0
Research Papers: Flows in Complex Systems

# Numerical Study on Creeping Flow of Burgers’ Fluids through a Peristaltic Tube

[+] Author and Article Information
Dharmendra Tripathi

Department of Mathematics,  Indian Institute of Technology, Ropar, Punjab-140001, Indiadtripathi@iitrpr.ac.in

J. Fluids Eng 133(12), 121104 (Dec 20, 2011) (9 pages) doi:10.1115/1.4005316 History: Received April 11, 2011; Revised October 13, 2011; Published December 20, 2011; Online December 20, 2011

## Abstract

Motivated by the objective of improving an understanding of the complex rheological fluid dynamics in fluid engineering and biomedical engineering, we consider the creeping flow of Burgers’ fluid with a fractional model through a peristaltic tube in the present article. Homotopy analysis method is used to solve the problem and obtain the approximate analytical solution in terms of axial velocity, volumetric flow rate, pressure gradient, stream function and mechanical efficiency under the long wavelength approximation. It is assumed that the cross-section of the tube varies sinusoidally along the length of tube. The impacts of fractional parameters, material constants, time and amplitude on the pressure difference, frictional force across one wavelength and trapping, are depicted numerically. It is found that the second material constant helps the flow pattern, whereas the other three material constants resist it through the peristaltic tube. The effects of fractional parameters on flow pattern are found to be opposite to each other.

###### FIGURES IN THIS ARTICLE
<>
Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

## Figures

Figure 1

Geometry of peristaltic tube

Figure 2

ℏ -curves for the pressure difference at different values of α at φ=0.5, Q¯=0.2, t=0.4, β=4/5, λ1=4,λ2=1,λ3=1,λ4=1

Figure 3

Pressure difference versus averaged flow rate for various values of α at φ=0.5, t=0.4, β=4/5, λ1=4,λ2=1,λ3=1,λ4=1

Figure 4

Pressure difference versus averaged flow rate for various values of β at φ=0.5, t=0.4, α=1/5, λ1=4,λ2=1,λ3=1,λ4=1

Figure 11

Pressure difference versus averaged flow rate for various values of φ at t=0.4, α=1/5, β=4/5, λ1=4,λ2=1,λ3=1,λ4=1

Figure 10

Pressure difference versus averaged flow rate for various values of t at φ=0.5, α=1/5, β=4/5, λ1=4,λ2=1,λ3=1,λ4=1

Figure 9

Pressure difference versus averaged flow rate for different fractional models (a) φ=0.5, t=0.4, α=1/5, β=4/5, λ1=4,λ2→0,λ3=1,λ4=0, (b) φ=0.5, t=0.4, α=1/5, β=4/5, λ1=4,λ2→0,λ3=0,λ4=0, (c) φ=0.5, t=0.4, α=1/5, β=4/5, λ1=4,λ2=1,λ3=1,λ4=1

Figure 8

Pressure difference versus averaged flow rate for various values of λ4 at φ=0.5, t=0.4, α=1/5, β=4/5, λ1=4,λ2=1,λ3=1

Figure 7

Pressure difference versus averaged flow rate for various values of λ3 at φ=0.5, t=0.4, α=1/5, β=4/5, λ1=4,λ2=1,λ4=1

Figure 6

Pressure difference versus averaged flow rate for various values of λ2 at φ=0.5, t=0.4, α=1/5, β=4/5, λ1=4,λ3=1,λ4=1

Figure 5

Pressure difference versus averaged flow rate for various values of λ1 at φ=0.5, t=0.4, α=1/5, β=4/5, λ2=1,λ3=1,λ4=1

Figure 20

Streamlines in the wave frame at Q¯=0.7 for (a) φ=0.5, (b) φ=0.4, (c) φ=0.3, (d) φ=0.2

Figure 19

Frictional force versus averaged flow rate for various values of φ at t=0.4, α=1/5, β=4/5, λ1=4,λ2=1,λ3=1,λ4=1

Figure 18

Frictional force versus averaged flow rate for various values of t at φ=0.5, α=1/5, β=4/5, λ1=4,λ2=1,λ3=1,λ4=1

Figure 17

Frictional force versus averaged flow rate for various values of λ4 at φ=0.5, t=0.4, α=1/5, β=4/5, λ1=4,λ2=1,λ3=1

Figure 16

Frictional force versus averaged flow rate for various values of λ3 at φ=0.5, t=0.4, α=1/5, β=4/5, λ1=4,λ2=1,λ4=1

Figure 15

Frictional force versus averaged flow rate for various values of λ2 at φ=0.5, t=0.4, α=1/5, β=4/5, λ1=4,λ3=1,λ4=1

Figure 14

Frictional force versus averaged flow rate for various values of λ1 at φ=0.5, t=0.4, α=1/5, β=4/5, λ2=1,λ3=1,λ4=1

Figure 13

Frictional force versus averaged flow rate for various values of β at φ=0.5, t=0.4, α=1/5, λ1=4,λ2=1,λ3=1,λ4=1

Figure 12

Frictional force versus averaged flow rate for various values of α at φ=0.5, t=0.4, β=4/5, λ1=4,λ2=1,λ3=1,λ4=1

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

• TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
• EMAIL: asmedigitalcollection@asme.org
Sign In