Gnielinski correlation

Adams et al. (1998) investigated turbulent, single-phase forced convection of water in circular micro-channels with diameters of 0.76 and 1.09 mm. The Nusselt numbers determined experimentally were higher than those predicted by traditional Nusselt number correlations such as the Gnielinski correlation (1976). The data suggest that the extent of enhancement (deviation) increases as the channel diameter decreases. Owhaib and Palm (2004) investigated the heat transfer characteristics... 

Concerning heat transfer,and the determination of the Nusselt number, the Gnielinski correlation valid for Re > 2300 is the most general [17] ... 

If the Nusselt number is plotted as a function of the Reynolds number, the curve in figure 6 is obtained. One can see the constant value for laminar flow. In the turbulent regime the Gnielinski correlation is compared to a Dittus-Boelter type correlation. 

Heat transfer in fully developed turbulent flow in elliptical ducts has been determined in several investigations. A comparison of the different results has been presented by Bhatti and Shah [45]. It was concluded that the Gnielinski correlation for circular ducts can confidently be used to calculate the fully developed Nusselt number for elliptical ducts for fluids of Pr 0.5. 

A more complex but also more accurate correlation for the convective heat transfer in the transition regime is the Gnielinski correlation [14] ... 

With /zlo taken from linear interpolation between the turbulent value using the Gnielinski correlation (given under Region I above) and the appropriate laminar value (for q" = CovT= C) using /zlo = (NuLo /-Dh)-... 

Figure 1736. Effective thermal conductivity and wall heat transfer coefficient of packed beds. Re = dpG/fi, dp = 6Vp/Ap, s -porosity, (a) Effective thermal conductivity in terms of particle Reynolds number. Most of the investigations were with air of approx. kf = 0.026, so that in general k elk f = 38.5k [Froment, Adv. Chem. Ser. 109, (1970)]. (b) Heat transfer coefficient at the wall. Recommendations for L/dp above 50 by Doraiswamy and Sharma are line H for cylinders, line J for spheres, (c) Correlation of Gnielinski (cited by Schlilnder, 1978) of coefficient of heat transfer between particle and fluid. The wall coefficient may be taken as hw = 0.8hp.

Gnielinski [3] derived a correlation for single particles, which represents all data measured with sufficient accuracy for technical applications ... 

The single-phase heat transfer coefficients in Eq. (17) were determined by asymptotic interpolation of standard correlations, i.e. Shah and London (SL) for Re < 2,300 and Gnielinski (G) for Re > 2,300. Thus,... 

These are the average laminar and transition to turbulent Nusselt numbers over the respective single-phase lengths L. In Gnielinski s correlation the friction factor is taken as / = (1.821ogjQ Re -1.64) . The bubble heat transfer coefficient, a, was determined by applying simple conduction theory through the liquid film ... 

Heat Transfer in Smooth Circular Ducts. For gases and liquids (Pr > 0.5), very little difference exists between the Nusselt number for uniform wall temperature and the Nusselt number for uniform wall heat flux in smooth circular ducts. However, for Pr < 0.1, there is a difference between NuT and NuH- Table 5.11 presents the fully developed turbulent flow Nusselt number in a smooth circular duct for Pr > 0.5. The correlation proposed by Gnielinski [69] is recommended for Pr > 0.5, as are those suggested by Bhatti and Shah [45]. In this table, the / in the equation is calculated using the Prandtl [52]-von Karman [53]-Nikuradse [43] Cole-brook [54] Filonenko [55] or Techo et al. [56] correlations shown in Table 5.8. 

The transition flow and fully developed turbulent flow Nusselt number correlation for a circular tube is given by Gnielinski as reported in Bhatti and Shah [46] as... 

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,/ , ... 

Higher heat transfer rates in turbulent microchannels than predicted by traditional large-scale correlations were observed by Adams et al. [23]. Based on the work of Gnielinski, a generalized correlation for turbulent single-phase flow in microchannels is derived ... 

The use of turbulent Nu correlations in the transition regime from laminar to turbulent flow must to be treated with caution. Heat transfer coefficient values will be overpredicted. An equation to calculate heat transfer rates in the transition region was proposed by Gnielinski [65] ... 

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