The melting duration in the photovoltaic/phase-change material (PV/PCM) system is a crucial parameter for thermal energy management such that its improvement can realize better energy management in respect to thermal storage capabilities, thermal conditions, and the lifespan of PV modules. An innovative and efficient technique for improving the melting duration is the inclusion of an exterior metal foam layer in the PV/PCM system. For detailed investigations of utilizing different metal foam configurations in terms of their convective heat transfer coefficients, the present paper proposes a newly developed mathematical model for the PV/PCM–metal foam assembly that can readily be implemented with a wide range of operating conditions. Both computational fluid dynamic (CFD) and experimental validations proved the good accuracy of the proposed model for further applications. The present research found that the average PV cell temperature can be reduced by about 12 °C with a corresponding improvement in PCM melting duration of 127%. The addition of the metal foam is more effective at low solar radiation, ambient temperatures far below the PCM solidus temperature, and high wind speeds in nonlinear extension. With increasing of tilt angle, the PCM melting duration is linearly decreased by an average value of (13.4–25.0)% when the metal foam convective heat transfer coefficient is changed in the range of (0.5–20) W/m2.K. The present research also shows that the PCM thickness has a positive linear effect on the PCM melting duration, however, modifying the metal foam configuration from 0.5 to 20 W/m2.K has an effect on the PCM melting duration in such a way that the average PCM melting duration is doubled. This confirms the effectiveness of the inclusion of metal foam in the PV/PCM system.