This study focuses on the modeling of a plasma arc heat source in the context ofelectric arc welding. The model was implemented in the open source CFD softwareOpenFOAM-1.6.x, coupling thermal fluid mechanics in three dimensions with electromagnetics.Different approaches were considered for modeling the electromagneticfields: i) the three-dimensional approach, ii) the two-dimensional axi-symmetric approach,iii) the electric potential formulation, and iv) the magnetic field formulation asdescribed by Ramírez et al. [1]. The underlying assumptions and the differencesbetween these models are detailed. The models i) to iii) reduce to the same quasione-dimensional limit for an axi-symmetric configuration with negligible radial currentdensity, contrary to the formulation iv). The models ii) to iv) cannot represent the samephysics when the radial current density is significant, such as for a short arc or anelectrode with a conical tip. The models i) to iii) were retained for doing numerical simulations.The corresponding solvers were tested against analytic solution for an infiniteelectric rod. Perfect agreement was obtained for all the models tested. The completesolver (thermal fluid coupled with electromagnetics) was tested against experimentalmeasurements for Gas Tungsten Arc Welding (GTAW). The shielding gas was argon,the arc was short (2mm), the electrode tip conical, and the configuration axi-symmetric.Anode and cathode were treated as boundary conditions. The models i) and ii) lead tothe same results, but not the formulation iii). It indeed neglects the radial current densitycomponent, resulting in a poor estimation of the magnetic field, and in turn of thearc velocity. Limitations of the complete solver were investigated changing also the gascomposition, and testing boundary conditions. These conditions, difficult to measureand to estimate a priori, significantly affect the simulation results.