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This article is cited in 25 scientific papers (total in 25 papers)
Heat and Mass Transfer and Physical Gasdynamics
On inverse boundary heat-conduction problems for recovery of heat fluxes to anisotropic bodies with nonlinear heat-transfer characteristics
V. F. Formalev, S. A. Kolesnik Moscow Aviation Institute (National Research University)
Abstract:
A closed method is proposed for recovering heat fluxes to anisotropic bodies under conditions of aero-gasdynamic heating from experimental temperature data at spatial-temporal nodes. The thermal protection of a body is made of anisotropic materials with components of thermal-conductivity tensor, which are dependent of temperature, i.e., are nonlinear. The method is based on approximating a spatial dependence of a heat flux by a linear combination of basis functions with sought coefficients (parameters), which are found by minimization of a quadratic functional of the residual (the discrepancy between experimental and theoretical temperature values) using the implicit method of gradient descent, as well as on constructing and numerically solving problems for the determination of sensitivity coefficients. To increase the degree of correctness of an inverse problem, along with a main functional, the regularizing functionals have been constructed and utilized on the basis of smoothness requirements for spatial functions of heat fluxes to have continuous first and second derivatives, which allowed heat fluxes with the coupled heat transfer to be recovered in the form of arbitrary functions: monotonic, nonmonotonic, having extrema, inflection points, etc. Numerous results of recovering heat fluxes to anisotropic bodies are obtained and discussed, with the regularization parameter being selected for every case.
Received: 14.06.2016 Accepted: 08.11.2016
Citation:
V. F. Formalev, S. A. Kolesnik, “On inverse boundary heat-conduction problems for recovery of heat fluxes to anisotropic bodies with nonlinear heat-transfer characteristics”, TVT, 55:4 (2017), 564–569; High Temperature, 55:4 (2017), 549–554
Linking options:
https://www.mathnet.ru/eng/tvt10746 https://www.mathnet.ru/eng/tvt/v55/i4/p564
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Abstract page: | 321 | Full-text PDF : | 89 | References: | 63 | First page: | 5 |
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