Wave heat transfer in heat-shielding materials with an exponential-like nonlinear dependence of thermal conductivity on temperature

The article studies heat transfer in a semi-infinite straight line with thermal conductivity depending exponentially on temperature. The introduction of a self-similar substitution reduces the heat conduction problem to a nonlinear ordinary differential equation. Its solution showed the wave nature of heat emission in the form of traveling heat waves. The solution gives a limiting time beyond which the heat flux is “locked” at some distance from the boundary of the body, despite the fact that the temperature or heat flux at the boundary can increase indefinitely. The limiting heating depth above which the computational domain remains cold (with the initial temperature) is determined.