# A GTA Welding Cooling Rate Analysis on Stainless Steel and Aluminum Using Inverse Problems
## 1 Introduction  
The gas tungsten arc (GTA) welding process is largely used in industrial applications nowadays. Due to its great welding quality and low equipment cost, this process is extensively applied to stainless steel, titanium alloy, and non-ferrous metals welds [1]. In the GTA welding process, a tungsten electrode is protected by a flow of inert gas; argon is usually employed, as well as helium, nitrogen, hydrogen, or mixtures. The knowledge of the heat flux, temperature gradients, and cooling process are thoroughly necessary for welding process studies. The thermal analysis is fundamentally based on models of heat transfer theory, which include the following phenomena: specific heat, latent heat, two-phase regions, moving interfaces, conservation of energy, fluid mechanics, conductivity, contact resistance, radiation emissivity, and convection [2]. The weld quality depends on several parameters that control the temperature of the workpiece. For instance, the electric current and the torch speed are important factors in the GTA welding process [3; 4]. The cooling rate is an important factor that affects all welding process quality. Heat loss, which occurs due to diffusion, free convection, and radiation, occur spontaneously; therefore, it is difficult to control the cooling rate during the welding process. There are several ways to control the heat loss in a welding process; one of them is to control the heat diffusion on the workpiece bypreheating of the sample [5]. Another one is to perform the process in a vacuum room, which will obliterate the free convection [6]. However, the thermal emission of radiation cannot be estimated. As a matter of fact, any matter at a temperature higher than absolute zero will emit thermal radiation, which limits the control. Several authors have been studying numerical models for the welding process. These models satisfactorily predict the temperature at the peak point [7; 8]. However, they fail to analyze the cooling rate because they use simple approaches for the radiation and heat transfer coefficient by convection. For instance, [PERSON] et al. [7] used a three-dimensional model based on the diffusion equation and the enthalpy method to model a TIG welding process. The authors' model used an empirical correction to estimate the heat transfer coefficient in the sample. However, this model did not consider the thermal emission by radiation. Thus, as expected, the model failed to predict the temperature after the TIG welding torch was turned off. The same pattern is seen in [PERSON] et al. [8]. In their work, the authors model a TIG welding process for the same stainless steel of [PERSON] et al. [7]. They used a linearization of the radiation equation of the Stefan-Boltzmann law and a constant heat transfer coefficient for the convection analysis. Although the authors' model covers radiation and convection, the use of a linear approach in a welding model is not recommended due to the high thermal gradient characteristic of the process. The author's model predicts the heating part of the problem well; on the other hand, it fails to analyze the cooling rate part. In [PERSON] et al. [9] previous work a numerical software, based on an inverse problem and enthalpy method, was developed in order to predict the thermal field in a GTA aluminum welding. The thermal field in any region of the plate or anytime was determined through the numerical solution of the three-dimensional heat diffusion equation. The inverse technique of BFGS was used to estimate the heat applied in the process. The finite difference method and the implicit Euler method for time discretization were used to solve the heat diffusion equation. Some improvements are made in relation to the previous work. In this work, a detailed analysis of the cooling rate is presented. Furthermore, the heat losses are presented separately under two headings: convection and radiation. In the same way, a comparison between the thermal fields of the Stainless steel AISI 304L and Aluminum 6065 T5 is presented.