Melting　heat　transfer　in　open-cell　metal　foams　embedded　in　phase-change　materials　(PCMS)　predicted　by　the　volume-averaged　method　(VAM)　was　systematically　compared　with　that　calculated　using　direct　numerical　simulation　(DNS),　with　particular　attention　placed　upon　the　contribution　of　natural　convection　in　the　melt　region　to　overall　phase　change　heat　transfer.　The　two-temperature　model　based　on　the　assumption　of　local　thermal　non-equilibrium　was　employed　to　account　for　the　large　difference　of　thermal　conductivity　between　metallic　ligaments　and　PCM　(paraffin).　The　Forchheimer　extended　Darcy　model　was　employed　to　describe　the　additional　flow　resistance　induced　by　metal　foam.　For　the　DNS,　a　geometric　model　of　metal　foam　based　on　tetrakaidehedron　cells　was　reconstructed.　The　DNS　results　demonstrated　significant　temperature　difference　between　ligament　surface　and　PCM,　thus　confirming　the　feasibility　of　local　thermal　non-equilibrium　employed　in　VAM　simulations.　Relative　to　the　DNS　results,　the　VAM　combined　with　the　two-temperature　model　could　satisfactorily　predict　transient　solid-liquid　interface　evolution　and　local　temperature　distribution,　although　pore-scale　features　of　phase　change　were　lost.　The　presence　of　natural　convection　affected　significantly　the　melting　front　shape,　temperature　distribution　and　full　melting.　The　contribution　of　natural　convection　to　overall　phase　change　heat　transfer　should　be　qualitatively　and　quantitatively　given　sufficient　consideration　from　both　macroscopic　(VAM)　and　microscopic　(DNS)　point　of　views.　Besides,　practical　significance　and　economic　prospective　using　metal　foam　in　TES　unit　for　WHR　system　to　provide　residential　heating　or　hot　water　is　discussed　and　analyzed.　©　2018　Elsevier　Ltd