Internal flow fully-developed

Friction Coefficient. In the design of a heat exchanger, the pumping requirement is an important consideration. For a fully developed laminar flow, the pressure drop inside a tube is inversely proportional to the fourth power of the inside tube diameter. For a turbulent flow, the pressure drop is inversely proportional to D where n Hes between 4.8 and 5. In general, the internal tube diameter, plays the most important role in the deterrnination of the pumping requirement. It can be calculated using the Darcy friction coefficient,, defined as... 

Consider steady, fully developed flow in a straight pipe of length L and internal diameter d,. As shown in Example 1.8, a force balance on a cylindrical element of the fluid can be written as... 

We start this chapter with a general physical description of internal flow, and the average velocity and average temperature. We continue with the discussion of the hydrodynamic, and thermal entry lengths, developing flow, and fully developed flow. We then obtain the velocity and temperature profiles for fully developed laminar flow, and develop relations for the friction factor and Nusselt nmnber. Hinally we present empirical relations for developing and full developed flows, and demonstrate their use. 

B Have a visual understanding of different flow regions in internal flow, such as Ihe entry and the fully developed flow regions, and calculate hydrodynamic and thermal entry lengths,... 

In practice, it is found convenient to express the pressure loss for all types of fully developed internal flosvs (laminar or turbulent flows, circular or noncLrcu-lar pipes, smooth or rough surfaces, horizontal or inclined pipes) as (Fig. 8-19)... 

Internal force flows are said to be fully developed once the... 

Ranade, V.V. (1999), Modelling of gas-solid flows in FCC riser reactor fully developed flow, 2nd International Conference on CFD, Melbourne. 

Lasheras, J. C., Eastwood, C., Marttnez-Bazan, C. Montanes, G. L. 2002 A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow. International Journal of Multiphase Flow 28, 247-278. 

Prakash and Liu [266] have numerically analyzed laminar flow and heat transfer in the entrance region of an internally finned circular duct. In this study, the fully developed / Re is compared with those reported by Hu and Chang [265] and Masliyah and Nandakumar [267]. The incremental pressure drop K(°°) and hydrodynamic entrance length L+hy together with /Re are given in Table 5.48, in which the term n refers to the number of fins, while / denotes the relative length of the fins. 

Gangal and Aggarwala [268] have analytically obtained the/Re and NuHi for fully developed flow in a square duct with four equal internal fins, as that shown in Fig., 5.43. The fins were treated as having zero thickness and 100 percent efficiency. The results of /Re and NuHm for fully developed flow are provided in Table 5.50. 

TABLE 5.51 The Fully Developed (f Re)rf and Nu,/ Values for Forced Convection of Laminar Flow in a Semicircular Duct With Internal Fins [274]... 

Dong and Ebadian [274] have used a very fine grid to perform a numerical analysis of fully developed laminar flow in a semicircular duct with internal longitudinal fins. The fins are considered to have zero thickness, and the number of fins n and relative fin length / = l/a are... 

An elliptical duct with four internal longitudinal fins mounted on the major and minor axes, as shown in Fig. 5.48, has been analyzed by Dong and Ebadian [275] for fully developed laminar flow and heat transfer. In this analysis, the fins are considered to have zero thickness. The thermal boundary condition is applied to the duct wall, and / is defined as a ratio of Ha a = Hbib. The friction factors and Nusselt numbers for fully developed laminar flow are given in Table 5.52. 

TABLE 5.52 Friction Factors and Nusselt Numbers for Fully Developed Flow in an Elliptical Duct With Internal Fins [275]... 

K. Nandakumar, and J. H. Masliyah, Fully Developed Viscous Flow in Internally Finned Tubes, Chem. Eng. J., (10) 113-120,1975. 

The solution of Eqs. 22 and 23a with the appropriate dynamic and thermal boundary conditions allows one to obtain the velocity and temperature distribution inside the microchannel for laminar fully developed flows. The analytical solution of Eqs. 22 and 23a has been obtained only for a few cross-sectional geometries. The numerical approach enables the calculation of the local and the average Nusselt number by means of which the internal convective heat transfer coefficients in microchannels can be computed. 

Sinai, Y. L., A Charnock-Based Estimate of Interfacial Resistance and Roughness for Internal, Fully-Developed Stratified Two-Phase Horizontal How, Int. J. Multiphase Flow, Vol. 9, pp. 13-19 (1983). 

For internal flows both the hydrodynamic boundary layer and the thermal boundary layer developing on the wall merge (at the center for symmetric channels) downstream of the entrance and provide thereafter a fully developed boundary layers. 

Worsoe-Schmidt PM. Heat transfer in the thermal entrance region of circular tubes and annular passages with fully developed laminar flow. International Journal of Heat and Mass Transfer 1967 10 541-551. 

For fully developed laminar flow (Section 3.2.2.1), the average Nu number for the heat transfer to the internal surface of the tube with uniform temperature, length L, and diameter dt is (Schluender, 1970 VDI, 1997, see Example 3.2.1) ... 

At some distance away from the entrance, the boundary layers meet and flow is assumed as viscous over the entire cross section of the channel. The internal flow is categorized into two distinct regions (i) hydrodynamic entrance region where velocity profile varies with the axial length of the channel and (ii) hydro-dynamic fully developed region where velocity profile remains invariable with the longitudinal distance along the channel, or becomes fully developed. 

For internal flows, thermal boundary layers develop from both top and bottom surfaces and develop into two regions thermal entry length and thermal fully developed regions similar to hydrodynamic internal flow as shown in Figure 6.8. 

Concentration entry length and fully developed region for internal flow in a charmel. 

Internal flow through tubes or channels regarding inlet flow or fully developed flow. 

From a force balance on the internal flow surface and conservation of energy, we can derive the following equation relating frictional pressure drop per unit length in a closed channel for fully developed flow ... 

Sand with a mean particle diameter of 0.2 mm is to be conveyed in water flowing at 0.5 kg/s in a 25 mm internal diameter horizontal pipe 100 m long. Assuming fully suspended flow, what is the maximum amount of sand which may be transported in this way if the head developed by the pump is limited to 300 kN/m2 ... 

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