Abstract
Natural convection of liquid metal in an annular enclosure under the influence of azimuthal static magnetic field was numerically studied. The liquid metal in the enclosure whose cross-sectional area is square was heated from an inner vertical wall and cooled from an outer vertical wall both isothermally whereas the other two horizontal walls were assumed to be adiabatic. The static azimuthal magnetic field was imposed by a long straight electric coil that was located at the central axis of the annular enclosure. The computations were carried out for the Prandtl number 0.025, the Rayleigh number 104, 5 × 105 and 107, and the Hartmann number 0–100,000 by using an in-house code. It was found that the contour map of the electric potential was similar to that of the Stokes stream function of the velocity regardless of the Hartmann number. Likewise, the contour map of the pressure was similar to the Stokes stream function of the electric current density in the case of the high Hartmann number. The average Nusselt number was decreased in proportion to the square of the Hartmann number in the high Hartmann number regime.
Highlights
Natural convection of liquid metal under an external magnetic field is a phenomenon encountered in liquid blankets of a thermonuclear fusion reactor, metallurgy process, manufacturing single crystals of semiconductors, and so on [1,2]
One of the characteristics of liquid metal is that it has very high thermal conductivity and it is classified as low-Prandtl-number fluid
The natural convection of liquid metal having such properties is affected by the inertial force because of its low Prandtl number characteristics, so it tends to be oscillatory or to exhibit turbulent in the high Rayleigh number regime
Summary
Natural convection of liquid metal under an external magnetic field is a phenomenon encountered in liquid blankets of a thermonuclear fusion reactor, metallurgy process, manufacturing single crystals of semiconductors, and so on [1,2]. In the case of natural convection of liquid metal in a rectangular container, the effect of enhancement of heat transfer by applying a magnetic field would be obtained when the conductivity of the container wall is small (insulating wall) and the Rayleigh number should be rather high, and likely be limited to the case where the axis of the main vortex of the convection and the applied magnetic field are parallel to each other In such a case, all the current generated in the core region comes into the Hartmann layer, so the influence of the electric potential is large, which is related to the quasi-two-dimensionality of the flow field. In this study, we attempted to consider natural convection of liquid metal in an annular vessel having a rectangular cross-sectional area under the influence of an azimuthal magnetic field
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