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Peristaltic flow of a nanofluid in a non-uniform tube

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An Erratum to this article was published on 01 November 2011

Abstract

The present analysis discusses the peristaltic flow of a nanofluid in a diverging tube. This is the first article on the peristaltic flow in nanofluids. The governing equations for nanofluid are modelled in cylindrical coordinates system. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Temperature and nanoparticle equations are coupled so Homotopy perturbation method is used to calculate the solutions of temperature and nanoparticle equations, while exact solutions have been calculated for velocity profile and pressure gradient. The solution depends on Brownian motion number N b , thermophoresis number N t , local temperature Grashof number B r and local nanoparticle Grashof number G r . The effects of various emerging parameters are investigated for five different peristaltic waves. It is observed that the pressure rise decreases with the increase in thermophoresis number N t . Increase in the Brownian motion parameter N b and the thermophoresis parameter N t temperature profile increases. Streamlines have been plotted at the end of the article.

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Abbreviations

c p :

Specific heat

b :

Wave amplitude

N b :

Brownian motion parameter

N t :

Thermophoresis parameter

λ:

Wave length

c 1 :

Wave speed

B r :

Local temperature Grashof

c :

Volumetric volume expansion coefficient

σ:

Nano particle phenomena

G r :

Local nano particle Grashof number

D B :

Brownian diffusion coefficient

k :

Thermal conductivity

K T :

Thermal—diffusion ratio

\( D_{{\bar{T}}} \) :

Thermophoretic diffusion coefficient

\( \bar{C} \) :

Nano particle phenomena

F :

Frictional forces

\( \bar{T} \) :

Temperature

T m :

Temperature of the medium

u :

Velocity component in r-direction

w :

Velocity component in z-direction

μ:

Viscosity

ρ p :

Density of the particle

ρ:

Density of the fluid

ν:

Kinematic viscosity

φ:

Wave amplitude

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Acknowledgments

Third author as a visiting Professor thanks the partial support of Global Research Network for Computational Mathematics and King Saud University for this work.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, 44000, Pakistan

    Noreen Sher Akbar, S. Nadeem & T. Hayat

  2. Department of Physics, Faculty of Science, King Saud University, P.O. Box 1846, Riyadh, 11321, Saudi Arabia

    T. Hayat & Awatif A. Hendi

Authors
  1. Noreen Sher Akbar
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  2. S. Nadeem
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  3. T. Hayat
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  4. Awatif A. Hendi
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Corresponding author

Correspondence to Noreen Sher Akbar.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s00231-011-0929-y.

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Akbar, N.S., Nadeem, S., Hayat, T. et al. Peristaltic flow of a nanofluid in a non-uniform tube. Heat Mass Transfer 48, 451–459 (2012). https://doi.org/10.1007/s00231-011-0892-7

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