Abstract 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.

中文翻译：

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考虑表面和深度吸收的指数热通量下聚合物的点火

摘要 在先前的研究中，利用表面或深度吸收或它们的组合，已经开发了解决恒定热通量下固体点火的分析模型。当遇到与时间相关的热通量时，大多数研究集中在多项式热通量和表面吸收假设上。然而，在分析模型中，特别是对于红外半透明固体，在与时间相关的热通量下也应考虑深度吸收。在这项工作中，建立了一个分析模型，旨在揭示指数时间增加热通量下半透明聚合物的点火机制，同时考虑表面和深度吸收。临界温度用作点火标准。四种典型的非炭化聚合物，聚甲基丙烯酸甲酯 (PMMA)、聚甲醛 (POM)、聚酰胺 6 (PA 6) 和聚丙烯 (PP) 被用作参考材料，并采用数值求解器来验证分析模型。结果表明，开发的分析模型提供了表面温度和点火时间的准确预测。对流和再辐射造成的表面热损失对表面温度、点火时间和临界能量影响不大，但对点火热通量影响很大。热渗透深度与恒定热通量下的热渗透深度不同，并且随着考虑表面热损失，热渗透深度变小。点火时间、热穿透深度和临界能量随着热通量增加率的增大而减小。同时，深度吸收的点火热通量高于表面吸收的点火热通量，并且两者都随着热通量的增加而增加。