## 1 Introduction  
In the steel industry, vertical strip galvanizing lines are used for the production of high-quality coated steel strips to be utilized, e.g., in making automotive body parts. The indirect-fired vertical strip annealing furnace in such a continuous strip galvanizing line (CGL) usually comprises of metallic radiant tubes (RT), arranged in several columns with the strip driven between them (Figure 0(a)). The furnace, commonly divided into heating and soaking sections, normally operates under a protective gas atmosphere to prevent oxidation of the steel strips. The radiant tubes serve the purpose of heating the steel strips and simultaneously separate the combustion gases from the protective gas atmosphere in the furnace. The annealing furnace of a 450,000 tonnes/year galvanizing line, operating in thyssenkrupp Steel Europe GmbH in Dortmund since 2001, can be taken as a typical example (comparable to Figure 1b). The radiant tube heating section of this furnace is equipped with a total of 189 double-P-type radiant tubes, amounting to a total heat input of 27 MW [1]. An annual tube mortality rate of approx. 20% is a reasonable assumption for strip annealing furnaces [2; 3]. At a typical cost of 7000 \(\upxi\) for a single double-P-type radiant tube, direct tube replacement costs of approx. 260,000 \(\upxi\) per annum could be expected for one such CGL alone. Additional costs of plant shutdowns and installation also need to be considered. Therefore, the potential for cost savings for several such CGLs justifies any effort to understand the factors influencing radiant tube lifetime. To this end, it is also important to develop reliable lifetime models not just to prevent radiant tube failures (Figure 2) but also to anticipate periods of service and change production recipes accordingly [4]. Radiant tube lifetime is influenced by its surroundings and their varying parameters resulting from process changes inherent in the operation of an annealing furnace of a CGL. The burners installed in recirculating radiant tubes are normally operated in on/off firing mode, in order to ensure better temperature uniformity on the tube as well as low NOx-emissions. The on-state corresponds to the burner operation at full-load (100% power). In temperature-controlled systems, the burner is switched to off-mode when a specified maximum temperature is reached. As soon as the temperature is too low, the burner is switched on again. Alternative furnace control systems operate based on the strip outlet temperature or the required energy input into the furnace. Model predictive control strategies can be used to anticipate the short term future process behavior and push the process towards its limits [5; 6]. Additionally, a sequential firing logic is implemented into the furnace control system to set the burner on/off firing cycles for each radiant tube [7]. A radiant tube in a CGL furnace not only experiences cyclic thermal loading due to burner on/off firing but is also exposed to changes in temperatures arising  
Figure 1: (**a**) Schematic of the annealing furnace of a continuous strip galvanizing line (CGL); (**b**) View from the bottom into the heating section of an annealing furnace. Figure 2: Examples of damaged recirculating and non-recirculating metallic radiant tubes in CGLs. from heat transfer (mainly radiative) to its neighboring tubes, the furnace chamber, and the passing strip. Figure 3 illustrates the influence of surroundings on the surface temperatures of a double-P-type radiant tube in an annealing furnace of a CGL for steel strips. The mass flow rate of strip is calculated as the product of the strip's cross-section, its velocity magnitude, and its density, thus representing the change of strip parameters. Region 1 presents the classic case of tube temperatures under burner on/off operation, with firing cycle times of approx. 100 s. In contrast, Region 2 shows drastic changes in tube temperatures, even though no change in the mass flow rate of the strip (similar to Region 1) is observed.