The periodic temperature oscillations in the near-surface layer of cylindrical structures

A hollow cylinder with thick walls and linear continuously acting variable heat sources are among the most difficult objects to calculate the unsteady temperature field, so this field is the least studied. However, such objects are found in many modern designs of heat generation and distribution systems. The proposed work considers the study of the temperature wave propagation in the wall of a hollow cylinder and in a cylindrical symmetric array around a variable linear heat source with a harmonious change in the temperature of the external or internal environment that occurs during its daily fluctuations or when regulating the heat distribution system. The result of approximate analytical solution of the problem by the method of separation of variables in the complex domain using cylindrical functions is presented. The data of numerical calculation of attenuation of temperature oscillations in the near-surface layer of the cylinder and around the variable linear heat source by means of an explicit finite-difference scheme of increased accuracy under boundary conditions of the first kind and their comparison with the analytical solution for its refinement are presented. The refined analytical dependences for the attenuation coefficient of the temperature wave suitable for use at low thermal inertia of the cylindrical layer and giving physically correct results at the boundary values of the parameters are proposed. The difference in the nature of the damping of oscillations in the direction of the temperature wave outside and inside the cylinder is noted. The presented dependences are proposed to be used for a refined analytical assessment of the amplitude of temperature fluctuations in the near-surface layer of cylindrical heated structures and around the heating and heat supply pipelines in variable modes, which will allow the use of engineering methods to verify compliance with the requirements of industrial safety.