A nonlinear wave equation in nonadiabatic flame propagation

Journal Article · Wed Jun 01 00:00:00 EDT 1988 · SIAM J. Appl. Math.; (United States)

DOI:https://doi.org/10.1137/0148030· OSTI ID:7199622

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

The authors 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 volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers 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.

• Research Organization: Dept. of Engineering Sciences and Applied Mathematics, Northwestern Univ., Evanston, IL (US)
• OSTI ID: 7199622
• Journal Information: SIAM J. Appl. Math.; (United States), Journal Name: SIAM J. Appl. Math.; (United States) Vol. 48:3; ISSN SMJMA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
DIFFERENTIAL EQUATIONS
ENERGY LOSSES
EQUATIONS
FLAMES
HEAT LOSSES
LOSSES
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS