Математическое моделирование влияния релаксационных процессов на температурные поля в упругом полупространстве

The article examines the relaxation processes that occur in an elastic solid medium when it is heated and cooled, especially their influence on the temperature field. Besides, we considered in this paper the heat equation of parabolic type arising in the theory of thermal conductivity for different modes of heating the border. We present a solution of the boundary value problem of nonstationary heat conduction for an infinite plate with the following regimes of loading the boundaries: a single slow temperature change at the border, a single instantaneous temperature variation at the border, and, finally, multiple instantaneous changes of temperature at the border. In order to solve these three heat problems, they were brought to a dimensionless form. Then the operational calculus method was applied. The essence of the method consists in the following. According to the obtained analytical solutions three-dimensional graphics characterizing the relaxations processes were built in the computer algebra system Wolfram Mathematica for different ranges of the Fourier criterion.