Using the local thermal non-equilibrium assumption,a numerical study is conducted on the natu-ral convection of Cu-water nanofluid in a porous square cavity with solid matrix of glass beads and foam a-luminum,respectively.The effects of dimensionless interphase heat transfer coefficient,Rayleigh number,porosity,and nanoparticle volume fraction on the heat transfer characteristics on the natural convection heat transfer characteristics of nanofluid in porous square cavity are investigated.The results show that the local thermal equilibrium model can replace the local thermal non-equilibrium model to calculate the natu-ral convection inside a porous cavity when the Rayleigh number is low.When the Rayleigh number is high,for the natural convection in the porous cavity filled with glass beads,the local thermal equilibrium model can be used to calculate the heat transfer when the porosity is high,while the local thermal non-equilibrium model should be used to calculate the heat transfer for the porous cavity filled with foam aluminum.When Cu-water nanofluid is used in the cavity filled with foam aluminum,the overall heat transfer rate remains unchanged.For the cavity filled with glass beads,the use of Cu-water nanofluid can significantly increase the heat transfer rate when the Rayleigh number is low,while the heat transfer rate of the cavity filled with glass beads decreases with the increase of the volume fraction of nanoparticles when the Rayleigh number is high.