Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field

Agnieszka Hudoba, Sergei Molokov, Svetlana Aleksandrova, Alex Pedcenko

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Abstract

Linear stability of buoyant convective flow in a horizontal layer of an electrically conducting fluid is considered with reference to horizontal Bridgman semiconductor crystal growth. The fluid flows owing to the horizontal temperature gradient in the presence of a vertical magnetic field. The main interest here is in the stability of the flow for a sufficiently strong magnetic field, for the Hartmann number Ha > 10, and increasing to high values, of the order of 103–104. The Prandtl number, Pr, has been fixed at Pr = 0.015. It is shown that besides the Hartmann number the instability strongly depends on the type of the thermal boundary conditions at the horizontal walls. For thermally conducting walls the basic temperature profile exhibits zones of unstable thermal stratification, which leads to instabilities owing to the Rayleigh-Bénard mechanism. However, the transitions between various, most unstable modes as Ha increases are not trivial. For sufficiently high values of Ha, the most unstable mode consists of transverse oscillatory rolls located in the region of unstable stratification. For thermally insulating walls, the transitions are simpler, and for sufficiently high Ha, the most unstable mode consists of longitudinal, steady, three-dimensional mode which is concentrated in the Hartmann layers at the horizontal boundaries. This mode has a combined dynamic-thermal origin and is owed to a strong shear in the Hartmann layers. The electrical boundary conditions do not qualitatively affect the picture of transitions between modes for both thermally conducting and thermally insulating walls.
Publisher Statement: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.

 

The following article appeared in Hudoba, A, Molokov, S, Aleksandrova, S & Pedcenko, A 2016, 'Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field' Physics of Fluid, vol 28, 094104 and may be found at https://dx.doi.org/10.1063/1.4962741

Original languageEnglish
Article number094104
JournalPhysics of Fluid
Volume28
DOIs
Publication statusPublished - 21 Sep 2016

Fingerprint

conducting fluids
convection
magnetic fields
Hartmann number
stratification
boundary conditions
conduction
convective flow
Prandtl number
temperature profiles
fluid flow
crystal growth
temperature gradients
shear
physics
fluids

Bibliographical note

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.

The following article appeared in Hudoba, A, Molokov, S, Aleksandrova, S & Pedcenko, A 2016, 'Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field' Physics of Fluid, vol 28, 094104 and may be found at https://dx.doi.org/10.1063/1.4962741

Keywords

  • Thermal conduction
  • Magnetic fields
  • Flow instabilities
  • Boundary value problems
  • Energy balance

Cite this

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title = "Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field",
abstract = "Linear stability of buoyant convective flow in a horizontal layer of an electrically conducting fluid is considered with reference to horizontal Bridgman semiconductor crystal growth. The fluid flows owing to the horizontal temperature gradient in the presence of a vertical magnetic field. The main interest here is in the stability of the flow for a sufficiently strong magnetic field, for the Hartmann number Ha > 10, and increasing to high values, of the order of 103–104. The Prandtl number, Pr, has been fixed at Pr = 0.015. It is shown that besides the Hartmann number the instability strongly depends on the type of the thermal boundary conditions at the horizontal walls. For thermally conducting walls the basic temperature profile exhibits zones of unstable thermal stratification, which leads to instabilities owing to the Rayleigh-B{\'e}nard mechanism. However, the transitions between various, most unstable modes as Ha increases are not trivial. For sufficiently high values of Ha, the most unstable mode consists of transverse oscillatory rolls located in the region of unstable stratification. For thermally insulating walls, the transitions are simpler, and for sufficiently high Ha, the most unstable mode consists of longitudinal, steady, three-dimensional mode which is concentrated in the Hartmann layers at the horizontal boundaries. This mode has a combined dynamic-thermal origin and is owed to a strong shear in the Hartmann layers. The electrical boundary conditions do not qualitatively affect the picture of transitions between modes for both thermally conducting and thermally insulating walls.Publisher Statement: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.   The following article appeared in Hudoba, A, Molokov, S, Aleksandrova, S & Pedcenko, A 2016, 'Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field' Physics of Fluid, vol 28, 094104 and may be found at https://dx.doi.org/10.1063/1.4962741",
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T1 - Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field

AU - Hudoba, Agnieszka

AU - Molokov, Sergei

AU - Aleksandrova, Svetlana

AU - Pedcenko, Alex

N1 - This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Hudoba, A, Molokov, S, Aleksandrova, S & Pedcenko, A 2016, 'Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field' Physics of Fluid, vol 28, 094104 and may be found at https://dx.doi.org/10.1063/1.4962741

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N2 - Linear stability of buoyant convective flow in a horizontal layer of an electrically conducting fluid is considered with reference to horizontal Bridgman semiconductor crystal growth. The fluid flows owing to the horizontal temperature gradient in the presence of a vertical magnetic field. The main interest here is in the stability of the flow for a sufficiently strong magnetic field, for the Hartmann number Ha > 10, and increasing to high values, of the order of 103–104. The Prandtl number, Pr, has been fixed at Pr = 0.015. It is shown that besides the Hartmann number the instability strongly depends on the type of the thermal boundary conditions at the horizontal walls. For thermally conducting walls the basic temperature profile exhibits zones of unstable thermal stratification, which leads to instabilities owing to the Rayleigh-Bénard mechanism. However, the transitions between various, most unstable modes as Ha increases are not trivial. For sufficiently high values of Ha, the most unstable mode consists of transverse oscillatory rolls located in the region of unstable stratification. For thermally insulating walls, the transitions are simpler, and for sufficiently high Ha, the most unstable mode consists of longitudinal, steady, three-dimensional mode which is concentrated in the Hartmann layers at the horizontal boundaries. This mode has a combined dynamic-thermal origin and is owed to a strong shear in the Hartmann layers. The electrical boundary conditions do not qualitatively affect the picture of transitions between modes for both thermally conducting and thermally insulating walls.Publisher Statement: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.   The following article appeared in Hudoba, A, Molokov, S, Aleksandrova, S & Pedcenko, A 2016, 'Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field' Physics of Fluid, vol 28, 094104 and may be found at https://dx.doi.org/10.1063/1.4962741

AB - Linear stability of buoyant convective flow in a horizontal layer of an electrically conducting fluid is considered with reference to horizontal Bridgman semiconductor crystal growth. The fluid flows owing to the horizontal temperature gradient in the presence of a vertical magnetic field. The main interest here is in the stability of the flow for a sufficiently strong magnetic field, for the Hartmann number Ha > 10, and increasing to high values, of the order of 103–104. The Prandtl number, Pr, has been fixed at Pr = 0.015. It is shown that besides the Hartmann number the instability strongly depends on the type of the thermal boundary conditions at the horizontal walls. For thermally conducting walls the basic temperature profile exhibits zones of unstable thermal stratification, which leads to instabilities owing to the Rayleigh-Bénard mechanism. However, the transitions between various, most unstable modes as Ha increases are not trivial. For sufficiently high values of Ha, the most unstable mode consists of transverse oscillatory rolls located in the region of unstable stratification. For thermally insulating walls, the transitions are simpler, and for sufficiently high Ha, the most unstable mode consists of longitudinal, steady, three-dimensional mode which is concentrated in the Hartmann layers at the horizontal boundaries. This mode has a combined dynamic-thermal origin and is owed to a strong shear in the Hartmann layers. The electrical boundary conditions do not qualitatively affect the picture of transitions between modes for both thermally conducting and thermally insulating walls.Publisher Statement: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.   The following article appeared in Hudoba, A, Molokov, S, Aleksandrova, S & Pedcenko, A 2016, 'Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field' Physics of Fluid, vol 28, 094104 and may be found at https://dx.doi.org/10.1063/1.4962741

KW - Thermal conduction

KW - Magnetic fields

KW - Flow instabilities

KW - Boundary value problems

KW - Energy balance

U2 - 10.1063/1.4962741

DO - 10.1063/1.4962741

M3 - Article

VL - 28

JO - Physics of Fluid

JF - Physics of Fluid

SN - 1070-6631

M1 - 094104

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