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

In the present study, the effects of close-contact melting (CCM) are studied for geometries suitable for latent heat thermal energy storage. Specifically, a vertical double pipe concentric storage unit with circumferentially finned inner tube is explored experimentally. It is demonstrated that CCM enhances significantly the heat transfer rate, shortening the melting time by almost 2.5 times in that specific laboratory-scale device. These results show that it is favorable to supply heat to the outer shell of a latent-heat storage unit in order to initiate close-contact melting and achieve higher heat transfer rates. In order to analyze the process more closely, a single-cell vertical enclosure containing a phase-change material (PCM) is explored. A numerical model, which combines an enthalpy method with CCM modeling, is developed and validated experimentally. The solid bulk of the PCM is allowed to sink, thus enabling close-contact melting on the non-isothermal fin surface. The fins are thus much more important than just extended surfaces for heat transfer enhancement. The agreement between the numerical predictions and experimental findings is very good both in terms of the total melting time and instant melting patterns. The validated numerical model is further used for a detailed study, in which time dependent melt fractions and heat transfer rates are obtained for various temperature conditions. In all cases, the findings are compared with a simplified analytical model which accounts for the close-contact melting only, revealing effects not predicted by common CCM modeling approaches in the literature. 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 FoSte^3/4 only, whereas the Nusselt number and the normalized layer thickness both depend also on the same additional group, Ste^1/4. Based on these findings, the numerically calculated melt fractions, Nusselt numbers and layer thicknesses are generalized completely, showing a remarkable agreement.