## 3 Discussion and Analysis
### Influence of Environmental Parameters on the Temperature Field Evolution
#### 3.1.2 Seawater Temperature  
This section mainly discusses the influence of seawater temperature change on the temperature change in the ballast tank. Considering that the seawater temperature generally changes in the range of \(-3\)\({}^{\circ}\)C-\(0\)\({}^{\circ}\)C, the seawater temperature is selected as \(0\)\({}^{\circ}\)C, \(-1\)\({}^{\circ}\)C, \(-2\)\({}^{\circ}\)C, \(-3\)\({}^{\circ}\)C and \(-4\)\({}^{\circ}\)C, the ambient temperature is maintained at \(-30\)\({}^{\circ}\)C, the ballast water height is 4.5 m, and other environmental conditions remain unchanged. Table 4 shows the environmental conditions under different working conditions, and Figure 10 shows a temperature field distribution cloud map of the freezing process under different seawater temperatures. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Cold Air Temperature/\({}^{\circ}\)C** & **Seawater Temperature/\({}^{\circ}\)C** & **Ballast Water Height/m** \\ \hline S1 & \(-30\) & \(0\) & \(4.5\) \\ S2 & \(-30\) & \(-1\) & \(4.5\) \\ S3 & \(-30\) & \(-2\) & \(4.5\) \\ S4 & \(-30\) & \(-3\) & \(4.5\) \\ S5 & \(-30\) & \(-4\) & \(4.5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Case of seawater temperature analysis. Figure 8: The temperature change curve with time at point a under different cold air temperatures. Figure 9: The temperature change curve with time at point c under different cold air temperatures. Figures 11 and 12 show the curves of temperature at a and b points with time at different seawater temperatures. As illustrated in Figure 10, changes in seawater temperature significantly impact the temperature distribution within the tank. As the seawater temperature decreases, the temperature variation in the air domain remains minimal, while the temperature change in the ballast water near the right bulkhead is substantial. The lower the seawater temperature, the more rapidly the temperature of the ballast water adjacent to the right bulkhead decreases. At 14,400 s, when the seawater temperature drops from 0 \({}^{\circ}\)C to \(-4\)\({}^{\circ}\)C, the temperature gradient on the right side of the ballast tank gradually increases, and the  
Figure 10: The temperature field evolution of the ballast tank under different seawater temperatures. low-temperature zone progressively extends into the ballast water. Comparing cases S1 and S5, it is evident that when the seawater temperature is 0 \({}^{\circ}\)C, the cooling range of the right bulkhead is limited. However, when the seawater temperature reaches \(-4\)\({}^{\circ}\)C, a distinct low-temperature freezing zone forms on the right bulkhead. Comparing and analyzing Figures 11 and 12, it is evident that as the seawater temperature decreases, the temperature change at point a is minimal, while the temperature change at point b is substantial. When the seawater temperature dropped from 0 \({}^{\circ}\)C to \(-4\)\({}^{\circ}\)C, the minimum temperature at point a decreased from \(-0.964\)\({}^{\circ}\)C to \(-1.091\)\({}^{\circ}\)C, representing a reduction of approximately 13.17%. In contrast, the minimum temperature at point b decreased from \(-0.587\)\({}^{\circ}\)C to \(-1.518\)\({}^{\circ}\)C, indicating a decrease of about 158.61%. This discrepancy can be attributed to the location of point a, which is situated at the center of the ballast water level, where convective heat transfer with the air is frequent. Consequently, it is less affected by seawater temperature fluctuations, resulting in a relatively stable temperature change. Conversely, point b is located near the right bulkhead, where the convective heat transfer coefficient between the ballast water and seawater is high, facilitating significant heat transfer. As the seawater temperature decreases, the heat released by the ballast water increases, leading to a more rapid temperature reduction. Figure 11: The temperature change curve with time at point a under different seawater temperatures. Figure 12: The temperature change curve with time at point c under different seawater temperatures.