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.

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 Rayleigh-Bénard convection in an elastico-viscous Walters’ (model B’) nanofluid layer

2015 ◽  
Vol 63 (1) ◽  
pp. 235-244 ◽  
Author(s):  
G.C. Rana ◽  
R. Chand
Keyword(s):  
Fluid Model ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Physical Parameters ◽  
Onset Of Convection ◽  
The Stability

Abstract In this study, the onset of convection in an elastico-viscous Walters’ (model B’) nanofluid horizontal layer heated from below is considered. The Walters’ (model B’) fluid model is employed to describe the rheological behavior of the nanofluid. By applying the linear stability theory and a normal mode analysis method, the dispersion relation has been derived. For the case of stationary convection, it is observed that the Walters’ (model B’) elastico-viscous nanofluid behaves like an ordinary Newtonian nanofluid. The effects of the various physical parameters of the system, namely, the concentration Rayleigh number, Prandtl number, capacity ratio, Lewis number and kinematics visco-elasticity coefficient on the stability of the system has been numerically investigated. In addition, sufficient conditions for the non-existence of oscillatory convection are also derived.

scholarly journals On the Onset of Thermal Convection in a Layer of Oldroydian Visco-Elastic Fluid Saturated by Brinkman–Darcy Porous Medium

2015 ◽  
Vol 37 (4) ◽  
pp. 3-10 ◽  
Author(s):  
Ramesh Chand
Keyword(s):  
Porous Medium ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Darcy Number ◽  
Horizontal Layer ◽  
Relaxation Parameter ◽  
Free Boundaries ◽  
Oscillatory Convection ◽  
Elastic Fluid ◽  
Mode Technique

AbstractThermal instability in a horizontal layer of Oldroydian visco-elastic fluid in a porous medium is investigated. For porous medium the Brinkman–Darcy model is considered. A linear stability analysis based upon perturbation method and normal mode technique is used to find solution of the fluid layer confined between two free-free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically. The influence of the Brinkman–Darcy, Prandtl–Darcy number, stress relaxation parameter on the stationary and oscillatory convection is studied both analytically and graphically. The sufficient condition for the validity of PES has also been derived.

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.

scholarly journals Thermal Instability in a Layer of Couple Stress Nanofluid Saturated Porous Medium

2017 ◽  
Vol 47 (1) ◽  
pp. 69-84 ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana ◽  
Dhananjay Yadav
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Couple Stress ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Mode Analysis ◽  
Brownian Diffusion

Abstract Thermal instability in a horizontal layer of Couple-stress nanofluid in a porous medium is investigated. Darcy model is used for porous medium. The model used for nanofluid incorporates the effect of Brownian diffusion and thermophoresis. The flux of volume fraction of nanoparticle is taken to be zero on the isothermal boundaries. Normal mode analysis and perturbation method is employed to solve the eigenvalue problem with the Rayleigh number as eigenvalue. Oscillatory convection cannot occur for the problem. The effects of Couple-stress parameter, Lewis number, modified diffusivity ratio, concentration Rayleigh number and porosity on stationary convection are shown both analytically and graphically.

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 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 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 Double Diffusive Convection in a Layer of Maxwell Viscoelastic Fluid in Porous Medium in the Presence of Soret and Dufour Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Viscoelastic Fluid ◽  
Fluid Layer ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Free Boundaries ◽  
Soret And Dufour Effects ◽  
Diffusive Convection ◽  
Double Diffusive

Double diffusive convection in a horizontal layer of Maxwell viscoelastic fluid in a porous medium in the presence of temperature gradient (Soret effects) and concentration gradient (Dufour effects) is investigated. For the porous medium Darcy model is considered. A linear stability analysis based upon normal mode technique is used to study the onset of instabilities of the Maxwell viscolastic fluid layer confined between two free-free boundaries. Rayleigh number on the onset of stationary and oscillatory convection has been derived and graphs have been plotted to study the effects of the Dufour parameter, Soret parameter, Lewis number, and solutal Rayleigh number on stationary convection.

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.

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