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.
The article considers the non-stationary initial-boundary problem of thermal conductivity in axially symmetric domain in Minkowski space, formulated as equivalent boundary integral equation. Using the representation of the solution in the form of a Fourier series expansion, the problem is reformulated as an infinite system of two-dimensional singular integral equations regarding expansion coefficients. The paper presents and investigates the explicit form for fundamental solutions used in the integral representation of the solution in the domain and on the border. The obtained results can be used in the construction of efficient numerical boundary element method for estimation of structures behavior under the influence of intense thermal loads in real-time.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.