Identification of conductivity in inhomogeneous
orthotropic media

Mahmood, MS; Lesnic, D

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.

Citation

orthotropic media. International Journal of Numerical Methods for Heat and Fluid Flow, 29(1), 165-183. https://doi.org/10.1108/HFF-11-2017-0469

• Journal Article Type: Article
• Acceptance Date: Jan 10, 2018
• Online Publication Date: Oct 30, 2018
• Publication Date: Oct 30, 2018
• Deposit Date: Jan 11, 2018
• Publicly Available Date: Nov 9, 2018
• Journal: International Journal of Numerical Methods for Heat and Fluid Flow
• Print ISSN: 0961-5539
• Publisher: Emerald
• Volume: 29
• Issue: 1
• Pages: 165-183
• DOI: https://doi.org/10.1108/HFF-11-2017-0469
• Publisher URL: https://doi.org/10.1108/HFF-11-2017-0469
• Related Public URLs: http://www.emeraldinsight.com/journal/hff
• Additional Information: Funders : Engineering and Physical Sciences Research Council (EPSRC); Projects : Robustness-performance optimisation for automated composite manufacture; Grant Number: EP/K-31430/1