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Couple stresses effect on linear instability and nonlinear stability of convection in a reacting fluid

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  • Harfash, Akil J.
  • Meften, Ghazi Abed

Abstract

We study the problem of convective movement of a reacting solute in a viscous incompressible fluid occupying a plane layer and subjected to a couple stresses effects. The thresholds for linear instability are found and compared to those derived by a global nonlinear energy stability analysis. In particular, we analyse the effect of no-slip boundary conditions on the stability and instability of convection. The conditions of no-slip at the boundary with couple stresses effect and non constant coefficients which are analysed for the first time in this article.

Suggested Citation

  • Harfash, Akil J. & Meften, Ghazi Abed, 2018. "Couple stresses effect on linear instability and nonlinear stability of convection in a reacting fluid," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 18-25.
    • Handle: RePEc:eee:chsofr:v:107:y:2018:i:c:p:18-25
    DOI: 10.1016/j.chaos.2017.12.013
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    References listed on IDEAS

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    1. Akil J. Harfash, 2016. "Stability analysis for penetrative convection in a fluid layer with throughflow," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(09), pages 1-21, September.
    2. Akinaga, Takeshi & Itano, Tomoaki & Generalis, Sotos, 2016. "Convection induced by instabilities in the presence of a transverse seepage," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 533-543.
    3. Harfash, Akil J., 2016. "Resonant penetrative convection in porous media with an internal heat source/sink effect," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 323-342.
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    Cited by:

    1. Badday, Alaa Jabbar & Harfash, Akil J., 2022. "Magnetohydrodynamic instability of fluid flow in a porous channel with slip boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    2. Meften, Ghazi Abed, 2021. "Conditional and unconditional stability for double diffusive convection when the viscosity has a maximum," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Harfash, Akil J. & Meften, Ghazi Abed, 2019. "Couple stresses effect on instability and nonlinear stability in a double diffusive convection," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 301-320.

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    1. Meften, Ghazi Abed, 2021. "Conditional and unconditional stability for double diffusive convection when the viscosity has a maximum," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Harfash, Akil J. & Meften, Ghazi Abed, 2019. "Couple stresses effect on instability and nonlinear stability in a double diffusive convection," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 301-320.
    3. Badday, Alaa Jabbar & Harfash, Akil J., 2022. "Magnetohydrodynamic instability of fluid flow in a porous channel with slip boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    4. Tripathi, Vinit Kumar & Mahajan, Amit, 2022. "Nonlinear stability analysis of double diffusive convection in a fluid saturated porous layer with variable gravity and throughflow," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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