## 2 Data Acquisition and Preprocessing
### Dataset Acquisition  
The temperature variation in the transcritical methane within the PCHE channels is significant, and the property changes along the corners of the regular hexagonal channels also require evaluation. Consequently, modeling and analyzing the entire PCHE channel as a single averaged sample is unreliable. This paper adopts a more reliable differential element analysis method. Considering the characteristics of the regular hexagonal geometry, the entire channel was uniformly divided into differential element segments at 1 mm intervals. The schematic diagrams of point sampling, division by temperature difference, and division by distance are illustrated in Figure 2.  
Figure 1: Grid independence verification. By employing the distance division method, the sample size is 2 to 3 times larger than that with the temperature difference method. At this point, the fluid properties within each 1 mm micro-element can be approximated as constant. The parameters of each micro-element were extracted, and the heat transfer coefficient was subsequently calculated. Through numerical simulation results under four distinct operating conditions, the data for liquidation flow heat transfer inside the PCHE microchannels were segmented to generate a substantial dataset. The dataset comprised a total of 1000 micro-element data points. The dataset information is presented in Table 1. The input feature variables included inlet temperature, inlet pressure, wall heat flux density, inner wall temperature, mass flow rate, temperature difference, inlet velocity, density, dynamic viscosity, channel diameter, hydraulic diameter, Prandtl number, and Reynolds number. The target variable is the heat transfer coefficient. The data have been open-sourced ([[https://github.com/mirror52/test1/blob/main/data_12](https://github.com/mirror52/test1/blob/main/data_12) mm-1.8 mm-liu-h.xlsx]([https://github.com/mirror52/test1/blob/main/data_12](https://github.com/mirror52/test1/blob/main/data_12) mm-1.8 mm-liu-h.xlsx) (accessed on 5 April 2025)), including data of four working conditions (1.2 mm diameter straight channel and hexagonal channel, 1.8 mm diameter straight channel and hexagonal channel). The histogram of the frequency distribution generated based on the dataset information is presented in Figure 3. All data exhibit a right-skewed distribution, meaning that lower values occur more frequently, while higher values occur less frequently. The distribution characteristics of heat transfer coefficients for the straight and hexagonal flow channels are \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Name** & \
\begin{tabular}{c} **Straight-Through Flow** \\ **Channel Range** \\ \end{tabular} &
\begin{tabular}{c} **Hexagonal Flow** \\ **Channel Range** \\ \end{tabular} \\ \hline \multirow{7}{*}{Feature variable (X)} & Inlet temperature Tin (Pa) & [111.15, 377.9662] & [111.15, 401.14103] \\  & Inlet pressure Pin (Pa) & [3.03, 11,865.28] & [79.26, 2412.52] \\  & Wall heat flux density qw (W/m\({}^{2}\)) & [73,696.66, 155,707.46] & [38,664.40, 123,604.93] \\  & Inner wall surface temperature Tinw (K) & [119.70, 443.74] & [124.51, 476.46] \\  & Mass flow rate V (G/kg/(m\({}^{2}\)/s)) & [118.13, 265.39] & [118.13, 265.39] \\  & Temperature difference Td (K) & [0.1497, 2.1355] & [\(-\)21.44, 28.31] \\  & Entrance density vin (m/s) & [0.27, 11.45] & [0.27, 5.21] \\  & Entrance density pin (kg/m\({}^{3}\)) & [23.43, 432.16] & [32.81, 432.16] \\  & Dynamic viscosity u (kg/(m\(\cdot\)s)) & [0.000073, 0.015] & [0.000006, 0.000733] \\  & Channel diameter D (mm) & [1.2, 1.8] & [1.2, 1.8] \\  & Hydraulic diameter Dh (m) & [0.0011, 0.001466] & [0.0011, 0.001466] \\  & Prandtl number Pr & [0.78, 2.95] & [0.00071, 0.0028] \\  & Reynolds number Re & [8.39, 4078.00] & [632.97, 24,610.42] \\  & Convective heat transfer coefficient h & [781.42, 20,806.38] & [554.168, 9625.993] \\  & (W/(m\({}^{2}\)-K)) & [781.42, 20,806.38] & [554.168, 9625.993] \\ \hline \hline \end{tabular}
\end{table}