## 6 Conclusions  
The focus of the present work was the evaluation of the effect of surrounding radiation on radiant tube lifetime in vertical strip annealing furnaces. For this purpose, the creep strains and associated thermomechanical stresses were calculated as service life-indicating parameters for various radiant tube setups. The setups consisted of two or three adjacent tubes, arranged in a horizontal row or a vertical column. The model boundary conditions were changed in order to identify their individual influences, which included changes in the burner firing mode, the strip's width, and its temperature. A reference case with a single radiant tube treated separately from the rest of the furnace was chosen to compare and classify the results. An in-house developed and validated numerical method was used to  
Figure 14: Von [PERSON] stresses at locations EL1, LG1, and EL2 after 400 h of process time for all nine cases. Figure 13: Creep strain at locations EL1 (= first elbow), LG1 (= first leg), and EL2 (= second elbow) after 400 h of process time for all nine cases. calculate the temperature distributions for every case. Subsequently, a creep analysis on the tubes was carried out to determine the lifetime indicating parameters. The following conclusions could be drawn from the assessment of the effect of surrounding radiation on radiant tube lifetime:  
1. Peak tube temperatures decreased, and the maximum tube temperature gradients at the burner-on and -off points invariably increased upon the introduction of adjacent tubes and a strip as radiating partners, compared to an isolated radiant tube. 2. Under synchronous burner firing, the presence of a passing strip--irrespective of its width--coupled with adjacent radiant tubes, resulted in an increase in the maximum tube deformation due to creep. 3. The choice of the asynchronous firing of burners in a furnace zone was preferable to synchronous firing with regard to the tube's creep deformation. 4. The full-load firing case expectedly showed the least creep rate. It might, however, be difficult to employ in practice for radiant tubes in a CGL furnace. 5. The higher the local tube temperature difference between the burner-on and -off points in a firing cycle, the greater was the creep rate at the respective tube region. This could be clearly seen while comparing the isolated tube, synchronous, and asynchronous firing cases. 6. The highest creep deformation was observed for the setup with three radiant tubes arranged horizontally compared to the vertical arrangement, even though the maximum and minimum tube temperatures and its gradients in a firing cycle were similar. Adjacent radiant tubes strongly affected each other as soon as a strip shielded a part of their radiation exchange area. 7. Changes in strip temperature had a marginal effect on the tube's creep deformation. Evaluating the radiant tube lifetime dependent on the tubes' positions in a CGL furnace, either near the strip entry or towards the strip exit seemed to be more complex than that. The strip cross-section was clearly a parameter of higher significance than locally changing strip temperatures. 8. The role played by the opposing effect, existing between creep deformation of the tube and its thermomechanical stresses, was evident. Therefore, a pattern elucidating a simple correlation between the two was difficult to observe, except, e.g., the asynchronous firing cases. 9. The investigations indicated that cyclic temperature changes--occurring either due to burner on/off firing or process changes--and the corresponding local temperature gradients were mainly responsible for the tube's creep deformation. In future investigations, attention would be shifted towards double-P-type radiant tubes due to their wide use in radiant tube heating and soaking sections of the CGL furnaces. In addition, an enlargement of the radiating surroundings is planned to include up to a matrix of nine radiant tubes.