Nonlinear wave equation in nonadiabatic flame propagation

M. R. Booty, M. Matalon, B. J. Matkowsky

Research output: Contribution to journalArticle

Abstract

We derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumetric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis number near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time.

Original languageEnglish (US)
Pages (from-to)519-535
Number of pages17
JournalSIAM Journal on Applied Mathematics
Volume48
Issue number3
DOIs
StatePublished - Jan 1 1988

Fingerprint

Hopf bifurcation
Nonlinear Wave Equation
Wave equations
Flame
Heat losses
Propagation
Thermal Model
Combustion
Extinction
Hopf Bifurcation
Critical value
Heat
Singularity
Hot Temperature

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Nonlinear wave equation in nonadiabatic flame propagation. / Booty, M. R.; Matalon, M.; Matkowsky, B. J.

In: SIAM Journal on Applied Mathematics, Vol. 48, No. 3, 01.01.1988, p. 519-535.

Research output: Contribution to journalArticle

Booty, M. R. ; Matalon, M. ; Matkowsky, B. J. / Nonlinear wave equation in nonadiabatic flame propagation. In: SIAM Journal on Applied Mathematics. 1988 ; Vol. 48, No. 3. pp. 519-535.
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