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An iterative finite-element algorithm for solving two-dimensional nonlinear inverse heat conduction problems
KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.ORCID iD: 0000-0001-8743-7157
KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering.
KTH, School of Engineering Sciences (SCI), Physics, Nuclear Engineering. Warsaw University of Technology, Poland.ORCID iD: 0000-0001-5595-1952
2018 (English)In: International Journal of Heat and Mass Transfer, ISSN 0017-9310, E-ISSN 1879-2189, Vol. 126, p. 281-292Article in journal (Refereed) Published
Abstract [en]

It is often useful to determine temperature and heat flux in multidimensional solid domains of arbitrary shape with inaccessible boundaries. In this study, an effective algorithm for solving boundary inverse heat conduction problems (IHCPs) is implemented: transient temperatures on inaccessible boundaries are estimated from redundant simulated measurements on accessible boundaries. A nonlinear heat equation is considered, where some of the material properties are dependent on temperature. The IHCP is reformulated as an optimization problem. The resulting functional is iteratively minimized using a conjugate gradient method together with an adjoint (dual) problem approach. The associated partial differential equations are solved using the finite-element package FEniCS. Tikhonov regularization is introduced to mitigate the ill-posedness of the IHCP. The accuracy of the implemented algorithm is assessed by comparing the solutions to the IHCP with the correct temperature values, on the inaccessible boundaries. The robustness of our method is tested by adding Gaussian noise to the initial conditions and redundant boundary data in the inverse problem formulation. A mesh independence study is performed.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 126, p. 281-292
Keywords [en]
nonlinear inverse problem, Tikhonov regularization, finite element, FEniCS, adjoint
National Category
Energy Engineering
Identifiers
URN: urn:nbn:se:kth:diva-227719DOI: 10.1016/j.ijheatmasstransfer.2018.04.104ISI: 000442979300022Scopus ID: 2-s2.0-85047095749OAI: oai:DiVA.org:kth-227719DiVA, id: diva2:1205258
Funder
Swedish Radiation Safety Authority, 47385
Note

QC 20180530

Available from: 2018-05-12 Created: 2018-05-12 Last updated: 2018-09-19Bibliographically approved

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Bergagio, Mattia

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