Modeling of anisotropic convection for the binary fluid in porous medium

 pdf (195K)  / List of references

We study an appearance of gravitational convection in a porous medium saturated by the double-diffusive fluid. The rectangle heated from below is considered with anisotropy of media properties. We analyze Darcy – Boussinesq equations for a binary fluid with Soret effect.

Resulting system for the stream function, the deviation of temperature and concentration is cosymmetric under some additional conditions for the parameters of the problem. It means that the quiescent state (mechanical equilibrium) loses its stability and a continuous family of stationary regimes branches off. We derive explicit formulas for the critical values of the Rayleigh numbers both for temperature and concentration under these conditions of the cosymmetry. It allows to analyze monotonic instability of mechanical equilibrium, the results of corresponding computations are presented.

A finite-difference discretization of a second-order accuracy is developed with preserving of the cosymmetry of the underlying system. The derived numerical scheme is applied to analyze the stability of mechanical equilibrium.

The appearance of stationary and nonstationary convective regimes is studied. The neutral stability curves for the mechanical equilibrium are presented. The map for the plane of the Rayleigh numbers (temperature and concentration) are displayed. The impact of the parameters of thermal diffusion on the Rayleigh concentration number is established, at which the oscillating instability precedes the monotonic instability. In the general situation, when the conditions of cosymmetry are not satisfied, the derived formulas of the critical Rayleigh numbers can be used to estimate the thresholds for the convection onset.

Keywords: convection, binary fluid, porous media, Soret effect, anisotropy, cosymmetry, finite-difference method
Citation in English: Abdelhafez M.A., Tsybulin V.G. Modeling of anisotropic convection for the binary fluid in porous medium // Computer Research and Modeling, 2018, vol. 10, no. 6, pp. 801-816
Citation in English: Abdelhafez M.A., Tsybulin V.G. Modeling of anisotropic convection for the binary fluid in porous medium // Computer Research and Modeling, 2018, vol. 10, no. 6, pp. 801-816
DOI: 10.20537/2076-7633-2018-10-6-801-816
According to Crossref, this article is cited by:
  • Leiv Storesletten, D. Andrew S. Rees. Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation. // Fluids. 2019. — V. 4, no. 2. — P. 75. DOI: 10.3390/fluids4020075
Please note that citation information may be incomplete as it includes data from Crossref cited-by program partners only.
Views (last year): 27.

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the List of Russian peer-reviewed journals publishing the main research results of PhD and doctoral dissertations.

International Interdisciplinary Conference "Mathematics. Computing. Education"

The journal is included in the RSCI

Indexed in Scopus