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KSME International Journal

, Volume 15, Issue 8, pp 1188–1195 | Cite as

Numerical study on the vertical bridgman crystal growth with thermosolutal convection

  • Moo Geun Kim
  • Geun Oh Kim
  • Byung Kyu Park
Thermal Engineering · Fluid Engineering · Energy and Power Engineering

Abstract

A numerical analysis has been carried out to investigate the influences of thermosolutal convection on the heat and mass transfer and solute segregation in crystals grown by the vertical Bridgman technique. The governing equations are solved by a finite-volume method using the power law scheme and the SIMPLE algorithm in which body-fitted coordinate system has been used. A primary convective cell driven by thermal gradients forms in the bulk of the domain, while a secondary convective cell driven by solutal gradients forms near interface. As the solutal Rayleigh number increases, secondary cell becomes to be stronger and has a great influence on the radial concentration along the interface.

Key Words

Thermosolutal Convection Solidification Melt-Solid Interface Bridgman Crystal Growth 

Nomenclature

C0

Average solute concentration [wt.%]

Cp

Specific heat [kJ/kgK]

D

Solutal diffusivity [m2/s]

g

Gravity [m/s2]

h

Heat transfer coefficient [W/m2K]

k

Segregation coefficient

ks

Thermal conductivity of solid [W/mK]

km

Thermal conductivity of melt [W/mK]

Pr

Prandtl number

P

Pressure [N/m2]

R

Radius of ampoule [m]

RaT

Thermal Rayleigh number

Ras

Solutal Rayleigh number

Sc

Schmidt number

T

Temperature [K]

u, v

Velocity [m/s]

Greek symbols

α

Thermal diffusivity [m2/s]

βT

Thermal expansion coefficient [K−1]

βS

Solutal expansion coefficient [wt.%−1]

ε

Emissivity of surface

ρ

Density [kg/m3]

ν

Kinematic viscosity [m2/s]

σ

Stefan-Boltzmann constant [W/m2K4]

Ψ

Stream function

Subscripts

C

Cold zone

h

Hot zone

L

Melt

m

Melting point

S

Solid

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References

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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2001

Authors and Affiliations

  • Moo Geun Kim
    • 1
  • Geun Oh Kim
    • 2
    • 3
  • Byung Kyu Park
    • 2
    • 3
  1. 1.School of Mechanical and Automotive EngineeringInje UniversityKyungnamKorea
  2. 2.Department of Thermal, FluidKorea Institute of Machinery and MaterialsTaejonKorea
  3. 3.Environmental EngineeringKorea Institute of Machinery and MaterialsTaejonKorea

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