Thermal storage modules offer a promising solution for efficient energy application. Thermal performance of flat-plate storage modules is analysed in rectangular, pentagonal, circular, and semicircular channels. Liquid fraction and average temperature of phase change materials are analysed in double-layer thermal storage modules. Compared with the rectangular channel case, the heat storage time of the thermal storage module with semicircular channels is reduced by 10.5%. The melting time of phase change materials decreases by 20.3% with an increase in the fluid inlet temperature from 338 K to 343 K. The heat release time of the thermal storage module with semicircular channels is shortened by 12.1% compared to that with rectangular channels. Compared to non-natural convection conditions, the melting rate of upper phase change materials increases by 36.7% under natural convection conditions, whereas the solidification rate of lower phase change materials increases by 12.8%. This work provides useful guidance for enhancing the heat transfer performance of thermal storage modules through semicircular channel configurations and natural convection.