This paper aims to study the effect of circular Y-shaped fin arrangement to improve the low thermal response rates of a double-tube heat exchanger containing Paraffin phase change material (PCM). ANSYS software is employed to perform the computational fluid dynamic (CFD) simulations of the heat exchanger, including fluid flow, heat transfer, and the phase change process. The optimum state of the fin configuration is derived through sensitivity analysis by evaluating the geometrical parameters of the Y-shaped fin. For the same height of the fins (10 mm), the solidification time is reduced by almost 22%, and the discharging rate is enhanced by almost 26% using Y-shaped fins compared with the straight fins. The results demonstrate that the solidification time is inversely proportional to the fin's length. The heat release rate for the case with the longest fins (stem length of 10 mm) is 39 W, almost 2.8 times higher than that with the fins' stem length of 5 mm. The case with the tributary's angle of 22.5o solidified in 55 min, faster than the other studied angles. Increasing the number of fins significantly affects the solidification time and discharging rate. By increasing the number of fins from 3 to 9, the heat transfer rate improves by 194%. The advantages of circular Y-shaped fins are well known in heat transfer applications and therefore are characterized toward higher performance in this study for the first time during the solidification process.