OBTAINING AND INVESTIGATION OF THE INTEGRAL REPRESENTATION OF SOLUTION AND BOUNDARY INTEGRAL EQUATION FOR THE NON-STATIONARY PROBLEM OF THERMAL CONDUCTIVITY

Grigoriy Zrazhevsky, Vera Zrazhevska

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.


Keywords


initial-boundary problem of thermal conductivity; boundary integral equation; method of weighted residuals; fundamental solution

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DOI: http://dx.doi.org/10.21303/2461-4262.2016.00216

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Copyright (c) 2016 Grigoriy Zrazhevsky, Vera Zrazhevska

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ISSN 2461-4262 (Online), ISSN 2461-4254 (Print)