Friction factors forced convection

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. 

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. 

The Pore Flow Model uses the Hagen-Poiseuille Equation to describe solvent flow through cylindrical pores of the membrane. No membrane characteristics other than pore size or pore density are accounted for, and neither limitation of flux due to friction nor diffusion is considered. Flux occurs due to convection under an applied pressure. The equation is derived from the balance between the driving force pressure and the fluid viscosity, which resists flow (Braghetta (1995), Staude (1992)). Solvent flux ( ) is described by equation (3.26) and solute flux (Js) by equation (3.27), where rp is the pore radius, np the number of pores, T the tortuosity factor. Ax the membrane thickness and ct the reflection coefficient. 

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