Separate mathematical models for determining the temperature distribution in the elements of turbogenerators have been developed, which are described geometrically by an isotropic half-space and a heat-sensitive space with locally concentrated sources of heating. For this purpose, using the theory of generalized functions in a convenient form, we write the initial differential equations of thermal conductivity with boundary conditions. For thermosensitive space (thermophysical parameters are temperature dependent), the original nonlinear thermal conductivity equation and the nonlinear boundary conditions are linearized using the Kirchhoff transform, for which a linear differential equation is obtained. An integral Hankel transform was used to solve the boundary value problems of thermal conductivity, and as a result analytical solutions in the images were obtained. These solutions were applied by the inverted Hankel integral transformation, which made it possible to obtain the final analytical solutions of the original problems. The analytical solutions obtained are presented in the form of non-native convergent integrals. For the construction material of the heat-sensitive space, a linear dependence of the thermal conductivity coefficient on the temperature was used. The result is a convenient formula for determining the temperature field, which allows to analyze temperature regimes in a heat-sensitive environment. To determine the numerical values of temperature in the above structures, as well as to analyze the heat exchange in the elements of the turbogenerators caused by different temperature regimes due to the heating of locally concentrated heat sources, computational programs have been developed. Using these programs are graphs that show the behavior of surfaces constructed using numerical values of the dimensionless temperature distribution depending on the spatial dimensionless coordinates. The obtained numerical values of temperature indicate that the mathematical models of determining the distribution of temperature to the actual physical process are consistent. The software also allows you to analyze locally heated environments for their heat resistance. As a consequence, it becomes possible to raise it, to determine the allowable temperatures of normal operation of the turbogenerators, to protect them from overheating, which can cause destruction not only of individual elements, but also of the whole structure.
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