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This study aims to study the discharging process to verify the influence of geometry modifications and heat transfer flow (HTF) patterns on the performance of a vertical triplex-tube latent heat container. The phase change material (PCM) is included in the middle tube, where the geometry is modified using single or multi-internal frustum tubes instead of straight tubes to enhance the discharging rate. The effects of the HTF flow direction, which is considered by the gravity and opposite-gravity directions, are also examined in four different cases. For the optimal geometry, three scenarios are proposed, i.e., employing a frustum tube for the middle tube, for the inner tube, and at last for both the inner and middle tubes. The effects of various gap widths in the modified geometries are investigated. The results show the advantages of using frustum tubes in increasing the discharging rate and reducing the solidification time compared with that of the straight tube unit due to the higher natural convection effect by proper utilization of frustum tubes. The study of the HTF pattern shows that where the HTF direction in both the inner and outer tubes are in the gravity direction, the maximum discharging rate can be achieved. For the best configuration, the discharge time is reduced negligibly compared with that for the system with straight tubes which depends on the dimensions of the PCM domain.