# A GTA Welding Cooling Rate Analysis on Stainless Steel and Aluminum Using Inverse Problems
## 3 Results and Discussion
### Stainless Steel  
In order to accomplish a complete analysis of the cooling rate in the GTA welding process, an analysis was performed on a stainless steel AISI 304L plate. Due to its melting temperature, the stainless steel achieved a higher temperature level than the aluminum. In this case, the thermal emission has a higher impact on the cooling rate analysis. The stainless steel has a lower thermal conductivity compared to the aluminum. Therefore, the heat conduction velocity of the AISI 304L is lower than the aluminum 6065 T5. Thus, although the stainless steel welding achieves higher temperature on the welding bead, its cooling rate is lower than the welding of aluminum. Videlicet, the average temperature in the stainless steel welding is lower than in aluminum welding when the samples have the same size. This pattern is well presented in Figure 11 where the thermal field for the two sample materials is presented. It may be noticed that the center of the weld bead of the stainless steel (Figure 11a) achieves a higher temperature than the aluminum. However, due to the high thermal conduction of the aluminum 6065 T5, the temperature outside the weld bead is higher than the temperature outside the stainless steel weld bead. It may also be observed that the isothermal curves in the stainless steel present oval shapes while in the aluminum they present circular shapes. The shape is related to the welding velocity and the thermal conductivity. As the welding velocity increases the shape becomes more oval. When the thermal conductivity is high the shape becomes circular.  
Figure 10: Evolution of the heat transfer coefficient, \(h\) (W/m\({}^{2}\)K), at instants (a) 7.8 s, (b) 15.6 s, (c) 23.4 s, and (d) 39.0 s for \(t\)+ = 2.0 ms.  
A comparison between the experimental temperature values for only a single thermocouple and the values obtained by the software are displayed in Figure 12. A good agreement between the curves may be observed. However, the temperature peak tends to be slightly lower when compared to the experimental temperature. This difference is related to the inherent error of the attributed values of the thermal properties. For a better precision of the calculated data at high temperatures, an estimation of the thermal conductivity and diffusivity for the stainless steel AISI 304L is required, mainly in the liquid phase. Unfortunately, there is a lack of technology development in this area. Therefore, those values are not easily found in the literature.  
This fundamental pattern has an important role in the cooling analysis. Thus, the cooling rate by free convection and radiation is lower in the stainless steel than in the aluminum welding. Figure 13 presents the cooling rate by convection and radiation for the stainless steel AISI 304L welding. The cooling rate achieves the highest value at 24 s when the arc torch is turned off. At this time interval, the cooling rate by convection reaches 11.7 W, while the cooling rate lost by radiation reaches 2.8 W.  
Figure 11: The numerical thermal fields for GTA welding in (**a**) stainless steel AISI 304L and (**b**) aluminum 6065 T5.  
The evolution of the heat transfer coefficient for the stainless steel presented is different from the aluminum. While the aluminum reaches a heat transfer coefficient of 11.5 (W/m\({}^{2}\)K) after the arc torch is off, the stainless steel reaches only 9 (W/m\({}^{2}\)K). Figure 14 presents the evolution of the heat transfer coefficient for the stainless steel.  
Figure 12: Numerical temperature (\(T_{mum}\)) and experimental temperature (\(T_{exp}\)) for GTA welding in stainless steel AISI 304L.  
Figure 13: Overall heat transfer by convection and radiation for the GTA stainless steel welding.