This study explores the enhancement of charging performance in a triplex-tube latent heat thermal energy storage system (TTHX) by integrating longitudinal fins and alumina nanoparticles in phase change materials (PCMs). Numerical simulations are conducted to systematically examine the influence of fin length, thickness, number, and orientation, alongside the impact of nano-enhanced PCMs (NEPCMs) to identify optimal configurations for improved charging performance. The results show that incorporating fins accelerates the melting process, with thinner, more numerous fins providing the greatest enhancement. The optimal configuration, consisting of 64 fins with a reduced thickness of 125 µm, achieved an 86% reduction in charging time compared to the baseline case without fins. While adding nanoparticles to the PCM further improved heat transfer, concentrations exceeding 4% led to a decline in the system's overall thermal storage capacity. Among the PCMs studied, RT80-HC outperformed RT82 due to its higher latent heat of fusion and narrower phase-change temperature range. Additionally, horizontal fin configurations demonstrated a slight advantage by increasing the solid–liquid interface area, further enhancing melting efficiency. This study provides a comprehensive analysis of fin optimization and NEPCM integration in TTHXs, offering a better insight into maximizing thermal energy storage performance. The findings contribute to the development of more efficient latent heat thermal energy storage systems, supporting advancements in renewable energy utilization.