Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-26T20:58:25.866Z Has data issue: false hasContentIssue false
  • English
  • Français

Criticality dependence on data and parameters for a problem in combustion theory

Published online by Cambridge University Press:  17 February 2009

K. K. Tam
K. K. Tam
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec, CanadaH3A 2K6
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 central problem in the theory of combustion, consisting of a nonlinear parbolic equation together with initial and boundary conditions, is considered. The influence of the initial and boundary data examined. In the main part of the study, a two-step linearization is developed such that the interesting features of the original problem are given by the solution of a non-liner and ordinary differential equation. Approximate solutions are obtained and upper and lower solutions are used to assess the validity of the approximations. Whenever possible, results are compared with those obtained previously and there is good agreement in all cases.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 4 , April 1986 , pp. 416 - 441
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]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
[2]Duff, G. F. D. and Naylor, D., Differential equations of applied mathematics (Wiley, 1966).Google Scholar
[3]Fenaughty, K. F., Lacey, A. A. and Wake, G. C., “The disappearance of criticality for small activation energy with arbitrary Biot number”, Combustion and Flame 45 (1982), 287–291.CrossRefGoogle Scholar
[4]Frank-Kamenetskii, D. A., Diffusion and heat transfer in chemical kinetics (Translation editor Appleton, J. P.), (Plenum Press, New York, 1959).Google Scholar
[5]Kordylewski, W., “Degenerate critical points of thermal explosion”, Komunikat I-20/K-020/78, (Technical University of Wroclaw 1978).Google Scholar
[6]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
[7]Sattinger, D. H., “A nonlinear parabolic system in the theory of combustion”, Quart. Appl. Math. (1975), 47–61.CrossRefGoogle Scholar
[8]Tam, K. K., “Construction of upper and lower solutions for a problem in combustion theory”, J. Math. Anal. Appl. 69 (1979), 131–145.CrossRefGoogle Scholar
[9]Tam, K. K., “Initial data and criticality for a problem in combustion theory”, J. Math. Anal. Appl. 77 (1980), 626–634.CrossRefGoogle Scholar
[10]Tam, K. K., “On the influence of the initial data in a combustion problem”, J. Austral. Math. Soc. Ser. B 22 (1980), 193–209.CrossRefGoogle Scholar
[11]Tam, K. K., “Computation of critical parameters for a problem in combustion theory,” J. Austral. Math. Soc. Ser. B 24 (1982), 40–46.CrossRefGoogle Scholar
[12]Tam, K. K., “On the Oseen linearization of the swirling flow boundary layer”, J. Fluid Mech. 75 (1976), 777–790.CrossRefGoogle Scholar
[13]Tam, K. K. and Chapman, P. B., “Thermal ignition in a reactive slab with unsymmetric boundary temperatures”, J. Austral. Math. Soc. Ser. B 24 (1983), 279–288.CrossRefGoogle Scholar
[14]Tam, K. K. and Kiang, M. T., “The response to a hot spot in a combustion problem,” J. Austral. Math. Soc. Ser. B 23 (1981), 95–102.CrossRefGoogle Scholar