Lattice Boltzmann Simulation of Magnetohydrodynamic Free Convection in a Square Enclosure with Non-Uniform Heating of the Bottom Wall

Abstract

A steady tow-dimensional Magnetohydrodynamic (MHD) free convection flow in a square cavity filled with an electrically conducting fluid which is get under a uniform magnetic field at different angles is numerically investigated using lattice Boltzmann method (LBM). The bottom wall is non-uniformly heated and vertical walls are maintained at cold temperature whereas the top wall is well isolated. The influence of pertinent parameters such as, Reyleigh number (103≤ Re ≤ 105), the Hartmann number (0 ≤ Ha ≤ 70) and the inclination angle of the magnetic field (0°≤ θ≤ 180°) on the flow and heat transfer characteristics have been examined. The obtained results indicate that the heat transfer rate decreases with an increase of the Hartmann number but increases with increase of the Rayleigh number. Also, for high Rayleigh number (Ra = 105) and for the range of Hartmann number, the heat transfer and fluid flow inside the enclosure depend strongly upon the magnetic field direction.