## 5 Conclusions  
The aim of this paper is to simulate the working principle of the TPS method by means of the finite element method in order to create a three-dimensional model for test use. The temperature rise profile of the sample is reproduced from this model. Additionally, this paper analyzes the current density distribution in the nickel metal strip within the sensor and its relationship with the heat source distribution through both transient and steady-state studies. The current density tends to increase along the inside of the bar curve. The temperature rise data obtained from the simulation closely match the corresponding experimental data for PMMA. The model is then used again to simulate tests on other materials and the corresponding thermal performance parameters are calculated, and these also match the reference results. This simulation has the potential to be utilized for future geometry and parameter estimate optimization, and provides a theoretical reference for detector design. Although we performed a detailed modeling of the transient plane source (TPS) method using finite element analysis and achieved good agreement with experimental data, certain limitations remain. Specifically, the model assumes uniform material properties, while in practical applications, materials may exhibit inhomogeneities, defects such as bubbles or impurities, which could influence thermal conductivity and lead to discrepancies between experimental results and simulation outcomes. For future research directions, we propose further exploration in the following areas: First, the scope of the study can be expanded to assess the thermal conductivity of different types of materials, particularly composite materials with complex structures or specialized properties. Second, the development of hybrid approaches that integrate data-driven models with  
Figure 8: (**a**) Temperature rise curves of stainless steel with different sensors. (**b**) Temperature rise curves of ceramic with different sensors. experimental techniques should be pursued to enhance the accuracy and efficiency of thermal conductivity measurements. Third, the impact of environmental factors should be considered to investigate how material properties vary under different conditions, thereby providing a more robust theoretical and experimental foundation for the application of new materials. Finally, we recommend establishing standardized testing procedures to enable the consistent comparison and validation of results across different laboratories and research teams. Conceptualization, J.S., S.Z., P.S. and Z.Y. ; data curation, J.S., S.Z., P.S. and Q.Z. ; formal analysis, J.S., S.Z., P.S. and Z.Y. ; methodology, J.S., S.Z., P.S., Z.Y., Y.Y. and Q.Z. ; resources, J.S., S.Z., P.S., Y.Y. and Z.Y. ; data curation, J.S., S.Z. and P.S. ; writing-original draft preparation, J.S., S.Z. and P.S. ; writing-review and editing, J.S., S.Z., P.S. and Z.Y. All authors have read and agreed to the published version of the manuscript. The authors are grateful to the support provided by the National Natural Science Foundation of China (Nos. 51606158, 11604311, 12074151); the funding from the Natural Science Foundation of Fujian Province (2022J011102, 2022H0048); the funded from the Guangxi Science and Technology Base and Talent Special Project (No. AD21075009); the funding from the Sichuan Science and Technology Program (No. 2021 JDRC0022); the funding from the Natural Science Foundation of Fujian Province (2022J011102); the funding from the Research Project of Fashu Foundation (MFK23006); the funding from the Open Fund of the Key Laboratory for Metallurgical Equipment and Control Technology of Ministry of Education in Wuhan University of Science and Technology, China (No. MECOF2022B01; MECOF2023B04); the funding from the Project supported by Guangxi Key Laboratory of Precision Navigation Technology and Application, Guilin University of Electronic Technology (No. DH202321). Not applicable.