Abstract
A model of a casting is presented which describes the freezing of a mushy zone, growing with a dynamically calculated undercooling at the dendrite tips. Equiaxed grains are introduced ahead of a columnar front. The model resembles a combination of the Stefan and mushy zone problems.
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Abbreviations
- c0 :
-
composition
- C :
-
heat capacity per unit volume
- C 1, C 2, C 3 :
-
parameters
- D:
-
solutal diffusion coefficient
- g:
-
weight fraction
- G:
-
temperature gradient
- h:
-
heat transfer coefficient
- H:
-
heat content or enthalpy per unit volume
- I:
-
nucleation rate per unit volume
- k:
-
distribution coefficient
- ki :
-
thermal conductivity (i = 5 or l)
- Ki :
-
thermal conductivity of a single phase (i = s or l)
- L:
-
latent heat per unit volume evolved at the front
- m :
-
liquidus slope
- N :
-
number of grain per unit volume
- N 0 :
-
number of substrate particles per unit volume
- r :
-
extended radius of a grain
- t :
-
time
- T :
-
temperature at time t
- v :
-
velocity
- x :
-
distance
- α :
-
width of control volume immediately ahead of the columnar front
- β :
-
width of control volume immediately behind the columnar front
- δ :
-
boundary layer thickness
- δt :
-
time discretisation interval
- δx :
-
spatial discretisation interval
- ΔH :
-
latent heat per unit volume
- ΔT :
-
undercooling
- χ :
-
pseudo heat transfer coefficient
- ω :
-
extended volume fraction of grains
- Ω :
-
volume fraction of grains
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© 1987 Martinus Nijhoff Publishers, Dordrecht
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Flood, S.C., Hunt, J.D. (1987). A model of a casting. In: Smith, T.J. (eds) Modelling the Flow and Solidification of Metals. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3617-1_3
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DOI: https://doi.org/10.1007/978-94-009-3617-1_3
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