Some features of the thermally concentrated convective motion of a hardening binary melt and the impurity distribution
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Abstract
Some features of the thermally concentrated convective motion of a binary melt, hardening in a closed rectangular region with movable boundaries, and the impurity distribution are investigated numerically.
Keywords
Statistical Physic Rectangular Region Convective Motion Impurity Distribution Movable BoundaryNotation
- x0
characteristic dimension
- xi (i=1, 2)
a dimensional coordinate
- li (i=1, 2)
height and width of the crystallizer cavity
- ri, ei (i=1, 2)
dimensional coordinates of the phase transition in the Ox1x2 coordinate system
- T, T0, and TK
current temperature, initial temperature, and melt crystallization temperature
- ρ
density of the melt
- P, Pmax, and Pmin
current pressure, maximum pressure, and minimum pressure in the system
- c, c0
current and initial impurity concentration
- e2
unit vector having the same direction as the direction as the force of gravity
- ¯g
acceleration due to gravity
- β
coefficient of thermal expansion
- γ
diffusion broadening coefficient
- ¯u
velocity of convective motion
- ν
kinematic viscosity
- k
equilibrium impurity distribution coefficient
- t
current time
- D
diffusion coefficient
- a
thermal diffusivity
- ΔT=t0-tK
initial overheating of the melt
- ηi=Xi/x0 (i=1, 2)
dimensionless coordinate
- ιi=L1/x0 (i=1, 2)
relative height and width of the crystallizer cavity in the coordinate system Oη1η2
- Ri=ri/x0, εi=εi/x0
dimensionless coordinates of the phase-transition boundary in the Oν1η2 coordinate system
- Ū=ū/u0
dimensionless velocity of convective motion
- Gr=¦¯g¦βΔTx03/ν2
Grashof hydrodynamic number
- GrD=¦¯g¦γc0X03/ν2
Grashof diffusion number
- Fo=Dt x02)
dimensionless time, Sm=ν/D, Schmidt number
- Lu=D/a
Lewis number
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Literature cited
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