A 2D mathematical model was developed for the GTAW arc welding process (Gas Tungsten Arc Welding). Computational simulations were performed by using the commercial software PHOENICS based on mass and momentum conservation equations as well as on Maxwell equations. The model predicts the electric characteristics of the arc column, flow patterns, temperature profiles, heat flux, total heat flow and the electrical potential, by varying the arc length and the applied current. By increasing the current the arc jet is stronger, hotter and provides more heat to the weld pool, while by increasing the arc length the maximum temperature, maximum velocity and heat flow are unchanged, although a short arc focuses the heat in a small area and a long arc spreads the heat in a wider area of the work piece.Keywords: Electric arc, heat transfer, fluid flow, mathematical modeling.