Bem-Fvm Solution Of Conjugate Heat Transfer Problems In Czochralski Crystal Growth Process


A technique of solving multi-mode heat transfer problems in semi transparent, phase changing medium is addressed. Simultaneous heat conduction, free and forced convection, radiation and change of phase during Czochralski crystal growth process are modeled. Heat conduction/convection problem is solved using a commercial code based on the Finite Volume Method with the enthalpy technique applied to capture the moving boundary problem. The model of energy, mass and momentum transfer in the melt encompasses both the forced and natural convection. The problem of radiation is solved using the an in-home code based on the boundary element method. Spectral dependent properties of the crystal and melt are accounted for. The condensed phase is treated as an emitting absorbing one the gas filling the apparatus is treated as a transparent medium. The coupling between the CFD model and the radiation is twofold. Heat radiation generates volumetric heat sources that arise in the energy transport equations in the condensed phase. The temperature field coming from the solution of the convection/conduction problem enters a forcing term in the equations of radiative heat exchange. The coupling is taken into account within an iterative loop by solving the convection and radiation equations in a sequence. Numerical example is included.

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Boundary Elements



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Article; Proceedings Paper

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0002468871 (Scopus)

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