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In this work, the two-dimensional laminar flow and the heat transfer in an open-ended rectangular porous channel (metal foam) including a phase change material (PCM; paraffin) under forced convection were numerically investigated. To gain further insight into the foam pore effect on charging/discharging processes, the Darcy–Brinkmann–Forchheimer (DBF) unsteady flow model and that with two temperature equations based on the local thermal non-equilibrium (LTNE) were solved at the representative elementary volume (REV) scale. The enthalpy-based thermal lattice Boltzmann method (TLBM) with triple distribution function (TDF) was employed at the REV scale to perform simulations for different porosities (0.7≤ε≤0.9) and pore per inch (PPI) density (10≤PPI≤60) at Reynolds numbers (Re) of 200 and 400. It turned out that increasing Re with high porosity and PPI (0.9 and 60) speeds up the melting process, while, at low PPI and porosity (10 and 0.7), the complete melting time increases. In addition, during the charging process, increasing the PPI with a small porosity (0.7) weakens the forced convection in the first two-thirds of the channel. However, the increase in PPI with large porosity and high Re number limits the forced convection while improving the heat transfer. To sum up, the study findings clearly evidence the foam pore effect on the phase change process under unsteady forced convection in a PCM-saturated porous channel under local thermal non-equilibrium (LTNE).