The elaborated model solves the coupled equations of a laminar fluid flow and heat transfer to predict the temperature distribution in the weld pool. The enthalpy-porosity technique was employed to account for the latent heat during melting and solidification. The coupled effects of buoyancy and Marangoni forces are considered in this model. The volume-of-fluid (VOF) method was employed to track free surfaces of weld pool. The molten temperature distribution, velocity field and molten shape were calculated using FLUENT software. The results clearly demonstrate Marangoni flow significantly alters the characteristics of the thawing and solidifying process, and makes the molten wider and shallower.