Prandtl correlation, friction factor

The dimensionless relations are usually indicated in either of two forms, each yielding identical results. The preferred form is that suggested by Colburn [Trarrs. Am. Inst. Chem. Eng., 29,17T-210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cG, the Prandtl number c[ /k, and the Reymolds number DG/p. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and IC/p for Reynolds number <10,000) is approximately equal to half of the Fanning friction factor 2. This product is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

Metzner and Friend [73] measured turbulent heat transfer rates with aqueous solutions of Carbopol, corn syrup, and slurries of Attagel in circular-tube flow. They developed a semi-theoretical correlation to predict the Stanton number for purely viscous fluids as a function of the friction factor and Prandtl number, applying Reichardt s general formulation for the analogy between heat and momentum transfer in turbulent flow ... 

In Section 2.5.1 of Hewitt (1992), prepared by Gnielinski, a more accurate and more widely applicable correlation is given, which accounts for tube diameter-to-tube length ratio for 0 < DJL 1, and IS apphcable to Avide ranges of Reynolds and Prandtl numbers of 2,300 to 1,000,000 and 0.6 to 2,000, respectively. The correlation has a semitheoretical basis in the Prandtl analogy to skin friction in terms of the Darcy friction factor,/ , ... 

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