The rate of production and the spatial distribution of ozone in the negative DC corona discharge are predicted with a numerical model. The results are compared to prior experimental data and to results previously presented by the authors for the positive corona discharge. In agreement with experimental data, ozone production rate in the negative corona is an order of magnitude higher than in the positive corona. The model reveals that this significant difference is due to the effect of discharge polarity on the number of energetic electrons in the corona plasma. The number of electrons is one order of magnitude greater and the chemically reactive plasma region extends beyond the ionization region in the negative corona. The paper also extends our prior modeling effort to lower velocities where the Joule heating reduces ozone production. The magnitude of the reduction is characterized by a new dimensionless parameter referred to as the electric Damkohler's third number (Da(III-e)).