I. I. Beilis and &. A. , Seval'nikov ; Column of an atmospheric-pressure electric arc High Temp, 1991.

P. Bertrand, M. Ignatiev, I. Smurov, and &. G. Flamant, Temperature monitoring during plasma-rc welding and cladding, TPP5 Proceedings, St Petersbourg, pp.13-16, 1998.

M. S. Benilov, A kinetic derivation of multifluid equations for multispecies non equilibrium mixtures of reacting gases Phys, Plasma, vol.4, issue.3, 1997.

D. Bershader, &. R. Landshoff, and V. L. Streeter, Magnetohydrodynamics Handbook of fluid dynamics, 1961.

R. Berton and . Magnétohydrodynamique, Collection Physique Fondamentale et Appliquée, 1991.

S. Bousrih, E. Ershov-pavlov, S. Megy, and &. Baronnet, Hydrogen/argon plasma jet with methane addition, Plasma Chemistry and Plasma Processing, vol.28, issue.No. 3, 1995.
DOI : 10.1007/BF01459702

B. Bowman, Properties of arcs in dc furnaces, 52 nd Electric Furnace Conference Proceeding, 1994.

B. Bowman, G. R. Jordan, and &. F. Fitzgerald, The physics of high current arcs, Journal of the Iron and Steel Institute, 1969.

D. M. Chen, K. C. Hsu, C. H. Liu, and &. E. Pfender, The Effects of Cold Gas Injection on a Confined Arc Column, IEEE Transactions on Plasma Science, vol.8, issue.4, 1980.
DOI : 10.1109/TPS.1980.4317351

D. M. Chen, K. C. Hsu, and &. E. Pfender, Two-temperature modeling of an arc plasma reactor, Plasma Chemistry and Plasma Processing, vol.16, issue.4, 1981.
DOI : 10.1007/BF00568837

Q. P. Chen and &. P. Biringer, The influence of arc constants on the characteristics of arc furnaces electrowärme international, p.4, 1991.

P. Conraux, Etude des phénomènes électromagnétiques présents dans une torche à plasma Thèse INPG, 1989.

P. Conraux, G. Meunier, F. Kassabji, and &. M. Moneuse, Computation of electromagnetic phenomena appearing in a plasma torch, IEEE Transactions on Magnetics, vol.24, issue.1, 1988.
DOI : 10.1109/20.43973

C. J. Cremers and &. H. Hsia, Thermal behavior of confined arcs with local fluid constriction Heat &, 1977.

C. J. Cremers, H. S. Hsia, and &. J. Mahan, Downstream Conditions in a Constricted ARC with Radial Injection, IEEE Transactions on Plasma Science, vol.1, issue.3, 1973.
DOI : 10.1109/TPS.1973.4316088

S. Delalondre, &. O. Zahrai, and . Simonin, Turbulence modelling in electric arc Collection des notes internes DER EDF, HE-44, 1994.

D. L. Evans and &. R. Tankin, Measurement of emission and absorption of radiation by an argon plasma The Physics of Fluids, p.10, 1967.

F. Fabry, Deuxième rapport intermédiaire relatif à l'article numéro 3 au contrat d'association n°E 26/L11-7C 6968-AEE 1674 établie entre CNRS, 1996.

F. Fabry, B. Ravary, P. Bertrand, J. M. Badie, L. Fulcheri et al., Smurov ; Comparison of experimental and theoretical temperature distribution in a plasma pilot reactor for carbon black production, TPP5 Proceedings, St Petersbourg, pp.13-16, 1998.

H. G. Fan and &. Y. Shi, Numerical simulation of the arc pressure in gas tungsten arc welding, Journal of Materials Processing Technology, vol.61, issue.3, p.61, 1996.
DOI : 10.1016/0924-0136(95)02190-6

P. Fauchais, La modélisation des plasmas thermiques, Ann. Chim. Fr, vol.8, 1983.
DOI : 10.1016/s0035-3159(99)80081-6

P. Fauchais and A. Vardelle, Pateyron ; Plasma spraying extractive and metallurgy : comparisons between mathematical modelling and measurements and between application and development Pure, J.F. Coudert & B. Appl. Chem, vol.57, issue.9, 1985.
DOI : 10.1351/pac198557091171

F. Inc, FLUENT User's guide V4, 1997.

L. Fulcheri and &. Y. Schwob, From methane to hydrogen, carbon black and water, International Journal of Hydrogen Energy, vol.20, issue.3, 1995.
DOI : 10.1016/0360-3199(94)E0022-Q

URL : https://hal.archives-ouvertes.fr/hal-01425269

P. Gardin, C. Soide, A. Dez, and &. I. Guillaume, Use of physical and numerical simulation methods to characterize gas flow in trielectrode arc furnace, Ironmaking & Steelmaking, 1992.

R. V. Giles, J. B. Evett, and &. Liu, Fluid mechanics & hydraulics, Schaum's outline series theory and problems Mc Graw Hill, 1994.

I. S. Gradshteyn and &. I. Ryzhik, Table of integrals, series and products Academic press, 1980.

J. Grey and &. F. Jacobs, Experiments on Turbulent Mixing in a Partially Ionised Gas, AIAA Journal, vol.2, issue.3, 1964.

J. Haidar and &. A. Farmer, Temperature measurements for high-current free-burning arcs in nitrogen, Journal of Physics D: Applied Physics, vol.26, issue.8, 1993.
DOI : 10.1088/0022-3727/26/8/011

N. J. Holt, J. A. Bakken, and &. R. Jensen, Numerical computation of heat transfer in a 300 kW plasma reactor High Temp, Chem. Processes, issue.2, 1993.

K. C. Hsu and &. E. Pfender, Two???temperature modeling of the free???burning, high???intensity arc, Journal of Applied Physics, vol.54, issue.8, 1983.
DOI : 10.1063/1.332672

K. C. Hsu, K. Etemadi, and &. E. Pfender, Study of the free???burning high???intensity argon arc, Journal of Applied Physics, vol.54, issue.3
DOI : 10.1063/1.332195

G. R. Jones and &. T. Fang, The physics of high-power arcs Rep, Prog. Phys, vol.43, 1980.

G. R. Jordan, B. Bowman, and &. D. Wakelam, Electrical and photographic measurements of high-power arcs, Journal of Physics D: Applied Physics, vol.3, issue.7, 1970.
DOI : 10.1088/0022-3727/3/7/313

M. E. Jordan, Process for production of highly amorphous carbon black, Brevet US Patent, vol.3431, p.74, 1969.

M. E. Jordan, H. M. Cole, V. Walpole, and W. G. , Carbon black product ans method of preparation thereof, p.554, 1967.

V. D. Khait, A channel model for an electric arc and the minimum power principle High Temp, 1979.

G. Kirschtein and &. F. Koppelmann, Der elektrischeLichtbogen in schnelströmenden Gas part I Wissenschaftliche Veroffenlichungen aus den Siemens-Werken, 1937.

G. Kirschtein and &. F. Koppelmann, Der elektrischeLichtbogen in schnelströmenden Gas part II Wissenschaftliche Veroffenlichungen aus den Siemens-Werken, 1937.

A. Laassouli, Thèse de doctorat, numéro 105C, p.22, 1990.

H. L. Larsen, AC electric arc models Dr, 1996.

H. L. Larsen and &. J. Bakken, A time dependent numerical model for an AC electric arc, Proceedings of the 3 rd European Congress on Thermal Plasma Processes, 1994.

H. L. Larsen, Channel model for AC electric arc SINTEF report, STF34 A93113, metallurgy, 1993.

J. J. Lowke, P. Kovitya, and &. H. Schmidt, Theory of free-burning arc columns including the influence of the cathode, Journal of Physics D: Applied Physics, vol.25, issue.11, 1992.
DOI : 10.1088/0022-3727/25/11/006

J. J. Lowke, R. L. Zollweg, and &. R. Liebermann, Theoretical description of ac arcs in mercury and argon, Journal of Applied Physics, vol.46, issue.2, 1975.
DOI : 10.1063/1.321681

S. Lynum, System for the production of carbon black, 1993.

J. R. Mahan and &. J. Cremers, The confined discharge plasma generator with local fluid constriction Transactions of the ASME, 1972.

J. W. Mckelliget and &. , El-Kaddah ; Theoretical prediction of the effect of coil gas configuration on gas mixing in an inductively coupled plasma torch Mat, Res. Soc. Symp, vol.98, 1987.

J. W. Mckelliget and &. J. Szekely, A mathematical model of the cathode region of a high intensity carbon arc, Journal of Physics D: Applied Physics, vol.16, issue.6, 1983.
DOI : 10.1088/0022-3727/16/6/010

H. Minoo, A. Arsaoui, A. Bouvier, and &. L. Jestin, Arc cathode root movements of a plasma generator at atmospheric pressure stabilized by a magnetic field and gas vortex flow, 1994.

M. Mitchner and &. C. Kruger-jr, Partially ionized gases J, 1973.

L. Msika, C. Delalondre, and &. O. Simonin, Modélisation d'un arc transféré dans l'azote à pression atmosphérique Collection des notes internes DER EDF, HE-44/92, 1992.

Z. Njah, J. Mosthaghimi, and &. M. Boulos, Mathematical modelling of the 3-D mixing in an induction plasma reactor, International Journal of Heat and Mass Transfer, vol.36, issue.16, p.16, 1993.
DOI : 10.1016/0017-9310(93)90141-R

Z. Njah, J. Mostaghimi, M. Fahgri, and &. M. Boulos, Study of 3D mixing of a cold jet in an induction plasma reactor, Int. J. Heat Mass Tranfer, vol.36, p.16, 1993.

S. Patankar, Numerical Heat Transfer & Fluid Flow Hemisphere Publishing Corp, 1980.

H. Pfeiffer, F. N. Fett, and &. H. Bebber, Model development for free burning AC plasma jets electrowärme international, p.3, 1989.

E. Pfender, J. Fincke, and &. R. Spores, Entrainment of cold gas into thermal plasma jets Plasma Chem, & Plasma Process, vol.11, issue.4, 1991.

K. , S. Bolouri, and &. J. Amouroux, Procédé et appareil de fabrication de noir de carbone à partir d'hydrocarbures, 1984.

O. Simonin, C. Delalondre, and &. P. Viollet, Modelling in thermal plasma and electric arc column Pure & Appl, Chem, vol.64, issue.5, 1992.

G. Soucy, J. W. Jurewicz, and &. I. Boulos, Mixing study of the induction plasma reactor. Part I : Axial injection mode Plasma Chem. & Plasma Process, 1994.

G. Soucy, J. W. Jurewicz, and &. I. Boulos, Mixing study of the induction plasma reactor. Part II : Radial injection mode Plasma Chem. & Plasma Process, 1994.

S. Vacquié, Etude des transferts. Rayonnement, diffusion et conduction thermique in : Club EDF Arc Electrique 'L'arc électrique et ses applications, 1984.

&. D. Veillette and . Simard, Electric arc characterization using high speed cinematography and spectroscopy, 42 nd Electric Furnace Conference Proceeding, p.42, 1984.

R. Westhoff and &. J. Szekely, A model of fluid, heat flow, and electromagnetic phenomena in a nontransferred arc plasma torch, Journal of Applied Physics, vol.70, issue.7, 1991.
DOI : 10.1063/1.349238

H. Wu, G. F. Carey, and &. E. Oakes, Numerical Simulation of AC Plasma Arc Thermodynamics, Journal of Computational Physics, vol.112, issue.1, 1994.
DOI : 10.1006/jcph.1994.1079

S. Zahrai, C. Delalondre, O. Simonin, and &. D. Andersson, Three dimensional simulations of transient high intensity electric arcs Collection des notes internes DER EDF, HE-44/93, 1996.