Model-based methodology coupled with a Laser-based experiment for non-destructive thermal parameter estimation of an Epoxy nanocomposite

This article addresses the estimation of the thermal conductivity k and the specific heat capacity Cp of a synthetic nanocomposite, by coupling a laser-based experiment and a reduced model-based inverse problem solved via a Finite Element Method (FEM) approach. The associated multiphysics problem can be described as an optical-radiative-thermal coupled process where a laser source is irradiating the sample corresponding to an Epoxy-Based Vitrimer (EV) with dispersed gold nanoparticles (NPs). A 1D reduced model for an infinite slab (having both boundaries subjected to natural convection and under certain conditions on both experiment and material properties) has been used to solve the forward radiative transfer problem involved, in order to achieve an initial approximation for the equivalent thermal source Q. This approximation is then used in the heat transfer equation, whose solution is computed using the finite element method (FEM). The corresponding statistical solution for the thermal conductivity k and the heat capacity Cp is calculated by the inversion of the T-thermocouple temperature time series measured at the center of the irradiated specimen, using a stochastic version of the Levenberg-Marquardt algorithm by embedding the algorithm inside a Monte Carlo routine. Reduced models have been analyzed for 1D and 2D reduced geometries as well as approximations for Q in the 3D case. Results show a confidence interval for the achieved estimates of the thermal parameters in a good agreement to the Differential Scanning Calorimetry (DSC) referential values. As a conclusion, even when the performed laser remote heating experiment has been developed as a self-healing process, it also appears to be a very promising Non-Destructive Testing (NDT) methodology for retrieving the thermal parameters along with the proposed computational approach in some thermosetting polymers, such as the EV studied here.