scholarly journals Linear stability of thermocapillary convection in cylindrical liquid bridges under axial magnetic fields

1999 ◽  
Vol 394 ◽  
pp. 281-302 ◽  
Author(s):  
M. PRANGE ◽  
M. WANSCHURA ◽  
H. C. KUHLMANN ◽  
H. J. RATH
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Magnetic Fields ◽  
Prandtl Number ◽  
Linear Stability ◽  
Thermocapillary Convection ◽  
Axial Magnetic Field ◽  
Unstable Mode ◽  
Linear Stability Theory ◽  
The Stability

The stability of axisymmetric steady thermocapillary convection of electrically conducting fluids in half-zones under the influence of a static axial magnetic field is investigated numerically by linear stability theory. In addition, the energy transfer between the basic state and a disturbance is considered in order to elucidate the mechanics of the most unstable mode. Axial magnetic fields cause a concentration of the thermocapillary flow near the free surface of the liquid bridge. For the low Prandtl number fluids considered, the most dangerous disturbance is a non-axisymmetric steady mode. It is found that axial magnetic fields act to stabilize the basic state. The stabilizing effect increases with the Prandtl number and decreases with the zone height, the heat transfer rate at the free surface and buoyancy when the heating is from below. The magnetic field also influences the azimuthal symmetry of the most unstable mode.

scholarly journals The effect of uniform magnetic field on spatial-temporal evolution of thermocapillary convection with the silicon oil based ferrofluid

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 4159-4171
Author(s):  
Shuo Yang ◽  
Rui Ma ◽  
Qiaosheng Deng ◽  
Guofeng Wang ◽  
Yu Gao ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Transverse Magnetic Field ◽  
Liquid Bridge ◽  
Thermocapillary Convection ◽  
Surface Deformation ◽  
Axial Magnetic Field ◽  
Transverse Magnetic ◽  
Surface Flow ◽  
Silicon Oil

A uniform axial or transverse magnetic field is applied on the silicon oil based ferrofluid of high Prandtl number fluid (Pr ? 111.67), and the effect of magnetic field on the thermocapillary convection is investigated. It is shown that the location of vortex core of thermocapillary convection is mainly near the free surface of liquid bridge due to the inhibition of the axial magnetic field. A velocity stagnation region is formed inside the liquid bridge under the axial magnetic field (B = 0.3-0.5 T). The disturbance of bulk reflux and surface flow is suppressed by the increasing axial magnetic field. There is a dynamic response of free surface deformation to the axial magnetic field, and then the contact angle variation of the free surface at the hot corner is as following, ?hot, B = 0.5 T = 83.34? > ?hot, B = 0.3 T = 72.16? > > ?hot,B = 0.1 T = 54.21? > ?hot, B = 0 T = 43.33?. The results show that temperature distribution near the free surface is less and less affected by thermocapillary convection with the increasing magnetic field, and it presents a characteristic of heat-conduction. In addition, the transverse magnetic field does not realize the fundamental inhibition for thermocapillary convection, but it transfers the influence of thermocapillary convection to the free surface.

ONSET OF INSTABILITY IN HYDROMAGNETIC COUETTE FLOW

2004 ◽  
Vol 02 (02) ◽  
pp. 145-159 ◽  
Author(s):  
ISOM H. HERRON
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Rotating Cylinders ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of viscous flow between rotating cylinders in the presence of a constant axial magnetic field is considered. The boundary conditions for general conductivities are examined. It is proved that the Principle of Exchange of Stabilities holds at zero magnetic Prandtl number, for all Chandrasekhar numbers, when the cylinders rotate in the same direction, the circulation decreases outwards, and the cylinders have insulating walls. The result holds for both the finite gap and the narrow gap approximation.

Thermocapillary convection in a cylindrical liquid-metal floating zone with a strong axial magnetic field and with a non-axisymmetric heat flux

1997 ◽  
Vol 345 ◽  
pp. 31-43 ◽  
Author(s):  
T. E. MORTHLAND ◽  
J. S. WALKER
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Free Surface ◽  
Liquid Metal ◽  
Thermocapillary Convection ◽  
Axial Magnetic Field ◽  
Hot Spot ◽  
Cold Spot ◽  
Floating Zone ◽  
Viscous Effects

This paper treats the steady three-dimensional thermocapillary convection in a cylindrical liquid-metal zone between the isothermal ends of two coaxial solid cylinders and surrounded by an atmosphere. There is a uniform steady magnetic field which is parallel to the common centrelines of the liquid zone and solid cylinders, and there is a non-axisymmetric heat flux into the liquid's free surface. The magnetic field is sufficiently strong that inertial effects and convective heat transfer are negligible, and that viscous effects are confined to thin boundary layers adjacent to the free surface and to the liquid–solid interfaces. With an axisymmetric heat flux, the axisymmetric thermocapillary convection is confined to the thin layer adjacent to the free surface, but with a non-axisymmetric heat flux, there is an azimuthal flow inside the free-surface layer from the hot spot to the cold spot with the circulation completed by flow across the inviscid central core region. This problem is related to the magnetic damping of thermocapillary convection for the floating-zone growth of semiconductor crystals in Space.

Thermocapillary convection in a cylinder with a strong non-uniform axisymmetric magnetic field

1994 ◽  
Vol 276 ◽  
pp. 369-388 ◽  
Author(s):  
Yu Yu Khine ◽  
John S. Walker
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Free Surface ◽  
Magnetic Fields ◽  
Thermocapillary Convection ◽  
Hartmann Number ◽  
Asymptotic Solutions ◽  
Cylinder Wall ◽  
Axial Component ◽  
Radial Temperature

This paper treats a surface-tension-driven liquid-metal flow in a cylinder with a steady externally applied non-uniform axisymmetric magnetic field. The top boundary consists of an annular free surface around a solid disk, modelling the Czochralski growth of silicon crystals. A radial temperature gradient produces a decrease of the surface tension from the disk edge to the vertical cylinder wall. The magnetic flux density is sufficiently large that inertial effects and convective heat transfer are negligible. First we present large-Hartmann-number asymptotic solutions for magnetic fields with either a non-zero or a zero axial component at the free surface. The asymptotic solutions indicate that a purely radial magnetic field at the free surface represents a singular limit of more general magnetic fields. Secondly we present numerical solutions for arbitrary values of the Hartmann number, and we treat the evolution of the thermocapillary convection as the axial magnetic field at the free surface is changed continuously from the full field strength to zero.

The stability of Couette flow in the presence of an axial magnetic field

1963 ◽  
Vol 17 (1) ◽  
pp. 52-60 ◽  
Author(s):  
Ulrich H. Kurzweg
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Taylor Number ◽  
Asymptotic Formulas ◽  
Magnetic Prandtl Number ◽  
The Mean ◽  
The Stability ◽  
Gap Spacing

The stability of Couette flow between concentric, co-rotating cylinders in an axial magnetic field is examined for fluids of arbitrary magnetic Prandtl number Pm = ν/η, where ν is the kinematic and η the magnetic viscosity of the fluid. It is assumed that the gap spacing d between the cylinders is small compared to the mean radius and that no magnetic disturbances penetrate into the cylinder walls. The critical Taylor number at which non-oscillatory disturbances are marginally stable is determined as a function of the magnetic Prandtl number and the dimensionless parameter S = (Vad/v)2, where Va is the Alfvén velocity. Asymptotic formulas relating the critical Taylor number to the magnitude of the magnetic field are derived for the limiting conditions of very small and very large magnetic Prandtl number.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

scholarly journals Hydromagnetic dynamos in rotating spherical fluid shells in dependence on the Prandtl number, density stratification and electromagnetic boundary conditions

2014 ◽  
Vol 44 (4) ◽  
pp. 293-312 ◽  
Author(s):  
Tomáš Šoltis ◽  
Ján Šimkanin
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Magnetic Fields ◽  
Prandtl Number ◽  
Inner Core ◽  
Polar Regions ◽  
Number Density ◽  
Magnetic Diffusion ◽  
Spherical Fluid ◽  
The Magnetic Field

Abstract We present an investigation of dynamo in a simultaneous dependence on the non-uniform stratification, electrical conductivity of the inner core and the Prandtl number. Computations are performed using the MAG dynamo code. In all the investigated cases, the generated magnetic fields are dipolar. Our results show that the dynamos, especially magnetic field structures, are independent in our investigated cases on the electrical conductivity of the inner core. This is in agreement with results obtained in previous analyses. The influence of non-uniform stratification is for our parameters weak, which is understandable because most of the shell is unstably stratified, and the stably stratified region is only a thin layer near the CMB. The teleconvection is not observed in our study. However, the influence of the Prandtl number is strong. The generated magnetic fields do not become weak in the polar regions because the magnetic field inside the tangent cylinder is always regenerated due to the weak magnetic diffusion.

scholarly journals Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field

2008 ◽  
Vol 12 (3) ◽  
pp. 103-110 ◽  
Author(s):  
Aiyub Khan ◽  
Neha Sharma ◽  
P.K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Growth Rate ◽  
Unstable Mode ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Streaming Velocity ◽  
The Stability ◽  
Conducting Fluids ◽  
Streaming Motion

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the taking account of effects of surface tension, when the whole system is immersed in a uniform horizontal magnetic field. The streaming motion is assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluid of uniform densities. The dispersion relation has been derived and solved numerically. It is found that the effect of viscosity, porosity and surface tension have stabilizing influence on the growth rate of the unstable mode, while streaming velocity has a destabilizing influence on the system.

Turbulence changes from magnetic fields in a stationary plasma

2010 ◽  
Vol 77 (4) ◽  
pp. 537-545 ◽  
Author(s):  
A. B. ALEXANDER ◽  
C. T. RAYNOR ◽  
D. L. WIGGINS ◽  
M. K. ROBINSON ◽  
C. C. AKPOVO ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Axial Magnetic Field ◽  
Turbulent Energy ◽  
Dominant Mode ◽  
Dc Glow Discharge ◽  
Turbulent Fluctuations ◽  
Stationary Plasma

AbstractWhen the krypton plasma in a DC glow discharge tube is exposed to an axial magnetic field, the turbulent energy and the characteristic dominant mode in the turbulent fluctuations are systematically and unexpectedly reduced with increasing magnetic field strength. When the index measuring the rate of transfer of energy through fluctuation scales is monitored, a lambda-like dependence on turbulent energy is routinely observed in all magnetic fields. From this, a critical turbulent energy is identified, which also decreases with increasing magnetic field strength.

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