Secondary flows induced in helical-coiled pipes significantly enhance the thermal storage performance of latent heat thermal energy storage units. This paper presents a three-dimensional model of a triple-pipe helical-coiled system to investigate the melting characteristics of phase change material within it. A correlation for the complete melting time was developed based on the simulation results. The findings indicate that the thermal-hydraulic fields of the heat transfer fluids and phase change material deflect from the vertical central axis at cross-sections. The secondary flows within the inner pipe are more effective in enhancing melting than those in the outer pipe. Melting performance improves with increasing inner pipe diameter, coil diameter (from 100 mm to 160 mm), inclination angle, or heat transfer fluid temperature, or decreasing helical pitch. The inner pipe diameter, helical pitch and heat transfer fluid temperature exhibit more pronounced influences. An inner pipe diameter of 30 mm, a coil diameter of 160 mm, a helical pitch of 80 mm, an inclination angle of 90°, a heat transfer fluid temperature of 360 K, and a heat transfer fluid Reynolds number of 2000, respectively produce a faster melting process. The developed correlation for the triple-pipe helical-coiled pipe thermal storage unit accurately predicts 96 % of the 45 data within ±11 %.