Simplified modeling approaches and analysis for combined close-contact and convective melting in vertical cylindrical enclosures

The present study deals with development and analysis of innovative simplified modeling approaches for combined close-contact and convective melting in vertical cylindrical enclosures. First, we suggest a new model for melting in peripherally isothermally heated vertical cylindrical enclosures, for which the outer shell thickness and thermal conductivity are finite, and the bottom of the enclosure is perfectly insulated. We show that our new model can accurately predict the melt fraction temporal evolution for a wide range of enclosure materials, aspect ratios, and outer temperatures. Second, we extend the newly suggested model for the case of combined close-contact and convective melting under isothermal wall conditions. Extensive comparison between our model predictions and existing results from the literature shows an excellent agreement. Then, we carry out dimensionless analysis for the model equations and reveal the governing dimensionless groups for the problem. Our analysis also shows that close-contact melting from the bottom of the enclosure is typically the most dominant heat transfer mechanism for isothermal wall conditions. Finally, we further extend the new model for the case of vertical cylindrical enclosures with a finite thickness and thermal conductivity. On contrary with the isothermal wall case, we show that the interplay between melting from the bottom and the peripheral walls of the enclosure is highly sensitive to the cylindrical enclosure thickness and thermal conductivity. For instance, we show that a 50-times increase in the thermal conductivity ratio between the phase change material and the outer shell can increase the total melting time by more than twice, whereas the initial molten layer thickness can decrease by more than twice. Our detailed analysis demonstrates very different trends for the temporal evolution of the liquid molten layer thickness, and the solid height and radius.