Hostname: page-component-84b7d79bbc-l82ql Total loading time: 0 Render date: 2024-07-30T02:01:43.393Z Has data issue: false hasContentIssue false

Travelling wave solutions for rich flames of reactive suspensions

Published online by Cambridge University Press:  17 February 2009

K. K. Tam
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada, H3A 2K6.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The modelling of the combustion of dust suspensions leads to a nonlinear eigenvalue problem for a system of ordinary differential equations defined over an infinite interval. The equations contain a number of parameters. In this study, the shooting method is used to prove the existence of a solution. Linearisation is then used to provide an approximate solution, from which an estimate of the eigenvalue and its dependence on the given parameters can be obtained.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Berestycki, H., Nicolaenko, B. and Scheurer, B., “Travelling wave solutions to combustion models and their singular limits”, SIAM J. Math. Anal. 16 (1985) 12071242.CrossRefGoogle Scholar
[2]Deshaies, B., and Joulin, G., “Radiative transfer as a propagation mechanism for rich flames of reactive suspensions”, SIAM J. Appl. Math. 46 (1986) 561581.CrossRefGoogle Scholar
[3]Ho, D. and Wilson, H. K., “On the existence of a similarity solution for a compressible boundary layer”, Arch. Rational Mech. Anal. 27 (1967) 165174.Google Scholar
[4]Serrin, J. and McLeod, J. B., “The existence of similar solutions for some laminar boundary layer problems”, Arch. Rational Mech. Anal. 41 (1968) 288303.Google Scholar
[5]Stewart, W. E., Ray, W. H. and Conley, C. C. (eds.), Dynamics and modelling of reactive systems (Academic Press, New York, 1980).Google Scholar
[6]Tam, K. K., “On the asymptotic solution of viscous incompressible flow past a heated paraboloid of revolution”, SIAM J. Appl. Math. 20 (1971) 714721.CrossRefGoogle Scholar
[7]Tam, K. K., “On the Lagerstrom model for flow at low Reynolds numbers”, J. Math. Anal. Appl. 49 (1975) 286294.CrossRefGoogle Scholar