Turbulent duct flow Nusselt number

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. 

TABLE 5.11 Fully Developed Turbulent Flow Nusselt Numbers in a Smooth, Circular Duct for Gases and Liquids (Pr > 0.5) [48]... 

Note that T 0 = 1 on the fluid side, which does not have fins. For fully developed turbulent flow through constant cross-sectional ducts, the Nusselt number correlation is of the form... 

The convective heat-transfer coefficient and friction factor for laminar flow in noncircular ducts can be calculated from empirically or analytically determined Nusselt numbers, as given in Table 5. For turbulent flow, the circular duct data with the use of the hydrauhc diameter, defined in equation 10, may be used. 

Flow in Noncircular Ducts The length scale in the Nusselt and Reynolds numbers for noncircular ducts is the hydraulic diameter, D), = 4AJp, where A, is the cross-sectional area for flow and p is the wetted perimeter. Nusselt numbers for fully developed laminar flow in a variety of noncircular ducts are given by Mills (Heat Transfer, 2d ed., Prentice-Hall, 1999, p. 307). For turbulent flows, correlations for round tubes can be used with D replaced by l. ... 

Thermally Developing Flow. Numerous investigators [80, 89-94] have carried out the investigation of turbulent thermally developing flow in a smooth circular duct with uniform wall temperature and uniform wall heat flux boundary conditions. It has been found that the dimensionless temperature and the Nusselt number for thermally developing turbulent flow have the same formats as those for laminar thermally developing flow (i.e., Eqs. 5.34-5.37 and Eqs. 5.50-5.53). The only differences are the eigenvalues and constants in the equations. 

TABLE 5.12 Nusselt Numbers for Fully Developed Turbulent Flow in the Fully Rough Flow Regime of a Circular Duct [45]... 

FIGURE 5.12 Local Nusselt numbers Nu, T and Nu, H for simultaneously developing turbulent flow in a smooth circular duct for Pr = 0.73 [92],... 

Presented in this section are the friction factor and Nusselt number for turbulent flow and heat transfer in concentric annular ducts. The effects of eccentricity on the friction factor and Nusselt number are also discussed. 

TABLE 5.27 Nusselt Numbers and Influence Coefficients for Fully Developed Turbulent Flow in a Concentric Annular Duct with Uniform Heat Flux at One Wall and the Other Wall Insulated [111]... 

Thermally Developing Flow. Kays and Leung [111] present experimental results for thermally developing turbulent flow in four concentric annular ducts, r = 0.192,0.255,0.376, and 0.500, with the boundary condition of one wall at uniform heat flux and the other insulated, that is, the fundamental solution of the second kind. In accordance with this solution, the local Nusselt numbers Nu and Nu at the outer and inner walls are expressed as... 

Simultaneously Developing Flow. Little information is available on simultaneously developing turbulent flow in concentric annular ducts. However, the theoretical and experimental studies by Roberts and Barrow [118] indicate that the Nusselt numbers for simultaneously developing flow are not significantly different from those for thermally developing flow. 

Analogous to circular ducts, the fully developed turbulent Nusselt numbers for uniform wall temperature and uniform wall heat flux boundary conditions in parallel plate ducts are nearly identical for Pr > 0.7 and Re > 105. This is also true for the Nusselt number of turbulent thermally developing flow in a parallel plate duct [147]. 

For fully developed Nusselt numbers for the turbulent flow of liquid metals in rectangular ducts, a simple correlation has been derived for the and boundary conditions [169]. This correlation follows ... 

The lower limit of Recrit is considered to be approximately 2000 in triangular ducts [45]. No reliable results for the friction factor and Nusselt number are available for transition flow in triangular ducts. In this section, the turbulent flow and heat transfer characteristics for equilateral, isosceles, and right triangular ducts are presented. 

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. 

In this section, emphasis will be given to the correlations used for calculating the friction factors and Nusselt numbers for laminar and turbulent flows in curved ducts, helicoidal pipes, and spiral ducts. These will be presented as the ratio of the friction factor in curved ducts to the friction factor in straight ducts fcJfs and the ratio of the Nusselt number in curved ducts to the Nusselt number in straight ducts Nuf/Nus, in most cases. The subscript c represents curved ducts or helicoidal pipes, while the subscript s denotes straight pipes of the same shape. 

The Nusselt numbers for turbulent flow in curved rectangular ducts have been studied by Butuzov et al. [230] and Kadambi [231], The correlation suggested by Butuzov et al. [230] is as follows ... 

A careful observation of accurate experimental friction factors for all noncircular smooth ducts reveals that ducts with laminar/Re < 16 have turbulent/factors lower than those for the circular tube, whereas ducts with laminar/Re > 16 have turbulent/factors higher than those for the circular tube [48], Similar trends are observed for the Nusselt numbers. If one is satisfied within 15 percent accuracy, Eqs. 17.87 and 17.88 for/and Nu can be used for noncircular passages with the hydraulic diameter as the characteristic length in / Nu, and Re otherwise, refer to Table 17.16 for more accurate results for turbulent flow. 

TABLE 17.16 Fully Developed Turbulent Flow Friction Factors and Nusselt Numbers (Pr > 0.5) for Technically Important Smooth-Walled Ducts [44]... 

Turbulent Flow. The thermal entry length solutions for smooth ducts for several cross-sectional geometries have been summarized [46]. As for laminar flow, the Nusselt numbers in the thermal region are higher than those in the fully developed region. However, unlike laminar flow, Nu,x and NuxHi are very nearly the same for turbulent flow. The local and mean Nusselt numbers for a circular tube with and boundary conditions are [46] ... 

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