Numerical modeling of radiative heat transfer in Bridgman solidification of semi-transparent BaF2 crystals

The radiative heat transfer during Bridgman solidification of semi-transparent barium fluoride (BaF2) crystals is numerically investigated by using the commercial software FIDAP. This code uses the P-1 approximation for the participating media modeling. The thermal field and the solid–liquid interface shape are computed for an opaque melt-crystal sample, a semi-transparent grey sample and a semi-transparent non-grey sample. The transient numerical analysis of the latent heat influence on the interface deflection shows a significant effect on the interface shape. In the case of an opaque sample, this effect is huge because of the small thermal conductivity of the BaF2 melt. The interface curvature is drastically reduced when the latent heat is taken into account, and the growth front, which has a convex shape, becomes flat when the growth rate increases. The latent heat effect is reduced in the case of the participating BaF2 sample because the effective thermal conductivity of the melt is augmented by the internal radiative heat transfer. The internal radiative effect is small at low solidified fractions but becomes significant when the crystal length increases, leading to a more curved interface. When the growth rates are greater than a critical value, the interface becomes concave and a destabilization of the growth process can occur. These results are in agreement with previous experimental measurements of the interface curvature and analytical investigations of the factors affecting the interface deflection.