Spatial Localization of Thermal Perturbations in Nonlinear Process of Heat Conduction

A one-dimensional boundary problem for a quasi-linear parabolic-type equation is considered. The problem describes the thermal perturbation propagation in a planar layer filled with the medium with volume heat absorption, whose specific power presents a power function of temperature. A difference scheme is used for finding a numerical solution to the problem. Results of calculations of temperature fields in the layer at different moments of time with the certain values of the problem parameters are given. Using theoretical inferences and data of performed numerical calculations, the nonlinear effect of spatial localization of thermal perturbations is established when thermal perturbations from the heated surface penetrate the medium only to a finite depth.

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