Rayleigh–Taylor Instability of Swirling Annular Layer With Mass Transfer

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Mukesh Kumar Awasthi
Keyword(s):  
Mass Transfer ◽  
Vapor Phase ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Interfacial Instability ◽  
Mode Analysis ◽  
Transfer Constant ◽  
Viscous Potential Flow ◽  
Annular Layer ◽  
The Stability

The interfacial instability of Rayleigh–Taylor type at the cylindrical boundary involving the liquid phase and vapor phase of a fluid has been considered when the vapor is warmer than the liquid. We use viscous potential flow theory to include the viscosity at the interface. To examine the stability of the arrangement, the normal-mode analysis is performed together with the effect of heat as well as mass transfer and free swirl. The physical system consists of an annular fluid layer restricted in a cylinder with vapor phase in the core. This work investigates the effect of a variety of variables on the instability of the interface. It is found that when the heat transfer constant increases, the range of stability increases. Also, the range of stability increases faster in the presence of swirling.

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.

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.

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.

Linearized theory of inhomogeneous multiple ‘water-bag’ plasmas

1973 ◽  
Vol 9 (2) ◽  
pp. 235-247 ◽  
Author(s):  
H. W. Bloomberg ◽  
H. L. Berk
Keyword(s):  
Boundary Conditions ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Special Boundary ◽  
Finite Region ◽  
Trapped Particles ◽  
Linearized Theory ◽  
Beam Approximation ◽  
The Stability

The problem of the stability of inhomogeneous, electrostatic, multiple water-bag plasmas is considered. Equations are derived for general stationary water-bag equilibria, as well as for the corresponding perturbations. Particular attention is directed to systems with trapped particles in periodic equilibria, and special boundary conditions for the perturbation equations at the trapped-particle turning points are introduced. A normal-mode analysis is carried out for a configuration involving trapped particles occupying a finite region in the vicinity of the trough of an equilibrium wave (BGK mode). The results confirm the validity of the bunched-beam approximation.

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 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.

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.

Surface instability of a dielectric fluid in an electric field

1968 ◽  
Vol 64 (4) ◽  
pp. 1203-1207 ◽  
Author(s):  
D. H. Michael
Keyword(s):  
Free Surface ◽  
Dispersion Relation ◽  
Gravity Waves ◽  
Normal Mode Analysis ◽  
Horizontal Layer ◽  
Mode Analysis ◽  
Dielectric Fluid ◽  
Inviscid Fluid ◽  
Static Displacement ◽  
The Stability

This paper is a sequel to a recent paper (1) in which the author discussed gravity waves on a horizontal layer of conducting fluid with a normal electrostatic field at the free surface. In this work results are given for waves in an incompressible dielectric fluid, in a similar configuration. Treating the dielectric as an inviscid fluid the stability of the system is first described in terms of the changes in potential energy in a small static displacement. The result so obtained is then confirmed by a normal mode analysis in which a dispersion relation is obtained for the inviscid model. The paper gives finally a discussion of the results for a viscous dielectric fluid, the main point of which is that, as in (1), in the transition from stable to unstable disturbances viscosity plays no part, and that the stability characteristics are the same as those for an inviscid dielectric fluid.

Baroclinic instability in an eccentric annulus

1976 ◽  
Vol 77 (4) ◽  
pp. 769-788 ◽  
Author(s):  
P. R. Gent ◽  
H. Leach
Keyword(s):  
Normal Mode Analysis ◽  
Baroclinic Instability ◽  
Analytical Investigation ◽  
Mode Analysis ◽  
Slow Rotation ◽  
Rotating Fluid ◽  
Mixed Flow ◽  
Eccentric Annulus ◽  
Baroclinic Waves ◽  
The Stability

A study has been made of baroclinic instability in a differentially heated, rotating fluid annulus whose channel width varies azimuthally. Both laboratory experiments and an a.nalytica1 model employing a linear normal-mode analysis have been used. The experiments show three types of flow. For slow rotation the flow is 'symmetric’, whereas at high rotation speeds baroclinic waves occur at all azimuths. At intermediate rotation speeds it is possible to have a mixed flow which is ‘symmetric’ in the narrow part but has baroclinic waves in the wide part of the annulus. This result suggested the analytical investigation of the stability of a barocIinic flow whose meridional scale varies downstream. It was found that this model also permits three possible types of flow: everywhere stable, everywhere unstable, and also a mixed flow which is locally unstable where the meridional scale is largest but locally stable where the scale is smallest.

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.

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