2006
DOI: 10.1016/j.ijthermalsci.2005.05.007
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Role of internal radiation during Czochralski growth of YAG and Nd:YAG crystals

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Cited by 14 publications
(6 citation statements)
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“…For a beaker diameter of 100 mm and a cylinder diameter of 50 mm, the largest Grashof number Gr was 3.2 × 10 6 , the largest Reynolds number Re of the rotating cylinder being 3.25 × 10 3 . Radius of the crucible is used as the length scale for nondimensionalization (Banerjee and Muralidhar, 2005). The mixed convection parameter, defined as Gr/Re 2 , could be varied.…”
Section: Apparatus and Instrumentationmentioning
confidence: 99%
See 1 more Smart Citation
“…For a beaker diameter of 100 mm and a cylinder diameter of 50 mm, the largest Grashof number Gr was 3.2 × 10 6 , the largest Reynolds number Re of the rotating cylinder being 3.25 × 10 3 . Radius of the crucible is used as the length scale for nondimensionalization (Banerjee and Muralidhar, 2005). The mixed convection parameter, defined as Gr/Re 2 , could be varied.…”
Section: Apparatus and Instrumentationmentioning
confidence: 99%
“…The images of the thermal field obtained using LCT are compared with the predictions of a numerical model (Banerjee and Muralidhar, 2005). The model assumes that the temperature and velocity fields are axisymmetric.…”
Section: Numerical Modelmentioning
confidence: 99%
“…Continuity: ·u=0,Momentum: u·u=ν2upρgβTTT0,Energy: ·Tu=αi2T+·qr,iρiCp,i,where u is the velocity vector, ρ is the density and ν is kinetic viscosity of the fluid; g is the gravitational acceleration vector, β T is the thermal expansion coefficient of the sapphire melt, T is the temperature, and T 0 is the reference temperature; α i and C p,i represent the thermal diffusivity and specific heat, respectively; qr,i is the radiative source term, solved by DO Model as described in Ref. , ·qr,i=κ4Ib2πIidΩi,where Ωi is the solid angle, Ib=σn2T4 is the radiation intensity of black body, and κ is absorption coefficient. Radiation intensity I i can be obtained by solving the radiative transfer equation, trueμ̃r(rI)r+ξ̃(I)z1r(η̃I)…”
Section: Mathematical Modelsmentioning
confidence: 99%
“…Since LMO single crystals have anisotropic mechanical properties such as elastic constants and thermal expansion coefficients, the exact thermal stress computation has to be performed in three dimensions by taking into account this anisotropy. Furthermore, for semitransparent crystals, such as LMO, internal radiation plays a key role in heat transfer and strongly affects crystal-melt interface convexity [9][10][11][12][13][14][15][16][17][18] . Therefore, temperature distribution inside the crystal is not uniform and, then, accurate computations of the stress inside the crystal requires to take into account the temperature dependence of anisotropic elasticity and thermal expansion tensors.…”
Section: Introductionmentioning
confidence: 99%