**4. Results**

In the present study, the results from experiments, the numerical modeling, and the analytical method are compared with regards to different energy densities. Equation (6) exhibits how the heat input can be calculated from the welding velocity and power. These parameters are of great importance because they affect the molten geometries and the heat transfer in the welding process. The calculated heat inputs in the present study are shown in Table 2.

$$E = P/V \tag{6}$$

Figure 4 demonstrates the heat transfer and a transverse-section molten pool achieved by the numerical modeling using an average power of 80 W, welding speed of 2 mm·s<sup>−</sup>1, and welding time of 4 *ms*. By using this model, further calculations of the fusion depth and width, growth rate, and temperature gradient can be enabled, and thus, the microstructure of welds becomes available to be estimated using these temperature-dependent parameters. Furthermore, the dimension of the partially melted zone (PMZ) of welds can be determined using experimental, Rosenthal equation, and FE modeling results. The results obtained from the numerical modeling, the analytical method, and the experiments are compared. The temperature gradient and growth rate determined by the two routes (numerical and analytical) will be evaluated owing to the importance of these parameters in the prediction of microstructure. Moreover, the PDAS (primary dendrite arm spacing) obtained from two approaches will be investigated.

**Figure 4.** *Cont*.

**Figure 4.** (**a**) Transverse-section (*x*-*z*) of the heat transfer; (**b**) molten pool achieved from the numerical modeling using an average laser power of 80 *W*, welding speed of 2 *mm*.*s*<sup>−</sup>1, and absorptivity of 0.36 at *t* = 4 *ms*.
