Extension of joseph's criterion to the nonlinear stability of mechanical equilibria in the presence of thermodiffusive conductivity

Georgescu, Adelina; Palese, Lidia

doi:10.1007/bf00455992

Cited by 4 publications

(5 citation statements)

References 2 publications

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“…Capone et al [13][14][15][16][17][18][19][20], Capone and De Luca [10][11][12], Capone et al [8,9], Capone and Rionero [21], Falsaperla et al [31], Georgescu and Palese [37], Hill and Malashetty [39], Rionero [87][88][89][90][91][92][93][94][95][96][97], Rionero and Vergori [98], Xu and Yang [113].…”

Section: Ltne Effectsmentioning

confidence: 99%

Nonlinear stability in microfluidic porous convection problems

Straughan

2014

Ricerche mat.

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This paper investigates classes of thermal convection problems which display effects which are predominant at small scales, i.e. at the microfluidic level. We concentrate on two effects. The first is the effect of local thermal non-equilibrium (LTNE), where the temperature of the saturating fluid may be different from the temperature of the solid skeleton of the porous body. The second is the effect of anisotropy where differences in the flow direction may change strongly depending on the inertia, permeability, thermal conductivity, and on the diffusion coefficient. The class of porous materials analysed are those of Forchheimer type. However, we employ a Forchheimer law recently in vogue in the literature where the nonlinear term which accounts for the variation from linear in the velocity-pressure gradient relationship is cubic in the velocity field as opposed to the classical quadratic one.

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Section: Ltne Effectsmentioning

confidence: 99%

Nonlinear stability in microfluidic porous convection problems

Straughan

2014

Ricerche mat.

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“…We observe anyhow, in this paper we applied an idea similar to [14] [15] [16] [18] [19], where, we modified the evolution equations obtaining equations with better symmetries, which incorporate the given equations. In this way, [14], [22], [23] , we preserve the contribution of some skewsymmetric terms, otherwise, if the initial evolution equations were used such contribution was null and, correspondingly, the stability criterion, weaker.…”

Section: ) ( 2 Lmentioning

confidence: 99%

“…In [14], [15] and [16] the hydrodynamic stability of the thermodiffusive equilibrium was investigated for a Newtonian fluid mixture in a horizontal layer heated from below and the thermoanisotropic effects on the hydrodynamic stability of the mechanical equilibrium have been evaluated.…”

Section: Introductionmentioning

confidence: 99%

“…We consider the initial-boundary value problem for the perturbation fields in Section 2, in Section 3 we formulate the mathematical problem in an equivalent form, in some suitable orthogonal Sobolev spaces, in Section 4 we study the Lyapunov stability, [14], [22], on a suitable linear space of admissible vector functions and, we derive a quadratic function We assume the fluid, heated and salted from below, subject to some constant vertical temperature and concentration gradients  and  , in rotation around the fixed vertical axis z with a constant angular velocity . = k…”

Section: Introductionmentioning

confidence: 99%

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Thermosolutal convection in a rotating couple-stress uid

Palese

2015

JAM

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In this paper we study the nonlinear Lyapunov stability of the conduction-diusion solution of a rotating couple-stress uid, in a layer heated and salted from below. After reformulating the perturbation evolution equations in a suit- able equivalent form, we derive the appropriate Lyapunov function and we prove that, if the principle of exchange of stabilities holds, the linear and nonlinear stability bounds are equal.The nonlinear stability bound is exactly the critical Rayleigh num-ber obtained solving the linear instability problem of the conduction- diusion solution.

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“…The papers [14], [15]and [16] dealt with an extension of the Joseph's parametric differentiation method applied to study of the stability of the conduction diffusion state for a binary mixture, in the presence of thermoanisotropic Soret and Dufour currents.…”

Section: Introductionmentioning

confidence: 99%

Steady Convection in MHD Bénard Problem with Hall and Ion-Slip Effects

Palese¹

2022

AnnalsARSciMath

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In this paper we study the nonlinear Lyapunov stability of the thermodiffusive equilibrium for a viscous thermoelectroconducting partially ionized fluid in a horizontal layer heated from below. The classical L 2 norm is too weak to evaluate some stabilizing or instabilizing effects of the electroanisotropic currents. A more fine Lyapunov function is obtained by reformulating the initial perturbation evolution problem in terms of the poloidal and toroidal scalar fields. In such a way, if instability occurs as stationary convection, we obtain the coincidence of linear and nonlinear stability bounds.

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Extension of joseph's criterion to the nonlinear stability of mechanical equilibria in the presence of thermodiffusive conductivity

Cited by 4 publications

References 2 publications

Nonlinear stability in microfluidic porous convection problems

Nonlinear stability in microfluidic porous convection problems

Thermosolutal convection in a rotating couple-stress uid

Steady Convection in MHD Bénard Problem with Hall and Ion-Slip Effects

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