Method of identification of non-stationary thermal processes in multilayer structures

1Matsevity, Yu.M, 2Sirenko, VN, 1Kostikov, AO, 1Safonov, NA, 1Ganchin, VV
1A. N. Podgorny Institute for Mechanical Engineering Problems of the NASU, Kharkiv, Ukraine
2Yangel Yuzhnoye State Design Office, Dnipro, Ukraine
Space Sci. & Technol. 2020, 26 ;(1):79-89
Publication Language: Russian
In the article, the method of A. N. Tikhonov with an effective algorithm for finding a regularization parameter is used to obtain a stable solution of the inverse problem of heat conduction (IPHC). Three inverse problems are considered. The first two determine the heat fluxes in the composite body with ideal and real thermal contact. In the third IPHC, the thermal contact resistance is determined with real thermal contact.
              The desired heat fluxes in multilayer bodies are represented as linear combinations of third-degree Schönberg splines with unknown coefficients, which are calculated by solving a system of linear algebraic equations. This system is a consequence of the necessary condition for the minimum of the functional based on the principle of least squares of the deviation of the simulated temperature from the temperature obtained as a result of a thermophysical experiment. To regularize IPHC solutions, a stabilizing functional with a regularization parameter as a multiplicative factor is used. It is the sum of the squares of the heat fluxes, their first and second derivatives with the corresponding multipliers. The regularization parameter search is performed using an algorithm similar to the non-linear equation root search algorithm.
Keywords: A. N. Tikhonov’s regularization method, approximation, functional, heat flow, identification, inverse heat conduction problem, regularization parameter, Schönberg spline of the third degree, stabilizer, thermal contact resistance
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