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Research Papers: Experimental Techniques

Thermovibrational Instability in a Fluid Saturated Anisotropic Porous Medium

[+] Author and Article Information
S. Saravanan1

Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, Indiasshravan@lycos.com

T. Sivakumar

Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, India

1

Corresponding author.

J. Heat Transfer 133(5), 051601 (Feb 01, 2011) (9 pages) doi:10.1115/1.4003013 History: Received February 16, 2010; Revised November 09, 2010; Published February 01, 2011; Online February 01, 2011

A comprehensive investigation is made to understand the effect of harmonic vibration on the onset of convection in a horizontal anisotropic porous layer heated either from below or from above. The layer is subject to vertical mechanical vibrations of arbitrary amplitude and frequency. The porous medium is assumed to be both mechanically and thermally anisotropic, and Brinkman’s law is invoked to model the momentum balance. Both continued fraction and Hill’s infinite determinant methods are used to determine the convective instability threshold with the aid of Floquet theory. The synchronous and subharmonic resonant regions of dynamic instability are determined and their critical boundaries are found. The results show that anisotropy in permeability favors convection whereas that in thermal conductivity suppresses it with a wider cellular pattern at the instability threshold. The influence of vibration parameters and heating condition on the anisotropy effects and the competition between the synchronous and subharmonic modes are discussed. This study also reveals the existence of a closed disconnected instability region in certain areas of the parameter space for the first time in literature.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Unmodulated critical Rayleigh number R0c for Kr=χr keeping χr/Kr=1

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Figure 2

Marginal curve with S mode for the case of low amplitude η=1 for Kr=χr=0.1

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Figure 3

Marginal curve with S (horizontal lines) and SH (cross lines) resonant loops for different values of Kr and χr with η=200 and ω=10

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Figure 4

(a) Rac and (b) αc against ω for Kr=1 and different values of χr and η

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Figure 5

(a) Rac and (b) αc against ω for χr=1 and different values of Kr and η

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Figure 6

(a) Rac and (b) αc against ω for different values of Kr, χr, and η

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Figure 7

Development of a CDL in the marginal curve with S (horizontal lines) and SH (cross lines) resonant loops for Kr=χr=0.1 and η=20

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Figure 8

Marginal curve with S (horizontal lines) and SH (cross lines) resonant loops for different values of Kr and χr with η=2 and ω=10

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Figure 9

(a) −Rac and (b) αc against ω for Kr=1 and different values of χr and η

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Figure 10

(a) −Rac and (b) αc against ω for χr=1 and different values of Kr and η

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Figure 11

(a) Enlarged view of −Rac against ω for Kr=0.1, χr=1, and η=2. (b) Behavior of marginal curve before and after the transitions marked in (a).

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Figure 12

(a) −Rac and (b) αc against ω for different values of Kr, χr, and η

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