The onset of electrohydrodynamic instability of an elastico-viscous Walters' (model B') dielectric fluid layer

Rana, G. C.; Chand, Ramesh; Yadav, Dhananjay

doi:10.5937/fmet1502154r

Cited by 12 publications

(12 citation statements)

References 19 publications

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“…The right hand sides of equations (52) and (55) are negative implying, thereby the AC electric Rayleigh number and nanoparticle Rayleigh number inhibit the stationary convection. Thus, AC electric Rayleigh number and nanoparticle Rayleigh number have destabilizing effects on the system which is in an agreement with the results derived by Nield and Kuznetsov (2009), Takashima (1976) and Shivakumara (2011), Rana et al (2012Rana et al ( , 2015 and .…”

Section: Resultssupporting

confidence: 90%

“…The right-hand side of equation 56is positive but it will be negative if Rn is negative implying thereby medium porosity has destabilizing effect on the system which is in an agreement with the results derived by Nield and Kuznetsov (2009), Rana et al (2012Rana et al ( , 2015 and .…”

Section: Resultssupporting

confidence: 88%

“…The dispersion relation (48) is also analyzed numerically. Graphs have been plotted by giving some numerical values to the parameters to depict the stability characteristics, e. g., 24 1010 Le  (Lewis number), 1 10 10 Rn   (nanoparticles Rayleigh number), 0.1 1   (porosity parameter) (Rana et al 2012(Rana et al , 2015 In Fig. 2, the variations of thermal Rayleigh number Ra with the wave number a for three different values of the modified Taylor number, namely, Ta = 1000, 2000 and 3000 which shows that thermal Rayleigh number increases with the increase in the modified Taylor number.…”

Section: Resultsmentioning

confidence: 99%

“…We know that keeping a constant volume fraction of nanoparticles at the horizontal boundaries will be almost impossible in a realistic situation. However, we assumed these conditions, which have also been previously adopted by several authors (Tzou 2008 a, b;Nield and Kuznetsov 2009;Sheu 2011;Chand and Rana 2012;Nield and Kuznetsov 2014;Chand et al 2014;Yadav and Kim 2015;Takashima and Ghosh 1979;Takashima and Hamabata 1984;Othman 2004;Shivakumara et al 2007;Ruo et al 2010;Shivakumara et al 2013;and Rana et al 2015, 2016.…”

Section: Formulation Of the Problem And Mathematical Modelmentioning

confidence: 99%

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Electrohydrodynamic Thermal Instability in a Walters’ (Model B') Rotating Nanofluid Saturating a Porous Medium

Rana¹,

Gautam²,

Saxena³

2019

JSSCM

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The onset of thermal instability in a dielectric rotating nanofluid layer saturating a porous medium with vertical AC electric field is investigated by employing Darcy model for porous medium. The rheology of the nanofluid is described by Walters' (model B') for calculating the shear stresses from the velocity gradients. The employed model incorporates the combined effects of movement of the molecules of the fluid striking the nanoparticles, thermophoresis and electrophoresis due to the embedded particles. The boundaries are considered to be stress free. It is assumed that nanoparticle flux is zero on the boundaries. The eigen-value problem is solved analytically using the first approximation of Galerkin method. The Darcy Rayleigh number for onset of nonoscillatory (stationary) modes is obtained. The effects of the modified Taylor number, the AC electric Rayleigh number, the Lewis number, the modified diffusivity ratio, nanoparticles Rayleigh number and medium porosity have been discussed. The kinematic viscoelasticity accounting for rheology of the nanofluid has no effect on the stationary convection for Walters' (model B') nanofluids and behaves like an ordinary Newtonian nanofluid. Oscillatory convection has been ruled out under the considered boundary conditions.

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Section: Resultssupporting

confidence: 90%

Section: Resultssupporting

confidence: 88%

Section: Resultsmentioning

confidence: 99%

Section: Formulation Of the Problem And Mathematical Modelmentioning

confidence: 99%

See 2 more Smart Citations

Electrohydrodynamic Thermal Instability in a Walters’ (Model B') Rotating Nanofluid Saturating a Porous Medium

Rana¹,

Gautam²,

Saxena³

2019

JSSCM

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“…To get an analytical result of Equations (19)–(21), the general Galerkin practice is used. Thus, we consider the following 35,50–60 :

V = E \sin π y, normalΘ = F \sin π y,

…”

Section: Perturbed Equationsmentioning

confidence: 99%

Influence of anisotropy on the Jeffrey fluid convection in a horizontal rotary porous layer

Yadav

2021

Heat Trans

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Stability analysis of thermal convection for a Jeffrey fluid with rotation in an anisotropic porous medium is examined utilizing a modified Jeffrey–Darcy model. The linear stability theory is applied to examine how the Jeffrey parameter, rotation parameter, and anisotropic parameters affect the convective motion. It is observed that the rotation and the anisotropic in the thermal diffusivity act to delay the start of Jeffery fluid convection, while the Jeffery parameter and the anisotropic in the permeability show a dual effect in the presence of rotation. The extent of the convection cell diminishes with rotation and Jeffery parameters, while it augments with the thermal anisotropy parameter. Also, some previous outcomes are regained as special cases of the current analysis.

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Volumetric heating and AC electric field effects on porous convection with general boundary conditions

Rachitha,

Nanjundappa,

Shivakumara

2024

Heat Trans

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The onset of convective instability in an internally heated dielectric fluid‐saturated porous layer under the influence of a uniform AC electric field for different types of boundary conditions is investigated. The flow in the porous medium is described by the Brinkman model with fluid viscosity different from effective viscosity. The lower adiabatic and the top with finite heat transfer coefficient to the external environment boundaries are considered to be either rigid or stress‐free. The presence of a uniform volumetric heat source alters the conduction profile of the temperature field from linear to quadratic in the vertical coordinate. A modal linear stability analysis of the basic motionless state is carried out and the general regime of linear instability is investigated by solving the stability eigenvalue problem numerically using the Galerkin method of weighted residual technique. The neutral stability condition as well as the critical value of the thermal Rayleigh number is computed for rigid–rigid, free–free, and rigid–free boundaries for various values of governing parameters. It is seen that the nature of boundaries affect the stability of the system only quantitatively, though not qualitatively. The rigid–rigid boundaries offer a more stabilizing effect against convection in comparison with rigid–free and free–free boundaries. The study found that the effect of increasing thermal electric Rayleigh number and the Darcy number is to hasten the onset of instability, while the opposite trend is perceived with an increase in the ratio of viscosities and Biot number. The outcomes of this investigation are found to be in good agreement with past studies under the limiting cases.

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The onset of electrohydrodynamic instability of an elastico-viscous Walters' (model B') dielectric fluid layer

Abstract: In this paper we investigate the effect of AC electric field on the onset of instability of an elastico-viscous Walters' (model B')

Cited by 12 publications

References 19 publications

Electrohydrodynamic Thermal Instability in a Walters’ (Model B') Rotating Nanofluid Saturating a Porous Medium

Electrohydrodynamic Thermal Instability in a Walters’ (Model B') Rotating Nanofluid Saturating a Porous Medium

Influence of anisotropy on the Jeffrey fluid convection in a horizontal rotary porous layer

Volumetric heating and AC electric field effects on porous convection with general boundary conditions

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