Approximate analytical solutions for temperature based transient mass flux and ignition time of a translucent solid at high radiant heat flux considering in-depth absorption

Most studies, employing ignition temperature as the ignition criterion, utilized surface absorption of radiant incident heat flux in analytical models when investigating the ignition mechanism of solid combustibles. However, in-depth absorption exerts its influence on ignition time significantly for translucent solid, especially at high radiant heat flux. In this work, we extend the previous researches from surface absorption to in-depth absorption to develop an approximate analytical ignition model using critical mass flux instead of critical temperature. An approximation methodology is proposed during derivation to study the in-depth absorption scenario. The comparison among this model, available experimental data of black PMMA in the literature and previous numerical simulations indicates that the proposed model provides relatively high accuracy in predicting ignition time. Furthermore, the pure surface absorption circumstance is also reexamined and compared with the classical ignition theory. The results show that surface absorption hypothesis accelerates the total mass flux, which consequently shortens the ignition time. However, in-depth absorption assumption eliminates the heat accumulation on surface and results in good prediction for ignition time at high heat flux. For in-depth absorption, the absorption coefficient affects the heat penetration depth and temperature distribution in this layer which consequently affects the thermal degradation reaction rate, mass flux and finally ignition time. Meanwhile, the ignition time considering both surface and in-depth absorption is discussed, and the relationship with pure surface and in-depth absorption conditions is obtained.