Instability and route to chaos in porous media convection

Research output: Contribution to journalReview article

2 Scopus citations

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.

Original languageEnglish (US)
Article number26
JournalFluids
Volume2
Issue number2
DOIs
StatePublished - Jun 1 2017

Keywords

  • Chaos
  • Feedback control
  • Lorenz equations
  • Natural convection
  • Porous media
  • Weak turbulence

ASJC Scopus subject areas

  • Mechanical Engineering
  • Fluid Flow and Transfer Processes
  • Condensed Matter Physics

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