This study evaluates the efficiency of a thermal storage system during the freezing process of a water-nanoparticle mixture in a uniquely designed curved container with fins. The container's enhanced conduction is attributed to the presence of nanoparticles, which are strategically placed to improve heat transfer. The finite element method (FEM) with an adaptive grid is used to simulate the unsteady phenomena, providing a robust analytical framework. The nanoparticle fraction ($\phi$) and diameter ($dp$) are key factors influencing the solidification rate. The results show that increasing $\phi$ from 0 to 0.04 reduces the freezing time by 21.31% and 8.79% for $dp$ values of 30 and 50 nm, respectively. The optimal size of $dp$ is found to be around 40 nm, where the freezing time is minimized. The study highlights the importance of carefully selecting parameters to optimize cold storage efficiency, contributing to a deeper understanding of freezing dynamics and practical insights for the design and enhancement of cold storage technologies.This study evaluates the efficiency of a thermal storage system during the freezing process of a water-nanoparticle mixture in a uniquely designed curved container with fins. The container's enhanced conduction is attributed to the presence of nanoparticles, which are strategically placed to improve heat transfer. The finite element method (FEM) with an adaptive grid is used to simulate the unsteady phenomena, providing a robust analytical framework. The nanoparticle fraction ($\phi$) and diameter ($dp$) are key factors influencing the solidification rate. The results show that increasing $\phi$ from 0 to 0.04 reduces the freezing time by 21.31% and 8.79% for $dp$ values of 30 and 50 nm, respectively. The optimal size of $dp$ is found to be around 40 nm, where the freezing time is minimized. The study highlights the importance of carefully selecting parameters to optimize cold storage efficiency, contributing to a deeper understanding of freezing dynamics and practical insights for the design and enhancement of cold storage technologies.