Increase in the heat transfer rate during melting and freezing of a phase change material (PCM) with a low thermal conductivity is demonstrated by inserting a high-porosity metal matrix into the PCM. A vertical annulus space (r1⩽r⩽r0,0⩽z⩽h)homogeneously fitted with water and an aluminum matrix, is selected for this study. The Navier-Stokes equations are modified to account for Darcy's effect. For both the melting and freezing cases, the density inversion phenomenon of water is considered. The irregularity and time-varying nature of the solid and the liquid regions are accounted for by a geometric coordinate transformation. The numerical results are presented in the form of solid-liquid interface movements, isotherms, streamlines, and heat transfer rates for some representative cases. The heat transfer rates for enhanced cases show an order-of-magnitude increase over the base case, where no metal matrix is inserted.