A numerical model of ozone generation in clean, dry air by positive DC corona discharges from a thin wire is presented. The model combines the physical processes in the corona discharge with the chemistry of ozone formation and destruction in the air stream. The distributions of ozone and nitrogen oxides are obtained in the neighborhood of the corona discharge wire. The model is validated with previously published experimental data. About 80% of the ozone produced is attributed to the presence of excited nitrogen and oxygen molecules. A parametric study reveals the effects of linear current density (0.1-100 muA/cm of wire), wire radius (10-1000 mum), temperature (300-800 K) and air velocity (0.05-2 m/s) on the production of ozone. The rate of ozone production increases with increasing current and wire size and decreases with increasing temperature. The air velocity affects the distribution of ozone, but does not affect the rate of production.