This study numerically intends to evaluate the effects of arc-shaped fins on the melting capability of a triplex-tube confinement system filled with phase-change materials (PCMs). In contrast to situations with no fins, where PCM exhibits relatively poor heat response, in this study, the thermal performance is modified using novel arc-shaped fins with various circular angles and orientations compared with traditional rectangular fins. Several inline and staggered layouts are also assessed to maximize the fin’s efficacy. The effect of the nearby natural convection is further investigated by adding a fin to the bottom of the heat-storage domain. Additionally, the Reynolds number and temperature of the heat-transfer fluid (HTF) are evaluated. The outcomes showed that the arc-shaped fins could greatly enhance the PCMs’ melting rate and the associated heat-storage properties. The melting rate is 17% and 93.1% greater for the case fitted with an inline distribution of the fins with a circular angle of 90° and an upward direction, respectively, than the cases with uniform rectangular fins and no fins, which corresponded to the shorter melting time of 14.5% and 50.4%. For the case with arc-shaped fins with a 90° circular angle, the melting rate increases by 9% using a staggered distribution. Compared to the staggered fin distribution, adding an extra fin to the bottom of the domain indicates adverse effects. The charging time reduces by 5.8% and 9.2% when the Reynolds number (Re) rises from 500 to 1000 and 1500, respectively, while the heat-storage rate increases by 6.3% and 10.3%. When the fluid inlet temperature is 55°C or 50°C, compared with 45°C, the overall charging time increases by 98% and 47%, respectively.