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Temporal instability of a power-law viscoelastic nanofluid layer

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Abstract

The stability of the interface formed by a viscoelastic nanofluid and viscous incompressible fluid is examined here. The layout is taken in such a way that the viscoelastic nanofluid lies above the viscous fluid, and therefore, the interface experiences Rayleigh–Taylor type instability. The power-law viscoelastic liquid is considered for the linear stability analysis and the potential flow theory of viscous fluids is enforced to solve the mathematical equations. This theory includes the viscosity of the fluids in the analysis, while the flow is considering as irrotational. The stress balance equation at the interface contains normal viscous stresses and their difference is neutralized by interfacial tension. An algebraic equation of second degree is achieved and stability/instability is discussed based on the negative/positive roots of this equation. The response of flow parameters is studied by the various plots based on the growth rate parameter. It is found that the perturbation grows rapidly in the case of viscoelastic nanofluid when compared with the Newtonian nanofluid.

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Abbreviations

\(\rho _{\mathrm{nf}}\) :

Density of power-law nanofluid

\(\mu _{\mathrm{nf}}\) :

Viscosity of power-law nanofluid

n :

Power-law index

\(\varphi _{\mathrm{ag}}\) :

Aggregate volume fraction

\(\varphi _{m}\) :

Maximum possible volume fraction for prolate spheroids

K :

Consistency coefficient

a :

Length of semi-major axis of nanoparticle

d :

Fractal index

\(h_{v}\) :

Width of viscous fluid layer

g :

Gravitational accelaration

\(\zeta \) :

Surface elevation

k :

Wave number

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

Equivalent volume fraction

\(\rho _{v}\) :

Density of viscous fluid

\(\mu _{v}\) :

Viscosity of viscous fluid

\(\omega \) :

Growth rate of disturbances

\(\delta \) :

Shape parementer of nano particle

\(\gamma \) :

Thickness of the interfacial layer

b :

Length of semi-minor axis of nanoparticle

\(h_{\mathrm{nf}}\) :

Width of power-law nanofluid layer

\(\varphi _{\mathrm{nf}}, \varphi _{v}\) :

Potential functions for naofluid and viscous fluid layer

\(\sigma \) :

Surface tension

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Acknowledgements

The author M. K. A. is thankful to UGC-BSR (New-Delhi, India) (project No.F.30-442/2018 (BSR)) for start-up-grant and research funding.

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Authors and Affiliations

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

    Mukesh Kumar Awasthi

  2. Department of Applied Sciences, SOET, BML Munjal University, Gurgaon, India

    Ziya Uddin & Rishi Asthana

Authors
  1. Mukesh Kumar Awasthi
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  2. Ziya Uddin
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  3. Rishi Asthana
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Contributions

MKA: writing—original draft. ZU: conceptualization, methodology. RA: software, writing–review & editing.

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Correspondence to Mukesh Kumar Awasthi.

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Awasthi, M.K., Uddin, Z. & Asthana, R. Temporal instability of a power-law viscoelastic nanofluid layer. Eur. Phys. J. Spec. Top. 230, 1427–1434 (2021). https://doi.org/10.1140/epjs/s11734-021-00038-8

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00038-8

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