Mathematical Models of Heat Ignition And Explosion Considering Local Non-Equilibrium of Processes

By using the heat balance equation and the modified Fourier's law formula, where the heat flux relaxation and temperature gradient were considered, the model of heat ignition non-equilibrium process for the plate with non-linear (exponentially changing depending on the temperature) inner heat source was developed. The studies performed at relaxed boundary third-class conditions have shown that consideration of non-locality results in the increased heat ignition time irrespective of the intensity of heat exchange with the ambient medium. This fact is explained by the resistance caused by the ambient medium, the process of change of its temperature condition which increases as the relaxation factors rise. It is also shown that with consideration of the relaxation phenomena boundary conditions of the first, second and third class may not be met immediately – they may be set only within a particular range of the initial time segment. This means that the immediate implementation of the thermal impact condition seems to be impossible, since the value of heat-transfer factor has a definite limit, which depends on the relaxation properties of the medium, which may not be exceeded under any conditions of heat exchange with the ambient medium. (paper)