Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 1, pp 71–86 | Cite as

Peristaltic biofluids flow through vertical porous human vessels using third-grade non-Newtonian fluids model

Original Paper


In this paper, the heat and flow characteristic of third-grade non-Newtonian biofluids flow through a vertical porous human vessel due to peristaltic wall motion are studied. The third-grade model can describe shear thinning (or shear thickening) and normal stress differences, which is acceptable for biofluids modeling. In order to solve the governing equations, the assumption of long-wavelength approximation is utilized. This hypothesis emphasizes that the wavelength of the peristaltic wall motion is large in comparison with the radius of the human vessel, which is widely acceptable in biological investigations. The analytical perturbation method is employed to solve the governing equations. Consequently, analytical expressions for the velocity profile, shear stress, temperature field, and biofluid flow rate are obtained. In addition, the effects of the governing parameters such as the third-grade non-Newtonian parameter, Grashof Number, Eckert number, and porosity, on the results are examined.


Peristaltic motion Third-grade non-Newtonian biofluid Porous vessels Perturbation method Long-wavelength approximation 



The author would like to acknowledge the Shahrood University of Technology, which supported this project.

Compliance with ethical standards

Conflict of interest

I wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Mechanical EngineeringShahrood University of TechnologyShahroodIran

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