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 Convection of a Plasma in Porous Medium

2021 ◽  
Vol 16 ◽  
pp. 110-119
Author(s):  
Pardeep Kumar ◽  
Sumit Gupta
Keyword(s):  
Magnetic Field ◽  
Thermal Convection ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Medium Permeability ◽  
Stabilizing Effect ◽  
The Magnetic Field

The effect of finite Larmor radius of the ions on thermal convection of a plasma is investigated. The case with vertical magnetic field is discussed. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of 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 is found to have a stabilizing effect. Medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain conditions in the presence of finite Larmor radius effect whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively. 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.

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 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 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.

Effect of Finite Larmor Radius on the Rayleigh-Taylor Instability of Two Component Magnetized Rotating Plasma

1998 ◽  
Vol 53 (12) ◽  
pp. 937-944 ◽  
Author(s):  
P. K. Sharma ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Horizontal Magnetic Field ◽  
Finite Larmor Radius ◽  
Neutral Particles ◽  
Rayleigh Taylor Instability ◽  
Superposed Fluids

Abstract The Rayleigh-Taylor (R-T) instability of two superposed plasmas, consisting of interacting ions and neutrals, in a horizontal magnetic field is investigated. The usual magnetohydrodynamic equations, including the permeability of the medium, are modified for finite Larmor radius (FLR) corrections. From the relevant linearized perturbation equations, using normal mode analysis, the dispersion relation for the two superposed fluids of different densities is derived. This relation shows that the growth rate unstability is reduced due to FLR corrections, rotation and the presence of neutrals. The horizontal magnetic field plays no role in the R-T instability. The R-T instability is discussed for various simplified configurations. It remains unaffected by the permeability of the porous medium, presence of neutral particles and rotation. The effect of different factors on the growth rate of R-T instability is investigated using numerical analysis. Corresponding graphs are plotted for showing the effect of these factors on the growth of the R-T instability.

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.

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.

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