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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**R. A. Handelsman and W. E. Olmstead,*Asymptotic solution to a class of Volterra integral equations*, SIAM J. Appl. Math.**22**, 373-384 (1972) MR**0310574****[2]**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) MR**0390690****[3]**A. K. Kapila,*Evolution of deflagration in a cold combustible subjected to uniform energy flux*, Internat. J. Engrg. Sci.**19**, 459-509 (1981).**[4]**D. G. Lasseigne and W. E. Olmstead,*Ignition of a combustible solid with reactant consumption*, SIAM J. Appl. Math.**47**, 332-342 (1987) MR**881353****[5]**A. Linan and F. A. Williams,*Theory of ignition of a reactive solid by constant energy flux*, Combustion Sci. Tech.**3**, 91-98 (1971)**[6]**W. E. Olmstead,*Ignition of a combustible half space*, SIAM J. Appl. Math.**43**, 1-5 (1983) MR**687785**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
80A25

Retrieve articles in all journals with MSC: 80A25

Additional Information

DOI:
https://doi.org/10.1090/qam/1106394

Article copyright:
© Copyright 1991
American Mathematical Society