A numerical modeling of natural convection under the influence of either axial (Bz) or radial (Br)magnetic field in a cylindrical configuration filled with a low-Prandtl number electrically conductingfluid, is studied. The finite volume method is used to discretize the equations of continuity, NavierStokes and energy. A computer program based on the SIMPLER algorithm is developed. The flowand temperature fields are presented by stream function and isotherms, respectively. Stabilitydiagrams are established according to the numerical results of this investigation. These diagrams putin evidence the dependence of the critical Grashof number,Grcrwith the increase of the Hartmannnumber,Ha. The strongest stabilization of the convective flows occurs when the magnetic field isapplied in the radial direction. This study confirms the possibility of stabilization of a liquid metalflow in natural convection by application of a radial magnetic field.