## 5 Discussion
### Relationship between Fin Size and Stress/Deformation  
According to the results of the finite element calculation, fin thickness had almost no impact on the yield range, while increasing the fin width enabled an increase in the yield range. In addition, the change in the fin thickness or width showed a minor effect on the longitudinal stress, but had a great influence on the flexural deformation. Figure 12 shows the effect of fin size on maximum deflection, where \(s_{\mathrm{i}}\) and \(b_{\mathrm{i}}\) are different fin widths and thicknesses, \(s_{\mathrm{0}}\) and \(b_{\mathrm{0}}\) are the typical fin width and thickness under actual working conditions (Table 1), \(y_{\mathrm{i}}\) is the maximum deflection under different fin size conditions, and \(y_{\mathrm{0}}\) is the maximum deflection under typical fin size conditions. One can notice that the maximum deflection deformation of the structure gradually decreased as the fin thickness increased (Figure 12a), while it first decreased and then increased with the increased fin  
Figure 10: Stress and deformation distribution curves along the path with different fin widths: (**a**) equivalent von Mises stress, (**b**) longitudinal stress, and (**c**) deflection. width (Figure 12b). When the fin thickness \(b_{0}\) was 8 mm and the fin width \(s_{0}\) was 17.5 mm, the maximum deflection was 1.62 mm. When the fin thickness was reduced by 25%, the maximum deflection decreased by -8%. However, when the fin thickness was increased by 50%, the maximum deflection decreased by about 72%. When the fin width was 0.57\(s_{0}\), the maximum deflection increased by 140%. When the fin width exceeded \(s_{0}\), the maximum deflection increased with an increase in fin width. When the fin width was 2.8\(s_{0}\), the maximum deflection increased by nearly 40%. Furthermore, when the width was four times the typical fin width in the structure, the structure became notably unstable, and the maximum deflection was -17 times that of the typical fin width. Therefore, compared with the welding rate and fin thickness, the maximum deflection of the flue-side wall structure was more sensitive to the changes in fin width. The thickness of the connecting fins had a visible effect on the flexural deformation, which was attributed to the varying mechanical properties in the welding area. Thicker fins had higher strength and rigidity, and possessed more resistance to thermal expansion and flexural deformation. Furthermore, the increased fin thickness implied deepened constraint conditions near the weld seam. Increasing the width of the connecting fins weakened the constraint effect, which induced more prone thermal shrinkage and deformation in the welding area, suggesting greater deflection deformation during the cooling process. Additionally, an upward temperature gradient in the welding area arose from the increase in the width of the connecting fins. Accordingly, a larger temperature gradient meant that the temperature difference on both sides of the weld increased, causing a larger thermal stress difference and ultimately greater deflection deformation. It also should be noted that, if the width of the connecting fins is too narrow, the distance between different weld seams will be close enough to produce the superimposed effect of the flexural deformation. Consequently, the maximum flexural deformation on the welding structure becomes larger. In short, the width of the flue-side wall fins should be comprehensively considered in the design process. Figure 11: Effect of welding rate on maximum deflection. Figure 12: Effect of fin size on maximum deflection: (**a**) fin width and (**b**) fin thickness. The effect of the tube number on the post-welding residual stress was investigated. As shown in Figure 7, it was found that, when the tube number was eight, the peak of longitudinal stress appeared in the middle of the connecting fins. However, as the tube number increased to 32, the peak value of the residual stress was inspected in the vicinity of the weld toe.