved using the finite-volume method, and the enthalpy-porosity formulation was employed to solve the energy equations in both the liquid and solid regions of the PCM. The effects of the Grashof and Stefan numbers on the thermal performance of the capsules of various diameters (20, 30, 40 and 50 mm) have been investigated. It was found that increasing the Grashof number from 1.32 × 104 to 2. 06 × 105 enhances the heat transfer. Also for a constant Grashof number (9.09 × 104) the PCM melts at a faster rate when the Stefan number increases from 0.077 to 0.097. Finally, appropriate dimensionless variables based on a combination of the Fourier, Grashof and Stefan numbers are introduced in order to obtain a generalized correlation for the liquid mass fraction and the Nusselt number during melting of sodium nitrate.