Improving the Accuracy of Transient Plane Source Thermal Conductivity Measurements: Novel Analytical Models, Fitting Approaches, and Systematic Sensitivity Analysis

Accurate thermal conductivity (λ) measurement is critical for optimizing material performance in applications where effective heat exchange and dissipation are paramount. Among contact methods, the transient plane source (TPS) method (ISO 22007-2:2022) is widely used for its efficiency and versatility, particularly for bulk solid samples. However, we reveal that for high-λ materials (λ > 30 W/(m·K)), TPS measurements can suffer from significant systematic errors—up to 97%—due to the limitations of traditional analytical models and fitting methods in addressing sensor/sample interface thermal resistance (R_c) and heat conduction within the sensor. Furthermore, the lack of in-depth investigation into measurement sensitivity and parameter correlations in the TPS method hampers the accurate fitting and identification of sample λ, particularly under the influence of other unknown parameters such as sample heat capacity (C) and R_c. This study addresses these challenges by: (1) developing two novel analytical models, termed realistic sensor model (RSM) and multilayer model (MLM), that account for heat transfer within the sensor and the R_c effect, both of which are neglected in the traditional model but crucial in the TPS study of high-λ materials; (2) proposing an innovative temperature derivative-based analysis approach using nonlinear regression (NR) to effectively suppress the influence of the R_c and the sensor geometry, which outperforms the conventional iterative linear regression of the raw temperature data; and (3) systematically analyzing the sensitivities of key parameters in different analytical and numerical models as well as parameter relationships via singular value decomposition (SVD) of the sensitivity matrix, providing deeper insights into the selection of the optimal time interval for fitting sample λ and C.

To reveal the limitations of traditional models and regression while evaluating our new analytical models and fitting methods, a reliable 3D finite element model (FEM) that replicates the actual TPS sensor with bifillar spiral heater was developed . The TPS experiments on four representative materials with significantly varied λ (polymethyl methacrylate, borosilicate glass, 304 stainless steel, and aluminum) and simulated TPS data for a broad range of materials (λ in 0.1–400 W/(m·K)) from our FEM simulations are utilized to systematically assess the performance of the proposed analytical model and fitting methods. We demonstrate that the proposed derivative-based approach combined with the new analytical models using two-parameters NR (NR-2) exhibits high robustness against R_c and improves the accuracy of the fitted λ, reducing errors from 50-97% to < 10% for high-λ material, which remain robust against significant variation in the input R_c (by up to ≈60 times), outperforming the iterative NR fitting involving R_c based on the raw temperature data. For materials with known C, the one-parameter NR fitting of λ can improve computational efficiency by 30-80% compared to NR-2, while maintaining the fitting error for λ of high-λ materials below 5%. To relax the requirement of large sample size in the derivative method, a ratio-based analysis was also developed. This work offers a comprehensive framework to improve the accuracy of the TPS measurement in real-world applications, especially for high-λ materials.