Identification of conductivity in inhomogeneous orthotropic media
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 30 October 2018
Issue publication date: 29 January 2019
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.
Keywords
Acknowledgements
The authors would like to acknowledge the Engineering and Physical Sciences Research Council (EPSRC) grant EP\K – 31430/1 entitled “Robustness Performance Optimisation for Automated Composite Manufacture” for supporting this research.
Citation
Mahmood, M.S. and Lesnic, D. (2019), "Identification of conductivity in inhomogeneous orthotropic media", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 1, pp. 165-183. https://doi.org/10.1108/HFF-11-2017-0469
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited