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TECHNICAL BRIEFS

Thermal Ignition in a Reactive Viscous Flow Through a Channel Filled With a Porous Medium

[+] Author and Article Information
O. D. Makinde

Applied Mathematics Department,  University of Limpopo, Private Bag X1106, Sovenga 0727, South Africamakindeo@ul.ac.za

J. Heat Transfer 128(6), 601-604 (Jan 28, 2006) (4 pages) doi:10.1115/1.2188511 History: Received May 17, 2005; Revised January 28, 2006

This paper examines the steady-state solutions of a strongly exothermic reaction of a viscous combustible material in a channel filled with a saturated porous medium under Arrhenius kinetics, neglecting reactant consumption. The Brinkman model is employed and analytical solutions are constructed for the governing nonlinear boundary-value problem using a perturbation technique together with a special type of Hermite-Padé approximants and important properties of the temperature field including bifurcations and thermal criticality are discussed.

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Copyright © 2006 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

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

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Figure 3

Fluid velocity profile:———β=1; oooooooβ=3.0; ++++++ β=5.0

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Figure 4

Fluid temperature profile:——λ=0.5; ooooooo λ=1.0; +++++++ λ=1.5

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