Corona discharges are due to the ionization of the gas between two electrodes when the electric field near one of them is very strong. The lack of a complete understanding of the physical processes in corona discharge in both positive and negative polarity means that interest in corona discharge is still current. In this work, we use a more realistic hydrodynamic plasma model which considers 12 charged species such electron, ions and molecules, and 32 chemical reactions present in the plasma. The digital algorithm based on the finite element method is implemented using the commercial software COMSOL Multiphysics (c). A geometrical configuration of a 1D-axisymmetric wire-cylinder is considered and the set of reactions takes place in the radial direction given the symmetry of the system. The results show that the electron density in the negative corona is four orders of magnitude greater than that in the positive corona. The total number of electrons in the plasma layer of the negative corona is more than 50 times that produced in the positive corona. Under identical temperature and pressure conditions, the weakest corona current in positive polarity, which implies a lower ignition DC voltage. Temperature has an opposite effect on the distribution of the electron density present in the plasma. While the rise in temperature causes a rapid increase in the density of electrons in negative corona, the increase is slower in positive corona. In both cases, the electric field is constant on the conductor surface, however the space charge modifies the local electric field.