Lattice Boltzmann simulation of magnetohydrodynamic natural convection heat transfer of Al 2 O 3 –water nanofluid in a horizontal cylindrical enclosure with an inner triangular cylinder

In this study the lattice Boltzmann method is applied to investigate the effect of magnetic field on natural convection heat transfer of Al2O3–water nanofluid in a two-dimensional horizontal annulus. In this model, the effect of Brownian motion on the effective thermal conductivity is also considered. The effective thermal conductivity and the effective viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. The effect of nanoparticle volume fraction for the enhancement of heat transfer was examined for several sets of values of Rayleigh and Hartmann numbers. Also, a correlation of the Nusselt number with physical parameters is presented. The obtained results indicate that the value of the maximum stream function decreases with increasing Hartmann number. Furthermore, we notice that the Nusselt number has a direct relationship with the Rayleigh number; but quite the opposite is true with the Hartmann number. The obtained results indicate that the Lattice Boltzmann method with double-population is a powerful approach for the simulation of natural convection heat transfer in nanofluids in regions with curved boundaries.