A lattice Boltzmann investigation of two-phase natural convection of Cu-water nanofluid in a square cavity

A numerical investigation of two-phase natural convection of Cu-water nanofluid in a square cavity is conducted by using a novel volume fraction-thermal lattice Boltzmann method to solve the governing equations of the flow field, temperature field, and nanoparticle volume fraction distribution field. The study explores the effects of the variable nanoparticle volume fraction at different Rayleigh numbers (10(3) <= Ra <= 10(6)) and initial nanoparticle volume fractions (0.01 <= phi(initial) <= 0.05) on streamlines, isotherms and the Nusselt number. The results have shown that the Nusselt number along side walls would decrease when the Rayleigh number is large, with the opposite effects on parts of the side walls when the Rayleigh number is small. The relative difference of Nusselt number has a positive correlation with both the Rayleigh number and the initial nanoparticle volume fraction. When the Rayleigh number or the initial nanoparticle volume fraction is relatively large, the slip mechanisms of nanoparticles play an important role, and the two-phase model should be adopted instead of the conventional homogeneous one-phase model.