Ignition or nonignition of a combustible solid with marginal heating
Authors:
D. Glenn Lasseigne and W. E. Olmstead
Journal:
Quart. Appl. Math. 49 (1991), 303-312
MSC:
Primary 80A25
DOI:
https://doi.org/10.1090/qam/1106394
MathSciNet review:
MR1106394
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Abstract: The possibility of achieving ignition of a combustible solid with only marginal external heating is investigated. The heating barely raises the temperature to a level where reaction occurs. A parameter indicating the duration of time spent near the crucial level governs the ignition process. If the parameter is below a critical value, no thermal runaway can occur; if it is sufficiently large, ignition will be achieved.
- Richard A. Handelsman and W. E. Olmstead, Asymptotic solution to a class of nonlinear Volterra integral equations, SIAM J. Appl. Math. 22 (1972), 373–384. MR 310574, DOI https://doi.org/10.1137/0122035
- W. E. Olmstead and Richard A. Handelsman, Asymptotic solution to a class of nonlinear Volterra integral equations. II, SIAM J. Appl. Math. 30 (1976), no. 1, 180–189. MR 390690, DOI https://doi.org/10.1137/0130020
A. K. Kapila, Evolution of deflagration in a cold combustible subjected to uniform energy flux, Internat. J. Engrg. Sci. 19, 459–509 (1981).
- D. Glenn Lasseigne and W. E. Olmstead, Ignition of a combustible solid with reactant consumption, SIAM J. Appl. Math. 47 (1987), no. 2, 332–342. MR 881353, DOI https://doi.org/10.1137/0147021
A. Linan and F. A. Williams, Theory of ignition of a reactive solid by constant energy flux, Combustion Sci. Tech. 3, 91–98 (1971)
- W. E. Olmstead, Ignition of a combustible half space, SIAM J. Appl. Math. 43 (1983), no. 1, 1–15. MR 687785, DOI https://doi.org/10.1137/0143001
R. A. Handelsman and W. E. Olmstead, Asymptotic solution to a class of Volterra integral equations, SIAM J. Appl. Math. 22, 373–384 (1972)
R. A. Handelsman and W. E. Olmstead, Asymptotic solution to a class of Volterra integral equations. II, SIAM J. Appl. Math. 30, 180–189 (1976)
A. K. Kapila, Evolution of deflagration in a cold combustible subjected to uniform energy flux, Internat. J. Engrg. Sci. 19, 459–509 (1981).
D. G. Lasseigne and W. E. Olmstead, Ignition of a combustible solid with reactant consumption, SIAM J. Appl. Math. 47, 332–342 (1987)
A. Linan and F. A. Williams, Theory of ignition of a reactive solid by constant energy flux, Combustion Sci. Tech. 3, 91–98 (1971)
W. E. Olmstead, Ignition of a combustible half space, SIAM J. Appl. Math. 43, 1–5 (1983)
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Article copyright:
© Copyright 1991
American Mathematical Society