The sporadic nature of energy resources, especially renewable ones, underscores the need for reliable energy storage. Phase change materials (PCMs) are of great importance regarding saving energy, however, their low thermal conductivity lengthens the transition evolution which is the main problem of this system. So, many methods address this issue among which fins and nanoparticles, used in this study, are expected to have significant positive effects on the solidification rate and PCM response time. Various cases based on the presence of fins and nanoparticles are introduced and solved with Galerkin Finite Element Method (GFEM) and validated with authentic data for the solidification process. A novel mixture of nanoparticles MoS2 - Fe3O4 called Hybrid Nano-Particles (HNP) is applied at different concentrations to the PCM to compensate for unfavorable ramifications of single-type nanoparticle. Also, the star shape triplex LHTESS with internal fins is the geometrical arrangement of storage unit. The results expose a substantial improvement by using each technique individually, while the lowest solidification rate is assigned to the combination usage of both techniques. Furthermore, the comparisons done in this work reveal the better performance of fins alone when juxtaposed with the result of HNPs alone. (C) Elsevier Ltd. All rights reserved.