Dynamics of the temperature field in a massive substrate under the effect of a concentrated heat flux

The results of an analytical solution to the problem of heat distribution inside a massive solid sample with concentrated heat supply to this sample surface are presented. Analytical expressions for the non-stationary temperature distribution inside the body are obtained using the integral cosine Fourier transform and the Hankel transform. Examples of solution application for estimating the characteristic times of reaching the Chernov points Ac1 and Ac3 in model hypoeutectoid steels under the effect of laser radiation are presented. The application of this solution to calculating the cooling dynamics of ceramic Al2O3 and SiO2 samples, affected by the air and water jets, is demonstrated.