In phase-change applications, once the melting process is completed, the natural convective heat transfer of liquid material may be promoted or degraded by the fins, which is the main motivation of this research. For this reason, the natural convection heat transfer inside a PCM container that can be a representative model for PV/PCM systems is numerically investigated in this study by considering three aspect ratios (AR = 1, 2 and 4), three Rayleigh numbers (Ra = 10(4), 10(5) and 10(6)), two types of fins as rectangular and tree-like branching fin, and three different length-to-height ratio of rectangular fin (w/ H = 0.3, 0.4 and 0.5). The rates of increment and decrement are presented taking the finless enclosure as the reference case. The computed results revealed that the natural convection is promoted up to 20%, depending on Ra and fin length by the inclusion of fins when the AR = 1, while it is degraded down by 5.5% for AR = 4. Interestingly, at AR = 2, the percentage increase and decrease of mean Nu numbers are slighter compared to other aspect ratios. Besides, it is also noticed in this study that utilizing a tree-like branching fin is not as effective as a rectangular fin with the same mass. (C) 2020 Elsevier Ltd. All rights reserved.