Hydromagnetic Instability Conditions for Viscoelastic Non-Newtonian Fluids

2000 ◽  
Vol 55 (3-4) ◽  
pp. 460-466
Keyword(s):  
Magnetic Field ◽  
Growth Rates ◽  
Stable Configuration ◽  
Horizontal Magnetic Field ◽  
Physical Conditions ◽  
Unstable Configuration ◽  
The Stability ◽  
Parameter Values ◽  
The Magnetic Field ◽  
Second Order Fluids

Abstract The effect of a horizontal magnetic field and a non-Newtonian stress tensor, as described by the Wal-ters B’ model, on the instability of two second order fluids of high kinematic viscosities and viscoelas-ticities is investigated. For the potentially stable configuration, it is found that the system is stable or unstable for a wavenumber range depending on the kinematic viscoelasticity. For the potentially un-stable configuration, it is found that the stability criterion is dependent on orientation and magnitude of the magnetic field which is found to stabilize a certain range of the unstable configuration related to the viscoelasticity values. The behaviour of growth rates with respect to Alfvén velocities are examined analytically, and it is found that the magnetic field has a dual role on the instability problem. For the exponentially varying stratifications, the system is found to be stable or unstable for the stable and un-stable stratifications under certain physical conditions, and the growth rates are found to increase or de-crease with increasing the stratification parameter values, according to some restrictions satisfied by the chosen wavenumbers range

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.

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.

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.

Rayleigh Taylor instability of a viscous Hall plasma with magnetic field

1972 ◽  
Vol 7 (1) ◽  
pp. 117-132 ◽  
Author(s):  
G. Bhowmik
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Larmor Frequency ◽  
Field Vector ◽  
Stable Configuration ◽  
Horizontal Magnetic Field ◽  
Wave Numbers ◽  
Hall Plasma ◽  
The Stability ◽  
The Magnetic Field

The influence of finite Larmor frequency on the stability of a viscous, finitely conducting liquid in a downward gravitational field under the influence of a uniform magnetic field directed along or normal to gravity, is investigated. The solution in each case is shown to be characterized by a variational principle Based on the variational principle, an approximate solution is obtained for the stability of a layer of fluid of constant kinematic viscosity and an exponentia density distribution. It has been found that finite resistivity and finite Larmor frequency do not introduce any instabifity in a potentially stable configuration. However, for a potentially unstable configuration we find that, for an ideal Hal plasma, the results depend on the orientation of the magnetic field, though the instability persists for all wave-numbers in the presence of non-ideal (finite resistivity and viscosity) effects. For the field aligned with gravity, it is found that a potentially unstable field-free configuration is stabilized if the buoyancy number B ( = gβ/12 V2) is less than unity. For B > 1, the instability arises for wave-numbers exceeding a critical value, which decreases on allowing for Hall terms in the generalized Ohm's law, suggesting a destabilizing influence of finite Larmor frequency. For an ambient horizontal magnetic field, it is found that an ideal plasma is stable, even for B > 0, for perturbations confined to a cone about the magnetic field vector. The angle of the cone of stable propagation, however, decreases on account of finite Larmor frequency.

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.

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.

Stability of Viscous Rotating Gravitating Streams in a Magnetic Field

2006 ◽  
Vol 61 (5-6) ◽  
pp. 258-262
Author(s):  
Prem Kumar Bhatia ◽  
Ravi Prakash Mathur
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Dispersion Relation ◽  
Horizontal Magnetic Field ◽  
The Stability ◽  
The Magnetic Field ◽  
Perturbation Equations

We have studied the stability of two superposed viscous compressible gravitating streams rotating about an axis perpendicular to the direction of a horizontal magnetic field. For wave propagation parallel to the direction of the magnetic field the dispersion relation is derived by solving the linearized perturbation equations. Both the viscosity and rotation are found to suppress the instability of the system

scholarly journals Hydromagnetic Stability Analysis of a Partially Ionized Medium

2020 ◽  
pp. 53-57
Author(s):  
Pardeep Kumar ◽  
Hari Mohan
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Growth Rates ◽  
Variable Density ◽  
Composite Medium ◽  
Horizontal Magnetic Field ◽  
Stability And Instability ◽  
Stabilizing Effect ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

Rayleigh-Taylor instability of a composite medium with variable density and viscosity is considered by taking into account the frictional effect of collisions of ionized with neutral atoms in the presence of a variable horizontal magnetic field. The criteria determining stability and instability are independent of the effects of viscosity and collisional effects. The magnetic field stabilizes the system which is otherwise unstable in the absence of the magnetic field. The viscosity of the medium has stabilizing as well as destabilizing effect on the growth rates. The collisional frequency has stabilizing effect on the growth rates, but has also destabilizing effect in some region.

Numerical and Experimental Analyses of Magnetic Convection of Paramagnetic Fluid in a Cylinder

2005 ◽  
Vol 128 (2) ◽  
pp. 183-191 ◽  
Author(s):  
Piotr Filar ◽  
Elzbieta Fornalik ◽  
Toshio Tagawa ◽  
Hiroyuki Ozoe ◽  
Janusz S. Szmyd
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Convective Flow ◽  
Buoyancy Force ◽  
Side Wall ◽  
Stable Configuration ◽  
Magnetic Buoyancy ◽  
Unstable Configuration ◽  
Magnetic Convection ◽  
The Magnetic Field

The magnetic convection of paramagnetic fluid in a cylindrical enclosure is studied experimentally and numerically. The upper side wall of the cylinder is cooled and the lower side wall heated, an unstable configuration. The whole system is placed coaxially in a bore of a superconducting magnet in the position of the minimum radial component of magnetic buoyancy force at the middle cross section of the enclosure. The stable configuration— when the whole system is placed inversely and the horizontal axial case are also considered. As a paramagnetic fluid an aqueous solution of glycerol with the gadolinium nitrate hexahydrate is used. The isotherms in the middle-height cross section are visualized by thermochromic liquid crystal slurry. For the unstable configuration the magnetic buoyancy force acts to assist the gravitational buoyancy force to give multiple spoke patterns at the mid cross section. The stable configuration gives an almost stagnant state without the magnetic field. Application of the magnetic field induces the convective flow similar to the unstable configuration. For the horizontal configuration a large roll convective flow (without the magnetic field) is changed under the magnetic field to the spoke pattern. The numerical results correspond to the experimental results.

scholarly journals Hydrodynamic and Hydromagnetic Stability of Two Superposed Elastico – Viscous Fluids of Different Permeability with Dust in Porous Medium

2015 ◽  
Vol 20 (2) ◽  
pp. 407-416
Author(s):  
M. Singh ◽  
C.B. Mehta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Viscous Fluids ◽  
Wave Number ◽  
Dust Particles ◽  
Unstable Configuration ◽  
Unstable Case ◽  
The Stability ◽  
Stable Arrangement ◽  
The Magnetic Field

Abstract Rayleigh-Taylor instability of two superposed Walters’ B has elastico-viscous fluids in a uniform magnetic field through a porous medium with different permeability been studied to include the suspended (dust) particles effect. Using normal mode technique a dispersion relation has been derived. The stability analysis has been carried out. The magnetic field stabilizes the unstable configuration for the wave number band K > K* in which the system is unstable in the absence of the magnetic field. It is also found that for a potential stable arrangement for Walters B’ elastico-viscous fluids of different permeabilities in the presence of suspended particles through a porous medium the system is stable, whereas in the potentially unstable case instability of the system occurs.

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