Proceedings of the International scientific and practical conference ―Science at the Frontier of Civilizations: Challenges and Perspectives‖ (December 27-29, 2025) / Publisher website: www.naukainfo.com. – Helsinki, Finland, 2026. – 252 p.

188 heterogeneity, an exact formulation of the temperature field problem leads to substantial mathematical difficulties. At the same time, determining the full temperature field of the rotor barrel is not necessary for calculating rotor deflections, because only integral temperature characteristics are involved in the deflection equations. This work is devoted to the development of a methodology for studying the influence of local overheating on the characteristics of the temperature field and the resulting deformations of a straight rod with a multiply connected cross section, with application to the analysis of thermal deflections and vibration levels of a turbogenerator rotor. In this study, a three-dimensional non-stationary heat conduction problem for a straight rod with a multiply connected cross section is reduced to a one-dimensional problem. The formulation is expressed in terms of the average temperature and temperature analogs of bending moments under conditions of Newtonian convective heat transfer on the external surface and imperfect thermal contact on the surfaces of longitudinal cutouts (slots) interacting with surrounding media. The corresponding boundary and initial conditions are formulated. The derived heat conduction equations for a rod with a multiply connected cross section are used to determine the temperature field of the barrel of a TGV-500-4 turbogenerator rotor. For this purpose, the rotor barrel is modeled as a straight hollow rod with 56 longitudinal rectangular slots defined in a polar coordinate system. Convective heat exchange conditions are applied on the outer and inner cylindrical surfaces of the rod. Heat transfer through intermediate layers of different thicknesses and thermal conductivities occurs on the slot surfaces. In the absence of overheating, the temperatures of the media in all slots are assumed to be identical. In the case of overheating in one or several slots, the temperature in these slots is assumed to increase to a certain level. In the considered case, due to the symmetry of the rotor barrel cross section with respect to the selected coordinate system, the system of heat conduction equations is significantly simplified. The solution of this system of differential equations is