Empirical correlations for natural convection, Δ and keff

•Nusselt number (Nu) correlations are used to quantify convection at solid–liquid interface.•Correlations for simultaneous heat and mass transfer, Nu(Gr,Pr, Sc), are presented.•Empirical correlations are used to determine Δ(Nu,Pe), and keff. (k0, Δ).•For CZ growth of 20 cm diameter Si crystals, natural convection is dominant below ~5 RPM.

Natural convection in semiconductor melts is quantified using empirical correlations for Nusselt numbers, Nu, developed in laboratory experiments with liquid metals. Nu is a dimensionless coefficient used to quantify the complex boundary condition of convection, involving advection and diffusion. A dozen of empirical correlations for heat transfer Nusselt numbers, Nu(Gr,Pr), was transformed into correlations for simultaneous heat and mass transfer, Nu(Gr,Pr, Sc), and used to calculate the parameter Δ=Pe/Nu and effective segregation coefficient, keff(Pe, Nu, k0), for horizontal Bridgman and Czochralski growth.