KOBILSKAYA E. Nonlocal and boundary problems for heat conductivity equation in metallurgy

In the thesis the new mathematical models of temperature field for the mobile isotropic environment with periodically and constantly operating heat sources are built. Existing mathematical models, such as nonlinear boundary and nonlocal problems for the heat conductivity equation and also the problems with a moving boundary are specified. The mathematical model of the thermal process in the mobile environment in the form of a nonlocal problem with integral condition was built. It is shown that in contrast to the boundary value problems, the solutions of nonlocal problems more accurately show the process of heating and temperature distribution both at the borders and within the region. The possibility and the limits of the integral condition for finding the solution of inverse problems and determining the main parameters of control the temperature field is shown. The method of search of parameter of control the temperature field is offered. Existence theorems for nonlocal problems of the heat conductivity equation are proved. Search method of temperature field control parameters with integral condition instead of the boundary one is offered. Numerical investigation of temperature distributions are carried out. The parameters of control for the temperature field for different materials and different environmentalconditions of heat exchange surface of the cylinder are obtained.