Linear and nonlinear mathematical models for determining the temperature field and subsequently analyzing temperature regimes in isotropic spatial media with semi-through foreign inclusions subjected to internal and external thermal loads are developed.
A study of the temperature field in metal structures of transport facilities with corrosion-resistant coating under the conditions of changes in ambient temperature has been conducted. The results of experimentally determined temperature distribution in the surface vicinity of a galvanized metal sheet are presented. The data were obtained over the day at positive and negative surface temperatures. Given a generalized boundary condition for the heat conduction problem, with a solid heated by a localized heat flow through a thin coating, there has been obtained and ana
Linear and nonlinear mathematical models for determining the temperature field, and later the analysis of temperature regimes in isotropic spatial inhomogeneous media exposed to internal and external thermal loads have been developed. To do this, the thermal conductivity for such structures is described as a whole using symmetric unit functions, which allows us to consider boundary thermal conductivity problems with one linear and nonlinear differential equation of thermal conductivity with discontinuous coefficients and linear and nonlinear boundary conditions on boundary surfaces.
Nonlinear mathematical models for the analysis of temperature regimes in a thermosensitive isotropic plate heated by locally concentrated heat sources have been developed. For this purpose, the heat-active zones of the plate are described using the theory of generalized functions. Given this, the equation of thermal conductivity and boundary conditions contain discontinuous and singular right parts. The original nonlinear equations of thermal conductivity and nonlinear boundary conditions are linearized by Kirchhoff transformation.
The results of the mathematical modeling and experimental studies for the stress-strain state of the annular section of the reinforced concrete shell with the protective structure are presented. Computer simulation has been formulated as a stationary temperature problem. The distribution of deformations and stresses is shown using the equations of the elastic theory. A comparison of theoretical dependences on the results of experimental studies of physical models is given.
A mathematical model of heat exchange analysis between an isotropic two-layer plate heated ba point heat source concentrated on the conjugation surfaces of layers and the environment has been developed.
Previously developed  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.
Goal. Investigation of the conditions of formation of operational tightness of the end of the output capillary - the rod of the ionization chamber with simultaneous provision of the temperature regime in the process of formation of the welded joint.
Practical importance. The analytical and numerical results obtained can be used in the study of the stress state and, respectively, to evaluate the strength and stiffness of curvilinear tubular structural elements, in particular, the pipeline bends and pipes of economizers.
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.