D-optimization of three-layer experimental set-ups for simultaneous estimation of transport thermal properties of FRP composites using contact and non-contact rear temperature measurements

A D-optimization problem, dealing with three-layer experimental set-ups for simultaneous estimation of the transport thermal properties of FRP composites, is faced. These experimental set-ups are two different configurations of the plane-source method, and they consist of a thin electrical heater placed between two larger composite specimens of the same thickness. Both set-ups are modeled through only one orthotropic rectangular plate (sample) partially heated at the front boundary through a surface heat flux (2D heat diffusion), while just the opposite boundary is subject to a third kind boundary condition. The related heat transfer coefficient simulates the operating conditions when recording temperature readings at the sample backside using either non-contact techniques or thermocouples. Indeed, in the first case it accounts only for free convection with the surrounding air, while in the latter it accounts for both an insulating material and convective heat transfer with the environment. This paper offers a systematic approach for the optimization of the whole experiment (i.e., the experimental variables and the set of unknown parameters) for thermal properties estimation of FRP composites. As the set-up optimization problem is often faced only partially by the experimentalists, the systematic approach here shown is the novelty of the work. In detail, the optimum set-up is designed for different thermal conductivity ratios of the sample through a D-optimization procedure, named Δ+ criterion. Its systematical application not only allows to find the optimum set of parameters to be estimated, but it also allows the heating and experiment times, sample aspect ratio, width of the heated region and measurement points location to be optimized. Expected standard deviations of the estimates are also computed. Optimization results show that the sample should be heated up to 80 % of its height, while the optimum sample aspect ratio is found to be related to the thermal conductivity ratio.