# A GTA Welding Cooling Rate Analysis on Stainless Steel and Aluminum Using Inverse Problems
## 3 Results and Discussion  
### Aluminum 6065 T5  
Figure 4 presents a comparison between the temperature signals measured by thermocouples \(T_{1}\), \(T_{2}\), \(T_{3}\), and \(T_{4}\). The respective numerical temperature was calculated from the previously-developed C++ code [9] for the welding conditions \(t+\) = 2 ms, \(t+\) = 7 ms, \(t+\) = 11 ms, and \(t+\) = 13 ms. It must be pointed out that the highest temperatures are obtained by the thermocouples soon after the GTA arch is turned off at \(t\) = 24 s [9]. Figure 3: Scheme representation of the numerical performed analysis. The dimensionless Richardson number, \(Ri\ =\ Gr_{l}\ /\ Re_{l}^{2}\), remained much higher than 1 (\(Ri\) > 1000) in all calculated points; consequently, the problem could be treated as purely free convection [12]. Thus, the empirical correlations from [PERSON] et al. [12] were used to calculate \(Nu_{l}\), local Nusselt number and \(h\) in any position on the plate. Figure 5 presents the average \(Nu\) profile. The average Nusselt number \(Nu\) is obtained from the arithmetic average of all \(Nu_{l}\) on the surface of the plate. From the analysis of Figure 5, it may be noticed that \(Nu\) increases in the first seconds of the process and it stabilizes until the arch torch is turned off. After the process, the average \(Nu\) starts to increase again. This behavior is due to the non-linear characteristics of the thermal properties for air adopted in this study. It may also be noticed that \(Nu\) is not sensitive to the positive polarity. As the average temperature increases due to the positive polarity, the \(Nu\) number remains almost at the same value for all cases studied. Figure 4: Evolution of the experimental and numerical temperatures for different \(t+\) conditions. Figure 5: Average \(Nu\) on the plate in relation to time. Figure 6 shows the average heat transfer coefficient, \(h\), for the four \(t+\) welding conditions. It may be observed that the average heat transfer coefficient achieves the maximum value when the GTA torch is turned off. After this, it decreases slowly. The heat transfer coefficient by convection will return to zero when the sample reaches room temperature. It is also noticed that the heat transfer coefficient by convection increases as the positive polarity increases, however, inexpressively. When all cases were compared, the heat transfer rate by convection had not increased more the 2 W when the difference between \(t+=13\) ms and \(t+=2\) ms was analyzed. The heat transfer rate lost by convection and radiation must be pointed out. As the heat transfer coefficient does not present an expressive difference from one positive polarity to another (Figure 6), the cooling rate presented almost the same values for all positive polarity conditions. Therefore, the cooling rate analysis was presented only for the experimental condition \(t+=2\) ms (Figure 7). For this case, the estimated heat transfer rate using the BFGS technique was nearly 601 W. In order to compare the heat transfer rate by using constant emissivity and a heat transfer coefficient by convection, the values of \(\varepsilon=0.2\) for the aluminum 6065, [19] and \(h=20\) W/m\({}^{2}\) were used. Although the natural convection represents a large part of the overall cooling process, the heat loss by radiation significantly affects the cooling process while the GTA welding is performed. In Figure 7, for emissivity and heat transfer coefficient dependent on temperature, the heat rate loss by radiation reaches 311 W at \(t=24\) s while, at the same time, the heat rate loss by free convection is only 247 W. However, in this case, the heat rate loss by radiation decreases considerably when the TIG arch torch is turned off.