Heat and Mass Transfer

, Volume 48, Issue 3, pp 451–459 | Cite as

Peristaltic flow of a nanofluid in a non-uniform tube

  • Noreen Sher AkbarEmail author
  • S. Nadeem
  • T. Hayat
  • Awatif A. Hendi


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.


Homotopy Perturbation Method Heat Transfer Fluid Nanoparticle Volume Fraction Peristaltic Transport Peristaltic Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Specific heat


Wave amplitude


Brownian motion parameter


Thermophoresis parameter


Wave length


Wave speed


Local temperature Grashof


Volumetric volume expansion coefficient


Nano particle phenomena


Local nano particle Grashof number


Brownian diffusion coefficient


Thermal conductivity


Thermal—diffusion ratio

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

Thermophoretic diffusion coefficient

\( \bar{C} \)

Nano particle phenomena


Frictional forces

\( \bar{T} \)



Temperature of the medium


Velocity component in r-direction


Velocity component in z-direction

Greek symbols




Density of the particle


Density of the fluid


Kinematic viscosity


Wave amplitude



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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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Noreen Sher Akbar
    • 1
    Email author
  • S. Nadeem
    • 1
  • T. Hayat
    • 1
    • 2
  • Awatif A. Hendi
    • 2
  1. 1.Department of MathematicsQuaid-i-Azam University 45320IslamabadPakistan
  2. 2.Department of Physics, Faculty of ScienceKing Saud UniversityRiyadhSaudi Arabia

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