scholarly journals Hall Effect on Bénard Convection of Compressible Viscoelastic Fluid through Porous Medium

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mahinder Singh ◽  
Chander Bhan Mehta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Linear Stability Theory ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
Rayleigh Numbers ◽  
The Magnetic Field ◽  
Mode Technique

An investigation made on the effect of Hall currents on thermal instability of a compressible Walter’s B′ elasticoviscous fluid through porous medium is considered. The analysis is carried out within the framework of linear stability theory and normal mode technique. For the case of stationary convection, Hall currents and compressibility have postponed the onset of convection through porous medium. Moreover, medium permeability hasten postpone the onset of convection, and magnetic field has duel character on the onset of convection. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection have been obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. The magnetic field, Hall currents found to introduce oscillatory modes, in the absence of these effects the principle of exchange of stabilities is valid.

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 Thermal instability of Walters B' viscoelastic fluid permeated with suspended particles in hydromagnetics in porous medium

2004 ◽  
Vol 8 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Pardeep Kumar ◽  
Jit Singh ◽  
Roshan Lal
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Newtonian Fluid ◽  
Viscoelastic Fluid ◽  
Thermal Instability ◽  
Suspended Particles ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
The Magnetic Field

The effect of suspended particles on the thermal instability of Walters B' viscoelastic fluid in hydromantic in porous medium is considered. For stationary convection, Walters B' viscoelastic fluid behaves like a Newtonian fluid. The medium permeability and suspended particles has ten the onset of convection whereas the magnetic field postpones the onset of convection, for the case of stationary convection. The magnetic field and viscoelasticity intro duce oscillatory modes in the system which was non-existent in their absence.

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 Double-Diffusive Magnetoconvection of a Dusty Micropolar Fluid Saturating a Porous Medium

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Parul Aggarwal ◽  
Urvashi Gupta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Micropolar Fluid ◽  
Fluid Layer ◽  
Suspended Particle ◽  
Suspended Particles ◽  
Linear Stability Theory ◽  
Stationary Convection ◽  
Medium Permeability ◽  
Solute Gradient

The paper deals with the theoretical investigation of the effect of dust/suspended particles on a layer of electrically conducting micropolar fluid heated and dissolved from below in the presence of a uniform vertical magnetic field in a porous medium. The presence of coupling between thermosolutal and micropolar effects and magnetic field brings oscillatory motions in the system. A dispersion relation governing the effects of solute gradient, magnetic field, and suspended particles is obtained for a fluid layer contained between two free boundaries using linear stability theory and normal mode technique. Graphs have been plotted by giving numerical values to various parameters involved to depict the stability characteristics for both cases of stationary convection and overstability. It has been found that, for permissible values of various parameters under consideration, the effect of magnetic field and solute gradient is stabilizing and that of medium permeability, suspended particles, and micropolar coefficient is destabilizing. Further it is found that the Rayleigh number for overstability is always less than that for stationary convection except for high values of suspended particle factor.

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 Effect of Magnetic Field on Thermal Instability of Oldroydian Viscoelastic Rotating Fluid in Porous Medium

2013 ◽  
Vol 18 (2) ◽  
pp. 555-569 ◽  
Author(s):  
R.C. Thakur ◽  
G.C. Rana
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Rotating Fluid ◽  
Medium Permeability ◽  
Effects Of Rotation ◽  
The Magnetic Field

In this paper, we investigate the effect of a vertical magnetic field on thermal instability of an Oldroydian visco-elastic rotating fluid in a porous medium. By applying the normal mode analysis method, the dispersion relation governing the effects of rotation, magnetic field and medium permeability is derived and solved analytically and numerically. For the case of stationary convection, the Oldroydian viscoelastic fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has a stabilizing effect while the magnetic field and medium permeability have a stabilizing/destabilizing effect under certain conditions on thermal instability of the Oldroydian viscoelastic fluid in a porous medium. The oscillatory modes are introduced due to the presence of rotation, the magnetic field and gravity field. It is also observed that the ‘principle of exchange of stability’ is invalid in the presence of rotation and the magnetic field.

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.

scholarly journals Convection of a Rotatory Plasma in Porous Medium

2021 ◽  
Vol 16 ◽  
pp. 68-78
Author(s):  
Pardeep Kumar ◽  
Gursharn Jit Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Medium Permeability ◽  
The Magnetic Field

The thermal convection of a plasma in porous medium is investigated to include simultaneously the effect of rotation and the finiteness of the ion Larmor radius (FLR) in the presence of a vertical magnetic field. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of a uniform rotation, finite Larmor radius and magnetic field introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, finite Larmor radius, rotation, medium permeability and magnetic field are found to have stabilizing (or destabilizing) effects under certain conditions. In the absence of rotation, finite Larmor radius has stabilizing effect on the thermal instability of the system whereas the medium permeability and the magnetic field may have stabilizing or destabilizing effect under certain conditions. The conditions κ<[ε+(1-ε) (ρ_S C_S)/(ρ_0 C)]η and κ<(ε^2 [ε+(1-ε) (ρ_S C_S)/(ρ_0 C)]ν)/(P^2 [εP{√U (x-2)+√(T_(A_1 ) )}^2-2Q_1 ] ) are the sufficient conditions for non-existence of overstability, the violation of which does not necessary involve an occurrence of overstability.

scholarly journals On Thermal Instability of Kuvshiniski Fluid with Suspended Particles Saturated in a Porous Medium in the Presence of a Magnetic Field June 13, 2017

2017 ◽  
Vol 22 (4) ◽  
pp. 981-994
Author(s):  
M. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Thermal Instability ◽  
Sufficient Conditions ◽  
Suspended Particles ◽  
Linear Stability Theory ◽  
Horizontal Magnetic Field ◽  
Medium Permeability ◽  
The Stability

Abstract The thermal instability of a Kuvshiniski viscoelastic fluid is considered to include the effects of a uniform horizontal magnetic field, suspended particles saturated in a porous medium. The analysis is carried out within the framework of the linear stability theory and normal mode technique. For the case of stationary convection, the Kuvshiniski viscoelastic fluid behaves like a Newtonian fluid and the magnetic field has a stabilizing effect, whereas medium permeability and suspended particles are found to have a destabilizing effect on the system, oscillatory modes are introduced in the system, in the absence of these the principle of exchange of stabilities is valid. Graphs in each case have been plotted by giving numerical values to the parameters, depicting the stability characteristics. Sufficient conditions for the avoidance of overstability are also obtained.

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.

Sign in / Sign up

Export Citation Format

Share Document