Ignition of polymers under exponential heat flux considering both surface and in-depth absorptions

Analytical models addressing ignition of solids under constant heat flux have been developed in previous studies utilizing surface or in-depth absorption or combination of them. When encountering time-dependent heat flux, the majority of the studies focused on polynomial heat flux and surface absorption assumption. However, in-depth absorption also should be taken into account under time-dependent heat flux in analytical models especially for infrared translucent solids. In this work, an analytical model aiming at revealing the ignition mechanism of translucent polymers under exponential time-increasing heat flux is established considering both surface and in-depth absorptions. Critical temperature is employed as ignition criterion. Four typical non-charring polymers, polymethyl methacrylate (PMMA), polyoxymethylene (POM), polyamide 6 (PA 6) and polypropylene (PP), are utilized as the reference materials, and a numerical solver is employed to validate the analytical model. The results show that the developed analytical model provides accurate predictions of surface temperature and ignition time. Surface heat loss by convection and reradiation has little effect on surface temperature, ignition time and critical energy, but it affects the ignition heat flux greatly. Thermal penetration depth differs from the one under constant heat flux, and it gets smaller as the surface heat loss is considered. The ignition time, thermal penetration depth and critical energy decrease as the heat flux increasing rate gets larger. Meanwhile, the ignition heat flux for in-depth absorption is higher than that for surface absorption, and both increase with heat flux increasing rate. Furthermore, the linearity between ignition time and the squared critical energy, proposed in constant and linear heat flux scenarios, is also found valid under this exponential heat flux condition.