A unified fluid flow and heat transfer model is developed by taking into account the coupled transport mechanisms of the plasma arc, weld pool and keyhole in stationary plasma arc welding. The local thermodynamic equilibrium-diffusion approximation method is used to treat the interface between the arc plasma and the weld pool. The volume-of-fluid method is employed to track the keyhole boundary, and the underlying physics in the whole domain are self-consistent. The whole welding process from arc ignition to penetrated keyhole formation, including the weld pool surface depression, blind keyhole expansion, dynamic coupling between the arc plasma and keyhole, interaction of keyhole and weld pool, and the transient behaviors of temperature, fluid flow and electromagnetic fields in the arc column, keyhole and weld pool, are numerically simulated. The dynamic variations of the current density, plasma arc pressure and heat flux at the weld pool surface with the evolution of keyhole boundary are quantitatively analyzed. It is found that as the keyhole depth increases the plasma arc shape, temperature profile and current density distribution undergo dynamic evolution so that the heat flux on the keyhole wall (plasma arc-weld pool interface) changes continuously. However, the plasma jet velocity is insensitive to the keyhole depth so that the plasma arc pressure at the keyhole wall is almost stable. The stationary plasma arc welding experiments are performed, and the macrographs of welds are made to validate the model. (C) 2015 Elsevier Ltd. All rights reserved.