Abstract
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.
Highlights
Pyrolysis and the subsequent ignition under external incident heat flux (HF) are important for fire protection since they determine the occurrence of fire propagation and are easier to be controlled at early stage
PMMA is selected for computation to validate the proposed analytical model
The comparison of surface temperature of PMMA between the developed analytical model and simulation results is illustrated in Fig. 4. acri is crucial for ignition and the ranges of a used in Fig. 4 are in the vicinity of acri
Summary
Equation [6] or [7] is the transient in-depth temperature in solid. Lautenberger replaced the pyrolysis rate by a power law function, and Snegirev used the Frank-Kamenetskii decomposition to simplify the Arrhenius function. All these works were conducted under constant HF. We extend Lautenberger’s8 study from constant to time-decreasing boundary condition. Both linearly and quadratically decreasing HFs are examined. As the approximation results in ref., the pyrolysis rate can be replaced by a power law function when the pyrolysis temperature is between 250 °C and 450 °C and the Ta ranges from 10000 K to 30000 K: exp −
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