Abstract The conjugate flow and heat transfer of phase change materials (PCMs)-metal foam confined between two annuli is addressed. A pulse heat load is employed at the inner surface of annuli, while the outer surface is subject to convection cooling. (This content of this sentence is the same as that in other sentences.) The enthalpy-porosity approach is utilized to model the phase change, and the natural convection in the porous medium is taken into account using Darcy-Brinkman model. The governing equations are transformed into non-dimensional form and solved by the finite element method. The finite element method is employed to solve the governing equations in the non-dimensional form. An automatic grid adaptation technique is employed to capture the phase change interface. The results are compared with theoretical and experimental studies available in the literature and found in good agreement. The steady-state solution and transient characteristics are addressed. The results demonstrate that the heatsink filled with PCM-metal foam can enhance the heat transfer at the hot surface, particularly at low external cooling power (Biot number