A new heat transfer correlation for transition and turbulent fluid flow in tubes

The objective of the paper is to develop a correlation for the Nusselt number Nu in terms of the friction factor ξ (Re), Reynolds number Re, and also Prandtl number Pr, which is valid for transitional and fully developed turbulent flow. After solving the equations of energy conservation for turbulent flow in a circular tube subject to a uniform heat flux, the Nusselt number values were calculated for different values of Reynolds and Prandtl numbers. Then, the form of the correlation Nu = f (Re, Pr) was selected which approximates the results obtained in the following ranges of Reynolds and Prandtl numbers: 2300 ≤ Re ≤ 106, 0.1 ≤ Pr ≤ 1000. The form of the correlation was selected in such a way that for the Reynolds number equal to Re = 2300, i.e. at the point of transition from laminar to transitional flow the Nusselt number should change continuously. Unknown coefficients x1,…,xn appearing in the heat transfer correlation expressing Nusselt number as a function of the Reynolds number and Prandtl number were determined by the method of least squares. To determine the values of the coefficients at which the sum of the difference squares is a minimum, the Levenberg-Marquardt method is used. The proposed correlation was validated by comparing with experimental data.