Huntul, MJ, Hussein, MS, Lesnic, D orcid.org/0000-0003-3025-2770 et al. (2 more authors) (2019) Reconstruction of an orthotropic thermal conductivity from nonlocal heat flux measurements. International Journal of Mathematical Modelling and Numerical Optimisation, 10 (1). pp. 102-122. ISSN 2040-3607
Abstract
Raw materials are anisotropic and heterogeneous in nature, and recovering their conductivity is of utmost importance to the oil, aerospace and medical industries concerned with the identification of soils, reinforced fibre composites and organs. Due to the ill-posedness of the anisotropic inverse conductivity problem certain simplifications are required to make the model tracktable. Herein, we consider such a model reduction in which the conductivity tensor is orthotropic with the main diagonal components independent of one space variable. Then, the conductivity components can be taken outside the divergence operator and the inverse problem requires reconstructing one or two components of the orthotropic conductivity tensor of a two-dimensional rectangular conductor using initial and Dirichlet boundary conditions, as well as non-local heat flux over-specifications on two adjacent sides of the boundary. We prove the unique solvability of this inverse coefficient problem. Afterwards, numerical results indicate that accurate and stable solutions are obtained.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article is protected by copyright. This is an author produced version of a journal article published in the International Journal of Mathematical Modelling and Numerical Optimisation. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | inverse problem; orthotropic thermal conductivity; two-dimensional heat equation; nonlinear optimisation |
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: | 14 Jun 2019 12:55 |
Last Modified: | 26 Dec 2020 01:38 |
Status: | Published |
Publisher: | Inderscience Publishers |
Identification Number: | 10.1504/IJMMNO.2020.104327 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147209 |