It is well recognized that the fluid flow is an important factor in overall heat and mass transfer in molten pools during arc welding, affecting geometry of the pool and temperature distribution in the pool and in the HAZ. These in turn influence solification behavior, which determine the mechanical properties and quality of the weld fusion zone. Here, a comprehensive numerical model of the time dependent weld pool flow in GTA welding, with a moving heat source has been developed. This model included heat transfer, radiation, evaporation, electromagnetic forces and Marangoni stress in the free surface boundary. With this 3D, fully time dependent model, the true chaotic time dependent melt flow is obtained. The time dependent properties of flow velocities and temperature of numerical results are examined. It shows that the temperature fields axe strongly affected by convection at the weld pool surfaces. The fluid flow in the weld pool is highly complex and it influences the weld pool's depth and width. Moreover, the velocity field at the surface of the specimen determines the streamlines defining the traveling paths of inclusions such as slag particles.