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Technical Briefs

Analysis of Non-Newtonian Reactive Flow in a Cylindrical Pipe

[+] Author and Article Information
Oluwole Daniel Makinde

Faculty of Engineering, Cape Peninsula University of Technology, P.O. Box 652, Cape Town 8000, South Africamakinded@cput.ac.za

J. Appl. Mech 76(3), 034502 (Mar 13, 2009) (5 pages) doi:10.1115/1.3086587 History: Received January 17, 2008; Revised January 27, 2009; Published March 13, 2009

In this paper, a mathematical investigation on the effect of convective cooling on a reactive third-grade fluid flowing steadily through a cylindrical pipe is performed. It is assumed that the system exchange heat, with the ambient following Newton’s cooling law and the reaction, is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The simplified governing nonlinear equations of momentum and energy are obtained and solved using a special type of the Hermite–Padé approximation technique. The important properties of the overall flow structure including velocity field, temperature field, bifurcations, and thermal criticality conditions are discussed.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of the problem

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Figure 2

Velocity profile: ______, γ=0; oooooo, γ=0.4; ++++++, γ=0.8

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Figure 3

Temperature profile for Bi=1; m=1; ε=0; γ=0.1; ______, λ=0.1; ooooo, λ=0.2; +++++, λ=0.3

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Figure 4

Temperature profile for λ=0.1; m=1; ε=0; γ=0.1; ______, Bi=1; ooooo, Bi=3; +++++, Bi=5

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Figure 5

A slice of approximate bifurcation diagram in the (λ,Nu) plane

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Figure 6

A bifurcation diagram in the (γ,Cf) plane for a third-grade liquid

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