Heat transfer regimes and hysteresis in porous media convection

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

Results of an investigation of different heat transfer regimes in porous media convection are presented by using a truncated Galerkin representation of the governing equations that yields the familiar Lorenz equations for the variation of the amplitude in the time domain. The solution to this system is obtained analytically by using a weak non-linear analysis and computationally by using Adomian's decomposition method. Expressions for the averaged Nusselt number are derived for steady, periodic, as well as weak-turbulent (temporal-chaotic) convection. The phenomenon of Hysteresis in the transition from steady to weak-turbulent convection, and backwards, is particularly investigated, identifying analytically its mechanism, which is confirmed by the computational results. While the post-transient chaotic solution in terms of the dependent variables is very sensitive to the initial conditions, the affinity of the averaged values of these variables to initial conditions is very weak. Therefore, long-term predictability of these averaged variables, and in particular the Nusselt number, becomes possible, a result of substantial practical significance. Actually, the only impact that the transition to chaos causes on the predicted results in terms of the averaged heat flux is a minor loss of accuracy. Therefore, the predictability of the results in the sense of the averaged heat flux is not significantly affected by the transition from steady to weak-turbulent convection. The transition point is shown to be very sensitive to a particular scaling of the equations, which leads the solution to an invariant value of steady-state for sub-transitional conditions, a result that affects the transition point in some cases.

Original languageEnglish (US)
Pages (from-to)145-156
Number of pages12
JournalJournal of Heat Transfer
Volume123
Issue number1
DOIs
StatePublished - Feb 2001
Externally publishedYes

Fingerprint

Porous materials
Hysteresis
convection
heat transfer
hysteresis
Heat transfer
transition points
Nusselt number
Heat flux
heat flux
dependent variables
Nonlinear analysis
Chaos theory
affinity
chaos
Decomposition
decomposition
scaling
Convection
causes

Keywords

  • Chaos
  • Free convection
  • Heat flux
  • Hysteresis
  • Lorenz equations
  • Porous media
  • Weak turbulence

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Physical and Theoretical Chemistry
  • Mechanical Engineering

Cite this

Heat transfer regimes and hysteresis in porous media convection. / Vadasz, Peter.

In: Journal of Heat Transfer, Vol. 123, No. 1, 02.2001, p. 145-156.

Research output: Contribution to journalArticle

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