Strongly Nonequilibrium Model of Thermal Ignition with Account for Space–Time Nonlocality

Abstract

A modified Fourier law with account for heat flux relaxation and scalar value of the temperature gradient serves as a basis for the mathematical model of the locally nonequilibrium process of thermal ignition of systems with a hear source exponentially changing due to temperature. It is shown by the studies performed under the boundary conditions of the first kind that accounting for the space–time nonlocality increases the time delay of thermal ignition. Moreover, it is shown that, when the relaxation properties of the material are considered, the boundary conditions can only be accepted after a certain time rather than instantaneously. Consequently, the amount of heat fed to the system has a limit that depends on the physical properties (including relaxation properties) of the medium.