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Research Papers: Porous Media

Effect of Gravity Modulation on Electrothermal Convection in a Dielectric Fluid Saturated Anisotropic Porous Layer

[+] Author and Article Information
Mahantesh S. Swamy

Department of Mathematics,
Government College,
Gulbarga 585 105, India
e-mail: mssmaths@gmail.com

I. S. Shivakumara

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

N. B. Naduvinamani

Department of Mathematics,
Gulbarga University,
Gulbarga 585 106, India

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 2, 2013; final manuscript received October 2, 2013; published online November 28, 2013. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 136(3), 032601 (Nov 28, 2013) (10 pages) Paper No: HT-13-1276; doi: 10.1115/1.4025684 History: Received June 02, 2013; Revised October 02, 2013

This paper deals with linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated anisotropic Brinkman porous layer subject to the combined effect of AC electric field and time-periodic gravity modulation (GM). In the realm of linear theory, the critical stability parameters are computed by regular perturbation method. The local nonlinear theory based on truncated Fourier series method gives the information of convection amplitudes and heat transfer. Principle of exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system several qualitative results on stability are discussed. The sensitive dependence of the solution of Lorenz system of electrothermal convection to the choice of initial conditions points to the possibility of chaos. Low frequency g-jitter is found to have significant stabilizing influence which is in turn diminished by an imposed AC electric field. The role of other governing parameters on the stability threshold and on transient heat transfer is determined.

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References

Figures

Grahic Jump Location
Fig. 1

Variation of correction Rayleigh number with frequency for different values of RaE and Da

Grahic Jump Location
Fig. 2

Variation of correction Rayleigh number with frequency for different values of ξ and RaE

Grahic Jump Location
Fig. 3

Variation of correction Rayleigh number with frequency for different values of η and RaE

Grahic Jump Location
Fig. 4

Variation of correction Rayleigh number with frequency for different values of χ and M

Grahic Jump Location
Fig. 5

Variation of Nusselt number with time for different (a) amplitude, (b) frequency, (c) RaE and (d) Da

Grahic Jump Location
Fig. 6

Variation of Nusselt number with time for different (a) ξ, (b) η, (c) M, and (d) χ

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