Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous media

Capone, Florinda; Luca, Roberta De; Massa, G

doi:10.1007/s00707-021-03002-8

Cited by 13 publications

(3 citation statements)

References 33 publications

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“…Accounting for the discussion made in [26], in this paper, we focus the attention on a single‐temperature bi‐disperse porous medium, that is,

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. Bi‐disperse convection has been widely analyze under various physical assumptions, for instance: In [27, 28], double diffusive bi‐dispersive convection was investigated, and papers [29–33] analyzed the onset of convection in anisotropic bi‐disperse porous media. The novelty of this paper is the investigation of penetrative convection in bi‐disperse porous media.…”

Section: Introductionmentioning

confidence: 99%

Penetrative convection in a bi‐disperse porous medium

Arnone

Capone

Luca

et al. 2023

Math Methods in App Sciences

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The present paper investigates penetrative convection in a bi-disperse porous medium. In particular, penetrative convection is modeled via a quadratic dependence on the temperature for the fluid density. For the problem under examination, convection can occur only through a secondary stationary motion since the validity of the principle of exchange of stabilities is proved. Via linear instability analysis of the conduction solution, the critical Rayleigh number for the onset of penetrative convection is determined. Moreover, the nonlinear stability is investigated via weighted energy method. In order to analyze the behavior of the stability and instability thresholds, numerical simulations are performed through Chebyshev-𝜏 method, proving the stabilizing effect of the upper boundary layer temperature on the onset of convective motion.

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“…Accounting for the discussion made in [26], in this paper, we focus the attention on a single‐temperature bi‐disperse porous medium, that is,

T&amp;#x0003D;{T}&amp;#x0005E;f&amp;#x0003D;{T}&amp;#x0005E;p

Section: Introductionmentioning

confidence: 99%

Penetrative convection in a bi‐disperse porous medium

Arnone

Capone

Luca

et al. 2023

Math Methods in App Sciences

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“…The mathematical models describing the onset of convective motions in horizontal layers of fluids heated from below are well known for both clear fluids and fluid-saturated porous media (see [1,2] and references therein) and have been widely analysed under various assumptions: in [3,4,5] the authors analysed the effect of the local thermal non-equilibrium hypothesis on the onset of convection in horizontal porous layers; in [6] the Darcy-Bénard problem for Bingham fluids has been studied, while in [7,8] the authors examined the onset of convection in an inclined horizontal layer of porous medium; convective instabilities in horizontal layers of bi-disperse porous media have been analysed in [9,10,11,12,13], the onset of penetrative convection has been studied in [14,15,16]. Usually, the fluid is assumed as Newtonian and incompressible.…”

Section: Introductionmentioning

confidence: 99%

Compressibility effect on Darcy porous convection

Arnone¹,

Capone²,

Luca³

et al. 2022

Preprint

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Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variation. In this paper the linear analysis of the Darcy-Bénard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor β which describes the compressibility of the fluid and plays an essential role in the instability results. In particular, in the Oberbeck-Boussinesq approximation, a more realistic constitutive equation for the fluid density is employed in order to obtain more thermodynamic consistent instability results. Via linear instability analysis of the conduction solution, the critical Rayleigh-Darcy number for the onset of convection is determined as a function of a dimensionless parameter β proportional to the compressibility factor β, proving that β enhances the onset of convective motions.

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“…This model has been widely used to investigate the onset of thermal convection in BDPM incorporating various effects. In particular, the effect of the uniform rotation about a vertical axis has been investigated in [7][8][9][10][11] for isotropic and anisotropic BDPM with or without the inertia term; the double-diffusive thermal convection has been analyzed in [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Instability of Vertical Throughflows in Bidisperse Porous Media

Capone¹,

Luca²

2021

Physics

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In this paper, the instability of a vertical fluid motion, or throughflow, is investigated in a horizontal bidisperse porous layer that is uniformly heated from below. By means of the order-1 Galerkin approximation method, the critical Darcy–Rayleigh number for the onset of steady instability is determined in closed form. The coincidence between the linear instability threshold and the global nonlinear stability threshold, in the energy norm, is shown.

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Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous media

Cited by 13 publications

References 33 publications

Penetrative convection in a bi‐disperse porous medium

Penetrative convection in a bi‐disperse porous medium

Compressibility effect on Darcy porous convection

Instability of Vertical Throughflows in Bidisperse Porous Media

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