scholarly journals Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field

2005 ◽  
Vol 2005 (23) ◽  
pp. 3727-3737 ◽  
Author(s):  
Jitender Singh ◽  
Renu Bajaj
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Critical Value ◽  
Annular Space ◽  
Rotating Cylinders ◽  
The Stability

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratioΩ∗of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

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

1961 ◽  
Vol 262 (1311) ◽  
pp. 443-454 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Rotating Cylinders ◽  
Counter Rotation ◽  
Angular Velocities ◽  
The Stability

The theory developed in an earlier paper (Chandrasekhar 1953) is extended to allow for counter-rotation of the two cylinders. Explicit results are given for the case when the two cylinders rotate in opposite directions with equal angular velocities.

The effect of a radial magnetic field on the stability of Couette flow

1994 ◽  
Vol 72 (5-6) ◽  
pp. 258-265 ◽  
Author(s):  
M. A. Ali
Keyword(s):  
Magnetic Field ◽  
Eigenvalue Problem ◽  
Incompressible Fluid ◽  
Couette Flow ◽  
Wave Number ◽  
Rotating Cylinders ◽  
Radial Magnetic Field ◽  
Electrically Conducting ◽  
Angular Velocities ◽  
The Stability

The effect of a radial magnetic field on the stability of an electrically conducting incompressible fluid between two concentric rotating cylinders is considered. The eigenvalue problem for determining the critical Taylor number TC and the corresponding wave number aC is solved numerically for different values of ±μ(= Ω2/Ω1), (where Ω1, and Ω2 are me angular velocities of the inner and outer cylinders, respectively) and for different gap sizes. It is observed that the radial magnetic field stabilizes the flow. This effect is more pronounced for cylinders that are corotating as compared with counter-rotating cylinders or the situation where only the inner one is rotating.

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.

Formation of the hexagonal pattern on the surface of a ferromagnetic fluid in an applied magnetic field

1977 ◽  
Vol 82 (3) ◽  
pp. 401-413 ◽  
Author(s):  
A. Gailītis
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Flat Surface ◽  
Critical Value ◽  
Minimization Principle ◽  
Magnetic Forces ◽  
Hexagonal Pattern ◽  
Equilibrium Configurations ◽  
Ferromagnetic Fluid ◽  
Gravity Surface

When a ferromagnetic fluid with a horizontal free surface is subjected to a uniform vertical applied magnetic field B0, it is known (Cowley & Rosensweig 1967) that the surface may be unstable when the field strength exceeds a certain critical value Bc. In this paper we consider, by means of an energy minimization principle, the possible forms that the surface may then take. Under the assumption that |μ − 1| [Lt ] 1 (where μ is the magnetic permeability of the fluid), it is shown that when B0 is near to Bc there are three equilibrium configurations for the surface: (i) flat surface, (ii) stationary hexagonal pattern, (iii) stationary square pattern. Configuration (i) is stable for B0 < Bc, (ii) is stable for B0 > Bc and B0−Bc sufficiently small, and (iii) is stable for some higher values of B0. In each configuration the fluid is static, and the surface is in equilibrium under the joint action of gravity, surface tension, and magnetic forces. The amplitude of the surface perturbation in cases (ii) and (iii) is calculated, and hysteresis effects associated with increase and decrease of B0 are discussed.

ON THE HESSIAN OF THE ENERGY FORM IN THE GINZBURG–LANDAU MODEL OF SUPERCONDUCTIVITY

2004 ◽  
Vol 16 (04) ◽  
pp. 421-450 ◽  
Author(s):  
MYRIAM COMTE ◽  
MYRTO SAUVAGEOT
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Radial Solutions ◽  
Ginzburg Landau ◽  
Landau Model ◽  
The Stability

The purpose of this work is to study the stability of radial solutions of degree d for the Ginzburg–Landau model of superconductivity with an applied magnetic field in a disk of radius [Formula: see text]. We consider the branch of solutions introduced in [24] as a branch with the radius of the ball as parameter. We prove that for small radii the branch is stable while it is unstable for large radii, see [6]. We then study in detail the Hessian of the energy at the symmetric vortex at the stability transition. Finally under a couple of extra assumptions, we construct a branch of solutions bifurcating from the radial one at this point, and describe it.

Finite deformations and incremental axisymmetric motions of a magnetoelastic tube

2017 ◽  
Vol 23 (6) ◽  
pp. 950-983 ◽  
Author(s):  
Prashant Saxena
Keyword(s):  
Magnetic Field ◽  
Internal Pressure ◽  
Applied Magnetic Field ◽  
Axial Magnetic Field ◽  
Cylindrical Tube ◽  
Axial Stretch ◽  
Mechanical Waves ◽  
Wave Guides ◽  
The Stability ◽  
Circular Cylindrical Tube

A thick-walled circular cylindrical tube made of an incompressible magnetoelastic material is subjected to a finite static deformation in the presence of an internal pressure, an axial stretch and an azimuthal or an axial magnetic field. The dependence of the static magnetoelastic deformation on the intensity of the applied magnetic field is analysed for two different magnetoelastic energy density functions. Then, superimposed on this static configuration, incremental axisymmetric motions of the tube and their dependence on the applied magnetic field and deformation parameters are studied. In particular, we show that magnetoelastic coupled waves exist only for particle motions in the azimuthal direction. For particle motion in radial and axial directions, only purely mechanical waves are able to propagate when a magnetic field is absent. The wave speeds as well as the stability of the tube can be controlled by changing the internal pressure, axial stretch and applied magnetic field that demonstrates the applicability of magneto-elastomers as wave guides and vibration absorbers.

scholarly journals Effects of magnetic fields on capillary-gravity waves in the presence of magnetic surfactants

2018 ◽  
Vol 185 ◽  
pp. 09002
Author(s):  
Alexander V. Zhukov
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
External Magnetic Field ◽  
Elastic Constant ◽  
Gravity Waves ◽  
Wave Motion ◽  
Liquid Surface ◽  
Critical Value ◽  
Surfactant Film ◽  
The Stability

The stability of capillary-gravity wave motion on horizontal free surface of viscous noncompressible fluid in the presence of magnetic surfactant in an external magnetic field was studied. It is shown that for normal as well as for tangential external magnetic field the horizontal free liquid surface is unstable for field strength exceeding some critical value that does not depend on the elastic constant of the surfactant film. However, for oblique external magnetic field the stability of the free surface depends not only on the field value but also on the surfactant elastic constant.

scholarly journals Stability of a viscous liquid contained between two rotating cylinders

1923 ◽  
Vol 102 (718) ◽  
pp. 541-542 ◽  
Keyword(s):  
Viscous Fluid ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Outer Cylinder ◽  
Steady Motion ◽  
Annular Space ◽  
Rotating Cylinders ◽  
High Speeds ◽  
Approximate Form ◽  
The Stability

Part I .—The stability for symmetrical disturbances of a viscous fluid in steady motion between concentric rotating cylinders is investigated mathematically. It is shown that at slow speeds the motion is always stable, but that at high speeds the motion is only stable when the ratio of the speed of the outer cylinder to that of the inner one exceeds a certain value. When the ratio is less than this or when it is negative the motion becomes unstable at high speeds. The “criterion” for stability is found, and in cases suitable for experimental verification an approximate form for the “criterion” is developed which is useful for numerical computation. The type of instability which may be expected to appear when the speed of the cylinders is slowly increased is shown to consist of symmetrical ring-shaped vortices spaced at regular intervals along the length of the cylinders. These vortices rotate alternately in opposite directions. Their dimensions are calculated and it is shown that they are contained in partitions of rectangular cross-section. In the case when the instability arises while both cylinders are rotating in the same direction, these rectangles are squares, so that the vortices are spaced at distances apart equal to the thickness of the annular space between the two cylinders. In the case when the cylinders rotate in opposite directions the spacing, or distance between the centres of neighbouring vortices, is smaller than this; and at the same time two systems of vortices develop—an inner system which is similar to the system which appears when the two cylinders rotate in the same direction, and an outer system, which is much less vigorous and rotates in the opposite direction to the adjacent members of the inner system.

STRANGE QUARK MATTER IN STRONG MAGNETIC FIELD

1994 ◽  
Vol 09 (39) ◽  
pp. 3611-3618 ◽  
Author(s):  
SOMENATH CHAKRABARTY ◽  
ASHOK GOYAL
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Quark Matter ◽  
Strange Quark ◽  
Critical Value ◽  
Strange Quark Matter ◽  
Zero Magnetic Field ◽  
Zero Temperature ◽  
Mit Bag Model ◽  
The Stability

Using conventional MIT bag model of confinement, the stability of bulk strange quark matter (SQM) in the presence of a strong magnetic field at zero temperature and zero pressure has been investigated. The binding energy of SQM increases in the presence of strong magnetic field greater than or of the order of some critical value at which the cyclotron lines begin to occur. At finite temperature the pressure dependence of the system has also been presented, which differs significantly from zero magnetic field case.

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