Prediction of turbulent heat fluxes and temperature fluctuations

It is shown that the conventional turbulent Prandtl number approach is grossly inadequate to predict turbulent heat fluxes in other than the cross-stream direction. A theory is presented which shows that the turbulent diffusivity is a second order tensor consisting of two parts. Based on this theory, a heat flux model is formed and has been applied to fully developed pipe flow. Excellent agreement with measurements has been obtained by adjusting the model constants. Temperature fluctuations in fully developed pipe flow have also been calculated from a model transport equation. Best agreement with experiment is achieved with the model constants assuming values different to those recommended by previous workers