A numerical model has been developed to analyze arc-anode attachment in direct-current electric arcs. The developed model fully couples a plasma flow with electromagnetic fields in a self-consistent manner. Electrons and heavy species are assumed to have different temperatures. Species continuities are taken into account to address the chemical nonequilibrium with the Self-Consistent Effective Binary Diffusion (SCEBD) formulation. Electric and magnetic field equations are determined with a newly developed Ohm's law, an improvement over the conventional generalized Ohm's law. The governing equations are discretized and solved using the Finite Volume Method (FVM) and Gauss-Seidel Line Relaxation (GSLR) method in a two-dimensional domain. The model is applied to a two-dimensional axisymmetric high-intensity argon arc. The results are compared favorably with experimental and other numerical data. A significant electric potential drop has been observed in the vicinity of the anode due to the thermal and chemical nonequilibrium effects.