Hartmann number

About: Hartmann number is a research topic. Over the lifetime, 2593 publications have been published within this topic receiving 61342 citations.

Numerical study of convection in the horizontal Bridgman configuration under the action of a constant magnetic field. Part 1. Two-dimensional flow

Abstract: Studies of convection in the horizontal Bridgman configuration were performed to investigate the flow structures and the nature of the convective regimes in a rectangular cavity filled with an electrically conducting liquid metal when it is subjected to a constant vertical magnetic field. Under some assumptions analytical solutions were obtained for the central region and for the turning flow region. The validity of the solutions was checked by comparison with the solutions obtained by direct numerical simulations. The main effects of the magnetic field are first to decrease the strength of the convective flow and then to cause a progressive modification of the flow structure followed by the appearance of Hartmann layers in the vicinity of the rigid walls. When the Hartmann number is large enough, Ha > 10, the decrease in the velocity asymptotically approaches a power-law dependence on Hartmann number. All these features are dependent on the dynamic boundary conditions, e.g. confined cavity or cavity with a free upper surface, and on the type of driving force, e.g. buoyancy and/or thermocapillary forces. From this study we generate scaling laws that govern the influence of applied magnetic fields on convection. Thus, the influence of various flow parameters are isolated, and succinct relationships for the influence of magnetic field on convection are obtained. A linear stability analysis was carried out in the case of an infinite horizontal layer with upper free surface. The results show essentially that the vertical magnetic field stabilizes the flow by increasing the values of the critical Grashof number at which the system becomes unstable and modifies the nature of the instability. In fact, the range of Prandtl number over which transverse oscillatory modes prevail shrinks progressively as the Hartmann number is increased from zero to 5. Therefore, longitudinal oscillatory modes become the preferred modes over a large range of Prandtl number.

Natural Convection Heat Transfer in a Rectangular Enclosure With a Transverse Magnetic Field

Abstract: The effect of a transverse magnetic field on buoyancy-driven convection in a shallow rectangular cavity is numerically investigated (horizontal Bridgman configuration). The enclosure is insulated on the top and bottom walls while it is heated from one side and cooled from the other. Both cases of a cavity with all rigid boundaries and a cavity with a free upper surface are considered. The study covers the range of the Rayleigh number, Ra, from 10 2 to 10 5 , the Hartmann number, Ha, from 0 to 10 2 , the Prandtl number, Pr, from 0.005 to 1 and aspect ratio of the cavity, A, from 1 to 6. Comparison is made with an existing analytical solution (Garandet et al.), based on a parallel flow approximation, and its range of validity is delineated. Results are presented for the velocity and temperature profiles and heat transfer in terms of Ha number. At high Hartmann numbers, both analytical and numerical analyses reveal that the velocity gradient in the core is constant outside the two Hartmann layers at the vicinity of the walls normal to the magnetic field.