The solidification process in a multi-tube latent heat energy system is affected by the natural convection and the arrangement of heat exchanger tubes, which changes the buoyancy effect as well. In the current work, the effect of the arrangement of the tubes in a multi-tube heat exchanger was examined during the solidification process with the focus on the natural convection effects inside the phase change material (PCM). The behavior of the system was numerically analyzed using liquid fraction and energy released, as well as temperature, velocity and streamline profiles for different studied cases. The arrangement of the tubes, considering seven pipes in the symmetrical condition, are assumed at different positions in the system, including uniform distribution of the tubes as well as non-uniform distribution, i.e., tubes concentrated at the bottom, middle and the top of the PCM shell. The model was first validated compared with previous experimental work from the literature. The results show that the heat rate removal from the PCM after 16 h was 52.89 W (max) and 14.85 W (min) for the cases of uniform tube distribution and tubes concentrated at the bottom, respectively, for the proposed dimensions of the heat exchanger. The heat rate removal of the system with uniform tube distribution increases when the distance between the tubes and top of the shell reduces, and increased equal to 68.75 W due to natural convection effect. The heat release rate also reduces by increasing the temperature the tubes. The heat removal rate increases by 7.5%, and 23.7% when the temperature increases from 10 °C to 15 °C and 20 °C, respectively. This paper reveals that specific consideration to the arrangement of the tubes should be made to enhance the heat recovery process attending natural convection effects in phase change heat storage systems.