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• The mathematical model can accurately predict the melting heat transfer process of PCMs. • The Rayleigh number increased with the heat flux, and the higher the heat flux, the larger the amplitude. • Increasing the heat flux improved the integrated heat transfer coefficient and thermal storage performance of the CPCMs. • Conduction was the primary heat transfer mechanism; however, the proportion of natural convection increased with the heat flux. To investigate the effect of heat flux on the enhanced heat transfer in phase change materials (PCMs) composed of copper metal foam (CMF) and paraffin wax (PX), a semi-cylindrical visualized heat storage device with a varied heat flux of 7.3 kW/m2, 8.5 kW/m2, 9.7 kW/m2, and 10.9 kW/m2 was established in this paper. Moreover, a 3-D mathematical model of composite phase change materials (CPCMs) was established using hybrid grid to study the temperature distribution, imbalance effect, flow, heat transfer mechanisms, and heat storage performance during the melting process. The results showed that the melting time of the CPCMs decreased as the heat flux increased. Compared with a heat flux of 7.3 kW/m2, the melting time was shortened by 10.05 %, 20.71 %, and 27.21 %, respectively. In addition, the Rayleigh number (Ra) increased with the increase in heat flux, and the amplitudes of Ra were 1.45×108,1.54×108,1.61×108, and 1.74×108, respectively, which indicated that the higher the heat flux, the larger the amplitudes. Moreover, the heat transfer mechanism during the melting process was dominated by conduction; however, with the increase in heat flux, the maximum flow velocity of the liquid paraffin increased, which caused the proportion of natural convection to increase from 27.80 % to 31.30 %. Hence, the integrated heat transfer coefficient of CPCMs increased from 5.69 W/(m·K) to 5.81 W/(m·K). However, the temperature imbalance effect of the CPCMs was exacerbated, as evidenced by the increased maximum temperature difference in the vertical direction of the center of the CPCMs from 24.7 K to 35.6 K. Besides, the heat storage performance was enhanced. Compared with a heat flux of 7.3 kW/m2, the heat storage capacities of the CPCMs increased by 4.21%, 9.46%, and 12.66 % with increasing heat flux, and the heat storage rates of the CPCMs increased by 15.3 %, 34.9 %, and 52.3 %, respectively. Furthermore, the relative error of the overall melting time was 3.4 %, indicating that the model provided reasonable predictions. [ABSTRACT FROM AUTHOR]