This study aims to numerically investigate the melting process of a phase change material in an H-type finned concentric shell tube configuration. The H-type fins are arranged in a manner that creates an annulus structure consisting of six identical H-type fin structures. These fins are evenly spaced with equal distances between them. The phase change material used in this study is RT42, which is stored within the annulus structure to absorb heat from the inner circular tube at a constant temperature input of 70 °C. The results of the study demonstrate that the phase change material within the H-type fin tube, with a uniform width of 3 mm, exhibit significantly faster melting rates compared to narrower fin tubes. Specifically, the phase change material in the 3 mm fin tube demonstrate melting rates that are 88% and 32% higher than those observed in fin tubes with widths less than 1 mm and 2 mm, respectively.Furthermore, the study considers two additional geometric factors, namely the varying curvy angles of the first and second circular layers of the H-type fins. Melting behavior is numerically featured by varying the ratios of these curvy angles within the range of 0.68 to 1.53. Among all the H-type annulus structures of the present study, the ratio of 1.21 is the most suitable design for increasing the total energy stored, while the ratio of 1.32 is an adequate choice for improving melting performance. Additionally, the latter ratio results in a 1.68 times reduction in melting time compared to the ratio of 1. Properly arranged H-type fin structures are possibly considered a preferable design that can either enhance heat transfer or increase the total stored energy, possibly expanding PCM applicability to a more latent heat thermal energy storage systems of practical interest.