Journal of Applied Mathematics and Decision Sciences
Volume 6 (2002), Issue 3, Pages 155-181

Ignition properties of thermally thin plastics: the effectiveness of non-competitive char formation in reducing flammability

M. I. Nelson,1 J. Brindley,2 and A. C. Mcintosh1

1Department of Fuel and Energy, The University of Leeds, Leeds LS2 9JT, UK
2School of Mathematics, The University of Leeds, LS2 9JT, Leeds, UK

Copyright © 2002 M. I. Nelson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The retardancy effect of char formation upon the flammability of thermally thin products is investigated. The char is formed in a single-step non-competitive scheme and is assumed to be thermally stable. The criterion for ignition is that of a critical mass flux of volatiles from the solid into the gas phase. Both steady-state and transient formulations of the model are considered. In the high activation energy limit the critical heat flux efficiency in the steady-state model is proportional to c/(1c), where c is the fraction of char formed. In the transient model the efficiency in reducing the maximum heat release rate, average heat release rate, and total heat released is given by c and is independent of activation energy and heat flux. The specific application that we have in mind for our model is piloted ignition in the cone calorimeter.