Design of a modular heat storage for heat commodification: Optimal aspect ratio of a laterally heated PCM enclosure

In this work, we numerically investigate a rectangular PCM tank with isothermal heating applied to one vertical wall, while the remaining walls are insulated. The effects of enclosure length ( L ) and height ( H ) on melting performance are systematically examined. It is shown that for each length, there exists an optimal height that minimizes the melting time. Moreover, this optimal height H o p t decreases with increasing enclosure length and wall temperature. A theoretical model is developed and validated against simulation results, revealing that the optimal enclosure aspect ratio follows the scaling law A R o p t ∼ R a L − 1 / 7 . This framework provides practical guidance for the design of insert-free PCM enclosures aimed at rapid thermal response and efficient energy storage. • Increasing the enclosure length leads to a linear increase in melting time. • An optimal height, H opt , exists that minimizes the overall melting duration. • Theoretical correlations show that the optimal aspect ratio scales with R a L − 1 / 7 . • For solidification, H opt grows linearly with length at small scales, then plateaus.