The heat transfer to the anode of an atmospheric pressure argon arc has been calculated using a numerical model for the anode region of the arc. The conservation equations are solved using a finite difference method for a given current and given temperature and velocity profiles at the column end of the computational domain. Local thermal equilibrium is assumed at this upstream boundary. In the anode boundary layer, a two-temperature model which also allows deviations from chemical equilibrium is adopted, and the composition is calculated taking diffusion into account. Results are obtained for two different upstream velocities, and two distinctly different arc attachments are observed: a low upstream velocity leads to a constricted attachment with steep gradients and high specific heat fluxes on the axis, whereas a higher upstream velocity results in lower gradients and heat fluxes distributed over a larger area. This model can serve as a basis for quantitative prediction of anode heat flux profiles for a variety of gas flows and arc currents.