- The present study deals with a latent heat thermal energy storage unit where an arbitrary number of phase-change materials (PCMs), arranged in a cascade, melt inside the tubes while a heat-transfer fluid flows across the tube bank. A mathematical model is solved numerically, and the effects of different parameters are explored, including the inlet velocity and temperature of the HTF, the number of rows, the number of materials, and the PCMs' melting temperature span. An optimal way is found to attain the shortest melting (charging) time for an entire multiple-PCM unit under given conditions. Generalization of the results is achieved for the optimal choice of uniformly-distributed melting temperatures. Unit behavior beyond optimum melting temperature span is also analyzed, and the overall limits for its improvement are defined. Furthermore, the model is re-defined to include the sensible heat capacity, comparing favorably with experimental results from the literature and demonstrating that the generalized results are applicable in this more realistic case as well.