Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-25T09:17:29.506Z Has data issue: false hasContentIssue false
  • English
  • Français

The response to a hot spot in a combustion problem

Published online by Cambridge University Press:  17 February 2009

K. K. Tam  and
M. T. Kiang
K. K. Tam
Affiliation:
Mathematics Department, McGill University, Montreal, Quebec, Canada
M. T. Kiang
Affiliation:
Mathematics Department, St. Mary's University, Halifax, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A simple model for a problem in combustion theory has multiple steady state solutions when a parameter is in a certain range. This note deals with the initial value problem when the initial temperature takes the form of a hot spot. Estimates on the extent and temperature of the spot for the steady state solution to be super-critical are obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 1 , July 1981 , pp. 95 - 102
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Boddington, T., Gray, P. and Wake, G. C., “Criteria for thermal explosions with and without reactant consumption”, Proc. Roy. Soc. A 357 (1977), 403–422.Google Scholar
[2]Chan, C. Y., “A first initial boundary value problem for a semi-linear heat equation”, SIAM J. Appl. Math. 22 (1972), 529–537.CrossRefGoogle Scholar
[3]Frank-Kamenetskii, D. A., Diffusion and heat transfer in chemical kinetics (Translation ed. Appleton, J. P.) (Plenum Press, New York, 1959).Google Scholar
[4]Gelfand, I. M., “Some problems in the theory of quasi-linear equations”, AMS Translations Ser. 2 29 (1963), 295–381.Google Scholar
[5]Parks, J. R., “Criticality criteria for various configurations of a self-heating chemical as functions of activation energy and temperature of assembly”, J. Chem. Phys. 34 (1961), 46–50.CrossRefGoogle Scholar
[6]Tam, K. K., “On the influence of the initial data in a combustion problem”, J. Austral. Math. Soc. B 22 (1980), 193–209.CrossRefGoogle Scholar
[7]Tam, K. K., “On the disapperance of criticality in the theory of thermal ignition”, ZAMP 31 (1980), 762–766.Google Scholar