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• A greater proportion of copper metal foam (CMF) can enhance the heat transfer of paraffin wax and reduce the temperature gradient. • A theoretical model was built to calculate the comprehensive heat transfer coefficient of composite PCMs and to determine the intensity change of heat conduction and natural convection of PCMs with different CMF proportions. • Melting time and heat storage capacity of CMF composite PCMs first increased and then decreased with increasing CMF proportion. • Heat storage rate and comprehensive heat transfer coefficient first decreased and then increased with increasing CMF proportion. • Composite PCMs with a CMF proportion of 0.86% exhibit the best heat storage performance. Phase-change materials (PCMs) can overcome the low energy density and utilization efficiency of solar energy. However, the low thermal conductivity of PCMs significantly affects the thermal efficiency of solar devices; thus, improving the thermal conductivity of PCMs has been the focus of many recent studies. In this study, copper metal foam (CMF) composite PCMs were prepared using paraffin wax and high-pore-density CMF. The effect of the CMF proportion on heat transfer enhancement in the PCM melting process was analyzed using experimental equipment for heat storage visualization. Comprehensive heat transfer coefficients of CMF composite PCMs were obtained. The experimental results showed that as the CMF proportion increased from 0 to 2.15%, the melting time of the CMF composite PCMs and their heat storage capacity first increased and then decreased, whereas the heat storage rate and comprehensive heat transfer coefficient first decreased and then increased. The minimum temperature gradient of 8.09 K was reached when the CMF proportion was 2.15%. More importantly, as the proportion of CMF increased from 0.43 to 2.15%, the proportion of natural convection decreased from 87.90 to 17.69%, and natural convection was the major heat transfer mechanism in the melting process of composite PCMs with a low CMF proportion. The composite PCMs with a CMF proportion of 0.86% has the best heat storage performance when the heat storage capacity and heat storage rate were both considered. [ABSTRACT FROM AUTHOR]