Mathematical modeling of high-intensity heatingprocesses of bodies with coatings during surfaceprocessing by laser radiation

The article presents a nonlinear mathematical model of heating a two-layer body with allowance of the finite velocity of heat propagation and the temperature dependence of the properties of materials. A numerical solution of the nonlinear hyperbolic heat conduction problem is obtained for the case when the absorption of the radiation energy is modeled by a volumetric heat source. The implementation of the grid method using a three-layer implicit difference scheme in solving a nonlinear heat conduction problem in a two-layer body with allowance for the relaxation of the heat flux and the conjugation conditions in the case of ideal contact at the interface junction is considered. The described algorithm for calculating the temperature field for high-intensity heating of a coated body, taking into account the dependence of the thermophysical characteristics of materials from temperature, is based on the implementation of the sweep method with iterative correction of the coefficients. Programs are developed and the results of calculating the temperature fields are presented using nonlinear hyperbolic heat conduction equations and the corresponding linear ones taking into account the average integrated thermal and optical characteristics of the materials. Based on a comparison of the results obtained the necessity of taking into account the temperature dependence of the properties of materials during the study of processes of high-intensity heating of bodies.The developed mathematical model on the basis of a system of nonlinear hyperbolic equations can be used to create technological processes using methods for processing the surface of multilayer bodies by laser radiation.