Fundamentals of Solidification

1
Fundamentals of Solidification

• Lecture 2 Heat transfer

2
Outline

• Heat transfer
• Latent heat
• Solidification rate
• Interface kinetics

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Heat transfer

• There are three ways of heat transfer
• Radiation
• Convection
• Conduction

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Heat transfer - radiation
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Heat transfer - radiation

• Thermal radiation is electromagnetic radiation
  emitted from the surface of an object which is
  due to the object's temperature.

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Heat transfer - radiation
Lab oven designed to reflect radiation and reduce
heat leak
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Heat transfer -convection
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Heat transfer - convection

• Flow-dependent heat transfer
• Need to solve hydrodynamic equation to get flow
  velocity field.
• Using diffusion-convection equation to solve
  temperature profile.
• There are many rough approximations used in
  industry

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Heat transfer - conduction

• Continuous casting

• Mould casting

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Heat transfer - conduction

• Fouriers first law of heat transfer

flow of heat K thermal conductivity
T1
T2
L
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Heat transfer - conduction
Thermal conductivity
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Latent heat
solid
liquid
Anything missing?
Solid-liquid interface
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Latent heat

• Latent heat is the amount of energy in the form
  of heat released or absorbed by a substance
  during a change of phase state
• Solidification Released
• Q mL (Q latent heat m mass L specific
  latent heat)

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Latent heat

• Heat produced due to latent
• Q mL (Q latent heat m mass L specific
  latent heat)
• The heat flow generated due to phase transition

? Is density, v is interface migration rate
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Solidification rate
solid
liquid
Solid-liquid interface
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Solidification rate

• Energy conservation gives
• Heat generated heat transferred in heat
  transferred out

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Interface kinetics
TS
TI
TL
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Interface kinetics
TS
TI
TL
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Interface kinetics
TLgtTI
TS
TI
TL
20
Interface kinetics
TLgtTI
TS
TI
TL
TS
TI
TL
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Interface kinetics
TLltTI
TS
TI
TL
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Interface kinetics
TLltTI
TS
TI
TL
TS
TI
TL
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Interface kinetics
TLltTI
Dendrite in stainless steel
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References

• Hasse Fredriksson and Ulla Åkerlind, Materials
  Processing during Casting, Wiley, (2006).
• M.C. Flemings, Solidification processing, (1976).
• http//cml.postech.ac.kr/rqin/gift702/