МАТЕМАТИЧНІ МОДЕЛІ ТЕПЛООБМІНУ В ЕЛЕМЕНТАХ ТУРБОГЕНЕРАТОРІВ (ПРОДОВЖЕННЯ)

Abstract

Previously developed [8] and presented new mathematical models for the analysis of temperature regimes in individual elements of turbo generators, which are geometrically described by isotropic half-space and space with an internal heat source of cylindrical shape. Cases are also considered for half-space, when the fuel-releasing cylinder is thin, and for space, when it is heat-sensitive. For this purpose, using the theory of generalized functions, the initial differential equations of thermal conductivity with boundary conditions are written in a convenient form. To solve the obtained boundary value problems of thermal conductivity, the integral Hankel transformation was used, and as a result, analytical solutions in the images were obtained. The inverse Hankel integral transformation was applied to these solutions, which made it possible to obtain the final analytical solutions of the initial problems. The obtained analytical solutions are presented in the form of improper convergent integrals. Computational programs have been developed to determine the numerical values ​​of temperature in the above structures, as well as to analyze the heat transfer in the elements of turbo generators due to different temperature regimes due to heating by internal heat sources concentrated in the cylinder volume. Using these programs, graphs are presented that show the behavior of curves constructed using numerical values ​​of the temperature distribution depending on the spatial radial and axial coordinates. The obtained numerical values ​​of temperature indicate the correspondence of the given mathematical models for determining the temperature distribution to the real physical process. The software also allows you to analyze media with internal heating, concentrated in the spatial figures of the correct geometric shape, in terms of their heat resistance. As a result, it becomes possible to increase it, to determine the allowable temperatures of normal operation of turbo generators, to protect them from overheating, which can cause the destruction of not only individual elements but also the entire structure.