Thermal Entry for Low Reynolds Number Turbulent Flow

Abstract

The thermal entrance problem for low Reynolds number, turbulent flow of gases in circular tubes is solved analytically by the method of Sparrow, Hallman, and Siegel. Fluid properties are considered constant. The solution is based on a Reynolds-number-dependent velocity profile developed, in a companion paper, by modifying Reichardt’s wall and middle law eddy diffusivity expressions. Tabular values of the eigenvalues and normalized Nusselt numbers are presented for a range of Reynolds numbers from 3,000 to 50,000. The axial variation of Nusselt number is found to be correlated by NuNu∞ = 1 + 0.8(1+70,000 Re−3/2) xD−1 to within ±5 percent for x/D ≥ 2. The fully developed value agrees with the Dittus-Boelter correlation. For the eigenvalues, λn 2 , and the associated constants, An , correlations of the form λn2 = a1,n Re−b1,n + c1,n Re−d1,nAn = a2,n Re−b2,n + c2,nRe−d2,n are obtained. Heat transfer data are presented, primarily for helium, for the conditions of the analysis. In the low Reynolds number turbulent regime, these data clearly support the present analytical solution.