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

  • M. HatamiEmail author
  • S. Mosayebidorcheh
  • D. Jing
Original Research Paper


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.


Sinusoidal channel Nanofluid Nanoparticle concentration Least square method Differential transformation method 

List of symblos


Half width of the channel


Wave amplitude


Velocity of the wave


Diffusion coefficient


Brownian diffusion coefficient


Thermophoretic diffusion coefficient


Nanoparticle volume fraction


Gravitational acceleration


Grashof number


Species Grashof number


Thermal Grashof number


Thermal conductivity


Reaction rate constant


Brownian motion parameter


Thermophoresis parameter


Prandtl number


Volume flow rate


Reynolds number


Axial velocity


Transverse velocity

Greek symbols

\( \beta \)

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



Mathematics Subject Classification

35: partial differential equations 



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

Compliance with ethical standards

Conflict of interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.


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Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringEsfarayen University of TechnologyEsfarayenIran
  2. 2.International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow in Power EngineeringXi’an Jiaotong UniversityXi’anChina
  3. 3.Department of Mechanical Engineering, Khomeinishahr BranchIslamic Azad UniversityKhomeinishahrIran

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