Abstract
This paper is concerned with an analytical study of the heat and mass transfer process of a single particle exposed to a thermal plasma, with emphasis on the effects which evaporation imposes on heat transfer from the plasma to the particle. The results refer mainly to an atmospheric-pressure argon plasma and, for comparison purposes, an argon-hydrogen mixture and a nitrogen plasma are also considered in a temperature range from 3000 to 16,000 K. Interactions with water droplets, alumina, tungsten, and graphite particles are considered in a range of small Reynolds numbers typical for plasma processing of fine powders. Comparisons between exact solutions of the governing equations and approximate solutions indicate the parameter range for which approximate solutions are valid. The time required for complete evaporation of a given particle can be determined from calculated values of the vaporization constant. This constant is mainly determined by the boiling (or sublimation) temperature of the particles and the density of the condensed phase. Evaporation severely reduces heat transfer to a particle and, in general, this effect is more pronounced for materials with low latent heat of evaporation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- A :
-
constant in Eq. (37)
- C p :
-
specific heat at constant pressure
- \(\bar C_p \) :
-
average specific heat at constant pressure
- D :
-
diffusion coefficient of vapor in mixture
- f :
-
mass fraction of vapor in mixture
- G :
-
total mass flux due to evaporation or sublimation
- h :
-
specific enthalpy
- K :
-
vaporization constant (m2/s)
- k :
-
thermal conductivity
- \(\bar k\) :
-
average thermal conductivity
- L :
-
latent heat of evaporation
- n :
-
constant in Eq. (37)
- M :
-
function defined in Eq. (16)
- m :
-
constant in Eq. (37)
- Nu:
-
Nusselt number
- Pr:
-
Prandtl number
- p :
-
pressure
- Q 0 :
-
total heat flux to a particle without evaporation
- q 0 :
-
specific heat flux to a particle without evaporation
- Q 1 :
-
total heat flux to a particle with evaporation
- q 1 :
-
specific heat flux to a particle with evaporation
- R :
-
radius of the outer edge of the computation domain
- r :
-
radius
- Re:
-
Reynolds number
- r s :
-
radius of particle
- r s0 :
-
initial radius of particle, Eq. (36)
- S :
-
heat conduction potential
- T :
-
temperature
- t :
-
time
- t v :
-
vaporization time, Eq. (36)
- u r :
-
r-component of velocity
- u θ :
-
θ-component of velocity
- v:
-
velocity vector
- θ :
-
angle from frontal stagnation point inr-θ coordinates
- λ :
-
bulk viscosity
- μ :
-
dynamic viscosity
- ρ :
-
density
- c :
-
condensed phase
- s :
-
at the surface of particle
- 0:
-
without evaporation
- 1:
-
with evaporation
- ∞:
-
far away from particle
References
I. G. Sayce, Plasma processes in extractive metallurgy,Advances in Extractive Metallurgy, Inst. of Min.-Met., London (1971).
B. Waldie, Review of recent work on the processing of powders in high-temperature plasmas. Part 1. Processing and economic studies,Chem. Eng. 259, 92 (1972).
B. Waldie, Review of recent work on the processing of powders in high-temperature plasmas. Part II. Particle dynamics, heat and mass transfer,Chem. Eng. 261, 188 (1972).
C. R. Veale,Fine Powders, Preparation, Properties and Uses Halsted Press, Wiley, New York (1972), p. 101.
S. F. Excell, R. Roggen, J. Gillot, and B. Lux, Preparation of ultrafine powders of refractory carbides in an arc plasma,Proceedings of the Fine Particles Symposium, 1965, Electrochemical Soc. (1973).
W. E. Kuhn, Morphology of boron nitride produced by arc vaporization of liquid boron oxide, proceedings of theFine Particles Symposium, Electrochemical Soc., 81 (1973).
M. I. Boulos and W. H. Gauvin, Powder processing in a plasma jet: a proposed model,Can. J. Chem. Eng. 52, June 1974.
J. Kenton and J. Grant, inFine Particle Second International Conference, William E. Kuhn and Jean Ehretsmann, eds., Electrochemical Society, Inc. (1974), p. 308.
P. Fauchais and J. M. Baronnet, State of the art of plasma chemical synthesis of homogeneous and heterogeneous products,Pure Appl. Chem. 52, 1669 (1980).
B. Mitrofanov, A. Mazza, E. Pfender, P. Ronsheim and L. E. Toth, D.C. arc plasma titanium and vanadium compound synthesis from metal powders and gas-phase non-metals,Mater. Sci. Eng. 48, 21–26 (1981).
P. Ronsheim, E. Pfender and L. E. Toth, Characteristics of particle growth in a thermal plasma jet,Fifth International Symposium on Plasma Chemistry, Vol. 2, Heriot-Watt University, Edinburgh, Scotland (1981).
P. Ronsheim, L. E. Toth, A. Mazza, E. Pfender and B. Mitrofanov, Direct current arc-plasma synthesis of tungsten carbides,J. Mater. Sci. 16, 2665–2674 (1981).
T. Yoshida and K. Akashi, Particle heating in a radio-frequency plasma torch,J. Appl. Phys. 48, 2252 (1977).
J. A. Lewis and W. H. Gauvin, Motion of particles entrained in a plasma jet, AIChE J.19, No. 5, 982 (1973).
M. I. Boulos, Heating of powders in the fire-ball of an inductive plasma,IEEE Trans. Plasma Sci. 4, No. 2, 93 (1978).
W. E. Ranz and W. R. Marshall, Jr., Evaporation from drops. Part II,Chem. Eng. Prog. 48, 173 (1952).
J. K. Fiszdon, Melting of powder grains in a plasma flame,Int. J. Heat Mass Trans. 22, 749 (1979).
Y. C. Lee, K. C. Hsu and E. Pfender, Modeling of particles injected into a d.c. plasma jet,Fifth International Symposium on Plasma Chemistry, Vol. 2, Heriot-Watt University, Edinburgh, Scotland (1981), p. 795.
C. Bonet, Thermal plasma processing,Chem. Eng. Prog.,72, 63 (1976).
C. Borgianni, M. Capitelli, F. Cramerossa, L. Triolo, and E. Molinari, The behavior of metal oxides injected into an argon induction plasma,Combust. Flame 13, 181 (1969).
P. D. Johnston, The rate of decomposition of silica particle in an augumented flame,Combust. Flame 18, 373 (1972).
Author information
Authors and Affiliations
Additional information
On leave from the Department of Engineering Mechanics, Tsinghua University, Beijing, P.R.C.
Rights and permissions
About this article
Cite this article
Chen, X., Pfender, E. Heat transfer to a single particle exposed to a thermal plasma. Plasma Chem Plasma Process 2, 185–212 (1982). https://doi.org/10.1007/BF00633133
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00633133