Optimal Experiment Design for Thermal Property Measurement of Orthotropic Materials using Infrared Thermography

The optimal set-up for a two-dimensional (2D) transient heat conduction experiment aimed at estimating simultaneously the thermal properties of orthotropic materials when using infrared (IR) thermography is designed. To this aim, a D-optimum criterion [1-2] ensuring the minimization of the confidence region of the estimated parameters is applied to define the optimum heating and experiment times. The optimal experiment is also sought in terms of the aspect ratio of the sample and the width of the heated region. In fact, the experimental apparatus here considered consists of a thin electrical heater between two larger samples of the same material and thickness. Moreover, temperature measurements useful for the estimation procedure are obtained non-intrusively from the unheated surface of the sample (exposed to the environment) using an IR camera [3]. For this reason, the heat transfer coefficient (h) is regarded as an unknown of the inverse problem, as well as the directional thermal conductivities (kx and ky) and volumetric heat capacity of sample (C). The 2D heat conduction problem is modeled through a rectangular plate (i.e., the sample) partially heated at the front boundary through a surface heat flux, while only the opposite boundary is subject to convection with the ambient air (all the other boundaries are kept insulated). Once the temperature solution to this problem is obtained starting from a generalized analytical solution available in the literature [4], the superposition principle is also applied to account for a finite heating period. Then, the so-called scaled sensitivity coefficients of temperature with respect to the parameters of interest are computed, and a sensitivity analysis is performed (see Fig. 1). Finally, the optimal experiment is designed through the so-called Δ+ criterion [1-2].