Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer

Charrier-Mojtabi, Marie-Catherine; Elhajjar, Bilal; Mojtabi, Abdelkader

doi:10.1063/1.2821460

Cited by 72 publications

(42 citation statements)

References 23 publications

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“…Using the boundary conditions (4), (6), and (7), the system of equations, which is dependent on the velocity, the temperature, and the mass fractions is solved. The temperature evolution is of the form…”

Section: Analytical Solution a Parallel Flowmentioning

confidence: 99%

“…Research on the transport properties in multicomponent mixtures is also of great interest to the scientific community (Legros et al; ), because such mixtures are involved in many natural and industrial processes. The case of binary mixtures has been widely studied, see for instance the work of Karimi-Fard et al 5 and Charrier-Mojtabi et al 6 There are several experimental techniques and numerical prediction models that allow the diffusion, thermal diffusion, and Soret coefficients in binary mixtures to be determined accurately, according to Blanco et al 7 Gebhardt et al 8,9 measured the diffusion, thermal diffusion, and Soret coefficients for binary and ternary mixtures. Three different optical techniques were employed, such as optical beam deflection, optical digital interferometry, and thermal diffusion forced Rayleigh scattering.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Thermal gravitational separation of ternary mixture n-dodecane/isobutylbenzene/tetralin components in a porous medium

Larabi¹,

Mutschler²,

Mojtabi³

2016

The Journal of Chemical Physics

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15922 Our present work focuses on the coupling between thermal diffusion and convection in order to improve the thermal gravitational separation of mixture components. The separation phenomenon was studied in a porous medium contained in vertical columns. We performed analytical and numerical simulations to corroborate the experimental measurements of the thermal diffusion coefficients of ternary mixture n-dodecane, isobutylbenzene, and tetralin obtained in microgravity in the international space station. Our approach corroborates the existing data published in the literature. The authors show that it is possible to quantify and to optimize the species separation for ternary mixtures. The authors checked, for ternary mixtures, the validity of the "forgotten effect hypothesis" established for binary mixtures by Furry, Jones, and Onsager. Two complete and different analytical resolution methods were used in order to describe the separation in terms of Lewis numbers, the separation ratios, the cross-diffusion coefficients, and the Rayleigh number. The analytical model is based on the parallel flow approximation. In order to validate this model, a numerical simulation was performed using the finite element method. From our new approach to vertical separation columns, new relations for mass fraction gradients and the optimal Rayleigh number for each component of the ternary mixture were obtained.

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Section: Analytical Solution a Parallel Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermal gravitational separation of ternary mixture n-dodecane/isobutylbenzene/tetralin components in a porous medium

Larabi¹,

Mutschler²,

Mojtabi³

2016

The Journal of Chemical Physics

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“…Furthermore, we expand our stability analysis to consider the physical significance of the nonlinear terms and the degree, if at all, to which they impact on the scheme's stability. This analysis has been used by Charrier-Mojtabi et al [51] in the study of Soret-driven convection in a horizontal porous layer. Furthermore, Patel and Meher [52] performed a stability analysis via the fixed point theorem method for the Adomian decomposition Sumudu transformation method, when solving for the heat transfer in a solid and porous fin with temperature dependent internal heat generation.…”

Section: Consideration Of Viability Of Linearised Systemmentioning

confidence: 99%

Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions

Jooma

Harley

2017

Advances in Mathematical Physics

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A time dependent nonlinear partial differential equation modelling heat transfer in a porous radial fin is considered. The Differential Transformation Method is employed in order to account for the steady state case. These solutions are then used as a means of assessing the validity of the numerical solutions obtained via the Crank-Nicolson finite difference method. In order to engage in the stability of this scheme we conduct a stability and dynamical systems analysis. These provide us with an assessment of the impact of the nonlinear sink terms on the stability of the numerical scheme employed and on the dynamics of the solutions.

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“…In particular, the roll convection and the corresponding stability mechanisms are well known (see Huke et al (2000)). For the system with porous medium, however, the standard of knowledge is much less developed, although there has been some work concerning the stability of the ground state and monocellular flow by Charrier-Mojtabi et al (2007), Elhajjar et al (2008) and Sovran et al (2001).…”

Section: Introductionmentioning

confidence: 99%

Roll convection of binary fluid mixtures in porous media

et al. 2010

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We investigate theoretically the nonlinear state of ideal straight rolls in the RayleighBénard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck-Boussinesq approximation, binary mixtures with positive separation ratio are studied and compared to one-component fluids. Our results for the structural properties of roll convection resemble qualitatively the situation in the Rayleigh-Bénard system without porous medium except for the fact that the streamlines of binary mixtures are deformed in the so-called Soret regime. The deformation of the streamlines is explained by means of the Darcy equation which is used to describe the transport of momentum. In addition to the properties of the rolls, their stability against arbitrary infinitesimal perturbations is investigated. We compute stability balloons for the pure fluid case as well as for a wide parameter range of Lewis numbers and separation ratios which are typical for binary gas and fluid mixtures. The stability regions of rolls are found to be restricted by a crossroll, a zigzag and a new type of oscillatory instability mechanism, which can be related to the crossroll mechanism.

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Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer

Cited by 72 publications

References 23 publications

Thermal gravitational separation of ternary mixture n-dodecane/isobutylbenzene/tetralin components in a porous medium

Thermal gravitational separation of ternary mixture n-dodecane/isobutylbenzene/tetralin components in a porous medium

Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions

Roll convection of binary fluid mixtures in porous media

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