Skip to main content
Springer Nature Link
Log in

Identification of the thermal conductivity coefficient in two dimension case

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In the paper the problem of determining the thermal conductivity coefficient that depends on temperature is studied. The consideration is based on the mixed boundary value problem for the two-dimensional unsteady-state heat equation. The inverse coefficient problem is reduced to a variation problem. The mean-root-square deviation of the heat flux obtained by solving initial-boundary value problem from the experimental data on the boundary of the considered domain is used as the objective functional. The optimal control problem is solved numerically. The objective functional is minimized using the gradient methods. It is well known that it is very important for the gradient methods to determine accurate values of the gradients. For this reason, in this paper we used the efficient fast automatic differentiation technique, which gives the exact functional gradient for the discrete optimal control problem. The examples of solving the inverse coefficient problem confirm the efficiency of the proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Alifanov, O.M., Cherepanov, V.V.: Mathematical simulation of high-porosity fibrous materials and determination of their physical properties. High Temp. 47, 438–447 (2009)

    Article  Google Scholar 

  2. Czel, B., Grof, Gyula: Inverse identification of temperature-dependent thermal conductivity via genetic algorithm with cost function-based rearrangement of genes. Int. J. Heat Mass Transf. 55(15), 4254–4263 (2012)

    Article  Google Scholar 

  3. Cui, M., Yang, K., Xu, X.L., Wang, S.D., Gao, X.W.: A modified Levenberg-Marquardt algorithm for simultaneous estimation of multi-parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems. Int. J. Heat Mass Transf. 97, 908–916 (2016)

    Article  Google Scholar 

  4. Matsevityi, YuM, Alekhina, S.V., Borukhov, V.T., Zayats, G.M., Kostikova, A.O.: Identification of the thermal conductivity coefficient for quasi-stationary two-dimensional heat conduction equations. J. Eng. Phys. Thermophys. 90(6), 1295–1301 (2017)

    Article  Google Scholar 

  5. Evtushenko, YuG: Computation of exact gradients in distributed dynamic systems. Optim. Methods Softw. 9, 45–75 (1998)

    Article  MathSciNet  Google Scholar 

  6. Zubov, V.I.: Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation. Comp. Math. Math. Phys. 56(10), 1743–1757 (2016)

    Article  MathSciNet  Google Scholar 

  7. Albu, A.F., Evtushenko, Y.G., Zubov, V.I.: Identification of Discontinuous Thermal Conductivity Coefficient using Fast Automatic Differentiation, Conference Proceedings: Learning and Intelligent Optimization. Lecture Notes in Computer Science, vol. 10556, pp. 295–300. Springer, Cham (2017)

    Google Scholar 

  8. Zubov, V., Albu, A.: The FAD-methodology and recovery the thermal conductivity coefficient in two dimension case. Optim. Appl. 1987, 39–44 (2017)

    Google Scholar 

  9. Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker, New York (2001)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Alla Albu & Vladimir Zubov

  2. Moscow Institute of Physics and Technology, Moscow, Russia

    Vladimir Zubov

Authors
  1. Alla Albu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Vladimir Zubov
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Alla Albu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Albu, A., Zubov, V. Identification of the thermal conductivity coefficient in two dimension case. Optim Lett 13, 1727–1743 (2019). https://doi.org/10.1007/s11590-018-1304-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-018-1304-4

Keywords