Advertisement

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

  • M. Hatami
  • S. Mosayebidorcheh
  • D. Jing
Original Research Paper
  • 18 Downloads

Abstract

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.

Keywords

Sinusoidal channel Nanofluid Nanoparticle concentration Least square method Differential transformation method 

List of symblos

a

Half width of the channel

b

Wave amplitude

c

Velocity of the wave

D

Diffusion coefficient

DB

Brownian diffusion coefficient

DT

Thermophoretic diffusion coefficient

F

Nanoparticle volume fraction

G

Gravitational acceleration

Gr

Grashof number

GrF

Species Grashof number

GrT

Thermal Grashof number

k

Thermal conductivity

k1

Reaction rate constant

Nb

Brownian motion parameter

Nt

Thermophoresis parameter

Pr

Prandtl number

Q

Volume flow rate

Re

Reynolds number

u

Axial velocity

v

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

λ

Wavelength

Mathematics Subject Classification

35: partial differential equations 

Notes

Acknowledgments

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.

References

  1. 1.
    Tripathi, Dharmendra, and O. Anwar Bég. 2014. A study on peristaltic flow of nanofluids: Application in drug delivery systems. International Journal of Heat and Mass Transfer 70: 61–70.CrossRefGoogle Scholar
  2. 2.
    Ghasemi, S.E., M. Vatani, M. Hatami, and D.D. Ganji. 2016. Analytical and numerical investigation of nanoparticle effect on peristaltic fluid flow in drug delivery systems. Journal of Molecular Liquids 215: 88–97.CrossRefGoogle Scholar
  3. 3.
    Hatami, M., D. Song, and D. Jing. 2016. Optimization of a circular-wavy cavity filled by nanofluid under the natural convection heat transfer condition. International Journal of Heat and Mass Transfer 98: 758–767.CrossRefGoogle Scholar
  4. 4.
    Tang, Wenhui, M. Hatami, Jiandong Zhou, and Dengwei Jing. 2017. Natural convection heat transfer in a nanofluid-filled cavity with double sinusoidal wavy walls of various phase deviations. International Journal of Heat and Mass Transfer 115: 430–440.CrossRefGoogle Scholar
  5. 5.
    Hatami, M. 2017. Nanoparticles migration around the heated cylinder during the RSM optimization of a wavy-wall enclosure. Advanced Powder Technology 28 (3): 890–899.CrossRefGoogle Scholar
  6. 6.
    Hatami, M., and D. Jing. 2017. Optimization of wavy direct absorber solar collector (WDASC) using Al2O3-water nanofluid and RSM analysis. Applied Thermal Engineering 121: 1040–1050.CrossRefGoogle Scholar
  7. 7.
    Zhou, Jiandong, M. Hatami, Dongxing Song, and Dengwei Jing. 2016. Design of microchannel heat sink with wavy channel and its time-efficient optimization with combined RSM and FVM methods. International Journal of Heat and Mass Transfer 103: 715–724.CrossRefGoogle Scholar
  8. 8.
    Rush, T.A., T.A. Newell, and A.M. Jacobi. 1999. An experimental study of flow and heat transfer in sinusoidal wavy passages. International Journal of Heat and Mass Transfer 42 (9): 1541–1553.CrossRefGoogle Scholar
  9. 9.
    Sui, Y., P.S. Lee, and C.J. Teo. 2011. An experimental study of flow friction and heat transfer in wavy microchannels with rectangular cross section. International Journal of Thermal Sciences 50 (12): 2473–2482.CrossRefGoogle Scholar
  10. 10.
    Greiner, M. 1991. An experimental investigation of resonant heat transfer enhancement in grooved channels. International Journal of Heat and Mass Transfer 34 (6): 1383–1391.CrossRefGoogle Scholar
  11. 11.
    Haghshenas Fard, M., M. Nasr Esfahany, and M.R. Talaie. 2010. Numerical study of convective heat transfer of nanofluids in a circular tube two-phase model versus single-phase model. International Communications in Heat and Mass Transfer 37: 91–97.CrossRefGoogle Scholar
  12. 12.
    Göktepe, Sinan, Kunt Atalık, and Hakan Ertürk. 2014. Comparison of single and two-phase models for nanofluid convection at the entrance of a uniformly heated tube. International Journal of Thermal Sciences 80: 83–92.CrossRefGoogle Scholar
  13. 13.
    Mohyud-Din, Syed Tauseef, Zulfiqar Ali Zaidi, Umar Khan, and Naveed Ahmed. 2015. On heat and mass transfer analysis for the flow of a nanofluid between rotating parallel plates. Aerospace Science and Technology 46: 514–522.CrossRefGoogle Scholar
  14. 14.
    Hayat, Tasawar, Maria Imtiaz, Ahmed Alsaedi, and Marwan A. Kutbi. 2015. MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation. Journal of Magnetism and Magnetic Materials 396: 31–37.CrossRefGoogle Scholar
  15. 15.
    Khan, J.A., M. Mustafa, T. Hayat, and A. Alsaedi. 2015. Three-dimensional flow of nanofluid over a non-linearly stretching sheet: An application to solar energy. International Journal of Heat and Mass Transfer 86: 158–164.CrossRefGoogle Scholar
  16. 16.
    Fakour, M., A. Vahabzadeh, D.D. Ganji, and M. Hatami. 2015. Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls. Journal of Molecular Liquids 204: 198–204.CrossRefGoogle Scholar
  17. 17.
    Ghasemi, Seiyed E., M. Hatami, A. Kalani Sarokolaie, and D.D. Ganji. 2015. Study on blood flow containing nanoparticles through porous arteries in presence of magnetic field using analytical methods. Physica E: Low-dimensional Systems and Nanostructures 70: 146–156.CrossRefGoogle Scholar
  18. 18.
    Ghasemi, S.E., M. Hatami, G.H.R. Mehdizadeh Ahangar, and D.D. Ganji. 2014. Electrohydrodynamic flow analysis in a circular cylindrical conduit using least square method. Journal of Electrostatics 72 (1): 47–52.CrossRefGoogle Scholar
  19. 19.
    Rahimi-Gorji, M., O. Pourmehran, M. Hatami, and D.D. Ganji. 2015. Statistical optimization of microchannel heat sink (MCHS) geometry cooled by different nanofluids using RSM analysis. The European Physical Journal Plus 130: 22.CrossRefGoogle Scholar
  20. 20.
    Domairry, G., and M. Hatami. 2014. Squeezing Cu–water nanofluid flow analysis between parallel plates by DTM-Padé Method. Journal of Molecular Liquids 193: 37–44.CrossRefGoogle Scholar
  21. 21.
    Ahmadi, A.R., A. Zahmatkesh, M. Hatami, and D.D. Ganji. 2014. A comprehensive analysis of the flow and heat transfer for a nanofluid over an unsteady stretching flat plate. Powder Technology 258: 125–133.CrossRefGoogle Scholar
  22. 22.
    Hatami, M., and D.D. Ganji. 2014. Thermal behavior of longitudinal convective–radiative porous fins with different section shapes and ceramic materials (SiC and Si3N4). Ceramics International 40 (5): 6765–6775.CrossRefGoogle Scholar
  23. 23.
    Hatami, M., and D.D. Ganji. 2014. Investigation of refrigeration efficiency for fully wet circular porous fins with variable sections by combined heat and mass transfer analysis. International Journal of Refrigeration 40: 140–151.CrossRefGoogle Scholar
  24. 24.
    Hatami, M., G.H.R. Mehdizadeh Ahangar, D.D. Ganji, and K. Boubaker. 2014. Refrigeration efficiency analysis for fully wet semi-spherical porous fins. Energy Conversion and Management 84: 533–540.CrossRefGoogle Scholar

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

Personalised recommendations