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 RayleighBénard 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, threedimensional mode which is concentrated in the Hartmann layers at the horizontal boundaries. This mode has a combined dynamicthermal 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.
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 language  English 

Article number  094104 
Journal  Physics of Fluid 
Volume  28 
DOIs  
Publication status  Published  21 Sept 2016 
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
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Alex Pedcenko
 School of Computing, Mathematics and Data Sciences  Assistant Professor Academic
Person: Teaching and Research