Effect of Near Wall Variation of Fluid Properties on the Nusselt Number in Forced Turbulent Convection at High Molecular Prandtl Number

The temperature-dependent variation of fluid properties is known to strongly challenge any universal description of convective heat transfer in terms of Nusselt number. This especially holds true for high Prandtl number liquids, where the fast drop in viscosity towards the heated wall enhances the turbulent mixing while the thermal fluctuations decrease. Most of the popular Nusselt number correlations grossly account for these basically counteracting effects on turbulent heat transfer by simply modifying a certain fictitious isothermal base correlation, representing the constant-fluid property reference, with the bulk-to-wall Prandtl number ratio raised to some power, (Prb/Prw)n. The present study revisits this widely used concept carrying out heated pipe flow experiments with a standard heat transfer oil at Prandtl numbers up to Prb ≈ 80. Considering the Gnielingski correlation [6] as a well representative formulation, it is shown that it consistently tends to overpredict the experiments for moderate Reynolds numbers (Reb < 104). As the thermal sublayer is shifted very close to the heated wall for high Prandtl numbers, the effective enhancement of turbulent motion due to the near wall increase of the local Reynolds number is low. Together with the low wall viscosity, this leads to a smaller skin-friction coefficient (cf), so that the Nusselt number should rather predicted lower. Correspondingly introducing a bulk-to-wall viscosity-ratio based correction of cf into the Nusselt number correlation is shown to reflect the experimentally observed trend adequately.