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Fluids 2017, 2(2), 26; doi:10.3390/fluids2020026

Instability and Route to Chaos in Porous Media Convection

Department of Mechanical Engineering, Northern Arizona University, Flagstaff, AZ 86011, USA
Academic Editors: D. Andrew S. Rees and Antonio Barletta
Received: 3 April 2017 / Revised: 26 April 2017 / Accepted: 27 April 2017 / Published: 18 May 2017
(This article belongs to the Special Issue Convective Instability in Porous Media)
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Abstract

A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed. View Full-Text
Keywords: chaos; porous media; natural convection; weak turbulence; Lorenz equations; feedback control chaos; porous media; natural convection; weak turbulence; Lorenz equations; feedback control
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Vadasz, P. Instability and Route to Chaos in Porous Media Convection. Fluids 2017, 2, 26.

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