Retrieving thermal conductivity of the solid sample using reduced order model inverse approach

Purpose - Prompted by the reliability and robustness of the previously proposed method of non-destructive measurement of thermal conductivity (TC) for anisotropic materials, the enhanced approach is presented in this study. The main improvement lies inthe substitution of the analytic solution of direct problem solver with a numerical one. This solver, used during the inverse procedure that fits measurement data into simulated ones, is proposed to be a numerical one (finite volume method). Moreover, the purpose of this study is to show the applicability of the reduce order model for retrieving thermal conductivity of solid body. Design/methodology/approach - In the proposed methodology, both the laser heat source and temperature measurements are performed on the same side of the sample material, which is the main difference with respect to the classic Parker flash method. To speed up the computational time, the full numerical model used in the course of inverse solution is replaced by the proper orthogonal decomposition (POD)-radial basis function (RBF) reduced order model, which is fast and accurate. Findings - The TCs measured using the proposed methodology are in good agreement with the well established (but destructive) measurement methods. The advantage of the proposed approach lies in the optimal approximation properties of the POD approximation basis used in reduced order model, as well as in its regularization properties. Practical implications - The proposed technique has high application potential in the design of novel apparatus for non-destructive measurement of TCs for both isotropic and anisotropic materials. Originality/value - This is the first time when the POD-RBF reduced order model is used in the procedure of non-destructive TC measurement for anisotropic bodies.