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Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions

Received: 16 May 2015     Accepted: 29 May 2015     Published: 16 June 2015
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Abstract

The aim of this study is to analyze the mixed convection under Soret effect in a liquid layer subjected to adverse temperature and concentration gradients and slip conditions. Theoretical linear stability analysis and numerical methods were performed to study the convective and absolute instabilities of the transverse rolls. It is found that, for convective instabilities, the problem has analytical solution and is a Galilean transformation of natural convection. The throughflow makes the rolls to propagate and the frequency shift is proportional to Reynolds number. For higher Rayleigh numbers, advection breaks Galilean invariance, and absolute instabilities settle. At the threshold of absolute instability, the presence of throughflow breaks the symmetry by the rotational invariance, and the system selects among an infinite number of unstable modes, the progressive waves, in the direction of the flow.

Published in American Journal of Mechanics and Applications (Volume 3, Issue 3)
DOI 10.11648/j.ajma.20150303.11
Page(s) 19-26
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Mixed Convection, Horizontal Liquid Layer, Critical Rayleigh, Linear Stability Analysis

References
[1] D.A. Nield, C.T. Simmons, A.V. Kuznetsov, and J.D. Ward, On the Evolution of Salt Lakes: Episodic Convection beneath an Evaporating Salt Lake, Water Resources Research, Vol. 44, article W02439, pp. 1-13, 2008
[2] J. Hu, H. Ben Hadid, and D. Henry, Linear stability analysis of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect, Phys. Fluids 19, 034101 (2007)
[3] J.K. Platten, J.C. Legros, Convection in Liquids, Springer-Verlag, Berlin, 1984
[4] H.W. Müller, M. Lücke, Transversal convection patterns in horizontal shear flow, Physical Review A, Vol. 45, Number 6, pp. 3714-3726, 1992
[5] Ben Hamed H., Bennacer R., Sammouda H., Poiseuille-Rayleigh-Bénartd problem in a horizontal duct of finite length in streamwise direction: stability analysis, Progress in Computational Fluid Dynamics, Vol. 8, N°6, pp. 342-350, 2008
[6] Carrière P., Monkewitz P.A., Convective versus absolute instability in mixed Rayleigh-Bénard-Poiseuille convection, Journal of Fluid Mechannics, Vol 384, pp. 2198-2207, 1999
[7] A Joulin. M.N Ouarzazi., Mixed convection of a binary mixture in a porous medium, C.R Acad. Sci. Paris, t, 328, Série II b, pp. 311-316, 2000
[8] T. A Campbell, J. N Koster.: Modeling of liquid encapsulated Gallium melt. Acta Astron. Vol. 35, pp. 805-812, 1995.
[9] S Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University, 1961.
Cite This Article
  • APA Style

    A. Kadiri, H. Ben Hamed, H. Beji. (2015). Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions. American Journal of Mechanics and Applications, 3(3), 19-26. https://doi.org/10.11648/j.ajma.20150303.11

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    ACS Style

    A. Kadiri; H. Ben Hamed; H. Beji. Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions. Am. J. Mech. Appl. 2015, 3(3), 19-26. doi: 10.11648/j.ajma.20150303.11

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    AMA Style

    A. Kadiri, H. Ben Hamed, H. Beji. Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions. Am J Mech Appl. 2015;3(3):19-26. doi: 10.11648/j.ajma.20150303.11

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  • @article{10.11648/j.ajma.20150303.11,
      author = {A. Kadiri and H. Ben Hamed and H. Beji},
      title = {Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions},
      journal = {American Journal of Mechanics and Applications},
      volume = {3},
      number = {3},
      pages = {19-26},
      doi = {10.11648/j.ajma.20150303.11},
      url = {https://doi.org/10.11648/j.ajma.20150303.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20150303.11},
      abstract = {The aim of this study is to analyze the mixed convection under Soret effect in a liquid layer subjected to adverse temperature and concentration gradients and slip conditions. Theoretical linear stability analysis and numerical methods were performed to study the convective and absolute instabilities of the transverse rolls. It is found that, for convective instabilities, the problem has analytical solution and is a Galilean transformation of natural convection. The throughflow makes the rolls to propagate and the frequency shift is proportional to Reynolds number. For higher Rayleigh numbers, advection breaks Galilean invariance, and absolute instabilities settle. At the threshold of absolute instability, the presence of throughflow breaks the symmetry by the rotational invariance, and the system selects among an infinite number of unstable modes, the progressive waves, in the direction of the flow.},
     year = {2015}
    }
    

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    T1  - Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions
    AU  - A. Kadiri
    AU  - H. Ben Hamed
    AU  - H. Beji
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    T2  - American Journal of Mechanics and Applications
    JF  - American Journal of Mechanics and Applications
    JO  - American Journal of Mechanics and Applications
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    AB  - The aim of this study is to analyze the mixed convection under Soret effect in a liquid layer subjected to adverse temperature and concentration gradients and slip conditions. Theoretical linear stability analysis and numerical methods were performed to study the convective and absolute instabilities of the transverse rolls. It is found that, for convective instabilities, the problem has analytical solution and is a Galilean transformation of natural convection. The throughflow makes the rolls to propagate and the frequency shift is proportional to Reynolds number. For higher Rayleigh numbers, advection breaks Galilean invariance, and absolute instabilities settle. At the threshold of absolute instability, the presence of throughflow breaks the symmetry by the rotational invariance, and the system selects among an infinite number of unstable modes, the progressive waves, in the direction of the flow.
    VL  - 3
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Author Information
  • LTI Laboratory, Jules Verne University of Picardie, Amiens, France

  • LTI Laboratory, Jules Verne University of Picardie, Amiens, France

  • LTI Laboratory, Jules Verne University of Picardie, Amiens, France

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