Circular ducts rough

The shear stress Ri at the pipe wall in the upper portion of the pipe may be calculated on the assumption that the liquid above the bed is flowing through a non-circular duct, bounded at the top by the wall of the pipe and at the bottom by the upper surface of the bed. The hydraulic mean diameter may then be used in the calculation of wall shear stress. However, this does not take account of the fact that the bottom boundary, the top surface of the bed, is not stationary, and will have a greater effective roughness than the pipe... 

Each term has the dimensions of energy per unit of mass - in this case, ft-lbp/lbM. The factor, a, in the kinetic energy term, Av /2agc, corrects for the velocity profile across a duct. For laminar flow in a circular duct, the velocity profile is parabolic, and a = 1/2. If the velocity profile is flat, a = 1. For very rough pipes and turbulent flow, a may reach a value of 0.77 [10]. In many engineering applications, it suffices to let a = 1 for turbulent flow. 

Fully Developed Flow. In this section, the characteristics of the fully developed turbulent flow and heat transfer are presented for both a smooth and a rough circular duct with a diameter of 2a. 

Velocity Distribution and the Friction Factor for Rough Circular Ducts. Fully developed velocity distribution in a completely rough circular duct has been expressed by Schlichting [57] as follows ... 

The friction factor correlations for fully developed turbulent flow in a rough circular duct are summarized in Table 5.9. The friction factor for turbulent flow in an artificially roughed circular duct can be found in Rao [59]. 

Moody s [58] plot, shown in Fig. 5.9, gives the friction factor for laminar and turbulent flow in both smooth and rough circular ducts. Relative roughness el Dk is used as a parameter for... 

FIGURE 5.9 Moody s [58] friction factor diagram for fully developed flow in a rough circular duct [45]. 

Heat Transfer in Rough Circular Ducts The Nusselt number for a complete, rough flow regime in a circular duct is given in Table 5.12. The term/in this table denotes the friction factor for fully rough flow. It is given by the Nikuradse [60] correlation shown in Table 5.9. The recommended equations for practical calculations are those correlations by Bhatti and Shah [45] shown in Table 5.12. 

Artificially roughed circular ducts are also often used to enhance heat transfer. The Nusselt numbers for artificially roughed ducts have been reviewed by Rao [59]. 

Hydrodynamtcally Developing Flow. An analytical, close-form solution for hydrodynami-cally developing flow in rough circular ducts has been obtained by Zhiqing [87]. The velocity distribution in the hydrodynamic entrance region is given as... 

TABLE 5.9 Fully Developed TUrbulent Flow Friction Factor Correlations for a Rough Circular Duct [48] (a = tube radius)... 

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

Fully developed fluid flow and heat transfer results for rough parallel plate ducts can be predicted using the results for rough circular ducts with the use of hydraulic diameter [45]. 

Chapter 4 is devoted to single-phase heat transfer. Data on heat transfer in circular micro-tubes and in rectangular, trapezoidal and triangular ducts are presented. Attention is drawn to the effect of energy dissipation, axial conduction and wall roughness on the thermal characteristics of flow. Specific problems connected with electro-osmotic heat transfer in micro-channels, three-dimensional heat transfer in micro-channel heat sinks and optimization of micro-heat exchangers are also discussed. 

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