The global demand of the heating and cooling applications gives a larger potential to study the thermal energy storage system. Phase change materials (PCM) that are used to charge, store, and discharge the heat energy are inferior in heat transfer characteristics. The properties of PCM can be improved by adding nanoparticles, changing the orientation of the enclosure or both. Two-dimensional transient numerical analysis on the effect of Grashoff number (5000, 13000, and 20000), nanoparticle type (Al2O3, CuO, and MWCNT), and volume concentration (0%, 1%, 3%, and 5%) added in RT 42 PCM and orientation of square enclosure (30, 45, and 60°) to enhance the heat transfer rate is carried out. The thermophysical properties of the nano-PCM are evaluated and presented. From the results, it is affirmed that the melt fraction of the PCM rises with the increase in Gr and volume concentration of the nanoparticles up to an optimum level. The MWCNT-based nano-PCM attained a larger portion of melt fraction followed by Al2O3, CuO, and pure PCM. It is noted that an orientation of 60° and 45° will convert more quantities of pure PCM and nano-PCM into liquid fraction, respectively. The (3% MWCNT/RT-42 PCM) filled in 45° oriented container attained the highest melt fraction by 3.4%, 2.04%, and 2.94% than (3% Al2O3/RT-42 PCM), (1%CuO/RT-42 PCM), and pure PCM. The variation in the maximum melt fraction of the nanomaterial is because of the change in thermophysical characteristics of the nano-PCM.