Analytical study on ignition time of PMMA exposed to time-decreasing thermal radiation using critical mass flux

This contribution addresses an analytical model to predict the ignition time of PMMA (Polymethyl methacrylate) subjected to a time-decreasing incident heat flux. Surface temperature, transient mass flux and ignition time of PMMA are thoroughly studied based on the exact solutions of in-depth temperature. Critical mass flux is utilized as the ignition criteria. An approximation methodology is suggested to simplify the unsolvable high order equations and deduce the explicit expressions of ignition time. A numerical model is employed to validate the capability of the developed model. The results show that no ignition occurs when the decreasing rate of heat flux increases larger than a critical value. The agreement of the transient mass flux between analytical and numerical models is good at high decreasing rate but turns worse as the decreasing rate declines. However, this enhanced discrepancy affects the ignition time prediction slightly. The inverse of the square root of the ignition time is linearly correlated with the decreasing rate of heat flux, and it becomes significantly sensitive to the decreasing rate when the decreasing rate approaching its critical value. Meanwhile, the value of critical mass flux has appreciable influence on the ignition time prediction.