scholarly journals Stability of Radial Flow Subjected to a Radial Magnetic Field

2013 ◽  
Vol 38 ◽  
pp. 41-48
Author(s):  
HA Jasmine
Keyword(s):  
Magnetic Field ◽  
Radial Flow ◽  
Inner Product ◽  
Local Velocity ◽  
Radial Magnetic Field ◽  
Concentric Cylinders ◽  
Product Method ◽  
Magnetic Stability ◽  
The Stability ◽  
The Magnetic Field

The linear stability of radial flow of a viscous fluid in the presence of a radial magnetic field is investigated. Basic velocity field q0 = (c/r,0,W) and magnetic field B0= (A/r,0,0) are considered in an annulus between two concentric cylinders. To analyze hydro-magnetic stability, inner product method is employed. The stability condition derived is found to remain valid even when the local velocity is not entirely radial, and that the magnetic field exerts a stabilizing effect on the flow. DOI: http://dx.doi.org/10.3329/rujs.v38i0.16547 Rajshahi University J. of Sci. 38, 41-48 (2010)

scholarly journals On the Hydromagnetic Stability of a Rotating Fluid Annulus

2010 ◽  
Vol 2 (2) ◽  
pp. 250-256
Author(s):  
H. A. Jasmine
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Velocity Component ◽  
Axial Direction ◽  
Inner Product ◽  
Rotating Fluid ◽  
Concentric Cylinders ◽  
Swirl Velocity ◽  
Product Method ◽  
Mhd Stability

The linear stability of a rotating fluid  in  the annulus  between two concentric cylinders is investigated in the presence of a magnetic field  which is  azimuthal as well as in axial direction. Several results of MHD stability have been derived by using the inner product method. It is shown that when the swirl velocity component is large, the hydromagnetic effects become small compared with those due to swirl. The presence of a velocity field and imposed magnetic field will lead to the basic state to more stability. Keywords: Hydromagnetic Stability; Rotating Fluid. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i2.3945                 J. Sci. Res. 2 (2), 250-256 (2010) 

Experiments on the stability of flow between rotating cylinders in the presence of a magnetic field

1962 ◽  
Vol 266 (1325) ◽  
pp. 272-286 ◽  
Keyword(s):  
Magnetic Field ◽  
Experimental Error ◽  
Rotating Cylinder ◽  
Torque Measurements ◽  
Concentric Cylinders ◽  
Theoretical Predictions ◽  
Supercritical Range ◽  
The Stability ◽  
The Magnetic Field ◽  
Cylinder Viscometer

The hydromagnetic stability of the flow of mercury between concentric cylinders has been determined by means of a rotating cylinder viscometer. The results agree with the theoretical predictions of Chandrasekhar (1953) and Niblett (1958) within experimental error. Torque measurements have been made well into the supercritical range of speeds and it is observed that an increasing magnetic field reduces the torque. It is shown that this may be due to the elongation of the cellular vortices which occurs as the magnetic field is increased. The results suggest that the shape assumption proposed by Stuart (1958) in his non-linear theory of supercritical flow may be valid in the hydromagnetic case as well.

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.

Magnetorheological fluid based on amorphous Fe-Si-B alloy magnetic particles

2021 ◽  
pp. 1045389X2110643
Author(s):  
Chuncheng Yang ◽  
Zhong Liu ◽  
Xiangyu Pei ◽  
Cuiling Jin ◽  
Mengchun Yu ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Rheological Property ◽  
Magnetic Particles ◽  
Annealing Treatment ◽  
Magnetorheological Fluid ◽  
The Stability ◽  
The Magnetic Field ◽  
Amorphous Particle ◽  
Better Than

Magnetorheological fluids (MRFs) based on amorphous Fe-Si-B alloy magnetic particles were prepared. The influence of annealing treatment on stability and rheological property of MRFs was investigated. The saturation magnetization ( Ms) of amorphous Fe-Si-B particles after annealing at 550°C is 131.5 emu/g, which is higher than that of amorphous Fe-Si-B particles without annealing. Moreover, the stability of MRF with annealed amorphous Fe-Si-B particles is better than that of MRF without annealed amorphous Fe-Si-B particles. Stearic acid at 3 wt% was added to the MRF2 to enhance the fluid stability to greater than 90%. In addition, the rheological properties demonstrate that the prepared amorphous particle MRF shows relatively strong magnetic responsiveness, especially when the magnetic field strength reaches 365 kA/m. As the magnetic field intensified, the yield stress increased dramatically and followed the Herschel-Bulkley model.

The stability of viscous flow in a curved channel in the presence of a magnetic field

1961 ◽  
Vol 264 (1317) ◽  
pp. 155-164 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Uniform Magnetic Field ◽  
Axial Direction ◽  
Electrical Conductor ◽  
Curved Channel ◽  
Coaxial Cylinders ◽  
Transverse Pressure ◽  
The Stability ◽  
The Magnetic Field

The stability of viscous flow between two coaxial cylinders maintained by a constant transverse pressure gradient is considered when the fluid is an electrical conductor and a uniform magnetic field is impressed in the axial direction. The problem is solved and the dependence of the critical number for the onset of instability on the strength of the magnetic field and the coefficient of electrical conductivity of the fluid is determined.

Stability of the Base Flow to Axisymmetric and Plane-Polar Disturbances in an Electrically Driven Flow Between Infinitely-Long, Concentric Cylinders

2000 ◽  
Vol 123 (1) ◽  
pp. 31-42
Author(s):  
J. Liu ◽  
G. Talmage ◽  
J. S. Walker
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Axial Magnetic Field ◽  
Normal Modes ◽  
Azimuthal Velocity ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Electrically Conducting ◽  
Concentric Cylinders ◽  
The Stability

The method of normal modes is used to examine the stability of an azimuthal base flow to both axisymmetric and plane-polar disturbances for an electrically conducting fluid confined between stationary, concentric, infinitely-long cylinders. An electric potential difference exists between the two cylinder walls and drives a radial electric current. Without a magnetic field, this flow remains stationary. However, if an axial magnetic field is applied, then the interaction between the radial electric current and the magnetic field gives rise to an azimuthal electromagnetic body force which drives an azimuthal velocity. Infinitesimal axisymmetric disturbances lead to an instability in the base flow. Infinitesimal plane-polar disturbances do not appear to destabilize the base flow until shear-flow transition to turbulence.

The stability of viscous flow between rotating cylinders in the presence of a magnetic field

1953 ◽  
Vol 216 (1126) ◽  
pp. 293-309 ◽  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Viscous Flow ◽  
Thermal Instability ◽  
Horizontal Layer ◽  
Rotational Stability ◽  
Marginal Stability ◽  
Inhibiting Effect ◽  
The Stability ◽  
The Magnetic Field

In this paper the theory of the stability of viscous flow between two rotating coaxial cylinders which has been developed by Taylor, Jeffreys and Meksyn is extended to the case when the fluid considered is an electrical conductor and a magnetic field along the axis of the cylinders is present. A differential equation of order eight is derived which governs the situation in marginal stability; and a significant set of boundary conditions for the problem is formulated. The case when the two cylinders are rotating in the same direction and the difference ( d ) in their radii is small compared to their mean (R 0 ) is investigated in detail. A variational procedure for solving the underlying characteristic value problem and determining the critical Taylor numbers for the onset of instability is described. As in the case of thermal instability of a horizontal layer of fluid heated below, the effect of the magnetic field is to inhibit the onset of instability, the inhibiting effect being the greater, the greater the strength of the field and the value of the electrical conductivity. In both cases, the inhibiting effect of the magnetic field depends on the strength of the field ( H ), the density ( ρ ) and the coefficients of electrical conductivity ( σ ), kinematic viscosity ( v ) and magnetic permeability ( μ ) through the same non-dimensional combination Q =μ 2 H 2 d 2 σ/ pv ; however, the effect on rotational stability is more pronounced than on thermal instability. A table of the critical Taylor numbers for various values of Q is provided.

Quantum Hall effects

Quantum 20/20 ◽  
2019 ◽  
pp. 303-322
Author(s):  
Ian R. Kenyon
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Energy Gap ◽  
Quantum Hall ◽  
Free Electrons ◽  
Electron Gases ◽  
Hall Conductance ◽  
Hall Effects ◽  
The Stability ◽  
The Magnetic Field

It is explained how plateaux are seen in the Hall conductance of two dimensional electron gases, at cryogenic temperatures, when the magnetic field is scanned from zero to ~10T. On a Hall plateau σ‎xy = ne 2/h, where n is integral, while the longitudinal conductance vanishes. This is the integral quantum Hall effect. Free electrons in such devices are shown to occupy quantized Landau levels, analogous to classical cyclotron orbits. The stability of the IQHE is shown to be associated with a mobility gap rather than an energy gap. The analysis showing the topological origin of the IQHE is reproduced. Next the fractional QHE is described: Laughlin’s explanation in terms of an IQHE of quasiparticles is presented. In the absence of any magnetic field, the quantum spin Hall effect is observed, and described here. Time reversal invariance and Kramer pairs are seen to be underlying requirements. It’s topological origin is outlined.

scholarly journals On the stability of a general magnetic field topology in stellar radiative zones

2019 ◽  
Vol 82 ◽  
pp. 365-371
Author(s):  
K. Augustson ◽  
S. Mathis ◽  
A. Strugarek
Keyword(s):  
Magnetic Field ◽  
Global Change ◽  
Magnetic Fields ◽  
Potential Energy ◽  
Massive Stars ◽  
Spherical Geometry ◽  
Stable Region ◽  
Magnetic Field Topology ◽  
The Stability ◽  
The Magnetic Field

This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. One such instability is the purely magnetic Tayler instability, which can occur for poloidal, toroidal, and mixed poloidal-toroidal axisymmetric magnetic field configurations. However, most of the magnetic field configurations observed at the surface of massive stars are non-axisymmetric. Thus, extending earlier studies in spherical geometry, we introduce a formulation for the global change in the potential energy contained in a convectively-stable region for both axisymmetric and non-axisymmetric magnetic fields.

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