Safer estimates of time-to-ignition of reactive porous solid of regular shapes

Time-to-ignition (time taken from an initial solid temperature to thermal ignition temperature) is an important parameter for safe practice in handling exothermically reactive solids, e.g. stockpiling, transportation etc. In this study, the well-known Thomasʹ approximation of the heat conduction term in Frank-Kamenetskiiʹs equation for thermal ignition of a porous solid slab has been examined. Initially, the constant boundary temperature condition (infinite Biot number) is considered. Using numerical simulation with the finite difference method, it can be shown that the Thomasʹ approximation overestimates the effect of conduction thus giving a greater time-to-ignition (the prediction is less safe) than reality. For conditions other than supercritical (that is when the solid size is sufficiently large to have annular ignition for a given reactivity), a semi-empirical modification has been made to enable a safer prediction of time-to-ignition (TTI). The new model is generalised to the case of finite Biot numbers and then, for different solid shapes. An analytical lower bound solution of TTI is also described.