Modeling Heat Transfer in Wall-Bounded Flows with the Spalart–Allmaras Model

We develop more accurate and general predictive schemes for forced turbulent thermal convection in low-Mach-number flow regimes based on the Spalart–Allmaras turbulence model. Using direct numerical simulation data, we derive corrections to the classical formulations of eddy kinematic viscosity and eddy thermal diffusivity, ensuring accurate asymptotic behavior near the wall and overcoming the limitations of the commonly used assumption of a constant turbulent Prandtl number. Numerical simulations for representative canonical turbulent flows, including turbulent boundary layers and turbulent pipe flow, demonstrate the enhanced predictive accuracy of the corrected model. In particular, the proposed model effectively captures turbulent heat transfer at moderate-to-high Prandtl numbers across a wide range of Reynolds numbers.