Identification of the Thermal Conductivity Coefficient for Quasi-Stationary Two-Dimensional Heat Conduction Equations
Article
First Online:
Received:
The problem of identifying the time-dependent thermal conductivity coefficient in the initial–boundary-value problem for the quasi-stationary two-dimensional heat conduction equation in a bounded cylinder is considered. It is assumed that the temperature field in the cylinder is independent of the angular coordinate. To solve the given problem, which is related to a class of inverse problems, a mathematical approach based on the method of conjugate gradients in a functional form is being developed.
Keywords
inverse heat conduction problem quasi-stationary heat conduction equation thermal conductivity coefficient method of conjugate gradients functional identificationPreview
Unable to display preview. Download preview PDF.
References
- 1.Yu. M. Matsevity, Inverse Heat Conduction Problems, in 2 vols., Vol. 1. Methodology, Institute for Problems in Mechanical Engineering, National Academy of Sciences of Ukraine, Kyiv (2008).Google Scholar
- 2.V. G. Rudychev, S. V. Alekhina, V. N. Goloshchapov, et al. (Yu. M. Matsevityi and I. I. Zalyubovskii Eds.), Safe Storage of Spent Nuclear Fuel [in Russian], Kharkovsk. Nats. Univ. im. V. N. Karazina, Kharkov (2013).Google Scholar
- 3.O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, Extreme Methods of Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1988).MATHGoogle Scholar
- 4.V. T. Borukhov and V. I. Timoshpol’skii, Functional identification of the nonlinear thermal-conductivity coefficient by gradient mehtods. I. Conjugate operators, J. Eng. Phys. Thermophys., 78, No. 4, 695–702 (2005).CrossRefGoogle Scholar
- 5.V. T. Borukhov, I. V. Gaishun, and V. I. Timoshpol′skii, Structural Properties of Dynamic Systems and Inverse Problems of Mathematical Physics [in Russian], Belaruskaya Navuka, Minsk (2009).Google Scholar
- 6.V. T. Borukhov, V. A. Tsurko, and G. M. Zayats, The functional identification approach for numerical reconstruction of the temperature-dependent thermal-conductivity coefficient, Int. J. Heat Mass Transf., 52, 232–238 (2009).CrossRefMATHGoogle Scholar
- 7.S. Alyokhina and A. Kostikov, Equivalent thermal conductivity of the storage basket with spent nuclear fuel of VVER-1000 reactors, Kerntechnik, 79, No. 6, 484–487 (2014).CrossRefGoogle Scholar
- 8.S. Alyokhina, V. Goloshchapov, A. Kostikov, and Yu. Matsevity, Simulation of thermal state of containers with spent nuclear fuel: Multistage approach, Int. J. Energy Res., 39, Issue 14, 1917–1924 (2015).CrossRefGoogle Scholar
- 9.Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Conjugate Operators [in Russian], Naukova Dumka, Kiev (1965).MATHGoogle Scholar
Copyright information
© Springer Science+Business Media, LLC, part of Springer Nature 2017