Thermal exploration of melting phenomena of four different annulus shapes’ (circular-circular, circular-rectangular, rectangular-circular, and rectangular-rectangular) beeswax-based phase change material for latent heat energy storage system is discussed here. To overcome the low efficiency in heat transfer because of low thermal conductivity of beeswax (the energy storage material in the current study), the composite-beeswax approach has been investigated numerically. Three metal oxides (Al2O3, MgO, and SiO2) with different volume concentrations (1%, 3%, and 5%) containing high thermal conductivity are dispersed into the pure beeswax. The 2-d continuity and momentum as well as energy transport mathematical model inside the composite-beeswax system have been adopted for the study, and we validated the model by available results in the literature. The obtained results revealed that both the melting rate and heat transfer are improved slightly in the case of rectangular-rectangular annulus shape. It was also shown from the result that the melting rate and heat transfer are improved significantly with the presence of metal oxide particles. Moreover, it was obtained that the types of particles have not affected noticeably the melting rate and heat transfer. For the three investigated nanoparticles, temperature of the system attained 346.4 K at 15000 s of process; at the same time, it is 341 K as noted for the beeswax, which shows an improvement of 1.4% in the case of circular-circular annulus and Al2O3. In the same conditions, melt fraction increases from 0.58 for beeswax to 0.91 for composite unit, thus showing 56.8% of improvement in the melting rate.