Linear and nonlinear mathematical models for determining the temperature field and, subsequently, for analyzing temperature regimes in an isotropic plate due to near-surface thermal loading have been developed.
The linear and nonlinear mathematical models for determining the temperature field and subsequently analyzing temperature regimes in isotropic spatial media subjected to external local thermal load are developed. In the case of a nonlinear boundary value problem, the Kirchhoff transform is applied to linearize the nonlinear heat conduction equation and nonlinear boundary conditions, resulting in a linearized second-order partial differential equation with a discontinuous right-hand side and partially linearized boundary conditions.
Linear and non-linear mathematical models for the determination of the temperature field, and subsequently for the analysis of temperature regimes in the braking systems of vehicles, which are geometrically depicted as isotropic spatial heat-active media that are subject to internal local thermal heating, have been developed. With the use of classical methods, it is not possible to obtain analytical solutions of linear and nonlinear boundary value problems of mathematical physics in a closed form.
Linear and non-linear mathematical models for the determination of the temperature field, and subsequently for the analysis of temperature regimes in isotropic spatial heat-active media subjected to internal local heat load, have been developed.
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.