Two time-dependent mathematical and numerical models with different levels of complexity and fidelity were developed to investigate the freezing of a PCM configured as a slab with an embedded serpentine microchannel evaporator of a vapor compression refrigeration system. The time-dependent PCM freezing process was first analyzed using finite-element modeling (FEM) of a representative 2-D domain. This model incorporates 2-D conduction and natural convection within the molten PCM. The FEM revealed that natural convection is negligible and that the freezing front advances in essentially 1-D fashion. However, the long execution time of FEM makes it unsuitable for repetitive design optimization of thermal storage devices. Consequently, a fast-executing quasi 2-D reduced-order model (ROM) was developed. The ROM is then utilized to study the freezing process in a multi-slab thermal storage device that is designed to store ∼500 W-h of “cooling” during ∼8 h of freezing operation at night, to be subsequently released for local cooling of room air during the day. The results show that (1) freezing rate is strongly affected by the frozen PCM thermal conductivity; (2) freezing almost ceases once the refrigerant is fully evaporated; (3) refrigerant exit quality drops precipitously toward the end of the freezing cycle.

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