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Conditional and unconditional stability for double diffusive convection when the viscosity has a maximum

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  • Meften, Ghazi Abed

Abstract

We here analyse two models of double-diffusive convection in fluid layer when viscosity depends on temperature quadratically. However, to a linearized instability analysis, conditional and global (unconditional) nonlinear stability theories are applied. For the first model, we establish an unconditional nonlinear energy stability. Moreover, in the second model the standard energy method does not yield unconditional stability so a conditional energy analysis is employed to achieve nonlinear results. In addition, the nonlinear stability bounds is found to be independent of the salt field and a presentation of the region of possible subcritical instabilities is given.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306470
    DOI: 10.1016/j.amc.2020.125694
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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. 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.
    3. 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.
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