## 2 Numerical Analysis Model
### Properties and Boundary Conditions  
Given the study's focus on a tube skid designed to withstand a maximum charging pressure of 450 bars, the simulation of the hydrogen charging process had to incorporate hydrogen properties at pressures up to 450 bars. While the ideal gas law is commonly employed for its simplicity in calculating gas properties at low pressures, it fails to account for molecular attractions [21], rendering it inadequate for high-pressure applications. Consequently, the van der Waals equation, which considers both the size of molecules and intermolecular forces as shown in Equation (6), was developed. Moreover, various cubic equations of state have been modified from the van der Waals equation to enhance accuracy. Among these, the Redlich-Kwong model [22] has been utilized in prior studies to simulate the hydrogen charging process [5; 7; 8; 9; 10].  
\[P=\frac{RT}{V-b}-\frac{a/\sqrt{T}}{V(V+b)} \tag{6}\]  
[PERSON] [23] evaluated the accuracy of three state equations--Redlich-Kwong, Soave-Redlich-Kwong, and Peng-Robinson--in predicting hydrogen's properties, finding that the Peng-Robinson equation exhibited a relative error of up to 5% against the National Institute of Standards and Technology (NIST) database. Although the Redlich-Kwong and Soave-Redlich-Kwong equations demonstrated smaller errors than the Peng-Robinson model, they still showed a relative error of up to 2%. While such discrepancies might be negligible in specific contexts, this study opted to utilize NIST's property data to enhance analysis accuracy by minimizing inherent errors in these equations. Therefore, the NIST real gas model [24], as provided by ANSYS Fluent v21.2, was employed to calculate hydrogen's thermodynamic properties based on the NIST database. This model, previously applied in studies [13; 14] simulating the hydrogen tank charging process, was chosen to represent the properties of high-pressure hydrogen accurately.  
Regarding the materials of the tank shell, ANSYS Fluent v21.2's default properties were used for aluminum, while property values for CFRP and PA were specified, as listed in Table 1.  
To assess the impact of environmental and operational conditions on the temperature distribution during charging, initial and boundary conditions were established, as outlined in Table 2. A total of five variables were considered to analyze their effect on the tank's  
\begin{table}
\begin{tabular}{c c c c} \hline
**Properties** & **Al6061** & **PA** & **CFRP** \\ \hline Density [kg/m\({}^{3}\)] & 2719 & 1100 & 1540 \\ Specific Heat [J/(kg K)] & 896 & 1872 & 1040 \\ Thermal Conductivity [W/(m K)] & 167 & 0.334 & 1.2 \\ \hline \end{tabular}
\end{table}
Table 1: Properties of tube skid materials.  
temperature rise. Seasonal variations, represented by summer (40 \({}^{\circ}\)C) and winter (\(-\)20 \({}^{\circ}\)C) conditions, informed the set values for inlet, ambient, and initial temperatures. In the initialization step of each case, both the fluid and solid regions were initialized to the initial temperature as shown in Table 2, and the pressure in the fluid region was specified as the initial pressure. The pressure of the inlet was regulated to increase linearly from the initial pressure to the maximum capacity of the tank (450 bar) during the charging time, and the temperature of the inlet stream was specified as the inlet temperature. It was assumed that convective heat transfer by the outside air continuously occurred on the outer wall of the tank, the temperature of the outside air was applied as the ambient temperature, and the convective heat transfer coefficient was set as 6 W/(m\({}^{2}\cdot\)K) assuming minimum air flow. Moreover, walls in contact with different materials share the mesh geometry and mediate heat transfer under coupled conditions.  
Analysis of Temperature Distribution Inside Tube Skid According to Operating and Environmental Conditions