Mala Y. Mathematical modeling of thermal conduction processes considering heat flow relaxation

The thesis is devoted to the development of nonlinear mathematical models of thermal conduction processes considering heat flow relaxation and which occur at using technologies of products processing with high-intensity energy flows and at devices operation where high-intensity energy flows appear; the development and improvement of methods for solving boundary value problems for systems of hyperbolic equations of thermal conduction. There was built the new mathematical model of thermal conduction processes in multilayer bodies considering finite heat distribution velocity and temperature dependence of the material thermophysical characteristics. There was derived structural solution with operational methods for the linear boundary value problem for systems of hyperbolic equations of thermal conduction. On the basis of this solution and the method of spatial and temporal quadrants there was developed approximate analytical method for solving nonlinear boundary value problems for systems of hyperbolic equations of thermal conduction. Using the obtained structural solution there was developed the calculation procedure of temperature fields in the contact connections at the time of switching short-circuit current. Developed mathematical models of bodies heating coated with laser considering finite heat distribution velocity and temperature dependence of thermophysical characteristics, and computational algorithm based on the developed approximate analytical method can be used for choosing rational modes of laser processing coatings. Proposed mathematical model, developed approximate analytical method and computational algorithms can be used at the practice of organizations where the researches of thermal processes under the influence of high-intensity energy flows on materials are performed.