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To study the effect of variable heat transfer coefficient of fireworks and crackers on thermal explosion critical ambient temperature and time to ignition, considering the heat transfer coefficient as the power function of temperature, mathematical thermal explosion steady state and unsteady-state model of finite cylindrical fireworks and crackers with complex shell structures are established based on two-dimensional steady state thermal explosion theory. The influence of variable heat transfer coefficient on thermal explosion critical ambient temperature and time to ignition are analyzed. When heat transfer coefficient is changing with temperature and in the condition of natural convection heat transfer, critical ambient temperature lessen, thermal explosion time to ignition shorten. If ambient temperature is close to critical ambient temperature, the influence of variable heat transfer coefficient on time to ignition become large. For firework with inner barrel in example analysis, the critical ambient temperature of propellant is 463.88 K and the time to ignition is 4054.9s at 466 K, 0.26 K and 450.8s less than without considering the change of heat transfer coefficient respectively. The calculation results show that the influence of variable heat transfer coefficient on thermal explosion time to ignition is greater in this example. Therefore, the effect of variable heat transfer coefficient should be considered into thermal safety evaluation of fireworks to reduce potential safety hazard.