Chinese Science Bulletin

, Volume 44, Issue 23, pp 2141–2145

# Analysis of electromagnetic pressure on thin plate melt

• Shen Jun
• Li Jianguo
• Fu Hengzhi
• Su Junyi
Notes

## Abstract

An equation used to calculate electromagnetic pressure for confining and shaping a plate-form melt with small or medium thickness is brought forward. The equation gives a precise relationship between electromagnetic pressure factorp and current frequencyf, melt thickness a and electromagnetic parameter μγ. The main results can be summarized as follows: (i) As thef, a and μγ are large enough, causing the ratio of melt thickness to current skin deptha/ δ to be larger than 2.2,p will be a constant (p = 1) and the electromagnetic pressure can be calculated withP m =B 2/2μ. (ii) As thef, a, and μγ are not large enough, and the ratioa/ δ is less than 2.2,p is no longer a constant but changes from 1 to 0 with the decrease ofa/δ. In this case, the value of electromagnetic pressure is determined not only by magnetic flux densityB but also by the current frequencyf, melt thickness a and electromagnetic parameter μγ.

## Keywords

electromagnetic confinement and shaping electromagnetic pressure magnetic flux density

## Symbols

Pm

Electromagnetic pressure

p.

electromagnetic pressure factor

P.

static pressure by melt

F

the value of electromagnetic body force in melt

B

the value of magnetic flux density on melt surface

B2

the value of magnetic flux density in melt

Bzo

the value of magnetic flux density at the center (x=0) of melt

(Bz0)m

amplitude of magnetic flux density at the center (x=0) of melt

Bz

the vector of magnetic flux density in melt

Hz

the vector of magnetic field density in melt

E2

the vector of electric field density in melt

J1

the vector of electric current density in melt

Bz

the phase form of magnetic flux density in melt

Bz0

the phase form of magnetic flux density at the center (x= 0) of melt

Hz

the phase form of magnetic field density in melt

Ė0

the phase form of electric field density in melt

J.

the phase form of electric current density in melt

j

the imaginary operator of complex number

μ

magnetic conductivity of melt

γ

electric conductivity of melt

α

melt thickness

f

electric current frequency

δ

electric current theoretic skin depth

K

√ηfμγ

k

√2jK

## References

1. 1.
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2. 2.
El-Kaddah, N., Martimer, J. H., New crucibleless melting process promises refractory-free melting for high-quality castings,Light Metal Age, 1990, 19(10): 37.Google Scholar
3. 3.
Sears, J. W., Current processes for cold-wall melting of titanium,Journal of Metals, 1990, 42(3): 17.Google Scholar
4. 4.
Sakane, J., Li, B. Q., Evans, J. W., Mathematical modeling of meniscus profile and melt flow in electromagnetic castings,Metallurgical Transations B, 1988, 19(6): 397.
5. 5.
Li, B. Q., Evans, J. W., Cook, D. P., An improved mathematical model for electromagnetic casters and testing by a physical model,Metallurgical Transactions B, 1991, 22(2): 121.

© Science in China Press 1999

## Authors and Affiliations

• Shen Jun
• 1
• 2
• Li Jianguo
• 1
• Fu Hengzhi
• 1
• Su Junyi
• 2
1. 1.State Key Laboratory of Solidification ProcessingNorthwestern Polytechnic UniversityXi’anChina
2. 2.Department of Mechanical EngineerirrgXi’an Jiaotong UniversityXi’anChina