In this paper, applying new structure and loading Graphene nanoparticles have been considered as promising techniques for enhancing thermal storage systems. The layers within the paraffin zone were made from aluminum and the melting temperature of paraffin is 319.55 K. The paraffin zone located in the middle section of the triplex tube and uniform hot temperatures (335 K) for both walls of annulus have been applied. Three geometries for the container were applied with changing the angle of fins (α = 7.5°, 15° and 30°). The uniform concentration of additives was assumed involving a homogeneous model for predicting properties. Results indicate that loading Graphene nanoparticles causes time of melting to decrease about 4.98% when α = 7.5° and the impact of ϕ improves about 5.2% with reduce of angle from 30° to 7.5°. In addition, as angle declines, the period of melting decreases around 76.47% which is associated with augmentation of driving force (conduction) in geometry with lower α.