Hostname: page-component-cb9f654ff-k7rjm Total loading time: 0 Render date: 2025-08-23T10:48:21.643Z Has data issue: false hasContentIssue false
  • English
  • Français

Combustion waves with reactant depletion

Published online by Cambridge University Press:  17 February 2009

J. Graham-Eagle  and
D. A. Schult
J. Graham-Eagle
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts Lowell, Lowell, MA 01854, USA.
D. A. Schult
Affiliation:
Department of Mathematics, Colgate University, Hamilton, NY 13346, USA.
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.

A simple model for the propagation of a combustion wave is proposed and the speed of propagation is predicted. It is assumed that the reactant ignites at a specified temperature and then burns until depleted with reaction rate dependent on temperature and reactant concentration. The exact solution and linear stability are determined in the case of constant heat generation and a numerical scheme is developed to generate traveling wave solutions in the more general case. This numerical method is applied to the case where the temperature dependence of the reaction rate is modeled by the Arrhenius function.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 1 , July 2001 , pp. 119 - 135
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Aris, R., The mathematical theory of diffusion and reaction in permeable catalysts (Oxford University Press, 1975).Google Scholar
[2]Bush, W. B. and Fendell, F. E., “Asymptotic analysis of laminar flame propagation for general Lewis numbers”, Combust. Sci. Tech. 1 (1970) 421–428.Google Scholar
[3]Frank-Kamenetskii, D. A., Diffusion and heat transfer in chemical kinetics, 2nd ed. (Plenum, New York, 1969).Google Scholar
[4]Gray, P. and Kordylewski, W., “Standing waves in exothermic systems”, Proc. Roy. Soc. Lond A 398 (1985) 281–288.Google Scholar
[5]Gray, P. and Kordylewski, W., “Traveling waves in exothermic systems”, Proc. Roy. Soc. Lond. A 416 (1988) 103–113.Google Scholar
[6]Mercer, G. N. and Weber, R. O., “Combustion wave speed”, Proc. Roy. Soc. bond. A 450 (1995) 193–198.Google Scholar
[7]Mercer, G. N. and Weber, R. O., “Combustion waves in two dimensions and their one-dimensional approximation”, Combust. Theory Modeling 1 (1997) 157–165.CrossRefGoogle Scholar
[8]Mercer, G. N., Weber, R. O., Gray, B. F. and Watt, S. D., “Combustion pseudo-waves in a system with reactant consumption and heat loss”, Math. Comput. Modelling 24 (1996) 29–38.Google Scholar
[9]Weber, R. O., Mercer, G. N., Sidhu, H. S. and Gray, B. F., “Combustion waves for gases (Le = 1) and solids (Le → ∞)”, Proc. Roy. Soc. Lond. A 453 (1997) 1105–1118.Google Scholar
[10]Weber, R. O. and Watt, S. D., “Combustion waves”, J. Austral. Math. Soc. Ser. B 38 (1997) 464–476.CrossRefGoogle Scholar
[11]Williams, F. A., Combustion theory (Benjamin/Cummings, New York, 1985).Google Scholar