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Zbl 1041.76002
Hayat, T.; Wang, Y.; Siddiqui, A. M.; Hutter, K.; Asghar, S.
Peristaltic transport of a third-order fluid in a circular cylindrical tube. (English)
[J] Math. Models Methods Appl. Sci. 12, No. 12, 1691-1706 (2002). ISSN 0218-2025

From the summary: 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.

MSC 2000:: *76A05 Non-Newtonian fluids
74F10 Fluid-solid interactions
76Z05 Physiological flows
92C35 Physiological flows

Keywords: non-Newtonian fluid; incompressible fluid; sinusoidal wave; numerical solutions; perturbation solution; asymptotic expansion; small Deborah number

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Zentralblatt MATH Berlin [Germany]