## 3 Results and Discussion
### Influence of Heat Flux  
The dynamic characteristics of the fuel at the outlet of the heating section with a change in the heat flux were studied. In this part, the benchmark case is under an outlet pressure of 5 MPa, a mass flow rate of 1 g/s, a \(T_{gi}\) is 673.15 K, and heat flux changes in the value of \(\pm 10\%\), \(\pm 20\%\), \(\pm 50\%\), and \(\pm 100\%\). As shown in Figure 13a, the cross-sectional average fuel and wall temperatures at the outlet of the heating section gradually decreased with a decrease in heat flux in the initial stage of the response and then approached a stable value. With a decrease in heat flux, the stable fuel temperature and wall temperature gradually decreased. In addition, with an increase in the inlet mass flow, the stable fuel temperature gradually increased (Figure 13b). The stable fuel temperatures and times are shown in Figure 14. With a decrease in heat flux, the stable time was longer when the fuel temperature was lower. Similarly, with an increase in the inlet mass flow, the higher the stable fuel temperature, the shorter the stable time. As shown in Figure 14, with the same \(\mathcal{A}r_{gd}\), the higher the \(T_{gi}\), the shorter the  
Figure 12: Dynamic process of adjacent temperature difference. (**a**) \(\mathcal{A}r_{m}\) decreases; (**b**) \(\mathcal{A}r_{m}\) increases. stable time. In addition, with a \(\mathcal{H}_{qf}\) of \(-100\%\), when the tube is heated no more, the stable time for the fuel temperature to decrease to room temperature in the four cases is almost the same, which is about 12.5 s.  
As shown in Figure 15a, the overall heat transfer coefficient gradually decreases with the decrease in heat flux at the initial stage of response. With the decrease in heat flux, the stable value of the overall heat transfer coefficient decreases gradually. As shown in Figure 15b, with a \(\mathcal{H}_{qf}\) of +100%, the change in the overall heat transfer coefficient is no longer a first-order response but increases first and then decreases with the increase in heat flux at the beginning of the response. In addition, with the increase in heat flux, the stable value of the overall heat transfer coefficient gradually increases. However, with a \(\mathcal{H}_{qf}\) of +100%, the overall heat transfer coefficient is smaller than the one with a \(\mathcal{H}_{qf}\) of +50%. Figure 14: Stable parameter distribution with \(\mathcal{H}_{qf}\). (**a**) Stable temperature distribution with \(\mathcal{H}_{qf}\); (**b**) Stable time distribution with \(\mathcal{H}_{qf}\). Figure 15: Change in the OHTC and SCHTC at X = 900 mm with \(\mathcal{H}_{qf}\) changes. (**a**) \(\mathcal{H}_{qf}\) decreases; (**b**) \(\mathcal{H}_{qf}\) increases. Figure 13: Dynamic process of fuel and wall temperature. (**a**) \(\mathcal{H}_{qf}\) decreases; (**b**) \(\mathcal{H}_{qf}\) increases. As shown in Figure 16a, with the decrease in the heat flux, the temperature difference exhibits a decreasing trend. In contrast, when the heat flux increased, the temperature difference was the opposite, and the stable value increased (Figure 16b). Combined with Figures 15a and 16a, the surface convective heat transfer coefficient exhibited a decreasing trend in the initial response. This trend was attributed to the decrease in the partial derivative of the adjacent wall fuel temperature, which was greater than the decrease in the adjacent wall temperature difference. Combined with Figures 15b and 17b, the surface convective heat transfer coefficient shows an increasing trend in the initial response. This was owing to the increase in the partial derivative of the adjacent wall fuel temperature, which was larger than the increase in the adjacent wall temperature difference. However, with a \(\Delta t_{qf}\) of +50%, the surface convective heat transfer coefficient shows a trend of decrease in the first 1-4 s time span. This was caused by an increase in the adjacent wall temperature difference, which was larger than the increase in the partial derivative of the adjacent wall fuel temperature.