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Temporal instability of nanofluid layer in a circular cylindrical cavity

The European Physical Journal Special Topics (2022)Cite this article

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

a, b :

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

d :

Fractal index

\(\sigma \) :

Surface tension

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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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Authors and Affiliations

  1. Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow, 226025, India

    Mukesh Kumar Awasthi &  Dharamendra

  2. Department of Mathematical and Physical Sciences, University of Nizwa, Nizwa, Oman

    Dhananjay Yadav

Authors
  1. Mukesh Kumar Awasthi
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  2. Dharamendra
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  3. Dhananjay Yadav
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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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  • DOI: https://doi.org/10.1140/epjs/s11734-022-00599-2