Abstract
Technological processes in the energy sector and engineering require the calculation of temperature regime of functioning of different constructions. Mathematical model of thermal loading of constructions is reduced to a non-stationary initial-boundary value problem of thermal conductivity. The article examines the formulation of the non-stationary initial-boundary value problem of thermal conductivity in the form of a boundary integral equation, analyzes the singular equation and builds the fundamental solution. To build the integral representation of the solution the method of weighted residuals is used. The correctness of the obtained integral representation of the solution in Minkowski space is confirmed. Singularity of the fundamental solution is investigated. The boundary integral equation and fundamental solution for axially symmetric domain for internal problem is built. The results of the article can be useful for numerical implementation of boundary element method.
Highlights
Intensive non-stationary thermal load of metal constructions can cause damage and destruction
The aim of this study is to obtain an integral representation of the solution in the Minkowski space, that allows to get a solution in the form of the boundary integral equation for a boundary value problem
This approach required the additional study of the behavior of the fundamental solution, and the interpretation of singular integrals in the boundary integral equation
Summary
Intensive non-stationary thermal load of metal constructions can cause damage and destruction. Processes in energy and engineering provide regular and emergency changes of temperature regimes Since cylindrical structures, such as pipelines, reactor vessel, constitute a substantial part of the production elements, calculation of critical temperature modes of their operation is important. Calculations and control of real constructions require the development of efficient numerical methods that allow to evaluate the behavior of structures under the influence of intense thermal loads in real time. One of these methods is the boundary element method that is one of numerous implementations of the method of boundary integral equations [5,6,7,8,9]
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