The stability of ferrofluid flow in a vertical layer subject to lateral heating and horizontal magnetic field

2010 ◽  
Vol 322 (17) ◽  
pp. 2596-2606 ◽  
Author(s):  
A.V. Belyaev ◽  
B.L. Smorodin
Keyword(s):  
Magnetic Field ◽  
Vertical Layer ◽  
Horizontal Magnetic Field ◽  
Lateral Heating ◽  
The Stability

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.

Hydromagnetic Stability of Two Rivlin-Ericksen Elastico-Viscous Superposed Conducting Fluids

1997 ◽  
Vol 52 (6-7) ◽  
pp. 528-532
Author(s):  
R. C. Sharma ◽  
P. Kumar
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Number Range ◽  
Wave Number Range ◽  
Unstable Configuration ◽  
The Stability ◽  
Superposed Fluids ◽  
The Magnetic Field ◽  
Conducting Fluids

Abstract The stability of the plane interface separating two Rivlin-Ericksen elastico-viscous superposed fluids of uniform densities when the whole system is immersed in a uniform horizontal magnetic field has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities and equal kinematic viscoelasticities. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the orientation and magnitude of the magnetic field. The magnetic field is found to stabilize a certain wave-number range of the unstable configuration. The behaviour of growth rates with respect to kinematic viscosity and kinematic viscoelasticity parameters are examined numerically.

Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids

2001 ◽  
Vol 56 (6-7) ◽  
pp. 416-439
Author(s):  
Mohamed Fahmy El
Keyword(s):  
Magnetic Field ◽  
Stable Configuration ◽  
Retardation Time ◽  
Horizontal Magnetic Field ◽  
Fluid Velocities ◽  
Unstable Configuration ◽  
The Stability ◽  
The Magnetic Field ◽  
Conducting Fluids ◽  
Alfven Velocity

Abstract The stability of the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in­ vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent of the viscosity and viscoelasticity, and to be dependent on the orientation of the magnetic field and the magnitudes of the fluids and Alfven velocities. It is also found that the potentially unstable configuration remains unstable in the absence of average fluid velocities, or in the presence of fluid velocities and absence of a magnetic field. The magnetic field is found to stabilize a certain wavenumbers range of the unstable configuration even in the presence of the effects of viscoelasticity. The behaviour of growth rates with respect to the stress relaxation time, strain retardation time, fluid and Alfven velocity parameters is examined analytically, and the stability conditions are obtained and discussed. -Pacs: 47.20.-k; 47.50.+d; 47.65.+a.

scholarly journals Larmor Radius and Collisional Effects on the Dynamic Stability of a Composite Medium

1972 ◽  
Vol 25 (3) ◽  
pp. 259 ◽  
Author(s):  
PK Bhatia ◽  
JM Steiner
Keyword(s):  
Magnetic Field ◽  
Dynamic Stability ◽  
Variable Density ◽  
Composite Medium ◽  
Larmor Radius ◽  
Combined Effects ◽  
Composite Media ◽  
Horizontal Magnetic Field ◽  
The Stability ◽  
Streaming Motion

The combined effects of a finite ion Larmor radius and collisions with neutral atoms on the dynamic stability of a composite medium are investigated. The stability analysis has been carried out for a semi-infinite composite medium of variable density in the presence and absence of a uniform streaming motion. Wave propagations transverse to the direction of the uniform horizontal magnetic field have been considered. It is found that the effects of the collisions as well as the finite ion Larmor radius are stabilizing on both streaming and non-streaming composite media.

Rayleigh-Taylor Instability of a Stratified Magnetized Medium in the Presence of Suspended Particles

1984 ◽  
Vol 39 (10) ◽  
pp. 939-944 ◽  
Author(s):  
R. K. Chhajlani ◽  
R. K. Sanghvi ◽  
P. Purohit
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Suspended Particles ◽  
Frequency Parameter ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Horizontal Magnetic Field ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
The Magnetic Field

Abstract The hydromagnetric Rayleigh-Taylor instability of a composite medium has been studied in the presence of suspended particles for an exponentially varying density distribution. The prevalent horizontal magnetic field and viscosity of the medium are assumed to be variable. The dispersion relation is derived for such a medium. It is found that the stability criterion is independent of both viscosity and suspended particles. The system can be stabilized for an appropriate value of the magnetic field. It is found that the suspended particles can suppress as well as enhance the growth rate of the instability in certain regions. The growth rates are obtained for a viscid medium with the inclusion of suspended particles and without it. It has been shown analytically that the growth rate is modified by the inclusion of the relaxation frequency parameter of the suspended particles.

Untersuchung der Stabilität eines gravitierenden Plasmas in gekreuzten Magnetfeldern

1958 ◽  
Vol 13 (12) ◽  
pp. 1016-1020 ◽  
Author(s):  
F. Meyer
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Field Strength ◽  
Equilibrium Configuration ◽  
Horizontal Magnetic Field ◽  
Large Wave ◽  
Small Wave ◽  
The Stability

Es wird die Stabilität einer Plasmaanordnung untersucht. Dabei wird ein gravitierendes Plasma mit horizontalem innerem Magnetfeld von einem dagegen um den Winkel α verdrehten horizontalen Vakuummagnetfeld getragen. Das Beispiel ist eine Erweiterung des von Kruskal und Schwarzschild untersuchten Falles α = 0 mit parallelem innerem und äußerem Feld. Es ergibt sich die Stabilisierbarkeit aller Störungen mit kleinen Wellenlängen einschließlich der Kruskal-Schwarzschild-Instabilität durch endliche Verdrehungswinkel α. Für große Wellenlängen tauchen stets instabile Störungen auf von der Art hydromagnetischer Rayleigh-Taylor-Instabilitäten.The stability of a plasma in crossed magnetic fields is investigated for the following equilibrium configuration. A plasma with an interior horizontal magnetic field is supported against gravity by a horizontal vacuum magnetic field which is inclined at some angle α to the interior field. This example is an extension of the case α=0 investigated by Kruskal und Schwarzschild. It is found that for all disturbances with small wave lengths, including those disturbances which give the Kruskal-Schwarzschild instability, stability can be restored by using a non-zero α. Perturbations of sufficiently large wave lengths are found unstable for every α and every ratio of field strength.

Magneto-gravitational convection in a vertical layer of ferrofluid in a uniform oblique magnetic field

2016 ◽  
Vol 795 ◽  
pp. 847-875 ◽  
Author(s):  
Habibur Rahman ◽  
Sergey A. Suslov
Keyword(s):  
Magnetic Field ◽  
Computational Cost ◽  
Three Dimensional ◽  
Vertical Layer ◽  
Gravitational Convection ◽  
Magnetic Parameters ◽  
Instability Modes ◽  
The Stability ◽  
Dimensional Instability ◽  
Oblique Magnetic Field

The stability of base gravitational convection in a layer of ferrofluid confined between two vertical wide and tall non-magnetic plates, heated from one side, cooled from the other and placed in a uniform oblique external magnetic field is studied. Two distinct mechanisms, thermo-gravitational and thermo-magnetic, are found to be responsible for the appearance of various stationary and wave-like instability modes. The characteristics of all instability modes are investigated as functions of the orientation angles of the applied magnetic field and its magnitude for various values of magnetic parameters when both the thermo-magnetic and gravitational buoyancy mechanisms are active. The original three-dimensional problem is cast in an equivalent two-dimensional form using generalised Squire’s transformations, which significantly reduces a computational cost. Subsequently, full three-dimensional instability patterns are recovered using the inverse Squire’s transformation, and the optimal field and pattern orientations are determined.

scholarly journals Hydromagnetic Instability of Two Viscoelastic Dusty-Fluids in Porous Medium

2021 ◽  
Vol 16 ◽  
pp. 137-144
Author(s):  
Pardeep Kumar ◽  
Sumit Gupta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Suspended Particles ◽  
Stable Configuration ◽  
Number Density ◽  
Horizontal Magnetic Field ◽  
Two Fluids ◽  
Medium Permeability ◽  
The Stability ◽  
The Magnetic Field

An attempt has been made to investigate the instability of the plane interface between two viscoelastic superposed conducting fluids in the presence of suspended particles and variable horizontal magnetic field through porous medium is studied. The cases of two fluids of uniform densities, viscosities, magnetic fields, and suspended particles number densities separated by a horizontal boundary; and of exponentially varying density, viscosity, suspended particles number density, and magnetic field are considered. It is found that the stability criterion is independent of the effects of viscoelasticity, medium porosity, and suspended particles but is dependent on the orientation and magnitude of the magnetic field. The magnetic field succeeds in stabilizing a certain range of wavenumbers which were unstable in the absence of the magnetic field. The system is found to be stable for potentially stable configuration/stratification. The growth rates are found to increase (for certain wavenumbers) and decrease (for other wavenumbers) with the increase in kinematic viscosity, suspended particles number density, magnetic field, medium permeability and stress relaxation time.

Stability Of Rotating Gravitating Streams

2005 ◽  
Vol 60 (7) ◽  
pp. 484-488 ◽  
Author(s):  
P. K. Bhatia ◽  
R. P. Mathur
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Critical Wave Number ◽  
Horizontal Magnetic Field ◽  
Axis Of Rotation ◽  
Streaming Velocity ◽  
The Stability ◽  
The Magnetic Field

This paper treats the stability of two superposed gravitating streams rotating about the axis transverse to the horizontal magnetic field. The critical wave number for instability is found to be affected by rotation for propagation perpendicular to the axis about which the system rotates. The critical wave number for instability is not affected by rotation when waves propagate along the axis of rotation. The critical wave number is affected by both the magnetic field and the streaming velocity in both cases. Both the magnetic field and the rotation are stabilizing, while the streaming velocity is destabilizing.

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