Close-contact melting in vertical annular enclosures with a non-isothermal base: Theoretical modeling and application to thermal storage

The analytical model yields theoretical expressions for the time-dependent melt fraction, heat transfer rate and molten layer thickness in a dimensionless form. For the conditions of the present study, the dimensional analysis indicates that the melt fraction depends on the Fourier and Stefan numbers combined as FoSte3/4 only, whereas the Nusselt number and the normalized layer thickness both depend also on the same additional group, Ste1/4. Based on these findings, the numerically calculated melt fractions, Nusselt numbers and layer thicknesses are generalized completely, showing a remarkable agreement.