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 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.

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.

Thermosolutal Convection in a Couple-Stress Fluid in Uniform Vertical Magnetic Field

2012 ◽  
Vol 67 (5) ◽  
pp. 275-281
Author(s):  
Mahinder Singh ◽  
Pardeep Kumar
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Thermosolutal Convection ◽  
Couple Stress Fluid ◽  
Vertical Magnetic Field ◽  
Stationary Convection ◽  
Gradient Magnetic Field ◽  
Electrically Conducting ◽  
Stabilizing Effect ◽  
Solute Gradient

The effect of a uniform vertical magnetic field on thermosolutal convection in a layer of an electrically conducting couple-stress fluid heated and soluted from below is considered. For the case of stationary convection, the stable solute gradient, magnetic field, and couple-stress parameter have stabilizing effect on the system. It is also observed that a stable solute gradient and a magnetic field introduce oscillatory modes in the system, but in the absence of a stable solute gradient and a magnetic field, oscillatory modes are not allowed and the principle of exchange of stabilities is valid.

scholarly journals Compressible Analysis of Bénard Convection of Magneto Rotatory Couple-Stress Fluid

2018 ◽  
Vol 23 (1) ◽  
pp. 91-105
Author(s):  
C.B. Mehta ◽  
M. Singh
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Thermal Instability ◽  
Sufficient Conditions ◽  
Couple Stress Fluid ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Linearized Stability ◽  
Exchange Of Stability ◽  
The Magnetic Field

AbstractThermal Instability (Benard’s Convection) in the presence of uniform rotation and uniform magnetic field (separately) is studied. Using the linearized stability theory and normal mode analyses the dispersion relation is obtained in each case. In the case of rotatory Benard’s stationary convection compressibility and rotation postpone the onset of convection whereas the couple-stress have duel character onset of convection depending on rotation parameter. While in the absence of rotation couple-stress always postpones the onset of convection. On the other hand, magnetic field on thermal instability problem on couple-stress fluid for stationary convection couple-stress parameter and magnetic field postpones the onset of convection. The effect of compressibility also postpones the onset of convection in both cases as rotation and magnetic field. Graphs have been plotted by giving numerical values to the parameters to depict the stationary characteristics. Further, the magnetic field and rotation are found to introduce oscillatory modes which were non-existent in their absence and then the principle of exchange of stability is valid. The sufficient conditions for non-existence of overstability are also obtained.

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.

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 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 Effect of Gravity Modulation on Single Component Convection in a Couple Stress Fluid with Maxwell-Cattaneo Law

2018 ◽  
Vol 7 (4.10) ◽  
pp. 657
Author(s):  
Maria Thomas ◽  
Sangeetha George K
Keyword(s):  
Heat Conduction ◽  
Couple Stress ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Gravity Modulation ◽  
Inertial Effects ◽  
Regular Perturbation ◽  
Onset Of Convection ◽  
Perturbed State

The outset of convection in a thin layer of couple stress fluid is analyzed using the linear stability analysis when the fluid is heated from below. In order to assimilate the inertial effects Maxwell-Cattaneo law is used in lieu of the classical Fourier's heat conduction law. The normal mode analysis is used to arrive at the eigenvalues of the perturbed state and a regular perturbation method to find the analytical solutions. The effect of Cattaneo number, couple stress parameter and Prandtl number is discussed and it is concluded that gravity modulation can delay or advance the onset of convection.  

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.

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