Thermal energy storage systems utilising phase change materials offer significantly higher energy densities compared to traditional solutions, and are therefore attracting growing interest in both research and application fields. However, the further development of this technology requires effective methods to enhance thermal efficiency. We propose a horizontal periodic shell-and-tube structure as an efficient latent heat thermal energy storage unit. This research aims to analyse heat transfer not only between the tube containing the heat transfer fluid and the phase change material but also between adjacent shell-and-tube units. The results obtained for a single cell within the periodic structure are compared with those of reference single shell-and-tube units with insulated adiabatic and highly conductive shells. The enthalpy–porosity approach, combined with the Boussinesq approximation, is applied to address the heat transfer challenges encountered during melting and solidification. The periodic horizontal shell-and-tube structure proves to be an efficient latent heat thermal energy storage unit with short melting and solidification times. In contrast, the non-periodic case with neglected conduction in the shell increases the melting and solidification times by 213.8% and 21%, respectively. The shortest melting and solidification times were recorded for the case with a periodic horizontal shell-and-tube structure and shell aspect ratios of 0.44 and 1, respectively.