Kobrinovich J. Mathematical modeling of the heat conduction of highspeed processes.

Subject of inquiry is the high-speed heat conductivity processes in multiply connected domains. Research objective is to develop mathematical models of the high-speed heat conductivity processes. Methods are structural and regional-structural methods, area boundary identification methods. A description method for the boundaries of the complex shape regions is developed, conservative analytical and regionally-analytical solutions of the heat conduction problems are constructed, construct exact solutions of the model problems of heat conduction are constructed, the high-speed heat conductivity processes models are build. The proposed structures have modular design and precisely satisfy the unsteady boundary conditions, this allows you to solve problems in parametric form that provides significant savings of computer time and accuracy in comparison to other research results. The results of the work were used in NTK " IPMash NAS of Ukraine " and introduced in the educational process at the M. Ostrogradskii Kremenchug National University. Application branches are mathematical modeling in industries of metal working, shaping details, aerospace industry.