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We present, in this paper, the MHD modeling of a dc plasma torch operating with air under very peculiar high-voltage low-current conditions. The model developed is 3-D, is time dependent, and assumes local thermodynamic equilibrium (LTE). The study has been carried out considering an axial injection of air with flow rates varying in the range of 0.16-0.5 g/s and currents varying in the range of 300-600 mA. The numerical modeling has been developed using Code_Saturne, a computational fluid dynamics software developed by EDF R&D which is based on colocated finite volume. After a detailed description of the model, the results are presented, analyzed, and discussed. The influence of current and that of air flow rate over the arc characteristics are studied in terms of temperature, velocity, electrical potential, Joule heating, and arc root motion. Regarding numerical issues, the MHD modeling of low-current high-voltage arc discharge is particularly tricky since, below 1 A, the self-induced magnetic field becomes negligible and the convection effects induce a highly irregular and unstable motion of the arc column. However, despite these difficulties, the numerical model has been successfully implemented. Numerical results have shown good correlation and good trends with experimental ones despite a discrepancy which is probably due to the LTE assumption. The model gave fruitful and significant information on parameters that could hardly be obtained experimentally. This preliminary work is likely to open the way toward a better understanding of low-current arc discharges, which technologies are currently encountering an important development in many application fields.