Abstract
Heat transfer to a copper particle immersed into an argon plasma is considered in this paper, including the effects of contamination of the plasma (transport coefficients) by copper vapor from the particle. Except for cases of high plasma temperatures, the vapor content in the plasma is shown to have a considerable influence on heat transfer to a nonevaporating particle, and, to a lesser extent, on heat transfer to an evaporating particle. Evaporation itself reduces heat transfer to a particle substantially as shown in a previous paper [Xi Chen and E. Pfender, Plasma Chem. Plasma Process.,2, 185 (1982)]. Comparisons of the calculated results with those based on a method suggested in the above reference show that the simplified assumptions employed, i.e., that the surface temperature is equal to the boiling point and that plasma properties based on a fixed composition are applicable, can be employed to simplify calculations for many cases. This study reveals that a considerable portion of a particle must be vaporized before a steady concentration distribution is established around the particle.
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Abbreviations
- C p :
-
specific heat at constant pressure
- D :
-
diffusion coefficient of copper in the mixture
- D a :
-
diffusion coefficient of copper atoms in the mixture
- D i :
-
ambipolar diffusion coefficient of copper ions in the mixture
- f :
-
mass fraction of copper in the mixture
- f a :
-
mass fraction of copper atoms in the mixture
- f i :
-
mass fraction of copper ions in the mixture
- f ∞ :
-
mass fraction of copper in the plasma far away from the particle
- f s :
-
mass fraction of copper at the particle surface
- G :
-
total mass flow rate due to evaporation
- G a :
-
mass flow rate of copper atoms
- G i :
-
mass flow rate of copper ions
- H :
-
function defined in Eq. (19)
- h :
-
specific enthalpy
- h s :
-
specify enthalpy at the particle surface
- h ∞ :
-
specific enthalpy corresponding toT ∞ andf ∞
- k :
-
thermal conductivity
- L :
-
latent heat of evaporation
- M 1 :
-
molecular weight of argon (M 1=39.99)
- M 2 :
-
molecular weight of copper (M 2=63.55)
- p 0 :
-
pressure of the gas mixture
- p s :
-
partial pressure of copper vapor at the particle surface
- Q 0 :
-
heat flux to a particle without evaporation
- Q 1 :
-
heat flux to a particle with evaporation
- R :
-
gas constant
- r :
-
radical coordinate
- r s :
-
particle radius
- S :
-
heat conduction potential defined in Eq. (4)
- S s :
-
surface value ofS, corresponding toT s andf s
- S ∞ :
-
free-stream value ofS, corresponding toT ∞ andf ∞
- T :
-
temperature
- T b :
-
boiling temperature of particle material
- T s :
-
particle surface temperature
- T ∞ :
-
plasma temperature
- ρ :
-
density
- ΔT :
-
temperature step for numerical integration
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Chen, X., Chyou, Y.P., Lee, Y.C. et al. Heat transfer to a particle under plasma conditions with vapor contamination from the particle. Plasma Chem Plasma Process 5, 119–141 (1985). https://doi.org/10.1007/BF00566210
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DOI: https://doi.org/10.1007/BF00566210