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Temporal instability of nanofluid layer in a circular cylindrical cavity

Abstract

The instability of an interface formed at the boundary of a circular cylindrical cavity is examined through an irrotational theory of viscous fluids. The cavity is assumed to be an infinite circular cylinder and the flow is considered to be two-dimensional. The cavity is filled with the Newtonian viscous fluid while the fluid outside the cavity is taken as Newtonian nanofluid. The normal mode procedure is employed and the growth rate parameter is calculated. The quadratic relationship in growth rate is achieved and for larger modes, it reduces to the case of the planar interface. The variety of nanofluids’ physical parameters is studied on the instability of the interface. The density of nanofluid makes the interface more unstable while nanofluid’s viscosity has stabilizing nature. The nanofluid with larger radius nanoparticles forms a more unstable interface than the smaller sized nanoparticles.

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Abbreviations

\(\rho _{n}\) :

Density of nanofluid

\(\rho _{u}\) :

Density of viscous fluid

\(\mu _{n} \) :

Viscosity of nanofluid

\(\mu _{u} \) :

Viscosity of viscous fluid

n :

Perturbation modes

\(\omega \) :

Growth rate of disturbances

\(\phi _{\text {ag}} \) :

Aggregate volume fraction

\(\delta \) :

Nanopartcle shape parameter

\(\phi _{\text {m}} \) :

Maximum possible volume fraction for prolate spheroids

\(\phi _{\bmod } \) :

Equivalent volume fraction

\(\gamma \) :

Thickness of the interfacial layer

ab :

Length of semi-major and semi-minor axes of nanoparticle

d :

Fractal index

\(\sigma \) :

Surface tension

References

  1. L. Rayleigh, Cambridge University Press, Cambridge. pp 200–207 (1890)

  2. G.I. Taylor, Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 201, 192–196 (1950)

    ADS  Google Scholar 

  3. D.H. Sharp, Phys. D 12, 3–18 (1984)

    Article  Google Scholar 

  4. Y. Zhou, Phys. Rep. 720, 1–136 (2017)

    ADS  MathSciNet  Google Scholar 

  5. Y. Zhou, Phys. Rep. 723, 1–160 (2017)

    ADS  MathSciNet  Google Scholar 

  6. G. Boffetta, A. Mazzino, Annu. Rev. Fluid Mech. 49, 119–143 (2017)

    ADS  Article  Google Scholar 

  7. H.J. Kull, Rev. Sec. Phys. Lett. 206, 197–325 (1991)

    Google Scholar 

  8. A.E. Radwan, H.A. Radwan, M.H. Hendi, Chaos Solitons Fractals 12, 1729–1735 (2001)

  9. J.B. Carpentier, F. Baillot, J.B. Blaisot, C. Dumouchel, Phys. Fluids 21, 023601 (2009). (8 pages)

  10. X.M. Chen, V.E. Schrock, P.F. Peterson, Nuclear Eng. Des. 177, 121–129 (1997)

  11. J.L. Vinningland, R. Toussaint, M. Niebling, E.G. Flekkoy, K.J. Maloy, Eur. Phys. J. Spec. Top. 204, 27–40 (2012)

    Article  Google Scholar 

  12. I. Ueno, J. Ando, Y. Koiwa, T. Saiki, T. Kaneko, Eur. Phys. J. Spec. Top. 224, 415–424 (2015)

    Article  Google Scholar 

  13. D.D. Joseph, T. Liao, Potential flows of viscous and viscoelastic fluids. J. Fluid Mech. 256, 1–23 (1994)

    ADS  MathSciNet  Article  Google Scholar 

  14. D.D. Joseph, J. Belanger, G.S. Beavers, Int. J. Multiphase Flow 25, 1263–1303 (1999)

    Article  Google Scholar 

  15. D.D. Joseph, G.S. Beavers, T. Funada, J. Fluid Mech. 453, 109–132 (2002)

    ADS  Article  Google Scholar 

  16. M.K. Awasthi, G.S. Agrawal, Int. J. Appl. Math. Mech. 7(12), 73–84 (2010)

    Google Scholar 

  17. R. Asthana, M.K. Awasthi, G.S. Agrawal, App. Mech. Math. 110–116, 769–775 (2012)

    Google Scholar 

  18. M.K. Awasthi, ASME-J. Fluid Eng. 141, 071202 (2019)

    Article  Google Scholar 

  19. A.K. Shukla, M.K. Awasthi, R. Asthana, Mater. Today Proc. 46, 10217–10220 (2021)

    Article  Google Scholar 

  20. M.K. Awasthi, S. Agarwal, ASME-J. Fluid Eng. 142, 094501 (2020)

    Article  Google Scholar 

  21. Z. Zhao, P. Wang, N. Liu, X. Lu, J. Fluid Mech. 900, A24 (2020)

    ADS  Article  Google Scholar 

  22. Y.O. El-Dib, G.M. Moatimid, A.A. Mady, M.H. Zekry, Indian J. Phys. (2021). https://doi.org/10.1007/s12648-021-02022-3

    Article  Google Scholar 

  23. G.M. Moatimid, M.F.E. Amer, J. Phys. 95, 47 (2021)

    Google Scholar 

  24. G.M. Moatimid, M.F.E. Amer, M.A.A. Mohamed, Indian J. Phys. (2021). https://doi.org/10.1007/s12648-021-02199-7

    Article  Google Scholar 

  25. M.K. Awasthi, S. Agarwal, Chin. J. Phys. 68, 866–873 (2020)

    Article  Google Scholar 

  26. M.A. Hassan, Differ. Equ. Dyn. Syst. (2020). https://doi.org/10.1007/s12591-020-00541-9

    Article  Google Scholar 

  27. G.M. Moatimid, M.A. Hassan, J. Egypt. Math. Soc. 25, 220–229 (2017)

    Article  Google Scholar 

  28. G.M. Moatimid, M. Gaber, J. Comp. Theo. Nanosci. 15, 1495–1510 (2018)

    Article  Google Scholar 

  29. G.M. Moatimid, M. Gaber, M.A.A. Mohamed, Microsyst. Technol. 26, 2123–2136 (2020)

    Article  Google Scholar 

  30. M.K. Awasthi, Z. Uddin, R. Asthana, Eur. Phys. J. Spec. Top. 230, 1427–1434 (2021)

    Article  Google Scholar 

  31. Y. Han, At. Sprays 32, 73–89 (2022)

    Article  Google Scholar 

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Acknowledgements

Dharamendra is thankful to the Council of Scientific and Industrial Research (CSIR), New Delhi for their financial support during this work. Dhananjay Yadav gratefully acknowledges the University of Nizwa Research Grant (Grant No.: A/2021-2022-UoN/3/CAS/IF), the Sultanate of Oman for supporting this work.

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Contributions

MKA: conceptualization, methodology. Dharamendra: writing—revised draft. DY: review and editing.

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Correspondence to Mukesh Kumar Awasthi.

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Awasthi, M.K., Dharamendra & Yadav, D. Temporal instability of nanofluid layer in a circular cylindrical cavity. Eur. Phys. J. Spec. Top. (2022). https://doi.org/10.1140/epjs/s11734-022-00599-2

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