Abstract: A steady two-dimensional axisymmetric model was developed in order to investigate heat and fluid flows in a free burning GTAW arc.The velocity and temperature profiles of the arc on the conditions of different currents were simulated,and the calculated results were compared.The conclusion is that with the increasing of the arc current,the energy transferred to the arc increases also,and all the parameters in the arc enhance,which are well consistent with classical arc theory.The control equations are solved by using a general thermo-fluid-mechanics computer program,PHOENICS (parabolic hyperbolic or elliptic numerical integration code series) code,which is based on the SAMPLE algorithm.