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The article is devoted to the study of the physical properties of gas. It discusses the concept of projective differential geometry. The invariance of the laws of thermodynamics with respect to projective transformations of specific parameters is shown on the example of an ideal single-component gas. The basic relations of projective differential geometry are also proved, as well as the invariance of all essential laws in thermodynamics with respect to projective transformations of specific parameters. [ABSTRACT FROM AUTHOR]

The work is devoted to the study of the thermally stressed state of fuel rods when their geometric shape changes. The temperature fields for the sphere and the ellipsoid are determined. It is shown that, while maintaining volumetric heat release, maximum stresses occur in fuel rods of circular cross-section. Similar results were obtained when changing the geometric shape of a spherical fuel cell: all other things being equal, maximum thermal stresses occur in spherical fuel cells. [ABSTRACT FROM AUTHOR]

The work is devoted to the issues of stationary heat transfer. In this article, the question of finding the temperature field of a heating element made in the form of a cylinder enclosed in a shell of the same cylindrical shape is considered. It is assumed that the thermal contact between the solid-coating systems is ideal. In this case, heat exchange occurs under boundary conditions of the third and fourth kind. In this paper, based on the methods of differentiation and integration, a solution was obtained to the problem of the distribution of the temperature field in both bodies. [ABSTRACT FROM AUTHOR]

In this article, attention is paid to the mathematical modeling of the ball lightning temperature field. The relevance of the work is due to the fact that the phenomenon itself is common, but in itself has not been sufficiently studied. Various models are used to describe its properties. In the article, ball lightning is considered as a plasma ball. The main purpose of the work is mathematical modeling of the lightning temperature field taking into account radiation heat transfer. Modeling of the thermal process is based on numerical integration of the heat equation. Also, based on the obtained result, an analysis of the behavior of the temperature field was carried out. [ABSTRACT FROM AUTHOR]

The article considers the question of finding the temperature field of a heating element made in the form of a cylinder enclosed in a shell of cylindrical shape. Heat exchange occurs under boundary conditions of the third and fourth kind. In this paper, based on the methods of differentiation and integration, a solution was obtained to the problem of the distribution of the temperature field in both bodies. The reliability of the obtained result is confirmed by the fact that one of the special cases leads the task to a problem with boundary conditions of the first kind, when the surface temperature is constant. [ABSTRACT FROM AUTHOR]

As is known, the fuel elements of nuclear reactors operate at sufficiently high temperatures. The heterogeneity of the temperature field leads to the appearance of so-called thermal stresses. The main objective of this work is mathematical modeling of temperature stresses of fuel elements of cylindrical and elliptical cross-section reactors. Based on mathematical modeling, it was shown that the level of thermal stresses arising during the transition from a circular cross-section to an elliptical one decreases. The optimal size of this section was also obtained. [ABSTRACT FROM AUTHOR]

In this article, attention was paid to the mathematical modeling of the plasma temperature field under boundary conditions of the third kind. The simulation of the thermal process is based on the numerical integration of the thermal conductivity equation. This takes into account the change in the thermal conductivity of the plasma and convective heat transfer. Based on the obtained result, the behavior of the temperature field is analyzed. [ABSTRACT FROM AUTHOR]