Numerical and experimental study of melting in a spherical shell

The present study explores numerically and experimentally the process of melting of a phase-change material (PCM) in spherical geometry. Its properties used in the simulations, including the melting temperature, latent and sensible specific heat, thermal conductivity and density in solid and liquid states, are based on a commercially available paraffin wax, which is manufactured to be used mainly in latent-heat-based heat storage systems. A detailed parametric investigation is performed for melting in spherical shells of 40, 60, and 80 mm in diameter, when the wall-temperature is uniform and varies from 2 °C to 20 °C above the mean melting temperature of the PCM. Transient numerical simulations are performed using the Fluent 6.0 software. These simulations show the melting process from the beginning to the end, and incorporate such phenomena as convection in the liquid phase, volumetric expansion due to melting, sinking of the solid in the liquid, and close contact melting. The results of the experimental investigation, which included visualization, compare favorably with the numerical results and thus serve to validate the numerical approach. The computational results show how the transient phase-change process depends on the thermal and geometrical parameters of the system, including the temperature difference between the wall and the mean melting temperature, and the diameter of the shell. Dimensional analysis of the results is performed and presented as the mean Nusselt numbers and PCM melt fractions vs. an appropriate combination of the Fourier, Stefan, and Grashof numbers. This analysis leads to generalization which encompasses the cases considered herein.