Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Linear stability analysis of cylindrical flames


Authors: Marc Garbey, Hans G. Kaper, Gary K. Leaf and Bernard J. Matkowsky
Journal: Quart. Appl. Math. 47 (1989), 691-704
MSC: Primary 80A25; Secondary 76E99
DOI: https://doi.org/10.1090/qam/1031685
MathSciNet review: MR1031685
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Abstract: This article is concerned with the linear stability of cylindrical flames in a velocity field generated by a line source of fuel of constant strength $ 2\pi \kappa $ per unit length. The mathematical model involves the equations of mass and heat transfer in the regions on either side of the flame sheet and a set of jump conditions across the flame sheet. It admits a basic solution representing a stationary flame front in the shape of a circular cylinder at a radial distance $ \kappa $ from the line source. The circular front loses stability if either (i) the Lewis number of the reaction-limiting component is less than some critical value less than 1 and $ \kappa $ is greater than a critical value, or (ii) the Lewis number is greater than a critical value greater than 1. In the former case the circular front evolves into a steady cellular front, in the latter into a pulsating front, which may also be cellular. The WKB method is employed to derive approximations for the pulsating and cellular branches of the neutral stability curve.


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DOI: https://doi.org/10.1090/qam/1031685
Article copyright: © Copyright 1989 American Mathematical Society


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