A new mean temperature model for incompressible wall-bounded turbulence over a wide range of Prandtl numbers

A new model of the mean temperature profiles within incompressible wall-bounded turbulence is developed based on a relationship between the momentum and thermal eddy diffusivities for a wide range of Prandtl numbers ( $ \textit{Pr}$ ). Flow media with $ \textit{Pr}$ and Schmidt numbers ( $ \textit{Sc}$ ) other than unity are of great engineering importance, and the proposed model for passive scalar mean profiles is able to suitably account for $ \textit{Pr}$ and $ \textit{Sc}$ variations and their effects. Existing models have a higher degree of error at the lower $ \textit{Pr}$ ranges due to significant inaccuracies of the modelled thermal eddy diffusivity in this region. Considering incompressible wall-bounded turbulence at $0.007 \leqslant \textit{Pr} \leqslant 10$ , the proposed methodology reduces the average error to just around $4\,\%$ across all cases considered, lower than previously proposed models due to its ability to capture low $ \textit{Pr}$ behaviour, showcasing a new temperature–velocity relationship that can account for variations in $ \textit{Pr}$ for all the cases considered.