Research of critical ambient temperature of cylindrical fireworks and crackers

To study the influence of temperature on cylindrical fireworks and crackers in production and storage, this article establishes a physical and mathematical model of thermal explosion critical ambient temperature of finite cylindrical fireworks with shell based on two-dimensional steady state thermal explosion theory. The numerical program is written by difference method and Newton-homotopy method. The partial differential equations of thermal explosion model are calculated in Matlab. Comparison of numerical solutions and classical solutions proves the accuracy of model. The influence of Biot number of each surface and length diameter ratio on critical ambient temperature is analyzed. It is founded that the scope of length diameter ratio is 0.08<H<4.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 0.08 < H < 4.3 $$\end{document} when Biot number tends to infinite. The thermal safety temperature of the fireworks without inner barrel when it is stored individually is obtained. This provides theoretical support for the safety of fireworks and crackers in production, storage transportation, and setting off process.