Revisiting the Reynolds-averaged energy equation in near-wall turbulence models

It is sometimes reported in the heat transfer studies of gaseous media using the near-wall turbulence models that their fully-developed Nu predictions deviate from the experimental correlations. This work approaches the rigorous formulation of the Reynolds-averaged equation in terms of temperature from a fundamental basis, in order to highlight the possible errors due to the usual overapproximation made for the Reynolds-averaged energy equation. It is suggested that Eq. (18) which is one of the rigorous forms of the Reynolds-averaged equation and free of the unknown correlation of the pressure diffusion term is suitable for the analysis of turbulent convective heat transfer in gaseous media.