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Two-dimensional modeling of non-transferred dc plasma torches have been performed using an axis symmetric geometrical configuration and boundary conditions. A control volume approach and SIMPLER algorithm is used to solve the governing equations for mass, momentum, and energy conservation coupled with the electric and magnetic fields. The results are compared with the ones obtained in 3-D simulation works of the authors. Results show substantial difference in control parameters as calculated from the two simulations, owing to local attachment of the arc over the anode surface.