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

This article is cited in 7 scientific papers (total in 7 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.

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


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

Bibliographic databases:

UDC: 536.21
Received: 14.06.2016

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
\by V.~F.~Formalev, S.~A.~Kolesnik
\paper On inverse boundary heat-conduction problems for recovery of heat fluxes to anisotropic bodies with nonlinear heat-transfer characteristics
\jour TVT
\yr 2017
\vol 55
\issue 4
\pages 564--569
\jour High Temperature
\yr 2017
\vol 55
\issue 4
\pages 549--554

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    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  crossref  isi  scopus
    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  isi
    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  isi
    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+  isi
    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  mathnet  crossref  crossref  isi  elib
    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  mathnet  crossref  crossref  isi  elib
    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  mathnet  crossref  crossref  isi  elib
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