Sudden or smooth transitions in porous media natural convection

Vadasz, Johnathan J.; Roy-Aikins, J. E. A.; Vadász, Péter

doi:10.1016/j.ijheatmasstransfer.2004.09.039

Cited by 13 publications

(1 citation statement)

References 18 publications

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“…Vadasz and Olek [4][5][6] and Vadasz [7,8] studied the transition to chaos in a porous layer and found that the transition from steady convection to a non-periodic (or chaotic) state occurs when the critical value associated with the loss of linear stability of the steady convection solution at a particular subcritical value of Rayleigh number is modeled by the familiar Lorenz system [1,9]. The question whether transitions during natural convection in porous media are sudden or smooth has been studied by Vadasz et al [10], who indicated that the transition remains sudden. In a recent study, Jawdat and Hashim [11] showed that a uniform internal heating can enhance the onset of chaotic convection in a porous medium.…”

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Effects of a magnetic field on chaos for low Prandtl number convection in porous media

Idris

Hashim

2010

Nonlinear Dyn

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The effects of a magnetic field on the route to chaos in a fluid-saturated porous layer were investigated based on the approach of dynamical systems. A low dimensional Lorenz-like model was obtained using Galerkin truncated approximation. The presence of a magnetic field helped delay the convective motion. The transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.

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