scholarly journals Analysis of Stability in Couple-Stress Magneto-Fluid

2021 ◽  
Vol 2 (2) ◽  
pp. 35-42
Author(s):  
Pardeep Kumar ◽  
Gursharn Singh
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Normal Mode Analysis ◽  
Boussinesq Approximation ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Electrically Conducting ◽  
Linearized Stability ◽  
Medium Permeability ◽  
Analysis Of Stability

The aim of the present research was to study the effect of magnetic field on the layer of electrically conducting couple-stress fluid heated from below in porous medium. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that the couple-stress parameter and magnetic field have stabilizing effect on the system whereas the medium permeability has a destabilizing effect on the system. The magnetic field introduces oscillatory modes in the system which was non-existent in its absence. A sufficient condition for the non-existent of overstability is also obtained.

scholarly journals Stability Analysis in Couple-Stress Rotatory Fluid

2021 ◽  
Vol 16 ◽  
pp. 49-58
Author(s):  
Pardeep Kumar
Keyword(s):  
Couple Stress ◽  
Normal Mode Analysis ◽  
Boussinesq Approximation ◽  
Mode Analysis ◽  
Sufficient Condition ◽  
Stationary Convection ◽  
Uniform Rotation ◽  
Linearized Stability ◽  
Medium Permeability ◽  
Stabilizing Effect

The aim of the present research was to study the effect of uniform rotation on the layer of a couple-stress fluid heated from below in porous medium. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that rotation has a stabilizing effect, whereas the couple-stress parameter and medium permeability have both stabilizing and destabilizing effects on the system. It is found that the presence of rotation introduces oscillatory modes in the system which were non-existent in its absence. A sufficient condition for the non-existent of overstability is also obtained.

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 Effect of hall currents on thermal instability of dusty couple stress fluid

2016 ◽  
Vol 37 (3) ◽  
pp. 3-18 ◽  
Author(s):  
Amrish Kumar Aggarwal ◽  
Anushri Verma
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Dust Particles ◽  
Couple Stress Fluid ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Stabilizing Effect

Abstract In this paper, effect of Hall currents on the thermal instability of couple-stress fluid permeated with dust particles has been considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For the case of stationary convection, dust particles and Hall currents are found to have destabilizing effect while couple stresses have stabilizing effect on the system. Magnetic field induced by Hall currents has stabilizing/destabilizing effect under certain conditions. It is found that due to the presence of Hall currents (hence magnetic field), oscillatory modes are produced which were non-existent in their absence.

Magneto Thermal Convection in a Compressible Couple-Stress Fluid

2010 ◽  
Vol 65 (3) ◽  
pp. 215-220 ◽  
Author(s):  
Mahinder Singh ◽  
Pardeep Kumar
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Linearized Stability ◽  
The Stability ◽  
The Magnetic Field

The problem of thermal instability of compressible, electrically conducting couple-stress fluids in the presence of a uniform magnetic field is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, couple-stress, and magnetic field postpone the onset of convection. Graphs have been plotted by giving numerical values of the parameters to depict the stability characteristics. The principle of exchange of stabilities is found to be satisfied. The magnetic field introduces oscillatory modes in the system that were non-existent in its absence. The case of overstability is also studied wherein a sufficient condition for the non-existence of overstability is obtained.

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.

scholarly journals TRIPLE-DIFFUSIVE CONVECTION IN WALTERS’ (MODEL B’) FLUID WITH VARYING GRAVITY FIELD SATURATING A POROUS MEDIUM

2013 ◽  
Vol 35 (3) ◽  
pp. 45-56 ◽  
Author(s):  
S.K. Kango ◽  
G.C. Rana ◽  
Ramesh Chand
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Gravity Field ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Analysis Theory ◽  
Diffusive Convection ◽  
Medium Permeability

Abstract The Triple-Diffusive convection in Walters’ (Model B') fluid with varying gravity field is considered in the presence of uniform vertical magnetic field in porous medium. For the case of stationary convection, the magnetic field, varying gravity field and the stable solute gradients have stabilizing effects whereas the medium permeability has destabilizing (or stabilizing) effect on the system under certain conditions. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset convection. The kinematic viscoelasticity has no effect on the stationary convection. The solute gradients, magnetic field, varying gravity field, porosity and kinematic viscoelasticity introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The results are also shown graphically.

Rotatory Thermosolutal Convection in a Couple-Stress Fluid

2009 ◽  
Vol 64 (7-8) ◽  
pp. 448-454
Author(s):  
Pardeep Kumar ◽  
Mahinder Singh
Keyword(s):  
Dispersion Relation ◽  
Couple Stress ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Thermosolutal Convection ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Solute Gradient

AbstractThe thermosolutal instability of couple-stress fluid in the presence of uniform vertical rotation is considered. Following the linearized stability theory and normal mode analysis, the dispersion is obtained. For the case of stationary convection, the stable solute gradient and rotation have stabilizing effects on the system, whereas the couple-stress has both stabilizing and destabilizing effects. The dispersion relation is also analyzed numerically. The stable solute gradient and the rotation introduce oscillatory modes in the system, which did not occur in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

scholarly journals The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium

2014 ◽  
Vol 62 (2) ◽  
pp. 357-362
Author(s):  
Gian C. Rana
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Convection ◽  
Couple Stress ◽  
Normal Mode Analysis ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Stress Parameter ◽  
Medium Permeability

Abstract In this paper, the effect of magnetic field on thermal convection in couple-stress fluid saturating a porous medium is considered. By applying linear stability theory and the normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter Pι the couple-stress parameter F and the Chandrasekher number Q, satisfy the inequality the result clearly establishes the stabilizing character of couple-stress parameter and magnetic field whereas destabilizing character of medium permeability.

Effect Of Rotation On Thermal Instability In Couple-Stress Elastico-Viscous Fluid

2004 ◽  
Vol 59 (7-8) ◽  
pp. 407-411
Author(s):  
Pardeep Kumar ◽  
Roshan Lal ◽  
Poonam Sharma
Keyword(s):  
Couple Stress ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Sufficient Condition ◽  
Stationary Convection ◽  
Uniform Rotation ◽  
System A ◽  
Linearized Stability ◽  
Stabilizing Effect

The thermal instability of a layer of a couple-stress fluid acted on by a uniform rotation is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection it is found that rotation has a stabilizing effect, whereas the couple-stress has both stabilizing and destabilizing effects. It is found that the presence of rotation introduces oscillatory modes in the system. A sufficient condition for the non-existence of overstability is also obtained.

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