## 5 Results and Discussion  
The first step in assessing the effect of the radiation exchange on the parameters indicating the tube's lifetime involved taking a closer look at the calculated temperature distribution of the individual cases with their boundary conditions. For each case, four characteristic temperature values are shown in Figure 7: the maximum tube temperature (T\({}_{\text{max}}\)) and the temperature difference (\(\Delta\)T) between the maximum and minimum magnitudes for both the burner-on point and -off point distributions. The introduction of a strip resulted in a decrease in maximum tube temperatures for all its respective cases. Higher temperature gradients were evident in both the tube temperature distributions \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **Name** & **Setup** & \begin{tabular}{c} **No. of** \\ **Tubes** \\ \end{tabular} & **Arrangement** & **Strip** & \begin{tabular}{c} **Burner** \\ **Firing** \\ \end{tabular} \\ \hline I & Ref & a & 1 & - & - & - \\ \hline II & WOSII & b & 2 & horizontal & - & sync \\ \hline III & WSII & \begin{tabular}{c} async-Off \\ wide \\ \end{tabular} & b & 2 & horizontal & wide & async-Off \\ \hline IV & WSII & \begin{tabular}{c} async-On \\ wide \\ \end{tabular} & b & 2 & horizontal & wide & async-On \\ \hline V & WSII & \begin{tabular}{c} sync \\ wide \\ \end{tabular} & b & 2 & horizontal & narrow & sync \\ \hline VII & WSII & \
\begin{tabular}{c} sync \\ vertical \\ wide-iso \\ \end{tabular} & b & 2 & horizontal & wide & sync \\ \hline IX & WSII &
\begin{tabular}{c} sync \\ wide-var \\ \end{tabular} & c & 3 & horizontal & wide, variable & sync \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Nine investigated cases and their radiant tube setups and boundary conditions. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Burner-on Point**} & **Burner-off Point** \\ \hline Strip & - isothermal & 820 \({}^{\circ}\)C & 850 \({}^{\circ}\)C \\  & - variable & 800–10–820–830 \({}^{\circ}\)C & 830–840–850–860 \({}^{\circ}\)C \\ \hline \multirow{2}{*}{Furnace chamber} & - with strip & 860 \({}^{\circ}\)C & 900 \({}^{\circ}\)C \\  & - without strip & 895 \({}^{\circ}\)C & 940 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Temperature boundary conditions for strip and furnace chamber used for all setups. Figure 7: Comparison of the temperature distributions of all nine cases with the help of characteristic values. (at burner-on and -off points) for all cases with a strip (III-IX) compared to the reference case of the isolated tube (I). The temperature gradients for cases with strip were also higher in magnitude than the case without the strip (II), with the exception of the vertical three-tube arrangement case (VII). The case without strip (II) also had a slightly higher maximum tube temperature (11 K) at the burner-off point, accompanied by a higher temperature difference. In contrast, the temperature values showed no significant change at the burner-on point. Spatially resolved, the temperature distributions of the reference case (I) showed high temperatures at the first elbow and minimum temperatures at the pinned support (XYZ) [35]. The cases II to IX that were influenced by surroundings showed similar locations of the maximum and minimum temperatures. However, the local distribution of temperatures in the legs and elbows changed accordingly, as shown in Figure 8. Figure 9a shows the creep strain distribution on the tube for case VI at a time of 250 of the total 400 calculated hours. The maximum creep strain occurred at the meeting point of the second elbow to the first leg, followed by the maximums in the first leg, first elbow, and the second elbow, respectively. To evaluate and compare the individual calculations, a point EL (= elbow) was selected on the second elbow. The position of the maximum occurring creep strain MX (= maximum) was not used since the numerical error could not be ruled out due to the proximity to the pinned support (XYZ).