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Travelling Combustion Waves in a Porous Medium. Part II—Stability

Norbury, J. and Stuart, A. M. (1988) Travelling Combustion Waves in a Porous Medium. Part II—Stability. SIAM Journal on Applied Mathematics, 48 (2). pp. 374-392. ISSN 0036-1399. doi:10.1137/0148019.

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The linear stability properties of the travelling combustion waves found in Part I are examined. The key parameters which determine the stability properties of the waves are found to be the (scaled) driving velocity and the solid specific heat. In particular, the destabilising influence of increasing either of these two parameters is demonstrated. The results indicate that travelling combustion waves whose reaction is turned off because the solid temperature becomes too low are always unstable, whereas travelling waves whose reaction is turned off due to depletion of solid reactant can be stable. Global techniques are employed to prove that, for large enough values of the scaled solid specific heat, combustion cannot be sustained in any form, and all initial conditions lead to extinction.

Item Type:Article
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Additional Information:© 1988 Society for Industrial and Applied Mathematics. Received by the editors August 11, 1986; accepted for publication (in revised form) April 23, 1987. The work of this author was supported by the Science and Engineering Research Council of the United Kingdom.
Funding AgencyGrant Number
Science and Engineering Research Council (SERC)UNSPECIFIED
Subject Keywords:combustion, travelling waves, stability
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ5
Issue or Number:2
Classification Code:AMS(MOS) subject classifications. 35B32, 35B35, 80A30
Record Number:CaltechAUTHORS:20170612-164819129
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Official Citation:Travelling Combustion Waves in a Porous Medium. Part II—Stability J. Norbury and A. M. Stuart SIAM Journal on Applied Mathematics 1988 48:2, 374-392
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78134
Deposited By: George Porter
Deposited On:13 Jun 2017 14:45
Last Modified:15 Nov 2021 17:37

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