Review of analytical studies of melting rate enhancement with fin and/or foam inserts

Phase change materials (PCMs) are extensively used in thermal energy storage (TES) applications but most of them own poor thermal conductivities. Melting of a PCM can be thermally enhanced by means of inserting high conducting fin and/or foam structures, nevertheless, relevant design guideline for a PCM system with these thermal enhancers is yet absent partly because our interpretation of such systems is limited to particular experiments or simulations that usually valid only over a certain (and narrow) range of parameter values. In order to develop such guideline for practicing engineers, one must gain a comprehensive understanding of melting characteristics under different conditions. Hence, this review concerns only on theoretical works of melting with/ without fin and foam structures. Isothermal melting without inserts inside a rectangular box under lateral, basal and inclined heating conditions will be firstly reviewed, afterwards, heat transport dimensions of melting in horizontal cylinder and sphere are clarified. Of a PCM system fin structures can be classified into straight and non-straight fins, whereas the former can be further subdivided into "short" lumped fins and "long" semi-infinite fins. Comparatively, only a few works of non-straight fins and porous foams are perceived due mainly to their irregular and complicated structures. Furthermore, different criteria for evaluating the performance of melting rate enhancement are summarized. Accordingly, the research gaps of theoretical works are remarked and several recommendations are introduced.