Identification of conductivity in inhomogeneous orthotropic media

Mahmood, MS and Lesnic, D 2018, 'Identification of conductivity in inhomogeneous orthotropic media' , International Journal of Numerical Methods for Heat and Fluid Flow .

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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, in order to obtain a stable solution, a nonlinear regularized least-squares approach is employed. For the numerical discretisation of the orthotropic heat equation, the finite-difference method is applied, whilst the nonlinear 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 tem- perature measurements taken at many points inside the sample and this may be too much information that is provided to identify a spacewise dependent only conductivity tensor.
Practical implications - Since noisy data are inverted, the study 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 generalising the conductivity to be orthotropic in addition of being heterogeneous. The originality lies in performing, for the first time, numerical simulations of inver- sion to find the anisotropic and inhomogeneous thermal conductivity form noisy temperature measurements. Further value and physical significance is 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.

Item Type: Article
Schools: Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre (SIRC)
Journal or Publication Title: International Journal of Numerical Methods for Heat and Fluid Flow
Publisher: Emerald
ISSN: 0961-5539
Related URLs:
Funders: Engineering and Physical Sciences Research Council (EPSRC)
Depositing User: MS Mahmood
Date Deposited: 11 Jan 2018 12:02
Last Modified: 10 Nov 2018 08:47
URI: http://usir.salford.ac.uk/id/eprint/44932

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