Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with linear temperature distribution

This paper examines the natural convection in a square enclosure filled with a water–Al2O3 nanofluid and is subjected to a magnetic field. The bottom wall is uniformly heated and vertical walls are linearly heated whereas the top wall is well insulated. Lattice Boltzmann Method (LBM) is applied to solve the coupled equations of flow and temperature fields. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number of the base fluid, Ra = 103 to 105, Hartmann number varied from Ha = 0 to 60, the inclination angle of the magnetic field relative to the horizontal plane γ = 0° to 180° and the solid volume fraction of the nanoparticles between ϕ = 0 and 6%. The results show that the heat transfer rate increases with an increase of the Rayleigh number but it decreases with an increase of the Hartmann number. Also for Ra ≥ 5 × 104 and for the range of Hartmann number study, we note that the heat transfer and fluid flow depend strongly upon the direction of magnetic field. In addition, according the Hartmann number, it observed that the magnetic field direction controls the effects of nanoparticles.