Modeling and calculation of thermal explosion time to ignition of cylindrical fireworks and crackers

Abstract

To analyze the thermal safety of cylindrical fireworks and crackers in storage and transportation, this article establishes a physical model and a mathematical model of thermal explosion time to ignition of finite cylindrical fireworks and crackers. And in order to simplify the thermal explosion model, effective Biot number about boundary condition is deduced according to the theory of heat transfer. The partial differential equation of thermal explosion model are calculated with difference method in Matlab program, to obtain the time to ignition as well as the temperature–time history before explosion system explodes. The rationality of effective Biot number and calculation method is proved through comparison of calculation solution and literature solution. Being the first to solve the problem of two-dimensional thermal explosion unsteady-state model of fireworks and crackers, where the upper surface, lower surface, and side surface have different heat dissipation conditions. Meanwhile, calculation steps were shown about a type of fireworks.