Weakly nonlinear interaction of mixed convection patterns in porous media heated from below

Delache, A.; Ouarzazi, M. N.

doi:10.1016/j.ijthermalsci.2007.06.015

Cited by 21 publications

(16 citation statements)

References 25 publications

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“…This will provide information on the influence of the modes on each other and how strong the interaction is (e.g. [50]).…”

Section: Nonlinear Stabilitymentioning

confidence: 99%

Convective instabilities of Maxwell–Cattaneo fluids

Eltayeb¹

2017

Proc. R. Soc. A.

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Motivated by the need to understand better the dynamics of non-Fourier fluids, we examine the linear and weakly nonlinear stabilities of a horizontal layer of fluid obeying the Maxwell–Cattaneo relationship of heat flux and temperature using three different forms of the time derivative of the heat flux. Linear stability mode regime diagrams in the parameter plane have been established and used to summarize the linear instabilities. The energy balance of the system is used to identify the mechanism by which the Maxwell–Cattaneo effect (i) introduces overstability, (ii) leads to preferred stationary modes with the critical Rayleigh and wavelengths either both increasing or both decreasing, (iii) gives rise to instabilities in a layer heated from above, and (iv) enhances heat transfer. A formal weakly nonlinear analysis leads to evolution equations for the amplitudes of linear instability modes. It is shown that the amplitude of the stationary mode obeys an equation of the Landau–Stuart type. The two equally excitable overstable modes obey two equations of the same type coupled by an interaction term. The evolution of the different amplitudes leads to supercritical stability, supercritical instability or subcritical instability depending on the model and parameter values. The results are presented in regime diagrams.

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“…This will provide information on the influence of the modes on each other and how strong the interaction is (e.g. [50]).…”

Section: Nonlinear Stabilitymentioning

confidence: 99%

Convective instabilities of Maxwell–Cattaneo fluids

Eltayeb¹

2017

Proc. R. Soc. A.

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“…Linear stability analysis was also able to demonstrate that lateral confinement of the channel in both configurations leads to stabilisation of the flow and selects either transverse rolls ( TRs ), whose axes are perpendicular to the main flow direction and the horizontal walls, for small Re or LRs otherwise [5] . The interaction between LRs and TRs in a flow through a rectangular channel heated from below was analyzed using a weakly nonlinear stability framework for both clear fluids [6] and in a porous medium [7] . Recently, there had been a renewed interest in RBP and RBC systems as prototype problems to understand convective and absolute instabilities [8][9][10][11] , viscous dissipation induced thermal instabilities [12,13] , binary fluid systems [14,15] as well as the influence of thermal stratification on transient growth [16] .…”

Section: Introductionmentioning

confidence: 99%

Linear onset of convective instability for Rayleigh-Bénard-Couette flows of viscoelastic fluids

Alves

Hirata

Ouarzazi

2016

Journal of Non-Newtonian Fluid Mechanics

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“…There are also many numerical and analytical studies of the transition of convective patterns from the stationary state to steady flows and then to unsteady chaotic regimes (see, e.g. [4,16,17]). 15 In this paper we focus on the Darcy convection in a two-dimensional container of porous material saturated with fluid [1,2,5] and heated from below.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, if we know a regular point u 0 in the family, we can continue the curve of equilibria by solving the Cauchy problem (17). Thus, the algorithm for computing families of equilibria in cosymmetric systems can be presented as follows [32]: 3.…”

mentioning

confidence: 99%

Selection of steady regimes of a one-parameter family in the problem of plane convective flow through a porous medium

Говорухин¹,

Shevchenko²

2013

Fluid Dyn

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We study convection in a two-dimensional container of porous material saturated with fluid and heated from below. This problem belongs to the class of dynamical systems with nontrivial cosymmetry. The cosymmetry gives rise to a hidden parameter in the system and continuous families of infinitely many equilibria, and leads to non-trivial bifurcations. In this article we present our numerical studies that demonstrate nonlinear phenomena resulting from the existence of cosymmetry. We give a comprehensive picture of different bifurcations which occur in cosymmetric dynamical systems and in the convection problem. It includes internal and external (as an invariant set) bifurcations of one-parameter families of equilibria, as well as bifurcations leading to periodic, quasiperiodic and chaotic behaviour. The existence of infinite number of stable steady-state regimes begs the important question as to which of them can realize in physical experiments. In the paper, this question (known as the selection problem) is studied in detail. In particular, we show that the selection scenarios strongly depend on the initial temperature distribution of the fluid. method, and numerical methods used to analyse cosymmetric systems are also described.

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Weakly nonlinear interaction of mixed convection patterns in porous media heated from below

Cited by 21 publications

References 25 publications

Convective instabilities of Maxwell–Cattaneo fluids

Convective instabilities of Maxwell–Cattaneo fluids

Linear onset of convective instability for Rayleigh-Bénard-Couette flows of viscoelastic fluids

Selection of steady regimes of a one-parameter family in the problem of plane convective flow through a porous medium

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