## 3 Numerical Simulations
### Simulation Results and Discussion  
Temperature nephograms obtained at curing temperatures of 220 \({}^{\circ}\)C and 230 \({}^{\circ}\)C are shown in Figure 21. The convective heat transfer coefficient of the coating surface was low, and the heat loss from this surface was also low. Therefore, in the initial phase of heating, the upper layer of the coating had a higher temperature. The coating surface was heated for 155 s to achieve a curing temperature of 220 \({}^{\circ}\)C. This curing temperature was maintained for 3 min. Then, the coating surface was heated for 187 s to achieve a curing  
Figure 20: Comparison of experimental and simulated temperatures during the curing process.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Time (s)** & 40 & 50 & 60 & 70 & 80 & 90 \\
**Experimental data (\({}^{\circ}\)C)** & 143.2 & 159.3 & 176.2 & 185.1 & 196.9 & 207.1 \\
**Simulated data (\({}^{\circ}\)C)** & 132.85 & 148.73 & 162.73 & 175 & 185.68 & 194.93 \\
**Relative error (\%)** & 7.23\% & 6.64\% & 7.64\% & 5.46\% & 5.70\% & 5.88\% \\ \hline
**Time (s)** & 100 & 110 & 120 & 130 & 140 & 150 \\
**Experimental data (\({}^{\circ}\)C)** & 211 & 218.1 & 221.4 & 225.7 & 228.5 & 232.5 \\
**Simulated data (\({}^{\circ}\)C)** & 202.91 & 209.75 & 215.61 & 220.61 & 224.85 & 228.46 \\
**Relative error (\%)** & 3.83\% & 3.83\% & 2.62\% & 2.26\% & 1.60\% & 1.74\% \\ \hline \hline \end{tabular}
\end{table}
Table 8: Relative errors for measured and simulated coating temperatures (\(\eta_{\text{tot}}=0.4\)).  
temperature of 230 \({}^{\circ}\)C. This curing temperature was maintained for 2 min. During this heating process, the temperature distribution of the coating became more uniform, with the highest temperature located in the middle of the coating. The internal temperature of the substrate was almost constant throughout the entire heating process.  
To further analyze the heat transfer during the curing process and to provide a reference for production, numerical simulations were used to predict the coating temperature with different substrate thicknesses. The effects of metal substrate thicknesses ranging from 1 mm to 10 mm on the coating temperature were calculated using a gas inlet flow of 0.2 m\({}^{3}\)/h. As shown in Figure 22, the rate at which the coatings were heated decreased with increasing substrate thickness. Figure 23 shows the predicted times required for the coating temperature to reach 220 \({}^{\circ}\)C or 230 \({}^{\circ}\)C with different substrate thicknesses. When the  
Figure 21: (a) Temperature nephogram of coating and substrate at a curing temperature of 220 \({}^{\circ}\)C. (b) Temperature nephogram of coating and substrate at a curing temperature of 230 \({}^{\circ}\)C.  
substrate thickness was 1 mm, the coating required 2.58 min to reach 220 \({}^{\circ}\)C and 3.12 min to reach 230 \({}^{\circ}\)C. The minimum times required to cure the coatings with this catalytic infrared heating equipment were 5.58 min and 5.12 min for curing temperatures of 220 \({}^{\circ}\)C and 230 \({}^{\circ}\)C, respectively. Moreover, a shorter total curing time was required with a curing temperature of 230 \({}^{\circ}\)C, resulting in energy savings. Therefore, it is recommended that a curing temperature of 230 \({}^{\circ}\)C should be used when the substrate thickness is 1 mm, and 220 \({}^{\circ}\)C should be used when the substrate thickness is \(\geq\)2 mm.