A steady laminar two-dimensional magneto-hydrodynamics (MHD) natural convection
flow in a square enclosure filled with an electrically conducting fluid is numerically investigated
using Lattice Boltzmann Method (LBM). The left and right vertical sidewalls of the square enclosure
are maintained at hot and cold temperatures respectively. The horizontal top and bottom walls
are considered thermally insulated. An adiabatic square shaped body is located in the center of a
square enclosure and an external magnetic field is applied parallel to the horizontal x-axis. In the
present work, the following parametric ranges of the non-dimensional groups are utilized: Hartmann
number is varied as 0 6 Ha 6 50, Rayleigh number is varied as 103 6 Ra 6 105, Prandtl number
is varied 0.05 6 Pr 6 5. It is found that the Hartmann number, Rayleigh number, and Prandtl
number have an important role on the flow and thermal characteristics. It is found that when the
Hartmann number increases the average Nusselt number decreases. The results also explain that the
effect of magnetic field on flow field increases by increasing Prandtl number. However, the Prandtl
number effect on the average Nusselt number with a magnetic field is less than the case without a
magnetic field. Comparisons with previously published numerical works are performed and good
agreements between the results are observed.