Kobilska O. Mathematical and computer modeling of thermal processes in complex systems with moving and stationary axisymmetric elements

In the dissertation work a new solution of an important scientific and applied problem is obtained, which consists in the development of new and improvement of existing mathematical models of temperature distributions in complex systems and methods of their research. The obtained solution differs from the existing solutions by a more complete reflection (temperature distributions) of heat transfer processes, development of new computational methods for solving initial-boundary and nonlocal 44 problems that arise in mathematical models, which allows to increase the efficiency of temperature control in complex systems. Mathematical models of thermal processes occurring in complex multilayer areas have been improved. Nonlocal integral conditions for finding solutions of inverse problems and determination of temperature field control parameters are proposed. Methods for solving inverse boundary value problems of thermal conductivity have been improved, which take into account variable boundary conditions and apply the integral condition of heat balance to construct a solution. The paper proposes a method for solving boundary value problems for the equation of thermal conductivity in a complex region – a multilayer cylinder, where in one part of the layers there are internal heat sources, and in the other – external. The results of work in the educational process of KrNU and the practice of designing technological processes and equipment at private enterprises of Ukraine and Europe are introduced.