Using phase change materials (PCMs) in energy storage systems provides various advantages such as energy storage at a nearly constant temperature and higher energy density. In this study, we aimed to conduct a numerical simulation for augmenting a PCM’s melting performance within multiple tubes, including branched fins. The suspension contained Al2O3/n-octadecane paraffin, and four cases were considered based on a number of heated fins. A numerical algorithm based on the finite element method (FEM) was applied to solve the dimensionless governing system. The average liquid fraction was computed over the considered flow area. The key parameters are the time parameter (100 ≤t≤600 s) and the nanoparticles’ volume fraction (0%≤φ≤8%). The major outcomes revealed that the flow structures, the irreversibility of the system, and the melting process can be controlled by increasing/decreasing number of the heated fins. Additionally, case four, in which eight heated fins were considered, produced the largest average liquid fraction values.