Convection friction factor

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. 

A study of forced convection characteristics in rectangular channels with hydraulic diameter of 133-367 pm was performed by Peng and Peterson (1996). In their experiments the liquid velocity varied from 0.2 to 12m/s and the Reynolds number was in the range 50, 000. The main results of this study (and subsequent works, e.g., Peng and Wang 1998) may be summarized as follows (1) friction factors for laminar and turbulent flows are inversely proportional to Re and Re ", respectively (2) the Poiseuille number is not constant, i.e., for laminar flow it depends on Re as PoRe ° (3) the transition from laminar to turbulent flow occurs at Re about 300-700. These results do not agree with those reported by other investigators and are probably incorrect. 

Tlie friction factor/and the Nusselt number relations are given in Table 8-1 for fully developed laminar flow in tubes of various cross sections. The Reynolds and Nu.sselt numbers for flow in these tubes are based on the hydraulic diameter D/, - 4AJp, where is the cross sectional area of the tube and p is its perimeter. Once the Nusselt number is available, the convection heat transfer coefficient is determined from h = / Nu/D. ... 

Any iiregiilarily or roughness on the surface disturbs- the laminar sublayer, and affects the flow. Therefore, unlike laminar flow, the friction factor and the convection coefficient in turbulent flow are strong functions of surface roughness. 

In turbulent flow, wall roughness increases the heat transfer coefficient h by a factor of 2 or more [Dipprey and Saber.sky (1963)]. The convection heat transfer coefficient for rough tubes can be calculated approximately from the Nusselt number relations such as Eq. 8-71 by using the friction factor determined from the Moody chart or the Colebrook equation. However, this approach is not very accurate since there is no further increase in h with/for /> 4/sn,ooih [Norris (1970)1 and correlations developed specifically for rough tubes should be used when more accuracy is desired. 

Tubes with rough surfaces have much higher heat transfer coefficients than tubes with smooth surfaces. Therefore, tube surfaces are often intentionally roughened, corrugated, or filmed in order to enhance the convection heat iraiisier coefficient and thus the convection heat transfer rate (Fig. 8-28). Heat transfer in turbulent flow in a lube has been increased by as much as 400 percent by roughening the surface. Roughening the surface, of course, also increases the friction factor and thus the power requirement for the pump or the fan. 

An enormous amount of experimental work on convective heat transfer and skin-friction pressure drop has been reported during the 1900s. This has been accompanied by theoretied developments. For laminar flow, heat transfer coefficients and friction factors for weD-... 

It is well known that the friction factor and the convective heat transfer coefficient can be influenced by the relative roughness of the walls of a channel. For microchannels the relative roughness, defined as the ratio between the mean height of the surface asperities and the hydraulic diameter of the chaimel, can assume large values. Especially for stainless steel commercial microtubes the relative roughness can reach values equal to 2-8 %. 

It should be added here that rounded or square-edged entrances can influence the values assumed by the convective heat transfer coefficient and, especially, the values assumed by the friction factor in the entrance region [1, 2]. Since the data cover only a few simple entrance geometries, the designer must exercise judgment in the application of the correlations proposed for calculating the friction factor and the convective heat transfer coefficient in the entrance region. 

It may now be added here that rounded entrances or square-edged entrances can influence the values assumed by the convective heat transfer coefficient but especially by the friction factor in the entrance region. 

Since data cover only a few simple entrance geometries, the designer must exercise judgment in the application of the correlations proposed to calculate the friction factor and the convective heat transfer coefficient in the entrance region of a microchannel. 

When Mam > 0.3 the hypothesis of incompressibility no longer holds and the gas acceleration leads to changes in the velocity profile not only in magnitude but also in shape. The magnitude increments produce additional pressure drop while the shape changes alter the friction factor at the walls. The continuous variation in shape of the velocity profile means that neither fully developed nor locally fully developed flows occur. This fact influences the convective heat transfer coefficient since no fully developed temperature profiles can occur if the flow is developing and the experimental Nusselt numbers differ by the theoretical values for fully developed flow. It is possible to demonstrate numerically that when the Mach number increases the Nusselt number decreases along the... 

The development of the velocity and temperature fields has a marked effect on the friction factor and the heat transfer coefficient near the channel entrance region. Correlations for the calculation of the friction factor and of the convective heat transfer coefficients in the entrance region of a microchannel are given in entrance region. 

The specific form of the distributed wall friction factor, Eq. [16.34], for natural-circulation flows, has been the subject of extensive investigations. Todreas and Kazimi (1990) present a summary to that time, including rod bundle data by Gruszynski and Viskanta (1983). Swapnalee and Vijayan (2011) and Ambrosini et al. (2004) are additional examples. The special consideration required for supercritical thermodynamic states has been noted earUer in this chapter (eg, Pioro and Duffey, 2003 Yadav et al., 2012b). Natural-circulation flows, having bulk motions, are somewhat different from natural convection and low-flow forced convection. The necessity for a continuous representation of the friction factor for wall-distributed resistance is an additional critical aspect of stability of NCLs as discussed in Section 16.10. 

J-factor A dimensionless factor used in heat and mass transfer of fluids with turbulent flowin pipes. It isafunctionofReynolds number, geometry, and boundary conditions from which the friction factor can be obtained and agrees well with convective heat transfer correlations orfor detemiiningheattransfercoefficients.lt was proposed by Americanchemi-cal engineer Allan P. Colburn (1904-55) and forms part of the Chilton-Colbum analogy, which is used in heat, momentum, and mass transfer. 

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