Magnetohydrodynamic convection in molten gallium

Juel, Anne; Mullin, T.; Hadid, H. Ben; Henry, Daniel

doi:10.1017/s0022112098003061

Cited by 54 publications

(41 citation statements)

References 29 publications

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“…BenHadid & Henry 1997) are symmetric to rotations of π about the y-axis (rotationsymmetry) and to reflections with respect to the L v plane (left-right symmetry). However, in the experimental flows of Hurle, Jakeman & Johnson (1974), Braunsfurth et al (1997) and Juel et al (1999) this rotation-symmetry is not usually observed. As in any physical system, imperfections tend to break the perfect symmetries assumed in models.…”

Section: Resultsmentioning

confidence: 95%

“…In a combined numerical and experimental study, Juel et al (1999) measure the vertical temperature difference at a given Grashof number for varying Hartmann numbers in a transverse applied field. Experimental and numerical results show excellent agreement and, in particular, flows observed in the calculations become increasingly two-dimensional with increasing Hartmann number.…”

Section: Introductionmentioning

confidence: 99%

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Magnetohydrodynamic damping of convective flows in molten gallium

Hof

Juel²,

Mullin

2003

J. Fluid Mech.

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We report the results of an experimental study of magnetohydrodynamic damping of sidewall convection in a rectangular enclosure filled with gallium. In particular we investigate the suppression of convection when a steady magnetic field is applied separately in each of the three principal directions of the flow. The strongest damping of the steady flow is found for a vertical magnetic field, which is in agreement with theory. However, we observe that the application of a field transverse to the flow provides greater damping than a longitudinal one, which seems to contradict available theory. We provide a possible resolution of this apparent dichotomy in terms of the length scale of the experiment.

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Section: Resultsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic damping of convective flows in molten gallium

Hof

Juel²,

Mullin

2003

J. Fluid Mech.

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“…They found that the average Nusselt number increases with Marangoni number, but decreases with Hartmann number. Some notable studies on the numerical simulation of combined buoyancy and/or thermocapillary convection in a differentially heated rectangular enclosures are due to Strani et al (1983), Srinivasan and Basu (1986), Bergman and Ramadhyani (1986), Bergman and Keller (1988), Juel et al (1999), Moessner and Mueller (1999) and Gelfgat and Bar-Yoseph (2001). The effect of magnetic field on the combined buoyancy and thermocapillary driven convection in a rectangular enclosure containing a heat generating substance has been numerically investigated by Hossain et al (2005).…”

Section: Introductionmentioning

confidence: 99%

Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure

Sankar

Venkatachalappa

2011

International Journal of Heat and Fluid Flow

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a b s t r a c tThe main objective of this article is to study the effect of magnetic field on the combined buoyancy and surface tension driven convection in a cylindrical annular enclosure. In this study, the top surface of the annulus is assumed to be free, and the bottom wall is insulated, whereas the inner and the outer cylindrical walls are kept at hot and cold temperatures respectively. The governing equations of the flow system are numerically solved using an implicit finite difference technique. The numerical results for various governing parameters of the problem are discussed in terms of the streamlines, isotherms, Nusselt number and velocity profiles in the annuli. Our results reveal that, in tall cavities, the axial magnetic field suppresses the surface tension flow more effectively than the radial magnetic field, whereas, the radial magnetic field is found to be better for suppressing the buoyancy driven flow compared to axial magnetic field. However, the axial magnetic field is found to be effective in suppressing both the flows in shallow cavities. From the results, we also found that the surface tension effect is predominant in shallow cavities compared to the square and tall annulus. Further, the heat transfer rate increases with radii ratio, but decreases with the Hartmann number.

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“…[8][9][10][11][12] In this paper, we provide insight into the damping mechanisms at play through the direct computation of Hopf bifurcation points and the analysis of the associated three-dimensional flow solutions. Similar continuation calculations have been performed in the absence of a magnetic field in a rectangular parallepiped enclosure, revealing multiple flow structures depending on the values of the aspect ratios and Prandtl number.…”

Section: Introductionmentioning

confidence: 99%

Directional effect of a magnetic field on oscillatory low-Prandtl-number convection

et al. 2008

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The directional effect of a magnetic field on the onset of oscillatory convection is studied numerically in a confined three-dimensional cavity of relative dimensions 4:2:1 ͑length:width:height͒ filled with mercury and subject to a horizontal temperature gradient. The magnetic field suppresses the oscillations most effectively when it is applied in the vertical direction, and is the least efficient when applied in the longitudinal direction ͑parallel to the temperature gradient͒. In all cases, however, exponential growths of the critical Grashof number, Gr c ͑Gr, ratio of buoyancy to viscous dissipation forces͒ with the Hartmann number ͑Ha, ratio of magnetic to viscous dissipation forces͒ are obtained. Insight into the damping mechanism is gained from the fluctuating kinetic energy budget associated with the time-periodic disturbances at threshold. The kinetic energy produced by the vertical shear of the longitudinal basic flow dominates the oscillatory transition, and when a magnetic field is applied, it increases in order to balance the stabilizing magnetic energy. Moreover, subtle changes in the spatial distribution of this shear energy are at the origin of the exponential growth of Gr c . The destabilizing effect of the velocity fluctuations strongly decreases when Ha is increased ͑due to the decay of the velocity fluctuations in the bulk accompanied by the appearance of steep gradients localized in the Hartmann layers͒, so that an increase of the shear of the basic flow at Gr c is required in order to sustain the instability. This yields an increase in Gr c , which is reinforced by the fact that the shear of the basic flow naturally decreases at constant Gr with the increase of Ha, particularly when the magnetic field is applied in the vertical direction. For transverse and longitudinal fields, the decay of the velocity fluctuations is combined with an increase of the shear energy term due to a sustained growth in stabilizing magnetic energy with Ha.

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Magnetohydrodynamic convection in molten gallium

Cited by 54 publications

References 29 publications

Magnetohydrodynamic damping of convective flows in molten gallium

Magnetohydrodynamic damping of convective flows in molten gallium

Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure

Directional effect of a magnetic field on oscillatory low-Prandtl-number convection

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