Determination of the wall temperature change for a cavity in a solid as a result of the temperature change of the gas flow in a cavity

The wall temperature change for a cylindrical cavity in a solid was found as a response to the temperature change of the gas flowing in a cavity. Three important special cases of the gas temperature dependence on time are considered: temperature is constant; temperature changes according to the linear law; temperature changes according to the harmonic law. The plots of five "$\theta$-functions" used to denote solutions are submitted. The plots are obtained by the means of the numerical integration of the Gauss quadrature formula applied to improper integrals containing cylindrical functions.