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
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 , where 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 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.