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Thermal ignition in a reactive slab with unsymmetric boundary temperatures

Published online by Cambridge University Press:  17 February 2009

K. K. Tam  and
P. B. Chapman
K. K. Tam
Affiliation:
Department of Mathematics, McGill University, Montreal, Quebec H3C 3G I, Canada.
P. B. Chapman
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6009.
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Abstract

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The problem of thermal ignition in a reactive slab with unsymmetric temperatures equal to 0 and T is considered. Steady state upper and lower solutions are constructed. It is found that T plays a critical role. Results similar to the case with symmetric boundary temperatures are expected when T is small. When T is sufficiently large, there is only one steady state upper or lower solution. The time dependent problem is then considered. Phenomena suggested by studying the upper and lower steady state solutions are confirmed.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 3 , January 1983 , pp. 279 - 288
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Frank-Kamenetskii, D. A., Diffusion and heat transfer in chemical kinetics (Plenum Press, 2nd Edition, 1969).Google Scholar
[2]Shouman, A. R. and Donaldson, A. B., “The stationary problem of thermal ignition in a reactive slab with unsymmetric boundary temperatures”, Combustion and Flame 24 (1975), 203–210.Google Scholar
[3]Tam, K. K., “Construction of upper and lower solutions for a problem in combustion theory”, J. Math. Anal. Appl. 69 (1979), 131–145.Google Scholar
[4]Tam, K. K., “Initial data and criticality for a problem in combustion theory”, J. Math. Anal. Appl. 77 (1980), 626–634.Google Scholar