Technical Briefs

Creeping Flow of Phan-Thien–Tanner Fluids in a Peristaltic Tube With an Infinite Long Wavelength

[+] Author and Article Information
Abd El Hakeem Abd El Naby1

Department of Mathematics, Faculty of Science, Mansoura University, New Damietta, Mansoura 3415, Egypthakeemnaby@yahoo.com


Present address: Department of Mathematics, College of Teachers, Madina Munawara, Kingdom of Saudi Arabia.

J. Appl. Mech 76(6), 064504 (Jul 27, 2009) (6 pages) doi:10.1115/1.3132183 History: Received May 15, 2008; Revised October 04, 2008; Published July 27, 2009

In this study both linearized and the exponential forms of the Phan-Thien–Tanner model (PTT) are used to simulate the peristaltic flow in a tube. The solutions are investigated under zero Reynolds number and infinitely long wavelength assumptions. Computational solutions are obtained for pressure rise and friction force. The results of the average chyme velocity in the small intestine show that the PTT model is in good agreement with the experimental results, as shown in Table 1. Also, the magnitude of pressure rise and friction force of the exponential PTT model are smaller than in linear PTT model for different values of flow rate. The peristaltic pumping and the augmented pumping are discussed for various values of the physical parameters of interest. The pressure rise and friction force of PTT were compared with other studies in both Newtonian and non-Newtonian cases.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Peristaltic transport in a uniform tube

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Figure 2

The pressure rise versus flow rate for ϕ=0.6 and ε=0.5

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Figure 3

The pressure rise versus flow rate for ϕ=0.6 and We=0.05

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Figure 4

The pressure rise versus ε1/2 We for ϕ=0.6

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Figure 5

The friction force versus flow rate for ϕ=0.6 and ε=0.5

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Figure 6

The friction force versus flow rate for ϕ=0.6 and We=0.05




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