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Mathematical model of fuel heat ignition considering space - time nonlocality

Using the formula of the Fourier law, which takes into account the relaxation of the heat flux and the temperature gradient, a mathematical model of thermal ignition for systems with an exothermic internal source of heat was developed, taking into account the space-time nonlocality of the heat exchange process. Studies of boundary conditions of the first and third kind showed that taking into account the local nonequilibrium leads to an increase in the delay time of thermal ignition, irrespective of the conditions of heat exchange with the environment. It is shown that if the relaxation properties of materials are taken into account, the boundary conditions (of the first, second, or third kind) cannot be taken instantly, but only in a certain range of initial time. Consequently, the amount of heat supplied to the system has a certain limit, depending on its relaxation properties. Therefore, it is possible to conclude that there is also a limit on the value of heat transfer coefficients, which cannot be exceeded under any conditions of heat exchange with the environment.