The plasma jet produced by a D.C. torch using a nozzle with a cylindrical part for the arc and a divergent part for the plasma expansion is studied. A model based essentially on the energy equation is developped to describe the thermal properties of the arc in the cylindrical channel. The energy equation is solved numerically and simultaneously with a calculation of the physical properties as a function of temperature and pressure. First, for the expansion zone, the momentum and energy equations are solved by a finite difference method. This model allows to investigate the behavior of numerical solutions of plasma equations near the wall. Then, a non equilibrium model is developped for the description of expanding plasma and the pressure, velocities, heavy particle and electron temperatures and densities are determined solving momentum, compositions and energy equations.