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Resonant penetrative convection in porous media with an internal heat source/sink effect

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  • Harfash, Akil J.

Abstract

We study the model of penetrative convection in a porous layer which involves a heat source which varies linearly with vertical height across the layer. This allows us to obtain very strong resonance between sub-layers. The mathematical analysis involves a linear instability technique which yields a definite instability boundary coupled with a global nonlinear energy stability analysis which yields a definite stability threshold. In addition to a linearized instability analysis, the global unconditional nonlinear stability thresholds are derived. Then, the accuracy of the linear instability thresholds are tested using a three dimensional simulation. The results support the assertion that the linear theory , in general, is accurate in predicting the onset of convective motion, and thus, regions of stability.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:281:y:2016:i:c:p:323-342
    DOI: 10.1016/j.amc.2016.01.006
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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, 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.
    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).
    5. 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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