Effect of Rotation and Magnetic Field on Thermal Stability of Ferromagnetic Fluid

2013 ◽  
Author(s):  
Amrish K. Aggarwal ◽  
Anushri Verma
Keyword(s):  
Magnetic Field ◽  
Thermal Stability ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Linearized Stability ◽  
Ferromagnetic Fluid ◽  
Exchange Of Stability ◽  
Thermal Stability Of

In this paper, the effect of rotation and magnetic field on thermal stability of a layer of ferromagnetic fluid heated from below has been investigated. For a fluid layer between two free boundaries, an exact solution is obtained using a linearized stability theory and normal mode analysis. For the case of stationary convection, it is found that magnetic field and rotation have stabilizing effect on the thermal stability of the system. The principle of exchange of stability is not valid for the problem under consideration, whereas in the absence of rotation and magnetic field, it is valid.

scholarly journals Effect of Magnetic Field on Thermosolutal Instability of Rotating Ferromagnetic Fluid Under Varying Gravity Field

2021 ◽  
Vol 26 (1) ◽  
pp. 201-214
Author(s):  
S. K. Pundir ◽  
P. K. Nadian ◽  
R. Pundir
Keyword(s):  
Magnetic Field ◽  
Gravity Field ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Magnetic Field Rotation ◽  
Stabilizing Effect ◽  
Ferromagnetic Fluid ◽  
Solute Gradient

AbstractThis paper deals with the theoretical investigation of the effect of a magnetic field, rotation and magnetization on a ferromagnetic fluid under varying gravity field. To find the exact solution for a ferromagnetic fluid layer contained between two free boundaries, we have used a linear stability analysis and normal mode analysis method. For the case of stationary convection, a stable solute gradient has a stabilizing effect, while rotation has a stabilizing effect if λ>0 and destabilizing effect if λ<0. Further, the magnetic field is discovered to have both a stabilizing and destabilizing effect for both λ>0 and λ<0. It is likewise discovered that magnetization has a stabilizing effect for both λ>0 and λ<0 in the absence of the stable solute gradient. Graphs have been plotted by giving numerical values of various parameters. In the absence of rotation, magnetic field and stable solute gradient, the principle of exchange of stabilities is found to hold true for certain conditions.

scholarly journals Hall effect on thermal stability of ferromagnetic fluid in porous medium in the presence of horizontal magnetic field

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 503-514 ◽  
Author(s):  
Amrish Aggarwal ◽  
Suman Makhija
Keyword(s):  
Magnetic Field ◽  
Thermal Stability ◽  
Porous Medium ◽  
Thermal Instability ◽  
Mode Analysis ◽  
Horizontal Magnetic Field ◽  
Linearized Stability ◽  
Medium Permeability ◽  
Ferromagnetic Fluid ◽  
Thermal Stability Of

This paper deals with the theoretical investigation of the effect of Hall currents on the thermal stability of a ferromagnetic fluid heated from below in porous medium. For a fluid layer between two free boundaries, an exact solution is obtained using a linearized stability theory and normal mode analysis. A dispersion relation governing the effects of medium permeability, a uniform horizontal magnetic field, magnetization and Hall currents is derived. For the case of stationary convection, it is found that the magnetic field and magnetization have a stabilizing effect on the system, as such their effect is to postpone the onset of thermal instability whereas Hall currents are found to hasten the onset of thermal instability. The medium permeability hastens the onset of convection under certain conditions. The principle of exchange of stabilities is not valid for the problem under consideration whereas in the absence of Hall currents (hence magnetic field), it is valid under certain conditions.

Finite-Resistivity Effects on Rayleigh-Taylor Instability of a Stratified Plasma Including Suspended Particles

1985 ◽  
Vol 40 (8) ◽  
pp. 826-833
Author(s):  
Rajkamal Sanghvi ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Kinematic Viscosity ◽  
Normal Mode Analysis ◽  
Longitudinal Mode ◽  
Transverse Mode ◽  
Suspended Particles ◽  
Wave Number ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Horizontal Magnetic Field

The Rayleigh-Taylor (RT) instability of a stratified and viscid magnetoplasma including the effects of "finite-resistivity and suspended particles is investigated using normal mode analysis. The horizontal magnetic field and the viscosity of the medium are assumed to be variable. The dispersion relation, which is obtained for the general case on employing boundary conditions appropriate to the case of two free boundaries, is then specialized for the longitudinal and transverse modes. It is found that the criterion of stable stratification remains essentially unchanged and that the unstable stratification for the longitudinal mode can be stabilized for a certain wave number band, whereas the transverse mode remains unstable or all wave numbers which can be stabilized by a suitable choice of the magnetic field for vanishing resistivity. Thus, resistivity is found to have a destabilizing influence on the RT configuration. The growth rates of the unstable RT modes with the kinematic viscosity and the relaxation frequency parameter of the suspended particles have been analytically evaluated. Dust (suspended particles) tends to stabilize the configuration when the medium is considered viscid with infinite conductivity. The kinematic viscosity has a stabilizing influence on the ideal plasma modes.

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.

Dufour and Soret Effects on the Thermosolutal Instability of Rivlin– Ericksen Elastico–Viscous Fluid in Porous Medium

2012 ◽  
Vol 67 (12) ◽  
pp. 685-691 ◽  
Author(s):  
Ramesh Chand ◽  
Gian Chand Rana
Keyword(s):  
Porous Medium ◽  
Viscous Fluid ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Oscillatory Convection ◽  
The Stability

Dufour and Soret effects on the convection in a horizontal layer of Rivlin-Ericksen elastico- viscous fluid in porous medium are considered. For the porous medium, the Darcy model is used. A linear stability analysis based upon normal mode analysis is employed to find a solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection has been derived analytically, and graphs have been plotted, giving various numerical values to various parameters, to depict the stability characteristics. The effects of the Dufour parameter, Soret parameter, solutal Rayleigh number, and Lewis number on stationary convection have been investigated.

scholarly journals Triple- Diffusive Convection in a Micropolar Ferrofluid in the Presence of Rotation

2013 ◽  
Vol 18 (2) ◽  
pp. 307-327
Author(s):  
S. Chand
Keyword(s):  
Spin Diffusion ◽  
Fluid Layer ◽  
Coupling Parameter ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Mode Analysis ◽  
Viscous Effect ◽  
Free Boundaries ◽  
Diffusive Convection ◽  
Solute Gradient

This paper deals with the theoretical investigation of the triple-diffusive convection in a micropolar ferrofluid layer heated and soluted below subjected to a transverse uniform magnetic field in the presence of uniform vertical rotation. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been employed to study the onset convection. The influence of various parameters like rotation, solute gradients, and micropolar parameters (i.e., the coupling parameter, spin diffusion parameter and micropolar heat conduction parameter) on the onset of stationary convection has been analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large value of the buoyancy magnetization parameter M1 (ratio of the magnetic to gravitational forces). The principle of exchange of stabilities is found to hold true for the micropolar fluid heated from below in the absence of micropolar viscous effect, microinertia, solute gradient and rotation. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia , solute gradient and rotation, which were non-existent in their absence. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability.

Thermal Instability of Rivlin–Ericksen Elastico-Viscous Nanofluid Saturated by a Porous Medium

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana
Keyword(s):  
Porous Medium ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Lewis Number ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Oscillatory Convection ◽  
The Stability

Thermal instability in a horizontal layer of Rivlin–Ericksen elastico-viscous nanofluid in a porous medium is considered. A linear stability analysis based upon normal mode analysis is used to find a solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically and graphs have been plotted by giving numerical values to various parameters to depict the stability characteristics. The effects of the concentration Rayleigh number, Vadasz number, capacity ratio, Lewis number, and kinematics viscoelasticity parameter on the stability of the system are investigated. Regimes of oscillatory and nonoscillatory convection for various parameters are derived and discussed in detail. The sufficient conditions for the nonexistence of oscillatory convection have also been obtained.

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