Numerical Simulation of the Effect of the Magnetic Field on Convective Heat Transfer in a Three-Dimensional L-Shaped Cavity

Abstract

This paper presents a numerical study of magnetohydrodynamic (MHD) natural convection in a three-dimensional L-shaped cavity using the lattice Boltzmann approach coupled with the finite difference method. The analysis focuses on the effect of a uniform vertical magnetic field on heat transfer, isotherms, and velocity field. The numerical code was validated by comparing our results with data available in the literature. The simulations revealed that, in the absence of a magnetic field, a significant improvement in heat transfer of 93.27% on the left vertical hot wall and 225.65% on the bottom hot wall was observed when the Rayleigh number (Ra) increased from 10^3 to 10^5. In the presence of the magnetic field, heat transfer decreased by 47.28% on the left vertical wall and 66.58% on the bottom wall, when the Hartmann number was increased from zero to 200 for Ra fixed at 10^5.