Peristaltic transport of a third-order fluid in a circular cylindrical tube

T. Hayat, Y. Wang, Abdul M. Siddiqui, K. Hutter, S. Asghar

Research output: Contribution to journalArticle

120 Citations (Scopus)

Abstract

The effect of a third-order fluid on the peristaltic transport is analysed in a circular cylindrical tube, such as some organs in the living body. The third-order flow of an incompressible fluid in a circular cylindrical tube, on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The wavelength of the peristaltic waves is assumed to be large compared to the tube average radius, whereas the amplitude of the wave need not be small compared to the average radius. Both analytic (perturbation) and numerical solutions are given. For the perturbation solution, a systematic approach based on an asymptotic expansion of the solution in terms of a small Deborah number is used and solutions up to the first order are presented in closed forms. The numerical solution, valid for any Deborah number, represents a new approach to peristaltic flows, and its features illuminate the physical behaviour much more than the analytical research on this problem. Comparison is made between the analytic (perturbation) and numerical results. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.

Original languageEnglish (US)
Pages (from-to)1691-1706
Number of pages16
JournalMathematical Models and Methods in Applied Sciences
Volume12
Issue number12
DOIs
StatePublished - Dec 1 2002

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Peristaltic Flow
Perturbation Solution
Tube
Fluid
Fluids
Radius
Numerical Solution
Non-Newtonian Fluid
Polyethylene oxides
Polyacrylates
Incompressible Fluid
Oxides
Asymptotic Expansion
Closed-form
Molecular weight
Valid
Wavelength
First-order
Perturbation
Numerical Results

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

Cite this

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abstract = "The effect of a third-order fluid on the peristaltic transport is analysed in a circular cylindrical tube, such as some organs in the living body. The third-order flow of an incompressible fluid in a circular cylindrical tube, on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The wavelength of the peristaltic waves is assumed to be large compared to the tube average radius, whereas the amplitude of the wave need not be small compared to the average radius. Both analytic (perturbation) and numerical solutions are given. For the perturbation solution, a systematic approach based on an asymptotic expansion of the solution in terms of a small Deborah number is used and solutions up to the first order are presented in closed forms. The numerical solution, valid for any Deborah number, represents a new approach to peristaltic flows, and its features illuminate the physical behaviour much more than the analytical research on this problem. Comparison is made between the analytic (perturbation) and numerical results. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.",
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Peristaltic transport of a third-order fluid in a circular cylindrical tube. / Hayat, T.; Wang, Y.; Siddiqui, Abdul M.; Hutter, K.; Asghar, S.

In: Mathematical Models and Methods in Applied Sciences, Vol. 12, No. 12, 01.12.2002, p. 1691-1706.

Research output: Contribution to journalArticle

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