Mahmood, MS and Lesnic, D orcid.org/0000-0003-3025-2770 (2019) Identification of conductivity in inhomogeneous orthotropic media. International Journal of Numerical Methods for Heat and Fluid Flow, 29 (1). pp. 165-183. ISSN 0961-5539
Abstract
Purpose: The purpose of this paper is to solve numerically the identification of the thermal conductivity of an inhomogeneous and possibly anisotropic medium from interior/internal temperature measurements.
Design/methodology/approach: The formulated coefficient identification problem is inverse and ill-posed, and therefore, to obtain a stable solution, a non-linear regularized least-squares approach is used. For the numerical discretization of the orthotropic heat equation, the finite-difference method is applied, while the non-linear minimization is performed using the MATLAB toolbox routine lsqnonlin.
Findings: Numerical results show the accuracy and stability of solution even in the presence of noise (modelling inexact measurements) in the input temperature data.
Research limitations/implications: The mathematical formulation uses temporal temperature measurements taken at many points inside the sample, and this may be too much information that is provided to identify a space-wise dependent only conductivity tensor.
Practical implications: As noisy data are inverted, the paper models real situations in which practical temperature measurements recorded using thermocouples are inherently contaminated with random noise.
Social implications: The identification of the conductivity of inhomogeneous and orthotropic media will be of great interest to the inverse problems community with applications in geophysics, groundwater flow and heat transfer.
Originality/value: The current investigation advances the field of coefficient identification problems by generalizing the conductivity to be anisotropic in addition of being heterogeneous. The originality lies in performing, for the first time, numerical simulations of inversion to find the orthotropic and inhomogeneous thermal conductivity from noisy temperature measurements. Further value and physical significance are brought in by determining the degree of cure in a resin transfer molding process, in addition to obtaining the inhomogeneous thermal conductivity of the tested material.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Emerald Publishing Limited. This is an author produced version of a paper published in International Journal of Numerical Methods for Heat & Fluid Flow. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Regularization; Inverse problem; Non-linear least-squares; Orthotropic and inhomogeneous media |
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: | 15 Jan 2018 14:53 |
Last Modified: | 13 Feb 2019 16:10 |
Status: | Published |
Publisher: | Emerald |
Identification Number: | 10.1108/HFF-11-2017-0469 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:126183 |