The dynamics of the melt spinning of metals by making use of the spinnability of glass are analyzed by deriving a set of simultaneous partial differential equations which have been developed to describe the spinning of polymers. For steady-state, equation of heat balance: where,
Lp=constant for
T=
Ts and
Lp=0 for
T_??_
Ts, equation of force balance: ∂
A∂
z=
-FAρ'
K/β
W, equation of material balance:
vz ∂
A/∂
z+
A∂
vz/∂
z=0. Where,
T: temperature,
z: distance from the bottom of the molten metal toward the winding drum, W: flow rate of metal,
Cp and
C'p: specific heat of metal and glass,
K: weight ratio of metal to glass,
Lp: heat of fusion of metal, ρ and ρ': density of metal and glass,
T∞: temperature of the atmosphere,
h and
hr: coefficient of heat transfer at the filament surface for convection and radiation,
Ts: temperature of solidification of metal,
F: spinning tension, β: tensile viscosity,
vz: local velocity,
A: cross-sectional area.
The solutions of the above equations corresponding to the melt spinning of copper, silver and stainless-steel using pyrex glass showed fairly good agreement with the experimentally measured values of thickness
A(
z) and temperature
T(
z). Compared to the melt spinning of polymers, the solidification of metal spin line is very rapid, for example,
A(
z) becomes constant within
z=0.5cm from the spinneret with the cooling rate amounting to as much as about 10
5°C/sec.
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