# Prediction of Transient Temperature Distributions for Laser Welding of Dissimilar Metals
## 1 Introduction
Using COMSOL Multiphysics, [PERSON] et al. [39] developed a model for AISI 316L stainless steel welding using a pulsed laser beam as a heat source [21; 22]. The thermal profiles were estimated in terms of surface temperature and isothermal contour, and hence, the temperature distribution was probed at radial directions from the centerline weld and on depth direction of the laser spot position. Their observations were discussed. Similarly, the thermal profile of the keyhole was predicted when the pulse was present and absent. The shape of the keyhole was viewed from both the top and front view [39]. The predicted keyhole was then compared with practical observation and results revealed that the temperature depended on the change in nonlinear physical properties such as density, thermal conductivity, thermal diffusivity, total enthalpy, inward heat flux, and Pacle number, which were plotted for the welding of AISI 316L stainless steel joint to study the change in microstructure and the mechanical properties [39]. [PERSON] et al. (2020) developed a (3D) axial symmetry model for laser welding of dissimilar materials in conduction welding mode [40]. To validate the model, experiments were carried out using a high power diode laser on dual phase steel and aluminum alloy in conduction mode. The model takes into account both the heat transfer and fluid flow. The temperature distribution of the weld pool and the weld pool geometry were contrasted against the empirical study observations [41; 42; 43]. The generation of the weld bead was aided by the laser energy density (LED). It was observed from the model that the peak temperature increased with escalated LED [40; 41; 42; 43]. Owing to the increase in temperature, the amount of heat conducted into the material increased, which resulted in higher penetration depth. At the temperature distribution along YZ plane at a LED of 371 J/mm\({}^{2}\), the model generated a weld width of 6400 \(\upmu\)m and a depth of 789 \(\upmu\)m. At a lower LED of 297 J/mm\({}^{2}\), the weld width and penetration depth were reduced to 5410 \(\upmu\)m and 393 \(\upmu\)m [40; 41; 42; 43]. The temperature profile was retrieved from the boundary by using six domain point probes positioned in the YZ plane along the weld's cross section [40; 41; 42; 43]. The temperature profile was depicted by the heating time and the cooling time for both cases at LED (371 J/mm\({}^{2}\) and 297 J/mm\({}^{2}\)). At higher LED (371 J/mm\({}^{2}\)), i.e., at lower scanning speed (8 mm/s), the laser remained in contact with the material for a longer time, which further resulted in increased heating time of 0.4 s and higher peak temperature of \(\sim\)8200 K [40; 41; 42; 43]. As the LED decreased (297 J/mm\({}^{2}\)), the heating time reduced to 0.25 s with a much lower peak temperature of \(\sim\)7800 K. Results also revealed that another phenomenon that governed the weld width and the depth was the Marangoni convection force. Marangoni effect was the mass transfer that occurred due to the gradient in the surface tension in the molten weld pool [40; 41; 42; 43]. The surface tension of the molten metal was increased with increase in temperature. The warmer liquid at point 'a' had lower surface tension and was pulled toward point 'b' [40; 41; 42; 43]. The surface tension gradient along the molten pool caused an outward shear stress. As a result, the molten metal moved from the weld's center to the pool's margins before returning below the pool's surface. At higher LED, the Marangoni convection increases, which result in larger weld width [40; 41; 42; 43]. The influence of surface tension and gravitational forces were minimal when compared to the Marangoni convection forces acting in the weld [40; 41; 42; 43]. In industries, welding of modern engineering materials including stainless steel and titanium alloys find a variety of applications due to the need to tailor the location of materials where a transition in mechanical properties, temperature, pressure, and/or performance in service is required.