DNS-informed formulas for temperature distributions and heat fluxes in forced thermal convection

We carry out DNS of forced thermal convection in turbulent pipe flow in a wied range of Reynolds and Prandtl numbers. The observed universaility of the thermal eddy diffusion coefficient is leverage to derive explicit formulas for the mean temperature distribution across the radial direction, and in turn explicit formulas for the heat transfer coefficients, which reproduce the DNS results with great accuracy. The resulting formulas are manipulated to a form similar to the classical form developed by Kader & Yaglom, however providing clear predictive improvement at low Prandtl numbers.