A numerical study of natural convection in a vertical annulus filled with gallium in the presence of magnetic field

Presets work aims to investigate the natural convection inside a cylindrical annulus mold containing molten gallium under a horizontal magnetic field in three-dimensional coordinates. The modeling system is a vertical cylindrical annulus which is made by two co-axial cylinders of internal and external radii. The internal and external walls are maintained isothermal but in different temperatures. The upper and lower sides of annulus are also considered adiabatic while it is filled by an electrical conducting fluid. Three dimensional cylindrical coordinates as (r, theta, z) are used to respond the velocity components as (u, v, w). The governing equations are steady, laminar and Newtonian using the Boussinesq approximation. Equations are nonlinear and they must be corresponded by applying the finite volume approach; so that the hybrid-scheme is applied to discretize equations. The results imply that magnetic field existence leads to generate the Lorentz force in opposite direction of the buoyancy forces. Moreover the Lorentz force and its corresponded electric field are more significant in both Hartmann layer and Roberts layer, respectively. The strong magnetic field is required to achieve better quality products in the casting process of a liquid metal with a higher Prandtl number.