Instability and Route to Chaos in Porous Media ConvectionReport as inadecuate


Instability and Route to Chaos in Porous Media Convection


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Department of Mechanical Engineering, Northern Arizona University, Flagstaff, AZ 86011, USA





Academic Editors: D. Andrew S. Rees and Antonio Barletta

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





Author: Peter Vadasz

Source: http://mdpi.com/



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