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.  

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.

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.

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 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.

scholarly journals Magneto-rotatory compressible couple-stress fluid heated from below in porous medium

2016 ◽  
Vol 38 (1) ◽  
pp. 55-63
Author(s):  
Chander Bhan Mehta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Couple Stress ◽  
Normal Modes ◽  
Sufficient Conditions ◽  
Couple Stress Fluid ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
Effects Of Rotation ◽  
The Magnetic Field

Abstract The study is aimed at analysing thermal convection in a compressible couple stress fluid in a porous medium in the presence of rotation and magnetic field. After linearizing the relevant equations, the perturbation equations are analysed in terms of normal modes. A dispersion relation governing the effects of rotation, magnetic field, couple stress parameter and medium permeability have been examined. For a stationary convection, the rotation postpones the onset of convection in a couple stress fluid heated from below in a porous medium in the presence of a magnetic field. Whereas, the magnetic field and couple stress postpones and hastens the onset of convection in the presence of rotation and the medium permeability hastens and postpones the onset of convection with conditions on Taylor number. Further the oscillatory modes are introduced due to the presence of rotation and the magnetic field which were non-existent in their absence, and hence the principle of exchange stands valid. The sufficient conditions for nonexistence of over stability are also obtained.

scholarly journals Global Stability For Double-Diffusive Convection In A Couple-Stress Fluid Saturating A Porous Medium

2019 ◽  
Vol 41 (1) ◽  
pp. 13-20
Author(s):  
Shalu Choudhary ◽  
Keyword(s):  
Porous Medium ◽  
Couple Stress ◽  
Linear Instability ◽  
Couple Stress Fluid ◽  
Brinkman Number ◽  
Onset Of Convection ◽  
Instability Theory ◽  
Diffusive Convection ◽  
Solute Gradient ◽  
Double Diffusive

Abstract We show that the global non-linear stability threshold for convection in a double-diffusive couple-stress fluid saturating a porous medium is exactly the same as the linear instability boundary. The optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It is also found that couple-stress fluid saturating a porous medium is thermally more stable than the ordinary viscous fluid, and the effects of couple-stress parameter (F ) , solute gradient ( S f ) and Brinkman number ( D a ) on the onset of convection is also analyzed.

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