Evaluation of momentum and thermal eddy diffusivities for turbulent flow in tubes

The present investigation deals with a differential formulation to estimate the eddy diffusivity together with the universal velocity for fully developed turbulent flows in a tube. The subsequent theoretical predictions of wall friction coefficients and Nusselt numbers are in reasonable agreement with the classical solution of Blasius wall friction coefficient and Dittus and Boelter correlation for heat transfer, Nu = 0.023 Re0.8 Pr1/3. The differential form of the eddy diffusivity equation is rendered into an explicit form by regression of the computer runs for wide range of 200 < R+ < 3000 and 1 < Pr < 1000: εmν=0.0195(y+u+)1-exp-y+u+1002. The prediction of Nusselt numbers from the eddy diffusivity expression satisfactorily agree with the Dittus and Boelter heat transfer correlation. In addition, the analysis can be further modified by altering the correction factor to agree with the predictions from Petukhov–Gnielinski correlation. Thus the efficacy of the model is established for different correlations with a modification in the correction factor for mixing length.