Peristaltic flow and heat transfer of nanofluids in a sinusoidal wall channel: two-phase analytical study


In this study, two-phase peristaltic nanofluid flow in two-dimensional wavy channel is modeled and the heat transfer analysis is performed for it. Both upper and lower channel walls are considered in a wavy shape by sinusoidal function. The governing equations are presented for the nanofluid based on the Buongiorno model and two analytical methods (least square method and differential transformation method). Maple 15.0 mathematical software is applied as the efficient solution methods for the governing equation. The effect of some parameters present in the governing equations (Brownian motion parameter, thermophoresis parameters, Grashof numbers and amplitude ratio of wavy channel), are discussed in terms of velocities, temperature and nanoparticles concentration functions. An important finding in this study is that, in order to have more nanoparticles concentration around the sinusoidal walls, thermophoresis parameter must be in lower values and vice versa.

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Half width of the channel


Wave amplitude


Velocity of the wave


Diffusion coefficient

DB :

Brownian diffusion coefficient

DT :

Thermophoretic diffusion coefficient


Nanoparticle volume fraction


Gravitational acceleration


Grashof number

GrF :

Species Grashof number

GrT :

Thermal Grashof number


Thermal conductivity

k1 :

Reaction rate constant

Nb :

Brownian motion parameter

Nt :

Thermophoresis parameter


Prandtl number


Volume flow rate


Reynolds number


Axial velocity


Transverse velocity

\( \beta \) :

Volumetric volume expansion coefficient

\( \phi \) :

Amplitude ratio

\( \mu \) :

Dynamic viscosity of the fluid

\( \upsilon \) :

Kinetic viscosity of the fluid

\( \delta \) :

Wave number

\( \rho_{f} \) :

Fluid density

\( \rho_{p} \) :

Density of nanoparticle mass

\( \varPhi \) :

Dimensionless nanoparticle volume fraction

λ :



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The authors gratefully acknowledge the general financial grant from the China Postdoctoral Science Foundation (No.2017M610638) and Shaanxi Provincial Postdoctoral Funds (2017BSHYDZZ16).

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Correspondence to M. Hatami.

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Hatami, M., Mosayebidorcheh, S. & Jing, D. Peristaltic flow and heat transfer of nanofluids in a sinusoidal wall channel: two-phase analytical study. J Anal 27, 913–929 (2019).

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  • Sinusoidal channel
  • Nanofluid
  • Nanoparticle concentration
  • Least square method
  • Differential transformation method

Mathematics Subject Classification

  • 35: partial differential equations