## 4 Results and Discussions
Despite this, nickel's high thermal conductivity and thermal diffusivity result in a uniform temperature distribution across sensor cross-sections over longer timescales, even when the sensor exists significant current density gradients, as shown in Figure 4b. Secondly, the structural design of the double helix curve is conducive to minimizing or completely counteracting the formation of a magnetic field around the nickel strip induced when a DC current flows through it. In this way, any AC impedance that may arise is canceled out. This is especially important for minimizing the rise time of the current pulse through the sensor at the beginning of the transient recording and for collecting accurate data. In the transient simulation, the TPS method is simulated by placing the detector between two identical media for testing (structure shown in Figure 2a). Since the actual sample size is not infinite in the TPS method, the measurement time needs to be limited to avoid the influence of boundary effects [63; 64] on the simulation results. In this simulation,  
Figure 6: (**a**,**b**) illustrate the variation curves of relative resistance and the number of mesh elements for Type I and Type II TPS sensors, respectively. The red line indicates the variation in the number of mesh elements, while the black line represents the change in the relative resistance of the sensors. the radius of sensors were set to 6.4 mm and 14 mm, respectively. The test samples were two identical PMMA blocks, each with a height of 20 mm and a radius of 25 mm. The simulation parameters are set to correspond to the actual experiment by selecting the appropriate heating current and measurement time. During the simulation, the temperature rise curves of the sensors were documented and subsequently compared with the recorded experimental data. Here, the calculation of the thermal properties of the material relies on the transient data obtained from the simulation by fitting Equation (4). Figure 7 presents the experimental and simulation temperature rise curves over time for the two types of sensor under different power levels. The experimental data points represent the average of three tests conducted under the same conditions, with a total uncertainty of less than 7%. The corresponding error bands are also plotted alongside the experimental data. In Figure 7a, the maximum temperature rise error between the experimental and simulation results is less than 0.2 K, while in Figure 7b, it is less than 0.3 K, indicating a high degree of consistency between the experimental and simulation results. Furthermore, it is noteworthy that the increase in power produced similar effects in both simulations and experiments. However, it is important to emphasize that different power levels were applied to the two sensors in order to achieve comparable temperature changes. This adjustment ensures that the temperature variations observed in each sensor are directly comparable, despite the different power levels used. Specifically, larger sensors require more power to achieve the same temperature rise. Subsequently, additional samples were subjected to further testing using the aforementioned model, the results of which are presented in Figure 8 below. Figure 8a,b illustrate the temperature rise curves over time for the stainless steel and ceramic materials, respectively. Ultimately, Equation (9) was employed for the purpose of fitting, with the objective of calculating the thermal performance parameters of PMMA, stainless steel, and ceramics, respectively. The relative errors were then calculated based on the reference values, and the results are presented in Table 3. The average relative error of both sensors is less than 3%. Figure 7: (**a**,**b**) show the temperature variation over time for Type I and Type II sensors, respectively. The solid lines represent the simulation curves, and the data points correspond to the experimental measurements.