We establish a mathematical model for the ignition of a thermally thin polymeric material in the Cone Calorimeter (autoignition mode). The model contains equations for solid phase and gas phase variables, and the two phases are couples nonlinearly. Of particular importance are the couplings through convective and radiative heat transfer. We use the model to evaluate the critical heat flux required for ignition and identify features of the model which require further experimental validation.
M.I. Nelson, J. Brindley, and A.C. McIntosh. A Mathematical Model of Ignition in the Cone Calorimeter. Combustion Science and Technology, 104:35-54, 1995.
We model char formation in isothermal and thermogravimetric experiments by a catalytic one-step reaction. For isothermal experiments there is an analytic solution and we show how the maximum amount of char formed, and the stability of the char, varies with the parameters in our model. For thermogravimetric experiments we use the concept of a `characteristic temperature' to provide bounds on parameter values and calculate the amount of char formed numerically. This approach can also be used to predict whether barrier-forming additives form char below or above the decomposition point of a polymeric solid.
M.I. Nelson and J. Brindley. Modelling Char-Formation in Isothermal and Non-Isothermal Thermogravimetric Experiments. Thermochimica Acta, 258:175-188, July 1995.
We use a mathematical model for the ignition of thermally thin thermoplastics to evaluate the critical heat flux, and the corresponding critical surface temperature, required for piloted ignition by using the concept that a sample ignites when the mass flux of fuel from the solid into the gas phase reaches a critical value. We shoe how the critical heat flux is related to the `characteristic temperature' determined in thermogravimetric experiments and investigate how this value is affected by dilution of the fuel with an inert additive and by the addition of a heat-sink additive. We suggest that experimental results should be presented in terms of a dilution factor rather than by the usual `% weight additive'. The specific application of the model we have in mind is piloted ignition in the cone calorimeter.
M.I. Nelson, J. Brindley, and A.C. McIntosh. The Dependence of Critical Heat Flux on Fuel and Additive Properties: A Critical Mass Flux Model. Fire Safety Journal, 24(2):107-130, 1995.