## 5 Results and Discussion
It should be noted that the evaluation of both points MX and EL did not show any qualitative deviations. The corresponding stress distribution in Figure 9b shows the maximum stress location at MX, with the next maximum lying on the first elbow. It could be observed that a direct causal relationship between the creep strains and thermomechanical stresses could not be ascertained. This gave the first indication of the existence of an opposing effect between the stresses and creep strains, caused by the local temperature gradients and the cyclic temperature changes in the radiant tube. The next step involved the division of results of the calculated creep strains into three parts in order to take a closer look on each of the investigated cases (II-IX): Each of the cases differed in terms of tube arrangement, strip parameters (width, temperature), and burner operating modes. Figure 10a illustrates the effects of the absence and presence of a strip, with two different strip widths (narrow and wide). For comparability, the creep strain of the reference was also shown. Basis  
Figure 8: Temperature distributions at the burner-on (**a**) and-off (**b**) points for case VI. Figure 9: Results for case VI showing: (**a**) creep strain; (**b**) stress distribution (burner-on point). of this investigation was setup (b) (Figure 5) with two horizontally adjacent tubes, operating with synchronous fired burners. The results showed a higher creep strain at the end of the 400 h of process time for the cases with a strip--regardless of the strip's width--compared to the cases without a strip (II) and the reference (I). In contrast, the maximum tube temperatures of the cases with a strip (III-IX) were below that of the reference. A narrower strip tended to cause the highest creep strains compared to the case with a wide strip. It could be noted that no causal correlations could be found between the maximum tube temperatures and the magnitudes of creep strain. For instance, the cases with a strip (III-IX) resulted in higher creep strains than the cases without a strip (II) and the reference (I), even though the latter two had higher maximum tube temperatures. To summarize, ignoring the strip during the analysis led to an overestimation of the tube's lifetime. Local temperature gradients and associated temperature changes due to cyclic loading had to be listed as being primarily responsible for the occurring creep strains. A correlation of creep strains solely with the tube temperatures magnitudes was, however, not possible. The creep strains at location EL for the reference case (I) and certain selected setups with the strip (VI-IX) are shown in Figure 10b. Three different radiant tube arrangements were considered, based on setups (b), (c), and (d) (Figure 5). The effect of two radiating tube partners in vertical direction led to a lower creep strain than two horizontally adjacent radiating partners. This could be ascribed to the fact that the strip's shielding of some of the neighbors' radiation strongly influenced the temperatures arising on the tube. In this context, it was also obvious that two neighboring tubes had a greater influence on the central tube than only one neighbor did. By considering horizontally arranged tubes, it became apparent to take a look at the strip's changing temperature during the passes. Compared to an isothermal strip, a variation in strip temperature led to an increase in the maximum creep strain in the tube. In addition to synchronous firing cases, the two-tube setup was also investigated with asynchronous burner operation (III-IV). Figure 11a shows the temperature-time-cycles at location EL, together with that of the reference. The corresponding creep strains are shown in Figure 11b. Both the asynchronous firing cases showed a lower creep rate than the calculation with synchronous firing. The creep rate was defined as the slope of the creep strain curve in its linear section (150 to 400 h). Also, a slightly lower creep rate could be observed compared to the reference.