Numerical simulation of natural convection and mixed convection of the nanofluid in a square cavity using Buongiorno model

A numerical study is carried out concerning natural and mixed convection heat transfer of nanofluid (Al2O3–water) in a laterally-heated square cavity. Two-dimensional continuity, Navier–Stokes, energy and volume fraction equations are solved using finite volume method. The effects of various design parameters such as Rayleigh number (102 ≤ Ra ≤ 107), volume fraction (0 ≤ φ ≤ 0.05), size of nanoparticles (25 nm ≤ dp ≤ 145 nm), Richardson number (0.01 ≤ Ri ≤ 1000) and Grashof number (102 ≤ Gr ≤ 104) on the heat transfer rate and distribution of nanoparticles for both natural and mixed convection cases are investigated. The simulation results indicate that there is an optimal volume fraction of the nanoparticles at each Rayleigh and Richardson number for which the maximum heat transfer rate can be obtained. It is also observed that at low Rayleigh numbers and high Richardson numbers, the particle distribution is fairly non-uniform while at high Ra and low Ri values particle distribution remains almost uniform for free and mixed convection cases, respectively.