scholarly journals The effect of aspect ratio and axial magnetic field on thermocapillary convection in liquid bridges with a deformable free-surface

2015 ◽  
Vol 10 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Yin Zhang ◽  
Hulin Huang ◽  
Xidong Zhang ◽  
Yong Zou ◽  
Shuojie Tang
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Aspect Ratio ◽  
Thermocapillary Convection ◽  
Axial Magnetic Field ◽  
Liquid Bridges

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.

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.

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.

Effect of Marangoni number on thermocapillary convection and free-surface deformation in liquid bridges

2016 ◽  
Vol 25 (2) ◽  
pp. 178-187 ◽  
Author(s):  
Yin Zhang ◽  
Hu-Lin Huang ◽  
Xiao-Ming Zhou ◽  
Gui-Ping Zhu ◽  
Yong Zou
Keyword(s):  
Free Surface ◽  
Marangoni Number ◽  
Thermocapillary Convection ◽  
Surface Deformation ◽  
Liquid Bridges ◽  
Free Surface Deformation

scholarly journals Spin-Up from Rest of a Liquid Metal with Deformable Free Surface in a Cylinder under the Influence of a Uniform Axial Magnetic Field

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 438
Author(s):  
Toshio Tagawa ◽  
Kewei Song
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Liquid Metal ◽  
Hartmann Number ◽  
Viscosity Ratio ◽  
Axial Magnetic Field ◽  
Density Ratio ◽  
Striking Difference ◽  
Gas Phases ◽  
Component Velocity

Spin-up from rest of a liquid metal having deformable free surface in the presence of a uniform axial magnetic field is numerically studied. Both liquid and gas phases in a vertically mounted cylinder are assumed to be an incompressible, immiscible, Newtonian fluid. Since the viscous dissipation and the Joule heating are neglected, thermal convection due to buoyancy and thermocapillary effects is not taken into account. The effects of Ekman number and Hartmann number were computed with fixing the Froude number of 1.5, the density ratio of 800, and the viscosity ratio of 50. The evolutions of the free surface, three-component velocity field, and electric current density are portrayed using the level-set method and HSMAC method. When a uniform axial magnetic field is imposed, the azimuthal momentum is transferred from the rotating bottom wall to the core region directly through the Hartmann layer. This is the most striking difference from spin-up of the nonmagnetic case.

Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface

1983 ◽  
Vol 126 ◽  
pp. 545-567 ◽  
Author(s):  
F. Preisser ◽  
D. Schwabe ◽  
A. Scharmann
Keyword(s):  
Free Surface ◽  
Aspect Ratio ◽  
Cylindrical Surface ◽  
Thermocapillary Convection ◽  
Cylinder Surface ◽  
Axially Symmetric ◽  
Zone Length ◽  
Aspect Ratios ◽  
Temperature Oscillations ◽  
Free Cylindrical Surface

In liquid columns (Prandtl number 8·9) with free cylindrical surface heated from above, strong thermocapillary convection (TC) has been observed. Stationary thermocapillary convection exists in the form of a single axially symmetric roll bound to the free surface. For aspect ratios l/a < 1 the radial extension of the roll equals the zone length. The stream velocities and the temperature distribution were measured.The influence of buoyant forces due to horizontal temperature gradients in the experiments was also studied. Buoyant forces become obvious for a contaminated free surface and in bulk regions far from the cylinder surface.The thermocapillary convection shows a transition to time-dependent oscillatory motion when a critical Marangoni number Mac is exceeded. A unique Mac = 7 × 103 has been found for zones with lengths l < 3·5 mm. The oscillatory state of thermocapillary convection has experimentally been proved to be a distortion of the laminar state in form of a wave travelling in the azimuthal direction. A unique non-dimensional wavenumber ≈ 2·2 (near Mac) of the distortion has been found. The non-dimensional frequency of the temperature oscillations is independent of zone size if the aspect ratio is held constant. However, the non-dimensional frequency of temperature oscillations increases linearly with the aspect ratio of the zone. This result is interpreted as a dependence of the phase velocity of the running disturbance on the aspect ratio.

Thermocapillary Instability With a Rotating Magnetic Field and System Rotation

2003 ◽  
Author(s):  
Nancy Ma ◽  
John S. Walker ◽  
Laurent Martin Witkowski
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Free Surface ◽  
Stability Analysis ◽  
Angular Velocity ◽  
Thermocapillary Convection ◽  
Rotating Magnetic Field ◽  
Azimuthal Direction ◽  
Critical Mode ◽  
Thermocapillary Instability

This paper presents a linear stability analysis for the thermocapillary convection in a liquid bridge bounded by two planar liquid-solid interfaces at the same temperature and by a cylindrical free surface with an axisymmetric heat input. The two solid boundaries are rotated at the same angular velocity in one azimuthal direction, and a rotating magnetic field is applied in the opposite azimuthal direction. The critical values of the Reynolds number for the thermocapillary convection and the critical-mode frequencies are presented as functions of the magnetic Taylor number for the rotating magnetic field and of the Reynolds number for the angular velocity of the solid boundaries.

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