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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
Original

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.

Keywords

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

cp

Specific heat

b

Wave amplitude

Nb

Brownian motion parameter

Nt

Thermophoresis parameter

λ

Wave length

c1

Wave speed

Br

Local temperature Grashof

c

Volumetric volume expansion coefficient

σ

Nano particle phenomena

Gr

Local nano particle Grashof number

DB

Brownian diffusion coefficient

k

Thermal conductivity

KT

Thermal—diffusion ratio

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

Thermophoretic diffusion coefficient

\( \bar{C} \)

Nano particle phenomena

F

Frictional forces

\( \bar{T} \)

Temperature

Tm

Temperature of the medium

u

Velocity component in r-direction

w

Velocity component in z-direction

Greek symbols

μ

Viscosity

ρp

Density of the particle

ρ

Density of the fluid

ν

Kinematic viscosity

φ

Wave amplitude

Notes

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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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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