An analytical solution is conducted on forced convection in a metal foam partially filled plate channel under asymmetric heat flux conditions, with the aim of optimizing heat transfer performance. The Darcy–Brinkman model and the local thermal non-equilibrium (LTNE) model are employed to predict heat transfer characteristics under varying heat flux ratios (q1/q2). Key parameters such as the free zone height, pore density, and thermal conductivity ratio significantly influence heat transfer efficiency. The results indicate that the height of the free region has a greater impact on the flow distribution than porosity and pore density. When the non-dimensional height of the free region is 0.3, the flow fraction in the free region reaches 80%. When the free zone height is H = 0.1, the heat exchanger heat transfer coefficient reaches its maximum value, and the combination of copper (Cu) and R134a refrigerant demonstrates superior convective heat transfer performance compared to the empty channel. Their optimization can lead to substantial improvements in the heat transfer effectiveness of the channel.