Research Papers: Heat and Mass Transfer

Analytical Solution for the Electric Arc Dynamics and Heat Transfer When Exposed to a Magnetic Cross-Field

[+] Author and Article Information
Youssef Abdo

MINES ParisTech,
PERSEE—Centre Procédés,
Énergies Renouvelables et
Systèmes Énergétiques,
PSL—Research University,
1 Rue Claude Daunesse,
Sophia Antipolis 06904, France
e-mail: youssef.abdo@mines-paristech.fr

Vandad Rohani, François Cauneau

MINES ParisTech,
PERSEE—Centre Procédés,
Énergies Renouvelables et
Systèmes Énergétiques,
PSL—Research University,
1 Rue Claude Daunesse,
Sophia Antipolis 06904, France

Laurent Fulcheri

MINES ParisTech,
PERSEE—Centre Procédés,
Énergies Renouvelables et Systèmes
PSL—Research University,
1 Rue Claude Daunesse,
Sophia Antipolis 06904, France

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 7, 2017; final manuscript received September 27, 2017; published online March 9, 2018. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 140(6), 062002 (Mar 09, 2018) (11 pages) Paper No: HT-17-1068; doi: 10.1115/1.4038602 History: Received February 07, 2017; Revised September 27, 2017

The motion of the gliding DC electric arc under the effect of magnetic field is investigated. The temperature distribution in the inside and the outside of the moving arc is computed. The temperature distribution for the fixed-spot arc is also obtained. It appears that the gas relative velocity inside the arc gives rise to heat convection, which has an impact on the arc motion. A practical analytical solution is derived using magneto gas dynamic equations in order to investigate the heat transfer occurring in the arc and its vicinity, to determine its characteristics, and to estimate its velocity when it is exposed to external and electrode-induced magnetic fields. Two methods are suggested: one for the free-burning arc and the other for arc burning between close surrounding walls.

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Grahic Jump Location
Fig. 1

Geometric parameters of the electrode-induced magnetic field

Grahic Jump Location
Fig. 2

Boundary conditions for bounded and unbounded domains

Grahic Jump Location
Fig. 3

Parameters S, Smax, and rmax as a function of a and α: (a) rmax function of a and α, (b) Smax function of a and α, and (c) S0 function of a and α

Grahic Jump Location
Fig. 4

Isotherms for the bounded domain for a = 5 mm: (a) isotherms: bounded case with α = 100 m−1 and (b) isotherms: Bounded case with α = 400 m−1

Grahic Jump Location
Fig. 5

Arc velocity with respect to magnetic field for 100 A. (Dashed line): Experimental results from Ref. [12].

Grahic Jump Location
Fig. 6

Arc velocity with respect to current for parallel rails. (Dashed line): MHD simulation results from Ref. [26].

Grahic Jump Location
Fig. 7

Isotherms for a fixed arc with α = 50 m−1 and a = 5 mm and an exponential current density



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