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 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.

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 Hydromagnetic thermosolutal instability of Rivlin-Ericksen rotating fluid permeated with suspended particles and variable gravity field in porous medium

2014 ◽  
Vol 6 (1) ◽  
pp. 24-45
Author(s):  
G. C. Rana
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Gravity Field ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Rotating Fluid ◽  
Medium Permeability ◽  
Variable Gravity ◽  
Solute Gradient

AbstractThe thermosolutal instability of Rivlin-Ericksen elasticoviscous rotating fluid permeated with suspended particles (fine dust) and variable gravity field 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, gravity field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation and stable solute gradient has stabilizing effects and 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. The effect of rotation, suspended particles, magnetic field, stable solute gradient and medium permeability has also been shown graphically.

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 Instability of Two Viscoelastic Dusty-Fluids in Porous Medium

2021 ◽  
Vol 16 ◽  
pp. 137-144
Author(s):  
Pardeep Kumar ◽  
Sumit Gupta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Suspended Particles ◽  
Stable Configuration ◽  
Number Density ◽  
Horizontal Magnetic Field ◽  
Two Fluids ◽  
Medium Permeability ◽  
The Stability ◽  
The Magnetic Field

An attempt has been made to investigate the instability of the plane interface between two viscoelastic superposed conducting fluids in the presence of suspended particles and variable horizontal magnetic field through porous medium is studied. The cases of two fluids of uniform densities, viscosities, magnetic fields, and suspended particles number densities separated by a horizontal boundary; and of exponentially varying density, viscosity, suspended particles number density, and magnetic field are considered. It is found that the stability criterion is independent of the effects of viscoelasticity, medium porosity, and suspended particles but is dependent on the orientation and magnitude of the magnetic field. The magnetic field succeeds in stabilizing a certain range of wavenumbers which were unstable in the absence of the magnetic field. The system is found to be stable for potentially stable configuration/stratification. The growth rates are found to increase (for certain wavenumbers) and decrease (for other wavenumbers) with the increase in kinematic viscosity, suspended particles number density, magnetic field, medium permeability and stress relaxation time.

scholarly journals Three-Dimensional Stability Characteristics of Finite Electrified Conducting Fluids Streaming through a Porous Medium

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
T. M. N. Metwaly ◽  
Zakaria M. Gharsseldien
Keyword(s):  
Porous Medium ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Mode Analysis ◽  
Three Dimension ◽  
Fluid Velocities ◽  
Medium Permeability ◽  
Medium Porosity ◽  
The Stability ◽  
Conducting Fluids

A novel procedure is utilized to investigate the surface waves between two finite conducting fluids streaming through a porous medium in the presence of a horizontal electric field. Normal mode analysis is applied to study two- and three-dimension disturbances cases. The quadratic dispersion equation of complex coefficients representing the system is derived and discussed. It is noted that based on appropriate data selections, the stability criteria do not depend on the medium permeability. It is found that electrical conductivities, viscosities, medium porosity, and surface tension enhance the stability of the system while the dimension and the fluid velocities decrease the stability of the system. Finally, the fluid depths have a dual role (stabilizing as well as destabilizing effects) on the system.

scholarly journals Triple Diffusive Convection of a Non-Newtonian Fluid Under the Combined Effect of Compressibility and Variable Gravity

2019 ◽  
Vol 24 (4) ◽  
pp. 1-11
Author(s):  
A.K. Aggarwal ◽  
D. Dixit
Keyword(s):  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Diffusive Convection ◽  
Medium Permeability ◽  
Stabilizing Effect ◽  
Variable Gravity

Abstract In this paper, triple diffusive convection in a Rivlin-Ericksen fluid layer, which is permeated with suspended particles in the porous medium under the effect of compressibility and variable gravity, is investigated. Linear stability theory and normal mode analysis have been used to study the problem under consideration. It is observed that, for stationary convection, suspended particles, compressibility and medium permeability have destabilizing/stabilizing effects under certain conditions. The variable gravity parameter destabilizes the system whereas stable solute gradients have a stabilizing effect.

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 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.

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