A new patented process can produce nano-sized carbon materials, in particular fullerenes, by treatment of carbon powders in a 3-phase AC plasma reactor. Computational Fluid Dynamics (CFD) of the reactor for this particular application has been carried out. A simplified model of the arc zone that had been developed earlier was used. The properties of the mixture of gas and carbon particles have been modelled for varying carbon concentration and temperature. The effect of sublimation of carbon particles on the mixture properties has been accounted for in a simplified manner. The theory selected to model the absorption coefficient of the mixture was the Mie theory associated to the Rayleigh limit. Simulations both in 2D and 3D have been performed and the results are discussed. The position of the injection of the particles has a large influence on the temperature field. Measurements are needed to validate the model.