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Heat transfer from a rarefied plasma flow to a metallic or nonmetallic particle

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Abstract

Heat transfer from a plasma flow to a metallic or nonmetallic spherical particle is studied in this paper for the extreme case of free-molecule flow regime. Analytical expressions are derived for the heat flux due to, respectively, atoms, ions, and electrons and for the floating potential on the sphere exposed to a two-temperature plasma flow. It has been shown that the local or average heat flux density over the whole sphere is independent of the sphere radius and approximately in direct proportion to the gas pressure. The presence of a macroscopic relative velocity between the plasma and the sphere causes substantially nonuniform distributions of the local heat flux and enhances the total heat flux to the sphere. The heat flux is also enhanced by the gas ionization. Appreciable difference between metallic and nonmetallic spheres is found in the distributions along the oncoming flow direction of the floating potential and of the local heat flux densities due to ions and electrons. The total heat flux to the whole sphere is, however, almost the same for these different spheres. For a fixed value of the electron temperature, the heat flux decreases with increasing temperature ratio Te/Th.

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Abbreviations

a j :

thermal accommodation coefficient for thejth gas species

e :

elementary charge

E I :

ionization energy (eV)

f − j :

velocity distribution function for thejth gas particles incident on the sphere surface

f + j :

velocity distribution function for thejth gas particles reflected from the sphere surface

k :

Boltzmann's constant

m :

gas particle mass (kg)

n :

number density of gas particles (m−3)

P :

pressure; any point on sphere surface

q j :

local heat flux density due to thejth gas species (W/m2)

Q j :

total heat flux to the whole sphere due to thejth gas species (W)

R o :

sphere radius (m)

S j :

velocity ratio,S j =U/(2kT j /m j )1/2

T e :

electron temperature (K)

T h :

heavy-particle temperature (K)

T w :

wall temperature (K)

U :

oncoming gas flow velocity (m/s)

v :

gas particle velocity,v=(v 2 x +v 2 y +v 2 z )1/2

\(\bar \upsilon \) :

thermal motion speed of gas particles,\(\bar \upsilon \) j =(8kT j /πm j )1/2

W s :

work function of sphere material (eV)

Θ :

angle measured from the frontal stagnation point of sphere

φ :

absolute value of the floating potential; angle

ψ :

particle flux density (m−2 s−1)

\(\bar \psi \) :

average flux over the whole sphere (m−2 s−1)

a :

atoms

e :

electrons

h :

heavy particles

i :

ions

j :

jth gas species

t :

resultant; total

References

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Authors and Affiliations

  1. Engineering Thermophysics Division, Department of Engineering Mechanics, Tsinghua University, 100084, Beijing, China

    Xi Chen & Ping He

Authors
  1. Xi Chen
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  2. Ping He
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Chen, X., He, P. Heat transfer from a rarefied plasma flow to a metallic or nonmetallic particle. Plasma Chem Plasma Process 6, 313–333 (1986). https://doi.org/10.1007/BF00565548

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  • DOI: https://doi.org/10.1007/BF00565548

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