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The combined effects of rotation and anisotropy on double diffusive bi-disperse convection

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Abstract

In the present paper, double-diffusive convection, taking into account Coriolis effects, in a horizontal layer of Brinkman-anisotropic bi-disperse porous medium is analysed. Via linear instability analysis, we find that convection can set in through stationary or oscillatory motions and the critical Rayleigh numbers for the onset of stationary secondary flow (steady convection) and overstability (oscillatory convection) are determined.

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References

  1. Nield, D.A., Bejan, A.: Convection in Porous Media, 5th edn. Springer, New York, NY (2017)

    Book  MATH  Google Scholar 

  2. Straughan, B.: Convection with Local Thermal Non-Equilibrium and Microfluidic Effects. Adv Mechanics and Matematics, Springer, Cham, Switzerland 32 (2015)

  3. Nield, D.A., Kuznetsov, A.V.: A two-velocity temperature model for a bi-dispersed porous medium: forced convection in a channel. Trans. Porous Media 59, 325–339 (2005)

    Article  Google Scholar 

  4. Nield, D.A., Kuznetsov, A.V.: Heat Transfer in Bidisperse Porous Media. In: Transport Phenomena in Porous Media III, 34–59 (2005)

  5. Nield, D.A., Kuznetsov, A.V.: The onset of convection in a bidisperse porous medium. Int. J. Heat Mass Transf. 49(17–18), 3068–3074 (2006)

    Article  MATH  Google Scholar 

  6. Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Dover Publicationas, New York (1981)

    MATH  Google Scholar 

  7. Vadasz, P.: Flow and Thermal Convection in Rotating Porous Media. In: Handbook of Porous Media, 395–440 (2000)

  8. Vadasz, P.: Coriolis effect on gravity-driven convection in a rotating porous layer heated from below. J. Fluid Mech. 376, 351–375 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Capone, F., Massa, G.: The effects of vadasz term, anisotropy and rotation on bi-disperse convection. Int. J. Non Lin. Mech. 135, 103749 (2021)

    Article  Google Scholar 

  10. Capone, F., Gentile, M., Massa, G.: The onset of thermal convection in anisotropic and rotating bidisperse porous media. Z. Angew. Math. Phys. 72, 169 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lombardo, S., Mulone, G.: Necessary and sufficient conditions of global nonlinear stability for rotating double-diffusive convection in a porous medium. Continuum Mech. Thermodyn 14, 527–540 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Straughan, B.: Bidispersive double diffusive convection. Int. J. Heat Mass Transf. 126(A), 504–508 (2018)

    Article  Google Scholar 

  13. Capone, F., De Luca, R.: On the stability-instability of vertical throughflows in double diffusive mixtures saturating rotating porous layers with large pores. Ric. Mat. 63(1), 119–148 (2014)

    MathSciNet  MATH  Google Scholar 

  14. Capone, F., De Luca, R., Massa, G.: The onset of double diffusive convection in a rotating bi-disperse porous medium. Eur. Phys. J. Plus 137(9), 1–16 (2022)

    Article  Google Scholar 

  15. Straughan, B.: Anisotropic bidispersive convection. Proc. R. Soc. A. 475, 20190206 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  16. Straughan, B.: Horizontally isotropic double porosity convection. Proc. R. Soc. A. 475, 20180672 (2019)

    Article  MATH  Google Scholar 

  17. Gentile, M., Straughan, B.: Bidispersive thermal convection. Int. J. Heat Mass Transf. 114, 837–840 (2017)

    Article  MATH  Google Scholar 

  18. Capone, F., De Luca, R., Gentile, M.: Coriolis effect on thermal convection in a rotating bidisperive porous layer. Proc. R. Soc. A. 476, 20190875 (2020)

    Article  MATH  Google Scholar 

  19. Falsaperla, P., Mulone, G., Straughan, B.: Bidispersive-inclined convection. Proc. R. Soc. A 472(2192), 20160480 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Capone, F., De Luca, R., Massa, G.: Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous media. Acta Mech. 232, 3393–3406 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  21. Capone, F., De Luca, R.: The effect of the Vadasz number on the onset of thermal convection in rotating bidispersive porous media. Fluids 5(4), 173 (2020)

    Article  Google Scholar 

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Acknowledgements

This paper was performed under the auspices of the GNFM of INdAM. The authors should like to thank an anonymous referee for suggestions which led to improvements in the manuscript.

Funding

No funding was received to assist with the preparation of this manuscript.

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Author notes

  1. Florinda Capone, Roberta De Luca, Giuliana Massa have contributed equally to this work.

Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni “R.Caccioppoli”, Università degli Studi di Napoli Federico II, Via Cintia, Monte S.Angelo, 80126, Napoli, Campania, Italy

    Florinda Capone, Roberta De Luca & Giuliana Massa

Authors
  1. Florinda Capone
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  2. Roberta De Luca
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  3. Giuliana Massa
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by F. Capone, R. De Luca and G. Massa. All authors read and approved the final manuscript.

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Correspondence to Florinda Capone.

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Capone, F., De Luca, R. & Massa, G. The combined effects of rotation and anisotropy on double diffusive bi-disperse convection. Ricerche mat (2022). https://doi.org/10.1007/s11587-022-00752-y

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