An extended Kays and Crawford turbulent Prandtl number model

For theoretical predictions of turbulent heat transfer in boundary layers and in duct flows, the knowledge of the turbulent Prandtl number is crucial. This is especially true for fluids with low molecular Prandtl numbers (liquid metals). The present formulation, which is an extended Kays and Crawford (Convective Heat and Mass Transfer, 3rd edn. McGraw-Hill, New York, 1993) turbulent Prandtl number model, can be used for accurately predicting the heat transfer for liquid metal flows. The Nusselt numbers calculated with the modified model for Prt are found to be in good agreement with experimental data for fully-developed pipe flows as well as for thermally developing pipe flows for various wall boundary conditions. The present model reduces to the one given in the above reference for liquids and gases with higher molecular Prandtl numbers.