Thermal energy storage is an important component in energy units to decrease the gap between energy supply and demand. Free convection and the locations of the tubes carrying the heat-transfer fluid (HTF) have a significant influence on both the energy discharging potential and the buoyancy effect during the solidification mode. In the present study, the impact of the tube position was examined during the discharging process. Liquid-fraction evolution and energy removal rate with thermo-fluid contour profiles were used to examine the performance of the unit. Heat exchanger tubes are proposed with different numbers and positions in the unit for various cases including uniform and non-uniform tubes distribution. The results show that moving the HTF tubes to medium positions along the vertical direction is relatively better for enhancing the solidification of PCM with multiple HTF tubes. Repositioning of the HTF tubes on the left side of the unit can slightly improve the heat removal rate by about 0.2 in the case of p5-u-1 and decreases by 1.6% in the case of p5-u-2. It was found also that increasing the distance between the tubes in the vertical direction has a detrimental effect on the PCM solidification mode. Replacing the HTF tubes on the left side of the unit negatively reduces the heat removal rate by about 1.2 and 4.4%, respectively. Further, decreasing the HTF temperature from 15 °C to 10 and 5 °C can increase the heat removal rate by around 7 and 16%, respectively. This paper indicates that the specific concern to the HTF tube arrangement should be made to improve the discharging process attending free convection impact in phase change heat storage.