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

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Bibliographic Details
Title: A new mean temperature model for incompressible wall-bounded turbulence over a wide range of Prandtl numbers.
Authors: Ip Sun, Justin E. Ka1, Fu, Lin1,2 linfu@ust.hk
Source: Journal of Fluid Mechanics. 5/25/2026, Vol. 1035, p1-29. 29p.
Subjects: Prandtl number, Thermal diffusivity, Fluid dynamics, Turbulence, Temperature distribution
Abstract: 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 (Pr). Flow media with Pr and Schmidt numbers (Sc) other than unity are of great engineering importance, and the proposed model for passive scalar mean profiles is able to suitably account for Pr and Sc variations and their effects. Existing models have a higher degree of error at the lower Pr ranges due to significant inaccuracies of the modelled thermal eddy diffusivity in this region. Considering incompressible wall-bounded turbulence at 0.007 x Pr x 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 Pr behaviour, showcasing a new temperature-velocity relationship that can account for variations in Pr for all the cases considered. [ABSTRACT FROM AUTHOR]
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Abstract: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 (Pr). Flow media with Pr and Schmidt numbers (Sc) other than unity are of great engineering importance, and the proposed model for passive scalar mean profiles is able to suitably account for Pr and Sc variations and their effects. Existing models have a higher degree of error at the lower Pr ranges due to significant inaccuracies of the modelled thermal eddy diffusivity in this region. Considering incompressible wall-bounded turbulence at 0.007 x Pr x 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 Pr behaviour, showcasing a new temperature-velocity relationship that can account for variations in Pr for all the cases considered. [ABSTRACT FROM AUTHOR]
ISSN:00221120
DOI:10.1017/jfm.2026.11582