In this study, we examine the melting behavior of paraffin wax mixed with Cu0 nanoparticles within a square cavity that incorporates a triangular double fin. The investigation focuses on different nanoparticle concentrations (1% and 2%) and considers the melting process under constrained conditions. Two different arrangements of double fin are analyzed based on melting performance keeping the total area of fin constant. Arrangement with lower fin having longer length and shorter base has better melting performance. Melting performance increases with the addition of nanoparticles. The addition of 1% nanoparticles results in a notable enhancement in the melt rate. However, when the volume fraction of nanoparticles is further increased to 2%, the increase in the melt fraction becomes negligible in comparison to the 1% nanoparticle concentration. This is due to the increase in effective viscosity which negatively impacts the occurrence of natural convection, resulting in a less notable increase in the melt rate. Compared to single nanoparticles hybrid nanoparticles (Al2O3+CuO) perform better in terms of melting. Impact of uniform magnetic field on the melting of NePCM is examined by introducing the Lorentz force term into the momentum equation. Magnetic field is found to decrease the phenomenon of natural convection and, hence melting rate. However, the influence of magnetic field is found to be insignificant in the initial phases of the melting process. due to weak natural convection. The present work could be used for the optimization of LHTES unit integrated with fins and subjected to magnetic field in industries.