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.
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Abbreviations
- 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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Shen, J., Li, J., Fu, H. et al. Analysis of electromagnetic pressure on thin plate melt. Chin. Sci. Bull. 44, 2141–2145 (1999). https://doi.org/10.1007/BF03182696
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DOI: https://doi.org/10.1007/BF03182696