Nusselt number duct flow

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. 

TABLE 5-4 Values of Limiting Nusselt Number in Laminar Flow in Closed Ducts... 

Consider a fully developed steady-state laminar flow of a constant-property fluid through a circular duct with a constant heat flux condition imposed at the duct wall. Neglect axial conduction and assume that the velocity profile may be approximated by a uniform velocity across the entire flow area (i.e., slug flow). Obtain an expression for the Nusselt number. 

Consider the fully-developed flow of a viscous fluid in a circular duct of radius a<,. Without neglecting viscous dissipation, derive an expression for the Nusselt number if the boundary condition at r = ao, is T = Tw < Tm, where T,n is the mean temperature of the fluid. 

Now, in duct flows, as previously discussed, it is usually convenient to utilize the mean fluid temperature, Tm, in defining the Nusselt number. This mean or bulk temperature is given as explained in Chapter 1 by ... 

Effect of wall thermal boundary condition oh the Nusselt number for hilly developed flow in a rectangular duct (Nusselt number based on hydraulic diameter)... 

Nusselt number and center line temperature variation in developing flow in a plane duct with a uniform wall temperature. 

Nusselt number variations for developing plane duct flow for... 

This chapter has been concerned with the analysis of laminar flows in ducts with various cross-sectional shapes. If the flow is far from the inlet to the duct or from anything else causing a disturbance in the flow, a fully developed state is reached in many situations, the basic characteristics of the flow in this state not changing with distance along the duct. If the diffusion of heat down the duct can be neglected, which is true in most practical situations, it was shown that in such fully developed flows, the Nusselt number based on the difference between the local wall and bulk mean temperatures is constant. Values of the Nusselt number for fully developed flow in ducts of various cross-sectional shape were discussed. 

In some situations it is possible to find the heat transfer rate with adequate accuracy by assuming that the velocity is constant across the duct. Le to assume that so-called slug flow exists. Find the temperature distribution and the Nusselt number in sllug flow in a plane duct when the thermal field is fully developed and when there is a uniform wall heat flux. 

Consider fully developed flow in a plane duct in which uniform heat fluxes qw and qwi are applied at the two walls. Derive expressions for the temperature distribution in the duct and the Nusselt number. 

Now in duct flow, the Nusselt number is defined in terms of the difference between the wall temperature and the mean fluid temperature, this mean temperature being defined by ... 

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. ... 

As a result of the development of the hydrodynamic and thermal boundary layers, four types of laminar flows occur in ducts, namely, fully developed, hydrodynamically developing, thermally developing (hydrodynamically developed and thermally developing), and simultaneously developing (hydrodynamically and thermally developing). In this chapter, the term fully developed flow refers to fluid flow in which both the velocity profile and temperature profile are fully developed (i.e., hydrodynamically and thermally developed flow). In such cases, the velocity profile and dimensionless temperature profile are constant along the flow direction. The friction factor and Nusselt number are also constant. 

Simultaneously developing flow is fluid flow in which both the velocity and the temperature profiles are developing. The hydrodynamic and thermal boundary layers are developing in the entrance region of the duct. Both the friction factor and Nusselt number vary in the flow direction. Detailed descriptions of fully developed, hydrodynamically developing, thermally developing, and simultaneously developing flows can be found in Shah and London [1] and Shah and Bhatti [2],... 

Heat Transfer on Walls With Uniform Heat Flux. For circular ducts with symmetrical heating, the same heat transfer results for fully developed flow and developing flow are obtained for boundary conditions through . Therefore, the uniform wall heat flux boundary conditions are simply designated as the boundary condition. Shah and Bhatti [2] have derived the temperature distribution and Nusselt number by recasting the results reported by Tyagi [6] for heat transfer in circular ducts. These follow ... 

FIGURE 5.1 Local and mean Nusselt numbers Nu, T and Num T for thermal developing flow in a circular duct. 

The local Nusselt number and mean Nusselt number computed from Eqs. 5.36 and 5.37 are shown in Fig. 5.1. The data corresponding to this figure can be found in Shah and London [1], The thermal entrance length for thermally developing flow in circular ducts can be obtained using the following expression ... 

Heat Transfer on Walls With Uniform Heat Flux. The temperature profile and the local and mean Nusselt numbers for thermally developing flow in a circular duct with uniform wall heat flux are provided by Siegel et al. [25] as follows ... 

Heat Transfer on Walls With Radiation. The local Nusselt numbers normalized with respect to Nu H have been obtained by Kadaner et al. [8] for thermally developing flow with the radioactive duct wall boundary condition . This is expressed as ... 

Heat Transfer on the Walls With Uniform Heat Flux. The solutions for simultaneously developing flow in circular ducts with uniform wall heat flux are reviewed by Shah and London [1], Recently, a new integral or boundary layer solution has been obtained by Al-Ali and Selim [33] for the same problem. However, the most accurate results for the local Nusselt numbers [1] are presented in Table 5.6. 

TABLE 5.6 Local Nusselt Number Nu, T3 for Simultaneously Developing Flow in a Circular Duct [1]... 

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. 

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