## 4 Multi-Factor Impact Analysis of Ice-Melting Performance and Energy Utilization Based on BPB-CFEH
### Analysis of the Effect of Burial Spacing and Rated Voltage on Ice-Melting Performance  
This section analyses the effects of burial spacing and rated voltage on region 1 (\(Q_{u}\)) and region 2 (\(Q_{d}\)) thermal transfer of the bridge pylon beam. Three types of burial spacing were considered: 5 cm, 7.5 cm, and 10 cm. Three kinds of rated voltage were used: 220 V, 260 V, and 300 V, for a total of nine groups of working conditions. In order to reduce energy consumption, the simulation was set at an ambient temperature of \(-\)5 \({}^{\circ}\)C, a wind speed of 4.5 m/s, and a heating time of 8 h. The design parameters for different pipe spacing values are detailed in Table 3.  
Figure 7: Effect of different ambient temperatures and wind speeds on paving power. As shown in Figures 8 and 9, \(Q_{u}\) and \(Q_{a}\) increase with increasing \(U\) and decreasing \(d\) during heating for 8 h. When the voltage is 220 V, the distance changes from 10 cm to 7.5 cm and 7.5 cm to 5 cm; \(Q_{u}\) changes by 25 KJ and 47.26 KJ, while \(Q_{a}\) changes by 262.46 KJ and 104.97 KJ, respectively. The amount of change in \(Q_{u}\) and \(Q_{a}\) was 9.6% and 45.02%, respectively. When the distance is 10 cm, and the voltage is changed from 220 V to 260 V and from 260 V to 300 V, \(Q_{u}\) changes by 78.65 KJ and 61.46 KJ and \(Q_{a}\) by 1739.64 KJ and 811.36 KJ, respectively. The amount of change in \(Q_{u}\) was 4.52%, and 3.39% of the change in \(Q_{a}\), respectively. It was found that changing \(U\) was effective in increasing \(Q_{u}\) and changing d had less of an effect on \(Q_{a}\). Changing \(U\) and d had almost the same effect on \(Q_{u}\). Quantitative analyses were carried out to analyze the effect of different spacing levels and different rated voltages on the amount of heat emitted from regions 1 and 2. Multiple regression was used to analyze the relationship between \(Q_{u}\), \(Q_{a}\) and, d and U, as shown in Equations (11) and (12):  
\[Q_{u}=-17.425d+1.941U-113.373~{}R^{2}=0.978 \tag{11}\]  
\[Q_{a}=-135.196d+48.482U-5063.629~{}R^{2}=0.992 \tag{12}\]  
Figure 8: Effect of \(d\) and \(U\) on thermal exchange in region 1. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**d/cm**} & **Number of Heating** & **Distance of Heating Cables** & **Total Length of** \\  & **Cables** & **from the Boundary/cm** & **Heating Cable/m** \\ \hline
10 & 4 & 10 & 7 \\
7.5 & 6 & 6 & 10.4 \\
5 & 8 & 5 & 13.8 \\ \hline \end{tabular}
\end{table} 
Table 3: Design parameters of BPB–CFEH with different pipe spacing values. Analysis of the Effect of \(d\) and \(U\) on the Energy Utilization of the Process from Stage 1 to Stage 2  
This section analyses the energy distribution of the stage 1 to stage 2 process based on the nine sets of working conditions detailed in Section 3.2. The effect of different spacing and rated voltage on _SEMI1R_ and _SEMI2R_ is analyzed. The energy utilization ratio is also presented for analysis. As shown in Figure 10, both _SEMI1R_ and _SEMI2R_ increase with increasing U, but the growth of _SEMI1R_ is not significant. With the same burial spacing, changing the rated voltage from 220 V to 260 V slowed the growth rate of _SEMI1R_ compared to changing the rated voltage from 260 V to 300 V. Increasing the voltage below the rated voltage of 260 V increases _SEMI1R_ more efficiently than increasing the spacing, whereas increasing the rated voltage to the maximum results in increasing _SEMI1R_ less efficiently. Figure 10: Effect of \(U\) and \(d\) on _SEMI1R_ and _SEMI2R_. Figure 9: Effect of \(d\) and \(U\) on thermal exchange in region 2. Changing the rated voltage greatly affects \(SEMI2R\) when the burial spacing is 5 cm. This is because when the burial spacing is 5 cm, there are more carbon fiber heating cables in region 2 compared to when the burial spacing is 7.5 cm and 10 cm. This leads to more significant thermal accumulation, as indicated in Table 3. On the other hand, the \(SEMI1R\) value is lowest when the burial spacing is 5 cm.