scholarly journals Stability Of Superposed Fluids Through Magnetic Field With Suspended Particles Of Different Permeability Saturated Through Porous Layer

2015 ◽  
Vol 20 (4) ◽  
pp. 889-898
Author(s):  
M. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Viscous Fluid ◽  
Suspended Particles ◽  
Wave Number ◽  
Mode Analysis ◽  
Dust Particles ◽  
Linearized Stability ◽  
Stable Arrangement ◽  
The Magnetic Field

Abstract The instability of plane interface between two superposed Rivlin-Ericksen elastico-viscous fluids saturated through a porous medium has been studied to include the suspended (dust) particles effect. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like Newtonian fluids. It found that for a potentially stable arrangement the Rivlin-Ericksen elastico-viscous fluid of different permeabilities in the presence of suspended particles in a porous medium is stable, whereas in a potentially unstable case instability of the system occurs. In the presence of a magnetic field for a potentially stable arrangement the system is always stable and for the potentially unstable arrangement, the magnetic field succeeds in stabilizing certain wave-number band which was unstable in the absence of the magnetic field.

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 Hall Effect on Thermal Instability of Viscoelastic Dusty Fluid in Porous Medium

2013 ◽  
Vol 18 (3) ◽  
pp. 871-886
Author(s):  
M. Singh ◽  
R.K. Gupta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
Rayleigh Numbers ◽  
The Magnetic Field

Abstract The effect of Hall currents and suspended dusty particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico viscous fluid in a porous medium is considered. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of the magnetic field. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers are depicted graphically. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the systems, which did not exist in the absence of these parameters

scholarly journals Hydromagnetic thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles in porous medium

2013 ◽  
Vol 35 (4) ◽  
pp. 75-88
Author(s):  
G.C. Rana ◽  
H.S. Jamwal
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Analysis Method ◽  
Rotating Fluid ◽  
Medium Permeability ◽  
The Magnetic Field

Abstract In this paper, the thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles (fine dust) in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B′) elastico-viscous fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has stabilizing effect, suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions

scholarly journals Thermosolutal Instability in Compressible Viscoelastic Dusty Fluid through Porous Medium

2013 ◽  
Vol 18 (1) ◽  
pp. 99-112 ◽  
Author(s):  
P. Kumar ◽  
H. Mohan
Keyword(s):  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
The Stability ◽  
Solute Gradient

Thermosolutal instability in a compressible Walters B’ viscoelastic fluid with suspended particles through a porous medium is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the Walters B’ viscoelastic fluid behaves like a Newtonian fluid and it is found that suspended particles and medium permeability have a destabilizing effect whereas the stable solute gradient and compressibility have a stabilizing effect on the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and viscoelasticity are found to introduce oscillatory modes in the system which are non-existent in their absence.

Double-Diffusive Magneto Convection in a Compressible Couple-Stress Fluid Through Porous Medium

2011 ◽  
Vol 66 (5) ◽  
pp. 304-310 ◽  
Author(s):  
Pardeep Kumar ◽  
Hari Mohan
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Couple Stress ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Onset Of Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
Solute Gradient ◽  
Double Diffusive

The double-diffusive convection in a compressible couple-stress fluid layer heated and soluted from below through porous medium is considered in the presence of a uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, stable solute gradient, magnetic field, and couple-stress postpone the onset of convection whereas medium permeability hastens the onset of convection. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and magnetic field introduce oscillatory modes in the system, which were non-existent in their absence. A condition for the system to be stable is obtained by using the Rayleigh-Ritz inequality. The sufficient conditions for the non-existence of overstability are also obtained.

Numerical Investigations on Rotatry Micropolar Fluid in Hydromagnetics Permeated with Suspended Particles Saturating Porous Medium

2021 ◽  
pp. 57-69
Author(s):  
Pushap Lata Sharma ◽  
Sumit Gupta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Field Intensity ◽  
Magnetic Field Intensity ◽  
Suspended Particles ◽  
Rotation Parameter ◽  
Wave Number ◽  
Stationary Convection ◽  
Micropolar Fluids ◽  
Medium Permeability

This paper deals with the convection of micropolar fluids heated and soluted from below in the presence of suspended particles (fine dust) and uniform vertical rotation and uniform vertical magnetic field in a porous medium. Using the Boussinesq approximation, the linearized stability theory and normal mode analysis, the exact solutions are obtained for the case of two free boundaries. It is found that the presence of the suspended particles number density, the rotation parameter, stable solute, magnetic field intensity and medium permeability bring oscillatory modes which were non–existent in their absence. It is found that the presence of coupling between thermal and micropolar effects, rotation parameter, solute parameter and suspended particles may introduce overstability in the system. Graphs have been plotted by giving numerical values to the parameters accounting for rotation parameter , magnetic field solute parameter, the dynamic microrotation viscosity and coefficient of angular viscosity to depict the stability characteristics, for both the cases of stationary convection and overstability. It is found that Rayleigh number for the case of overstability and stationary convection increases with increase in rotation parameter, as well as with magnetic field intensity, solute parameter and decreases with increase in micropolar coefficients and medium permeability, for a fixed wave number, implying thereby the stabilizing effect of rotation parameter, magnetic field intensity ,solute parameter and destabilizing effect of micropolar coefficients and medium permeability on the thermosolutal convection of micropolar fluids.

Finite-Resistivity Effects on Rayleigh-Taylor Instability of a Stratified Plasma Including Suspended Particles

1985 ◽  
Vol 40 (8) ◽  
pp. 826-833
Author(s):  
Rajkamal Sanghvi ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Kinematic Viscosity ◽  
Normal Mode Analysis ◽  
Longitudinal Mode ◽  
Transverse Mode ◽  
Suspended Particles ◽  
Wave Number ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Horizontal Magnetic Field

The Rayleigh-Taylor (RT) instability of a stratified and viscid magnetoplasma including the effects of "finite-resistivity and suspended particles is investigated using normal mode analysis. The horizontal magnetic field and the viscosity of the medium are assumed to be variable. The dispersion relation, which is obtained for the general case on employing boundary conditions appropriate to the case of two free boundaries, is then specialized for the longitudinal and transverse modes. It is found that the criterion of stable stratification remains essentially unchanged and that the unstable stratification for the longitudinal mode can be stabilized for a certain wave number band, whereas the transverse mode remains unstable or all wave numbers which can be stabilized by a suitable choice of the magnetic field for vanishing resistivity. Thus, resistivity is found to have a destabilizing influence on the RT configuration. The growth rates of the unstable RT modes with the kinematic viscosity and the relaxation frequency parameter of the suspended particles have been analytically evaluated. Dust (suspended particles) tends to stabilize the configuration when the medium is considered viscid with infinite conductivity. The kinematic viscosity has a stabilizing influence on the ideal plasma modes.

Kelvin-Helmholtz and Rayleigh-Taylor Instability of Two Superimposed Magnetized Fluids with Suspended Dust Particles

2009 ◽  
Vol 64 (7-8) ◽  
pp. 455-466 ◽  
Author(s):  
Ramprasad Prajapati ◽  
Raj Kamal Sanghvi ◽  
Rajendra Kumar Chhajlani ◽  
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Particle Density ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Mode Analysis ◽  
Dust Particles ◽  
Suspended Dust ◽  
The Magnetic Field

AbstractThe effect of a magnetic field and suspended dust particles on both the Kelvin-Helmholtz (K-H) and the Rayleigh-Taylor (R-T) instability of two superimposed streaming magnetized plasmas is investigated. The magnetized fluids are assumed to be incompressible and flowing on top of each other. The usual magnetohydrodynamic (MHD) equations are considered with suspended dust particles. The basic equations of the problem are linearized and the dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The general dispersion relation is found to be modified due to the presence of the suspended dust particles and of the magnetic field. The effect of the magnetic field appears in the dispersion relation if three-dimensional perturbations of the system are considered. The general conditions of the K-H instability as well as the R-T instability are derived for the considered medium. The stability of the system for both cases is discussed by applying the Routh-Hurwitz criterion. Numerical analysis is performed to show the effect of various parameters on the growth rates of the K-H and R-T instabilities. Three different cases of the present configurations are considered and the conditions of instability are obtained. It is found that the conditions for the K-H and R-T instabilities depend on the magnetic field, on the suspended dust particles and on the relaxation frequency of the particles. The magnetic field and particle density have stabilizing influence, while the density difference between the fluids has a destabilizing influence on the growth rate of the K-H and R-T configurations.

scholarly journals The effect of compressibility, rotation and magnetic field on thermal instability of Walters’ fluid permeated with suspended particles in porous medium

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 539-550 ◽  
Author(s):  
Kumar Aggarwal ◽  
Anushri Verma
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Elastic Parameter ◽  
Mode Analysis ◽  
Medium Permeability ◽  
Stabilizing Effect ◽  
Model Fluid ◽  
The Stability

The purpose of this paper is to study the effects of compressibility, rotation, magnetic field and suspended particles on thermal stability of a layer of visco-elastic Walters? (model) fluid in porous medium. Using linearized theory and normal mode analysis, dispersion relation has been obtained. In case of stationary convection, it is found that the rotation has stabilizing effect on the system. The magnetic field may have destabilizing effect on the system in the presence of rotation while in the absence of rotation it always has stabilizing effect. The medium permeability has destabilizing effect on the system in the absence of rotation while in the presence of rotation it may have stabilizing effect. The suspended particles and compressibility always have destabilizing effect. Due to vanishing of visco-elastic parameter, the compressible visco-elastic fluid behaves like Newtonian fluid. Graphs have also been plotted to depict the stability characteristics. The viscoelasticity, magnetic field and rotation are found to introduce oscillatory modes into the system which were non-existent in their absence.

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.

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