(untitled) (International Journal of Mathematics and Physics, 2023)
Many parts of internal combustion engines, gas turbine power plants, steam generators of nuclear power plants and manufacturing industries experience thermal effects of various forms. At the same time, a process of thermal expansion occurs on these parts and, as a result, a thermal stress-strain state arises on them with a value that in some cases can exceed the limit value. Therefore, knowledge of the stationary field of temperature distribution in the volume of partially thermally insulated parts of a complex configuration in the presence of a heat flux and heat exchange in parts of its surface is an urgent task. At the same time, it is very difficult to take into account all inhomogeneous boundary conditions when solving the problem of stationary heat conduction. Therefore, a new numerical method is proposed, based on the law of conservation of total thermal energy in combination with the finite element method. In this case, the procedure for minimizing the total thermal energy is used using quadrilateral bilinear finite elements. Partial thermal insulation, heat flux supplied to the local surface, and the process of heat exchange through the local surface area and ambient temperature are taken into account. Nodal temperature values are determined.