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 TVT, 2017, Volume 55, Issue 4, Pages 564–569 (Mi tvt10746)

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.

 Funding Agency Grant Number Russian Science Foundation 16-19-10340

DOI: https://doi.org/10.7868/S0040364417040068

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English version:
High Temperature, 2017, 55:4, 549–554

Bibliographic databases:

UDC: 536.21
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

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. F. Formalev, S. A. Kolesnik, “Temperature-dependent anisotropic bodies thermal conductivity tensor components identification method”, Int. J. Heat Mass Transf., 123 (2018), 994–998
2. V. F. Formalev, E. L. Kuznetsova, E. L. Kuznetsova, “Mathematical modeling of the Stefan's problems with the determination of the coordinates and the velocities of the dynamically moving borders of phase transformations”, Period. Tche Quim., 15:1 (2018), 377–389
3. V. A. Ripetskiy, I. T. Mirolyubova, S. A. Freylekhman, “Analysis of factors that determine the possibility for automation of smoothing of product electronic model, obtained through topological optimization for the purpose of its use in the technological preparation of additive manufacturing”, Period. Tche Quim., 15:1 (2018), 405–413
4. V. F. Formalev, S. A. Kolesnik, E. L. Kuznetsova, “Analytical study on heat transfer in anisotropic space with thermal conductivity tensor components depending on temperature”, Period. Tche Quim., 15:1 (2018), 426+
5. V. F. Formalev, S. A. Kolesnik, E. L. Kuznetsova, “Wave heat transfer in the orthotropic half-space under the action of a nonstationary point source of thermal energy”, High Temperature, 56:5 (2018), 727–731
6. V. F. Formalev, S. A. Kolesnik, E. L. Kuznetsova, “Effect of components of the heat conductivity tensor of heat-protection material on the value of heat fluxes from the gasdynamic boundary layer”, High Temperature, 57:1 (2019), 58–62
7. A. G. Vikulov, A. V. Nenarokomov, “Refined solution of the variational problem of identification of lumped parameter mathematical models of heat transfer”, High Temperature, 57:2 (2019), 211–221
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