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.
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.
Numerical results show the accuracy and stability of solution even in the presence of noise (modelling inexact measurements) in the input temperature data.
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.
As noisy data are inverted, the paper models real situations in which practical temperature measurements recorded using thermocouples are inherently contaminated with random noise.
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.
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.
