Two phase simulation of natural convection and mixed convection of the nanofluid in a square cavity

A numerical study is carried out concerning natural and mixed convection heat transfer of nanofluid in a two-dimensional square cavity with several pairs of heat source-sinks. Two-dimensional Navier-Stokes, energy and volume fraction equations are solved using the finite volume method. Effects of various design parameters such as external and internal heating, number of the coolers, Rayleigh number (10(3) <= Ra <= 10(7)), Richardson number (0.01 <= Ri <= 1000), nanoparticle volume fraction (0 <= phi <= 0.05), size (25nm 145nm) and type (Cu, Al2O3, TiO2) on the heat transfer rate and distribution of nanoparticles are investigated. The simulation results indicate that there is an optimal volume fraction of the nanoparticles for each Rayleigh number and Richardson number at which the maximum heat transfer rate occurs. It is also observed that at low Rayleigh numbers and high Richardson numbers, the particle distribution is fairly non-uniform. Moreover, it is found that thermophoretic effects are negligible for nanoparticles with high thermal conductivity. As a result, in such conditions the use of homogeneous and single-phase models is valid at any Ra and Ri. (C) 2015 Elsevier B.V. All rights reserved.