On the effect of heater heat capacity on thermal conductivity components estimation of composite materials when using the plane source method

The orthotropic behaviour of unidirectional fibre-reinforced composites is fully described by the out-of-plane thermal conductivity kx (in the perpendicular-to-fibre direction) and the in-plane thermal conductivity ky (in the along-fibre direction). The plane-source method [1] is a promising transient method to estimate simultaneously both these conductivity components. In particular, the experimental device here investigated consists of a flexible, thin electrical heater put in contact with two identical, larger samples of composite material. Additionally, temperature measurements involved in the estimation procedure may be obtained from the unheated surface of the sample through non-contact measuring techniques. For this reason the sample backside is subjected to free convection with the surrounding air. In this work the effect of the heater heat capacity on the estimates of the unknown parameters (i.e., kx, ky and the heat transfer coefficient h at the sample backside) is investigated when the tested sample is a fibre-reinforced-polymer (FRP) composite, and the Gauss-Newton method [2] for parameter estimation is used. For this purpose temperature measurements are simulated through a 3D FEM model, including both the heater and the insulating material around all the lateral boundaries of the experimental set-up. Random errors are then added to the numerical model results to simulate real temperature measurements. On the contrary, the thermal model describing the behaviour of the sample, completely neglects the presence of the heater. In fact, it considers only a 2D slab (sample) partially heated at one boundary, and exposed to free convection at the other one. Note that the exact analytical solution is already available in the literature [3, 4]. Then, the heater heat capacity effects are taken into account by applying the approximation error model (AEM) [5] to correct the original thermal model (reduced model). Results show that, although the heater thickness is very small, its heat capacity significantly the estimates, even when it is less than 10% of the sample heat capacity (see Table 1). As shown in this table, the AEM can improve the estimates of all the unknown parameters by compensating the modelling errors related to the heater thermal inertia.