Numerical analysis of three-dimensional MHD natural convection flow in a short horizontal cylindrical annulus

A numerical study of three-dimensional (3D) MHD laminar flow in a short horizontal cylindrical annulus has been performed to characterize the impacts of a uniform axial magnetic field on both hydrodynamic and thermal behaviors. This configuration corresponds to a horizontal annular mold containing molten iron or low carbon steel in electromagnetic casting (EMC). Complex nonlinear governing equations are solved numerically by means of the finite volume method based on artificial compressibility algorithm. The induced electric potential caused by the magnetic field is considered. Results show that a typical 3D steady spiral flow arises and the symmetry breaking occurs under a weak magnetic field of Ha < 10. As the Hartmann number increases, the spiral flow is distinctly suppressed, and then it changes to a helical flow with two transverse cells adjacent to each of the end walls. Correspondingly, the flow patterns and isotherms of fluid become symmetric with respect to the mid-axial plane of the annulus. Further increasing the Hartmann number, the fluid particle trajectories essentially lie in the cross-section of the annulus, as for two-dimensional solutions, with an extremely small axial dependency. In addition, both the values of local Nusselt number at the isothermal walls and its axial dependency, mainly in the upper region (−38π≤φ≤38π), are significantly affected by the magnetic field. The results of the present work can be useful in producing high-quality products by magnetic control.