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Abstract:

This Note is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [7]. The paper [7] derives, by means of a three-scale matched asymptotic expansion, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis number - i.e., the ratio between thermal and molecular diffusion - to be strictly less than unity. In this Note, we give the main ideas of a rigorous proof of the validity of this model, under the additional restriction that the Lewis number is close to 1. © 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

Registro:

Documento: Artículo
Título:Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames
Autor:Lederman, C.; Roquejoffre, J.-M.; Wolanski, N.
Filiación:Departamento de Matemática, Facultad Ciencias Exactas Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
UFR-MIG, UMR CNRS 5640, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France
Año:2002
Volumen:334
Número:7
Página de inicio:569
Página de fin:574
DOI: http://dx.doi.org/10.1016/S1631-073X(02)02299-9
Título revista:Comptes Rendus Mathematique
Título revista abreviado:C. R. Math.
ISSN:1631073X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1631073X_v334_n7_p569_Lederman

Referencias:

  • Audounet, J., Giovangigli, V., Roquejoffre, J.-M., A threshold phenomenon in the propagation of a point source initiated flame (1998) Phys. D, 121, pp. 295-316
  • Berestycki, H., Larrouturou, B., (1991) Quelques Aspects Mathématiques de la Propagation des Flammes Prémélangées, 10. , H. Brezis, Lions (Eds.), Collège de France Seminar Pitman-Longman, Harlow, UK
  • Buckmaster, J.D., Joulin, G., Ronney, P., The effects of radiation on flame balls at zero gravity (1990) Combustion and Flame, 79, pp. 381-392
  • Buckmaster, J.D., Ludford, G.S.S., (1982) Theory of Laminar Flames, , Cambridge University Press, Cambridge
  • Fernandez, J., Bonder Wolanski, N., A free-boundary problem in combustion theory (2000) Interfaces Free Bound, 2, pp. 381-411
  • Glangetas, L., Roquejoffre, J.-M., Bifurcations of travelling waves in the thermo-diffusive model for flame propagation (1996) Arch. Rational Mech. Anal., 134, pp. 341-402
  • Joulin, G., Point-source initiation of lean spherical flames of light reactants: An asymptotic theory (1985) Comb. Sci. and Tech., 43, pp. 99-113
  • Joulin, G., Preferential diffusion and the initiation of lean flames of light fuels (1987) SIAM J. Appl. Math., 47, pp. 998-1016

Citas:

---------- APA ----------
Lederman, C., Roquejoffre, J.-M. & Wolanski, N. (2002) . Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames . Comptes Rendus Mathematique, 334(7), 569-574.
http://dx.doi.org/10.1016/S1631-073X(02)02299-9
---------- CHICAGO ----------
Lederman, C., Roquejoffre, J.-M., Wolanski, N. "Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames " . Comptes Rendus Mathematique 334, no. 7 (2002) : 569-574.
http://dx.doi.org/10.1016/S1631-073X(02)02299-9
---------- MLA ----------
Lederman, C., Roquejoffre, J.-M., Wolanski, N. "Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames " . Comptes Rendus Mathematique, vol. 334, no. 7, 2002, pp. 569-574.
http://dx.doi.org/10.1016/S1631-073X(02)02299-9
---------- VANCOUVER ----------
Lederman, C., Roquejoffre, J.-M., Wolanski, N. Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames . C. R. Math. 2002;334(7):569-574.
http://dx.doi.org/10.1016/S1631-073X(02)02299-9