This study numerically investigates the charging and discharging behavior of multi-phase change materials (m-PCMs) enhanced in a semi-cylindrical enclosure equipped with rectangular and triangular fins. Organic (H395, H380, H355) and inorganic (PCM-S, PCM-M, PCM-C) PCMs are analyzed for liquid fraction and temperature distribution at nanofluid concentrations of 0.1%, 0.2%, and 0.3%. Key thermal parameters, including the Nusselt number, heat transfer coefficient, and pressure drop, are evaluated. Results reveal that using 0.3% nanofluids significantly improves heat transfer and accelerates melting and solidification. The rectangular fin configuration demonstrates superior performance, storing approximately 73,000 J compared to 55,000 J for the triangular fin. This improvement is attributed to optimized fin geometry, orientation, and enhanced thermal conductivity. Applications include solar heating, building energy management, and waste heat recovery. Furthermore, the Random Forest machine learning model effectively predicts energy storage performance, achieving an R² value of 0.99 for both training and testing datasets, confirming high predictive accuracy.