On the Identifiability of Thermal Conductivities Components of Composite Materials through an Optimum Experiment: a Numerical Investigation

A plane-source method-based optimum experiment useful to estimate simultaneously the out-of- and in-plane thermal conductivities, namely kx and ky , of composite materials is numerically simulated through a FEM (Finite Element Method) model. The experimental apparatus here investigated consists of a thin electrical heater put in contact with two larger samples of the same material and thickness. Moreover, temperature measurements useful for the estimation procedure are obtained exclusively from the unheated surface of the sample which is subjected to free convection with the surrounding air. For this reason non contact measuring techniques are here involved. This experimental set-up was previously optimized through a D-optimization criterion, known as Δ+ criterion, in terms of the heating and experiment times, the sample aspect ratio as well as the width of the heated region. An iterative experimental procedure based on the optimum experiment times is applied starting from a guess experiment, as they are not known beforehand. Two experiments are simulated in sequence to obtain reliable estimates of the unknowns. To this aim, the thermal behaviour of the composite sample is modelled through a two-dimensional orthotropic heat conduction model available in the literature, whereas the temperature measurements at the sample backside are simulated through a three-dimensional Finite Element (FE) model by adding random errors. Then the Gauss-Newton algorithm for parameter estimation is applied to retrieve simultaneously the conductivities kx and ky of the composite and the heat transfer coefficient at the sample backside.