Approximate analytical solutions for transient mass flux and ignition time of solid combustibles exposed to time-varying heat flux

An approximate analytical model was established in this study to predict the transient mass flux and ignition time of solid combustibles exposed to time-dependent exponentially increasing heat flux. Critical mass flux was employed as the ignition criterion in the developed model. A new approximation strategy was used to simplify the complicated exact solution and to derive explicit correlations between ignition time and heat flux. Linear and quadratic heat fluxes were focused and the conclusions under other heat fluxes can be extended through analogy. An equivalent ignition temperature, involving critical mass flux, thermodynamics and chemical kinetics, was found in this study. The negative square root of ignition time is linearly proportional to the heat flux at ignition time. Under linear and quadratic heat fluxes, the ignition heat flux increases with a(1/3) and a(1/5) (a is a constant in the heat flux expression), respectively, whereas the total heat absorbed by the solid before ignition is proportional to a(-1/3) and a(-1/5), respectively. The capability of the proposed model was validated by another analytical model, numerical simulations and experimental data of black PMMA (Polymethyl Methacrylate) and pine wood. Furthermore, the effect of surface heat loss on the predictions of the proposed model was estimated and parametric study based on critical mass flux was implemented.