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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

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.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of peristaltic tube

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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