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Anisotropic model of an emitting electric arc

Abstract

An analytical procedure is proposed for obtaining exponential dimensionless equations to calculate the characteristics of an electric arc in a plasmatron channel that is based on using an exponential approximation of the temperature dependence of electric conductivity with different exponents for longitudinal and transverse coordinates.

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Abbreviations

ρ:

density

C p :

specific heat at constant pressure

σ:

electrical conductivity

λ:

thermal conductivity

V :

velocity

T :

temperature

E :

electric-field strength

r, z :

radial and longitudinal coordinates

\(S = \int\limits_0^T \lambda dT\) :

thermal conductivity function

G :

gas flow rate

Q :

bulk radiation density

R, D :

radius and diameter of channel

I :

strength of current

\(\bar r\) :

r/R

\(\bar z\) :

z/R

m :

R/r *=1/r *

ΔS :

S−S *

b Q :

Q 0S 0

a, k,k σ,n σ,C 00, κ:

constants

J 0,J 1,Y 0 :

Bessel functions

μ1, α n :

roots of characteristic equations

j :

current density

q :

heat flux density

Po, Pe:

Pomerantsev and Pecklet numbers, respectively

Nu:

Nusselt number

Π K , Π U , Π q ,K Q ,K S :

similarity numbers

U :

voltage

α:

heat-transfer coefficient

z :

longitudinal component

*:

boundary of conducting band

0:

base value

1:

value on the wall

00:

axial value

I, II:

conducting and nonconducting bands, respectively

References

  1. 1.

    G. A. Stain, Investigations at High Temperatures [in Russian], Moscow (1967), pp. 94–112.

  2. 2.

    G. Mekker, A Moving Plasma [Russian translation], Moscow (1961), pp. 439–472.

  3. 3.

    A. V. Luikov, Theory of Heat Conduction [in Russian], Moscow (1967).

  4. 4.

    S. S. Kutateladze and O. I. Yas'ko, Inzh.-Fiz. Zh., 7, No. 4, 25–27 (1964).

  5. 5.

    A. F. Bublievskii and O. I. Yas'ko, Proc. of 11th Intern. Symposium on Plasma Chemistry. Loughborough University. Loughborough, England, Vol. 1, pp. 302–307 (1993).

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Additional information

Academic Scientific Complex “A. L. Luikov Institute of Heat and Mass Transfer of the Academy of Sciences of Belarus,” Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 5, pp. 820–826, September–October, 1995.

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Cite this article

Bublievskii, A.F. Anisotropic model of an emitting electric arc. J Eng Phys Thermophys 68, 667–672 (1995). https://doi.org/10.1007/BF00858069

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Keywords

  • Electric Conductivity
  • Statistical Physic
  • Analytical Procedure
  • Anisotropic Model
  • Exponential Approximation