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Research Papers: Forced Convection

Poiseuille Flow of Reactive Phan–Thien–Tanner Liquids in 1D Channel Flow

[+] Author and Article Information
T. Chinyoka

Center for Research in Computational and Applied Mechanics, University of Cape Town, Private Bag X3, Rondebosch 7701, South Africatchinyok@vt.edu

J. Heat Transfer 132(11), 111701 (Aug 10, 2010) (7 pages) doi:10.1115/1.4002094 History: Received June 27, 2009; Revised June 28, 2010; Published August 10, 2010; Online August 10, 2010

We investigate, using direct numerical simulations, the effects of viscoelasticity on pressure driven flows of thermally decomposable liquids in channels. A numerical algorithm based on the finite difference method is implemented in time and space with the Phan–Thien–Tanner as the model for the viscoelastic liquids. The strong dependence of fluid temperature on the Frank–Kamenetskii parameter is shown for various fluid types and the phenomenon of thermal runaway is demonstrated. It is shown that viscoelastic fluids have in general delayed susceptibility to thermal runaway as compared with corresponding inelastic fluids. This paper demonstrates the efficiency of using semi-implicit finite difference schemes in solving transient problems of coupled nonlinear systems. It also provides an understanding of nonisothermal flows of viscoelastic fluids.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematics of the model problem

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Figure 2

Newtonian results with zero initial conditions

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Viscoelastic results

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Effects of We on temperature profiles

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Figure 5

Effects of viscoelasticity on maximum temperature

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Variation of maximum temperature with We

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Temperature profiles for cases ranging from pure entropy to pure energy elasticity

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Figure 8

Temperature profiles for Newtonian, pure entropy to pure energy elasticity

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