Findings of numerical investigation of the synergistic relationship between heat conduction and thermal convection in convection-enhanced energy storage units with varying length longitudinal fin is reported. The influence of geometric parameters of rectangular, trapezoidal, and heptahedral energy storage containers, as well as the thickness of longitudinal fins, on the melting of RT42 is explored. The dependence of fin types (rectangular, trapezoidal, and triangular) on the continuous melting and solidification processes of PCM is revealed. The results indicate that the finned heptahedral container exhibits the most effective enhancement in thermal convection. Specifically, with a rectangular fin thickness of 0.2 mm, the optimal heptahedral unit reduces the melting completion time by 10.26% compared to the rectangular container, while increasing the heat storage rate by 11.1%. As fin thickness increases, the enhanced thermal conductivity of the fins decreases, leading to an increase in both the optimal length ratio of the upper and lower surfaces of the enclosures and the melting completion time. Moreover, incorporating non-uniform longitudinal fins with longer bottoms and shorter tops in convection-enhanced energy storage units can synergistically enhance both thermal conductivity and convective heat transfer. Among these configurations, the heptahedral enclosure with a triangle fin exhibits the best melting performance, resulting in a 13.16% reduction in melting time and a 13.7% increase in heat storage rate compared to the rectangular container with a rectangle fin. Conversely, rectangular containers exhibit a faster solidification rate, and adding a triangle fin further reduces the solidification time and improves heat release performance.