Effect of Horizontal Alternating Current Electric Field on the Stability of Natural Convection in a Dielectric Fluid Saturated Vertical Porous Layer

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
B. M. Shankar ◽  
Jai Kumar ◽  
I. S. Shivakumara
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Prandtl Number ◽  
Traveling Wave ◽  
Effective Viscosity ◽  
Darcy Number ◽  
Wave Mode ◽  
Dielectric Fluid ◽  
Fluid Viscosity ◽  
The Stability

The stability of natural convection in a dielectric fluid-saturated vertical porous layer in the presence of a uniform horizontal AC electric field is investigated. The flow in the porous medium is governed by Brinkman–Wooding-extended-Darcy equation with fluid viscosity different from effective viscosity. The resulting generalized eigenvalue problem is solved numerically using the Chebyshev collocation method. The critical Grashof number Gc, the critical wave number ac, and the critical wave speed cc are computed for a wide range of Prandtl number Pr, Darcy number Da, the ratio of effective viscosity to the fluid viscosity Λ, and AC electric Rayleigh number Rea. Interestingly, the value of Prandtl number at which the transition from stationary to traveling-wave mode takes place is found to be independent of Rea. The interconnectedness of the Darcy number and the Prandtl number on the nature of modes of instability is clearly delineated and found that increasing in Da and Rea is to destabilize the system. The ratio of viscosities Λ shows stabilizing effect on the system at the stationary mode, but to the contrary, it exhibits a dual behavior once the instability is via traveling-wave mode. Besides, the value of Pr at which transition occurs from stationary to traveling-wave mode instability increases with decreasing Λ. The behavior of secondary flows is discussed in detail for values of physical parameters at which transition from stationary to traveling-wave mode takes place.

scholarly journals Effect of Horizontal AC Electric Field on the Stability of Natural Convection in a Vertical Dielectric Fluid Layer

2016 ◽  
Vol 9 (6) ◽  
pp. 3073-3086 ◽  
Author(s):  
B. M. Shankar ◽  
J. Kumar ◽  
I. S. Shivakumara ◽  
S. B. Naveen Kumar ◽  
◽  
...  
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Fluid Layer ◽  
Dielectric Fluid ◽  
Ac Electric Field ◽  
The Stability

Experiments on Convective Instability of Large Prandtl Number Fluids in a Vertical Slot

1994 ◽  
Vol 116 (1) ◽  
pp. 120-126 ◽  
Author(s):  
S. Wakitani
Keyword(s):  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
Traveling Wave ◽  
Critical Rayleigh Number ◽  
Transition Process ◽  
Wave Mode ◽  
Vertical Slot ◽  
Increasing Trend ◽  
The Stability

The stability of thermal convection of large Prandtl number fluids in a vertical slot (aspect ratio = 10, 15, or 20) was studied experimentally. Secondary cells began to appear from the center of the slot and then prevailed. The critical Rayleigh number showed an increasing trend as the aspect ratio was increased, and became higher than that obtained from a linear stability analysis owing to a possible traveling wave mode of instability. As the Rayleigh number was increased, either the onset of the tertiary cells or the traveling waves occurred depending on the Prandtl number. In the transition process from laminar to turbulent flow, the secondary cells around the end regions split into smaller cells and an unsteady flow structure appeared with an original secondary cell in the center region and some smaller cells along the sidewalls.

The Stability of Natural Convection in an Inclined Fluid Layer in the Presence of AC Electric Field

1996 ◽  
Vol 65 (8) ◽  
pp. 2479-2484 ◽  
Author(s):  
Mohamed A. K. El Adawi ◽  
El Sayed F. El Shehawey ◽  
Safaa A. Shalaby ◽  
Mohamed I. A. Othman
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Fluid Layer ◽  
Ac Electric Field ◽  
Inclined Fluid Layer ◽  
The Stability

A rotating spherical liquid drop in an electric field

1972 ◽  
Vol 56 (2) ◽  
pp. 305-312 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Electric Field ◽  
Equilibrium Shape ◽  
Dielectric Fluid ◽  
Inviscid Fluid ◽  
Axis Of Rotation ◽  
Field Parallel ◽  
Electric Field Parallel ◽  
Fluid Drop ◽  
The Stability ◽  
Small Deformations

It is shown that the equilibrium shape of an incompressible dielectric fluid drop rotating with constant angular velocity in the presence of a uniform external electric field of appropriate magnitude along the axis of rotation is spherical. For an inviscid fluid drop, the stability of this spherical configuration to small deformations is investigated by means of Chandrasekhar's virial method. We find that a rotating drop in the presence of an electric field parallel to the axis of rotation is, in some respects, more stable than when either only the electric field or only rotation is present. This is due to the fact that the application of an electric field parallel to the axis of a rotating drop, or of rotation parallel to an electric field in which a drop is immersed, shifts the instability mechanism to another normal mode.

Natural Convection in Horizontal Porous Layers: Effects of Darcy and Prandtl Numbers

1989 ◽  
Vol 111 (4) ◽  
pp. 926-935 ◽  
Author(s):  
N. Kladias ◽  
V. Prasad
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Darcy Number ◽  
Solid Particles ◽  
Convection Regime ◽  
Porous Layers

Natural convection in horizontal porous layers heated from below is studied by employing a formulation based on the Brinkman–Forchheimer–extended Darcy equation of motion. The numerical solutions show that the convective flow is initiated at lower fluid Rayleigh number Raf than that predicted by the linear stability analysis for the Darcy flow model. The effect is considerable, particularly at a Darcy number Da greater than 10−4. On the other hand, an increase in the thermal conductivity of solid particles has a stabilizing effect. Also, the Rayleigh number Raf required for the onset of convection increases as the fluid Prandtl number is decreased. In the stable convection regime, the heat transfer rate increases with the Rayleigh number, the Prandtl number, the Darcy number, and the ratio of the solid and fluid thermal conductivities. However, there exists an asymptotic convection regime where the porous media solutions are independent of the permeability of the porous matrix or Darcy number. In this regime, the temperature and flow fields are very similar to those obtained for a fluid layer heated from below. Indeed, the Nusselt numbers for a porous medium with kf = ks match with the fluid results. The effect of Prandtl number is observed to be significant for Prf < 10, and is strengthened with an increase in Raf, Da, and ks/kf. An interesting effect, that a porous medium can transport more energy than the saturating fluid alone, is also revealed.

Effect of an electric field on the stability of binary dielectric fluid mixtures

2020 ◽  
Vol 152 (23) ◽  
pp. 234901
Author(s):  
Jonathan M. Martin ◽  
Kris T. Delaney ◽  
Glenn H. Fredrickson
Keyword(s):  
Electric Field ◽  
Dielectric Fluid ◽  
Fluid Mixtures ◽  
The Stability

Electrohydrostatic instability in electrically stressed dielectric fluids. Part 2

1975 ◽  
Vol 72 (1) ◽  
pp. 95-112 ◽  
Author(s):  
D. H. Michael ◽  
J. Norbury ◽  
M. E. O'Neill
Keyword(s):  
Electric Field ◽  
Point Of View ◽  
Dielectric Fluid ◽  
Sufficient Information ◽  
Physical Point ◽  
Dielectric Fluids ◽  
A Value ◽  
Asymmetric Equilibria ◽  
The Stability ◽  
Loading Parameter

The paper is the second part of a study of the failure of the insulation of a layer of dielectric fluid of arbitrary volume, occupying a hole in a solid dielectric sheet, when stressed by an applied electric field. In part 1 symmetric and asymmetric equilibria were found for the two-dimensional problem, using an approximation given by Taylor (1968) for the electric field, which is valid for large holes. In this paper axisymmetric equilibria are given for a circular hole, under the same conditions. In addition the points of bifurcation of asymmetric solutions have been found, and provide sufficient information to give the stability characteristics. It is found that when the volume-excess fraction δ exceeds a value of approximately −0·3 instability occurs in an asymmetric form reported earlier for large holes by Michael, O'Neill & Zuercher (1971) in the case δ = 0. For δ < −0·3 the nature of the instability changes to an axisymmetric form of failure associated with a maximum of the loading parameter.The analysis given shows that axisymmetric displacements of ‘sausage’ mode type, that is, symmetric about a centre-plane, are associated with small changes in the static pressure in the dielectric layer. Such modes have not previously been examined in this context, and in an appendix to this paper Michael & O'Neill give an analysis of them when δ = 0, valid for all hole sizes, by extending the small perturbation analysis of Michael, O'Neill & Zuercher. These modes however do not provide the most unstable displacements for any configuration, and do not therefore affect the stability from a physical point of view.

Finite Darcy–Prandtl Number and Maximum Density Effects on Gill's Stability Problem 

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
S. B. Naveen ◽  
B. M. Shankar ◽  
I. S. Shivakumara
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Wave Mode ◽  
Density Variation ◽  
Maximum Density ◽  
Time Dependent ◽  
Wave Number ◽  
Neutral Stability ◽  
The Stability ◽  
Darcy Rayleigh Number

Abstract The simultaneous effect of a time-dependent velocity term in the momentum equation and a maximum density property on the stability of natural convection in a vertical layer of Darcy porous medium is investigated. The density is assumed to vary quadratically with temperature and as a result, the basic velocity distribution becomes asymmetric. The problem has been analyzed separately with (case 1) and without (case 2) time-dependent velocity term. It is established that Gill's proof of linear stability effective for case 2 but found to be ineffective for case 1. Due to the lack of Gill's proof for case1, the stability eigenvalue problem is solved numerically and observed that the instability sets in always via traveling-wave mode when the Darcy–Prandtl number is not larger than 7.08. The neutral stability curves and isolines are presented for different governing parameters. The critical values of Darcy–Rayleigh number corresponding to quadratic density variation with respect to temperature, critical wave number, and the critical wave speed are computed for different values of governing parameters. It is found that the system becomes more stable with increasing Darcy–Rayleigh number corresponding to linear density variation with respect to temperature and the Darcy–Prandtl number.

Sign in / Sign up

Export Citation Format

Share Document