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 Instability through porous medium of two viscous superposed conducting fluids

1982 ◽  
Vol 5 (2) ◽  
pp. 365-375 ◽  
Author(s):  
R. C. Sharma ◽  
K. P. Thakur
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Number Range ◽  
Wave Number Range ◽  
Medium Permeability ◽  
The Stability ◽  
The Magnetic Field ◽  
Conducting Fluids

The stability of the plane interface separating two viscous superposed conducting fluids through porous medium is studied when the whole system is immersed in a uniform horizontal magnetic field. The stability analysis is carried out for two highly viscous fluids of equal kinematic viscosities, for mathematical simplicity. It is found that the stability criterion is independent of the effects of viscosity and porosity of the medium 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 viscosity, porosity and medium permeability are examined analytically.

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.

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.

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

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.

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.

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.

The character of equilibrium of an inviscid, infinitely conducting fluid of variable density in the presence of a horizontal magnetic field with Hall-current

1970 ◽  
Vol 4 (3) ◽  
pp. 523-530 ◽  
Author(s):  
P. D. Ariel
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Sufficient Conditions ◽  
Variable Density ◽  
Conducting Fluid ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Number Range ◽  
Finite Distance ◽  
Conditions Of Stability

The character of equilibrium of an inviscid, incompressible, infinitely conducting fluid of variable density in the presence of a horizontal magnetic field has been investigated taking into account the effects of Hall-currents. The solution is shown to be characterized by a variational principle. Making use of the existence of variational principle the solution is developed in the case of continuously stratified fluid of exponentially varying density confined between two horizontal planes at finite distance, from which the necessary and sufficient conditions of stability are obtained. The Hall-currents are found to destabilize the wave-number range which is stable otherwise.

On Superposed Couple-stress Fluids in Porous Medium in Hydromagnetics The Use of Quantum-Chemical Semiempirical Methods to Calculate the Lattice Energies of Organic Molecular Crystals. Part II: The Lattice Energies of - and -Oxalic Acid (COOH)2

2002 ◽  
Vol 57 (12) ◽  
pp. 955-960 ◽  
Author(s):  
◽  
R. C. Sharmab ◽  
R. S. Chandel
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Couple Stress ◽  
Kinematic Viscosity ◽  
Wave Number ◽  
Semiempirical Methods ◽  
Number Range ◽  
Lattice Energies ◽  
The Magnetic Field ◽  
Couple Stress Fluids

The Rayleigh-Taylor instability of two supersposed couple-stress fluids of uniform densities in a porous medium in the presence of a uniform horizontal magnetic field is studied. For mathematical simplicity, the stability analysis is carried out for two highly viscous fluids of equal kinematic viscosity and equal couple-stress kinematic viscosity. A potentially stable configuration remains stable under certain conditions, and a potentially unstable configuration is stable under certain conditions. The magnetic field stabilizes a certain wave-number range k>k*, which is unstable in the absence of the magnetic field.

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.

Sign in / Sign up

Export Citation Format

Share Document