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Numerical study on the vertical bridgman crystal growth with thermosolutal convection

  • Thermal Engineering · Fluid Engineering · Energy and Power Engineering
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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.

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Abbreviations

C 0 :

Average solute concentration [wt.%]

C p :

Specific heat [kJ/kgK]

D :

Solutal diffusivity [m2/s]

g :

Gravity [m/s2]

h :

Heat transfer coefficient [W/m2K]

k :

Segregation coefficient

k s :

Thermal conductivity of solid [W/mK]

k m :

Thermal conductivity of melt [W/mK]

Pr :

Prandtl number

P :

Pressure [N/m2]

R :

Radius of ampoule [m]

Ra T :

Thermal Rayleigh number

Ra s :

Solutal Rayleigh number

Sc :

Schmidt number

T :

Temperature [K]

u, v :

Velocity [m/s]

α:

Thermal diffusivity [m2/s]

β T :

Thermal expansion coefficient [K−1]

β S :

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

C :

Cold zone

h :

Hot zone

L :

Melt

m :

Melting point

S :

Solid

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Inje University, 621-749, Kyungnam, Korea

    Moo Geun Kim

  2. Department of Thermal, Fluid, Korea Institute of Machinery and Materials, 305-343, Taejon, Korea

    Geun Oh Kim & Byung Kyu Park

  3. Environmental Engineering, Korea Institute of Machinery and Materials, 305-343, Taejon, Korea

    Geun Oh Kim & Byung Kyu Park

Authors
  1. Moo Geun Kim
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  2. Geun Oh Kim
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  3. Byung Kyu Park
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Correspondence to Byung Kyu Park.

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Kim, M.G., Kim, G.O. & Park, B.K. Numerical study on the vertical bridgman crystal growth with thermosolutal convection. KSME International Journal 15, 1188–1195 (2001). https://doi.org/10.1007/BF03185099

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  • DOI: https://doi.org/10.1007/BF03185099

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