The onset of thermal convection in anisotropic and rotating bidisperse porous media

Capone, Florinda; Gentile, Maurizio; Massa, G

doi:10.1007/s00033-021-01592-w

Cited by 21 publications

(5 citation statements)

References 32 publications

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“…Anisotropic effects upon thermal convection in saturated porous media have been the subject of many recent investigations, see e.g. Capone et al [31][32][33][34][35], Hemanthkumar et al [36][37][38]. In particular the ramifications of anisotropy in porous media have proved of interest in the application to healthcare materials and in human tissues, see Fang et al [39], Mirbod et al [40].…”

Section: Effects On Penetrative Convectionmentioning

confidence: 99%

Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection

Straughan

2022

Environ Fluid Mech

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We investigate the effects of anisotropic permeability and changing boundary conditions upon the onset of penetrative convection in a porous medium of Darcy type and of Brinkman type. Attention is focussed on the critical eigenfunctions which show how many convection cells will be found in the porous layer. The number of cells is shown to depend critically upon the ratio of vertical to horizontal permeability, upon the Brinkman coefficient, and upon the upper boundary condition for the velocity which may be of Dirichlet type or constant pressure. The critical Rayleigh numbers and wave numbers are determined, and it is shown how an unconditional threshold for nonlinear stability may be derived. Highlights Shows how number of convection cells depends upon the temperature of the upper layer and the anisotropy of the permeability Shows how number of convection ceels depends upon the temperature of the upper layer and the Brinkman coefficient Shows how number of convection cells patters depends upon the upper boundary condition on the velocity or the ambient pressure

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Section: Effects On Penetrative Convectionmentioning

confidence: 99%

Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection

Straughan

2022

Environ Fluid Mech

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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

. 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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“…Essentially, BDPM can be seen as a permeable material that has undergone the creation of tunnels or cracks, with the terms “solid phase” and “fracture phase” replacing “ p ‐phase” and “ f ‐phase” in the current model. Convection in BDPM has gained increasing interest due to its practical applications, such as utilizing BDPM‐like absorbent and capillary wicks in heat pipes to enhance heat transfer efficiency 3–6 . Moreover, it has been observed that BDPM surpasses conventional porous media in addressing thermal insulation and system cooling challenges to a significant extent 7,8 …”

Section: Introductionmentioning

confidence: 99%

“…Convection in BDPM has gained increasing interest due to its practical applications, such as utilizing BDPM-like absorbent and capillary wicks in heat pipes to enhance heat transfer efficiency. [3][4][5][6] Moreover, it has been observed that BDPM surpasses conventional porous media in addressing thermal insulation and system cooling challenges to a significant extent. 7,8 The research on heat convection in BDPM was initially introduced by Nield et al [9][10][11][12] Their work specifically focused on forced convection in BDPM, analyzing uniform heat flux and constant wall temperature in a channel.…”

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confidence: 99%

Magnetohydrodynamic forced convection in bidisperse porous medium: Analysis of flow and temperature distributions in a parallel‐plate channel

Vanengmawia,

Ontela

2023

Heat Trans

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This study aims to explore magnetohydrodynamic forced convection in a parallel‐plate channel filled with a bidisperse porous medium, while emphasizing the significance of viscous dissipation. The study utilizes the two‐velocity two‐temperature model to analyze the flow and temperature distributions in both the fluid phase and solid phase. Convective boundary conditions at the channel walls are considered, and momentum slip is incorporated into the analysis. By nondimensionalizing the governing equations and employing the Homotopy Analysis Method, the velocity and temperature profiles for both phases are determined. Notably, the findings of the study highlight a notable discrepancy in the temperature increase between the solid phase and the fluid phase. Furthermore, the study investigates the impact of various parameters, such as the Darcy number, Biot number, slip parameter, Hartmann number, and Brinkman number, on velocity, temperature, Nusselt number, and skin friction.

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The onset of thermal convection in anisotropic and rotating bidisperse porous media

Abstract: The onset of thermal convection in anisotropic rotating bidisperse porous media is investigated. The optimal result concerning the coincidence between linear instability and nonlinear stability thresholds with respect the $$L^2$$ L 2 -norm is obtained.

Cited by 21 publications

References 32 publications

Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection

Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection

Penetrative convection in a bi‐disperse porous medium

Magnetohydrodynamic forced convection in bidisperse porous medium: Analysis of flow and temperature distributions in a parallel‐plate channel

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