Zhuo, L, Lesnic, D orcid.org/0000-0003-3025-2770 and Meng, S (2020) Reconstruction of the heat transfer coefficient at the interface of a bi-material. Inverse Problems in Science and Engineering, 28 (3). pp. 374-401. ISSN 1741-5977
Abstract
The knowledge of heat transfer behaviour of composite thermal systems requires the characterization of the heat transfer coefficient at the contact interfaces between the constituent materials. The present work is devoted to investigating an inverse problem with generalized interface condition containing an unknown space- and time-varying interface coefficient from non-invasive temperature measurements on an accessible boundary. The uniqueness of the solution holds, but the problem does not depend continuously on the input measured temperature data. A new preconditioned conjugate gradient method (CGM) is utilized to address the ill-posedness of the inverse problem. In comparison with the standard CGM with no preconditioning, this method has the merit that the gradient of the objective functional does not vanish at the final time, which restores accuracy and stability when the input data is contaminated with noise and when the initial guess is not close to the true solution. Several numerical examples corresponding to linear thermal contact and nonlinear Stefan-Boltzmann radiation condition are tested for determining thermal contact conductance and Stefan-Boltzmann coefficient, respectively. The numerical results in both one- and two-dimensions illustrate that the reconstructions are robust and stable.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in Inverse Problems in Science and Engineering on 08 Feb 2019, available online: http://www.tandfonline.com/10.1080/17415977.2019.1574781. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Thermal contact conductance; Stefan-Boltzmann coefficient; preconditioning; conjugate gradient method; nonlinear inverse problem |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Jan 2019 10:22 |
Last Modified: | 09 Mar 2020 11:38 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/17415977.2019.1574781 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:141136 |