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 densitySymbols
- 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
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References
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