Introduction to Solidification 1' Heat Transfer

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Introduction to Solidification1. Heat Transfer

• Rongshan QIN
• http//cml.postech.ac.kr/rqin

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In this lecture

• Heat
• Temperature
• The ways of heat transfer
• Heat transfer in solidification

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What is heat?

• Heat is a form of energy created by motion of
  atoms and molecules.

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What is temperature?

• Temperature measures the average kinetic energy
  of random motion of atoms and molecules

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Heat transfer

• Heat transfers from one body/location to another
  due to a difference in temperature.
• Heat transfers spontaneously from high
  temperature to low temperature areas.
• Heat cannot transfer from a low temperature
  object to high temperature object without a heat
  pump

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Heat transfer modes

• Conduction
• Media solid, liquid or gas
• Convection
• Media no solid
• Thermal radiation
• No media. Electromagnetic wave.

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Heat conduction

• Solid Phonons and electrons
• Liquid Phonons, electrons and transversal
  motion.
• Gas Motion and collision.

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Heat conduction
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Heat conduction

• The rate of heat transfer by conduction Q

k - thermal conductivity.
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    Table 1. Thermal conductivity
 
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Heat conduction

• Thermal resistance

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Heat conduction by composite media
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Fouriers 1st law of heat conduction

• qQ/A is the rate of heat transfer per unit
  cross-sectional area, or heat flux.

• The negative sign represents that heat flows in
  the direction opposite to temperature gradient

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One dimensional solidification

• The generated heat due to heat of fusion in
  solidification will be conducted away from
  interface to solid and liquid bulk phases.

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• Interface migration rate
• Single crystal growth
• Interface stability
• Maximum pulling speed

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Fouriers 2nd law of heat conduction

• Consider an infinite small volume in a thermal
  conductor
• heat conduction through the surface of the volume

• The rate of heat generation inside

• The heat storage due to temperature change

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Fouriers 2nd law of heat conduction
where ??c/k is the thermal diffusivity
 
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1D steady state heat conduction
Taxb
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1D unsteady state heat conduction
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Heat transfer by convection

• Convection can be caused by
• Residual flow due to filling of the mold.
• External forces such as imposed pressure
  gradients, mechanical stirring or magnetic
  forces.
• Density changes due to solidification as well as
  due to temperature and chemical compositional
  changes.
• Surface tension gradients.
• Buoyancy driven flow.
• Dragging force due to solid motion.

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Heat transfer by convection

• Heat convection possesses much larger heat
  transfer rate than heat conduction.
• Free convection is normally due to the
  temperature-density relationship.
• Forced convection is accelerated by external
  forces.

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Newtons law of cooling

• The rate of heat transfer from an object to the
  surround fluid by convection is given by

Q is the rate of heat transfer by convection to
the surrounding fluid. A is the objects exposed
area. T? and TW are the fluid free-stream
temperature and object temperature, respectively.
h is the convection heat transfer coefficient.
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Thermal radiation

• The thermal radiation is by electromagnetic wave
  propagation.
• There is no medium needed for thermal radiation
• The thermal radiation power of black body is

? is the Stefan-Boltzmann Constant.
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Thermal radiation

• The thermal radiation power of no-black body

where ? is emissivity of the material
Laboratory black body
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In summary

• Basic definitions of heat and temperature.
• Three modes of heat transfer
• Fouriers laws of heat conductions
• Application of heat transfer in solidification
• Pulling single crystal
• Sand casting

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References

• R.V. Kumar, Heat and mass transfer, Cambridge.
• C. Beckermann and R. Viskanta, Appl. Mech. Rev.,
  46 (1993) 1-27.
• M.C. Flemings, Solidification processing, 1974.