On temperature prediction at low Re turbulent flows using the Churchill turbulent heat flux correlation

The present work investigates the prediction of mean temperature profiles in turbulent channel flow using the fraction of the heat flux due to turbulence. According to this new model, suggested by Churchill and co-workers, fully developed flow and convection can be expressed as local fractions of the shear stress and the heat flux density due to turbulent fluctuations, respectively. The fully developed temperature profile can be predicted if the velocity field and the turbulent Prandtl number are known. Temperature profiles for Pr between 0.01 and 50,000 have been obtained theoretically and with simulations through the use of Lagrangian methods for both plane Poiseuille flow and plane Couette flow. The half channel height for all simulations was h = 150 in wall units. The theoretical predictions have been found to agree with the data quite well for a range of Pr, but there are deviations at very high Pr.