This research proposes an innovative configuration for modifying the thermal management system of the photovoltaic (PV) panel, integrated with a phase-change material (PCM) with an attached exterior metal-foam layer to the rear part of the PCM container. The configuration enables faster heat dissipation from the system leading to longer thermal-management duration for the PV panel during the energy storage (PCM charging) mode. Also, it supports faster energy recovery (PCM discharging) rate by decreasing the amount of heat trapped in the melted part of the PCM during the solidification mode. The effects of the foam-layer inclusion, PCM thickness, and PV tilt angle are numerically simulated and revealed. A mathematical model that accounts for natural convection effects of the melted PCM and non-Darcy effects of the metal foam, is formulated and validated via previous experiments. The results show that inclusion of an exterior foam layer could increase the PCM melting time, and the corresponding PV thermal-management duration, by up to 32% and 55% respectively, depending on the PCM thickness and PV tilt angle. The results also show that reducing the tilt angle from 90 degrees to 30 degrees increases the melting time by about 18%. Thus, a superior PCM-based thermal management is achieved. Moreover, utilizing PCM of thickness in the range of 20-30 mm lengthens the melting time by up to 54%, enhancing the potential for improved thermal management of PV panels.