The present study is devoted to the topic of the effectiveness of the use of metal foam in a cooling system based on phase change materials. The melting process of a material in a closed rectangular region with porous metal fins when heated from a source of constant volumetric heat generation was studied numerically. A mathematical model describing the heat transfer processes taking into account the presence of a moving boundary and convective mixing of the melt was formulated in dimensionless transformed variables: stream function, vorticity and temperature. Using the finite difference method, temperature fields and streamlines were obtained for two heat sinks with vertical and horizontal foam fins for different foam properties.