Laser welding is widely used in the industry for the advantage of small heat affected zone and short weld process time. Conduction limit welding can be used to modify the surface characteristic and it is important to identify the heat affecting area correctly for the improvement of manufacturing accuracy. Since time and length scale associated with laser welding process are extremely small, numerical study can be a useful tool. In this study, two-dimensional axi-symmetric version of energy equation with enthalpy method has been used to analyze the effect of laser input conditions on final shape by the laser welding process. The proposed numerical procedure has been benchmarked with several experimental results and compared well. The modified Marangoni and Peclet number have been introduced using controllable input variables. Simple parametric researches have been performed for high Pr number material. The results show that higher Marangoni number increase fluid mixing, thus generating convex type weld pool. On the other hand, the width of the weld pool is proportional to Peclet number.