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TECHNICAL PAPERS: Porous Media, Particles, and Droplets

Heat Transfer Regimes and Hysteresis in Porous Media Convection

[+] Author and Article Information
Peter Vadasz

Department of Mechanical Engineering, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa

J. Heat Transfer 123(1), 145-156 (Aug 17, 2000) (12 pages) doi:10.1115/1.1336505 History: Received September 13, 1999; Revised August 17, 2000
Copyright © 2001 by ASME
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References

Figures

Grahic Jump Location
A fluid saturated porous layer heated from below
Grahic Jump Location
The bifurcation diagram obtained analytically from Eqs. (101112): (a) X̃ versus R, (b) Ỹ versus R, and (c) Z̃ versus R.
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The critical time as a function of (R−Ro) for six values of initial conditions in terms of ro2. The transition from steady convection to chaos (or backwards) is linked to the existence (disappearance) of this critical time, explaining the mechanism for Hysteresis.
Grahic Jump Location
The computational results for the evolution of X(t) in the time domain for three values of Rayleigh number (in terms of R): (a) X as a function of time for R=23—the solution stabilizes to the fixed point; (b) the inset of Fig. 4(a) detailing the oscillatory decay of the solution; (c) X as a function of time for R=24.9—the solution exhibits chaotic behavior; (d) the inset of Fig. 4(c) detailing the chaotic solution; (e) X as a function of time for R=24.422—the solution is periodic; and (f ) the inset of Fig. 4(e) detailing the periodic solution (data points are connected).
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Transitional sub-critical values of Rayleigh number in terms of Rt/Ro as a function of the initial conditions ro. A comparison between the weak nonlinear solution (— analytical) and the computational results (• computational).
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(a) The impact of the accumulated effect of the variation of the mean Nusselt number as a function of the time range of the integration, τ1; (b) the inset of Fig. 6(a), highlighting the details of the oscillations.
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(a) The variation of the mean Nusselt number as a function of R as obtained by solving the system of Eqs. (141516) in terms of the rescaled variables, via constant initial conditions, forward and backward variation of R, and compared with the analytical relationship, Eq. (23), for sub-transitional values of R; (b) the inset of Fig. 7(a), highlighting the transition from steady convection to chaos, and the corresponding Hysteresis effect.
Grahic Jump Location
(a) The variation of the mean Nusselt number as a function of R as obtained by solving the system of Eqs. (101112), via forward and backward variation of R, and compared with the analytical relationship, Eq. (23), for sub-transitional values of R; (b) the inset of Fig. 8(a), highlighting the transition from steady convection to chaos, and the corresponding Hysteresis effect.

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