An autonomous system for chaotic convection in a porous medium using a thermal non-equilibrium model

Sheu, Long-Jye

doi:10.1016/j.chaos.2005.11.080

Cited by 36 publications

(18 citation statements)

References 17 publications

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“…The experimental observation of the chaotic behavior in this system was made by Libchaber and coworkers [2]. Other works in the chaotic convection are in simple fluids [4,5], in binary fluids [3,6,7], in viscoelastic fluids [8][9][10][11], in porous media [12][13][14], in magnetohydrodynamics [15], in magnetic fluids [16] or in dielectrics [17], just to mention a few examples.…”

Section: Introductionmentioning

confidence: 92%

Chaotic convection in a ferrofluid

Laroze

Siddheshwar

Pleiner

2013

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tWe report theoretical and numerical results on thermally driven convection of a magnetic suspension. The magnetic properties can be modeled as those of electrically non-conducting superparamagnets. We perform a truncated Galerkin expansion finding that the system can be described by a generalized Lorenz model. We characterize the dynamical system using different criteria such as Fourier power spectrum, bifurcation diagrams, and Lyapunov exponents. We find that the system exhibits multiple transitions between regular and chaotic behaviors in the parameter space. Transient chaotic behavior in time can be found slightly below their linear instability threshold of the stationary state.

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Section: Introductionmentioning

confidence: 92%

Chaotic convection in a ferrofluid

Laroze

Siddheshwar

Pleiner

2013

Communications in Nonlinear Science and Numerical Simulation

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“…The dimensionless group forming the coefficient to the time derivative term in the Darcy equation is 1 χ , where χ = φPr Da was named the Vadasz number by Straughan (2001Straughan ( , 2004, followed by Lombardo and Mulone (2002), Mulone and Straughan (2006), Sheu (2006), Bhadauria (2007), Mahmud and Hashim (2011), Roslan, Mahmud and Hashim (2011), Bhadauria and Kiran (2013 and more. It is only through this combined dimensionless group that Prandtl number is affecting the flow in porous media.…”

Section: −3mentioning

confidence: 99%

Chaotic and Periodic Natural Convection for Moderate and High Prandtl Numbers in a Porous Layer subject to Vibrations

2014

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A b s t r a c tThe analysis of natural convection for moderate and high Prandtl numbers in a fluid saturated porous layer heated from below and subject to vibrations is presented with a twofold objective. First, it aims at investigating the significance of including a time derivative term in Darcy's equation when wave phenomena are being considered. Second it is dedicated to reporting results related to the route to chaos for moderate and high Prandtl number convection. The results present conclusive evidence indicating that the time derivative term in Darcy's equation cannot be neglected when wave phenomena are being considered even when the coefficient to this term is extremely small. The results also show occasional chaotic "bursts" at specific values (or small range of values) of R , exceeding some threshold. This behavior is quite distinct from the case without forced vibrations, when the chaotic solution occupies a wide range of R values, interrupted only by periodic "bursts". Periodic and chaotic solution alternate as the value of the scaled Rayleigh number varies.

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“…In Equation (2) Ra is the gravity-related Rayleigh number in porous media defined in the form Ra = β * ∆T c g * H * k * /α e * ν * . The time derivative term was included in Darcy's Equation (2), where Va = φPr/Da is a dimensionless group including the porosity, the Prandtl, and Darcy numbers that Straughan [26] named the Vadasz number, or alternatively Vadasz coefficient Straughan [52] (see also Sheu [53]). Vadasz and Olek [8,10] have shown that when investigating wave phenomena, such as the present case, the time derivative in Equation (2) needs to be included irrespective of how large the value of Va is.…”

Section: Problem Formulationmentioning

confidence: 99%

Instability and Route to Chaos in Porous Media Convection

Vadász

2017

Fluids

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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.

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An autonomous system for chaotic convection in a porous medium using a thermal non-equilibrium model

Cited by 36 publications

References 17 publications

Chaotic convection in a ferrofluid

Chaotic convection in a ferrofluid

Chaotic and Periodic Natural Convection for Moderate and High Prandtl Numbers in a Porous Layer subject to Vibrations

Instability and Route to Chaos in Porous Media Convection

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