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Research Papers: Natural and Mixed Convection

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

[+] Author and Article Information
B. M. Shankar

Department of Mathematics,
PES University,
Bangalore 560 085, India
e-mail: bmshankar@pes.edu

Jai Kumar

ISRO Satellite Centre,
Bangalore 560 017, India

I. S. Shivakumara

Department of Mathematics,
Bangalore University,
Bangalore 560 001, India

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 21, 2014; final manuscript received December 4, 2014; published online January 7, 2015. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 137(4), 042501 (Apr 01, 2015) (9 pages) Paper No: HT-14-1424; doi: 10.1115/1.4029348 History: Received June 21, 2014; Revised December 04, 2014; Online January 07, 2015

## Abstract

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.

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## Figures

Fig. 1

Physical configuration

Fig. 2

Basic velocity profiles

Fig. 3

Neutral stability curves

Fig. 4

Variation of (a) Gc, (b) ac, and (c) cc with Pr for a fixed value of Rea (=500), Λ(=1) and for various values of Da. (——) Stationary modes, (········) traveling-wave modes.

Fig. 11

The disturbance streamlines (a)–(d) and isotherms (e)–(h) for different values of Pr when Λ = 2, Da = 10-1, Rea = 500

Fig. 5

The disturbance streamlines for different values of Pr when Λ = 1,Rea = 500, and Da = 10-1

Fig. 6

The disturbance isotherms for different values of Pr when Λ = 1,Rea = 500,and Da = 10-1

Fig. 7

The disturbance streamlines for different values of Pr when Λ = 1,Rea = 500,and Da = 10-2

Fig. 8

Variation of (a) Gc and (b) ac with Pr for a fixed value of Da(= 10-1), Λ(= 1) and for various values of Rea. (——) Stationary modes and (·······) traveling-wave modes.

Fig. 9

The disturbance streamlines (a)–(d) and isotherms (e)–(h) for different values of Pr when Λ = 1, Da = 10-1, and Rea = 200

Fig. 10

Variation of (a) Gc and (b) ac with Pr for a fixed value of Rea(=500), Da(= 10-1) and for various values of Λ. (——) Stationary modes and (········) traveling-wave modes.

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