Pogrebitskaya A. Asymptotic-numerical method of the thermal transfer problem solution.

The object of research is a process of heat exchange in the systems, which have various forms (cone, sphere and cylinder), and circular plates of radiator of trapezoidal and rectangular sections. The subject of research is approximate analytical solutions of problems of heat exchange for the systems that are reduced to linear and nonlinear ordinary differential equations with variable coefficients. The aim of dissertation work is the development and the application of hybrid asymptotic methods of research of linear and nonlinear differential equations with a small parameter, by means of which a modeling of processes of heat exchange in constructions with changeable geometry take place. Research methods are based on a mathematical modeling, asymptotic analysis, computing technique. For the first time the extended WKB-Galerkin and double hybrid asymptotic methods, used for research of the systems of heat exchange of constructions with changing parameters, were offered. The method of phase integrals, direct numeral methods and hybrid method of perturbations-Galerkin are used for description of behavior of the linear and nonlinear systems of thermal radiation. Results of the research are implemented in learning process of Zaporizhzhya National University. Application domain: engineer, aircraft building, building and aerospace technique.