Laminar flow in tubes

Geometrically Similar Scaleups for Laminar Flows in Tubes. The pressure drop for this method of scaleup is found using the integrated form of the Poiseuille equation ... 

Constant-Pressure Scaleups for Laminar Flows in Tubes. As shown in the previous section, scaling with geometric similarity, Sr = Sr = 5 /, gives... 

Hausen [4] presents the following empirical relation for fully developed laminar flow in tubes at constant wall temperature ... 

Thirty years later, Gerhard Damkohler (1937) in his historic paper, summarized various reactor models and formulated the two-dimensional CDR model for tubular reactors in complete generality, allowing for finite mixing both in the radial and axial directions. In this paper, Damkohler used the flux-type boundary condition at the inlet and also replaced the assumption of plug flow with parabolic velocity profile, which is typical of laminar flow in tubes. 

There have been several empirical heat transfer relationships for laminar flow in tubes proposed which attempt to allow for variation in rheological properties. Empirical equations developed by several authors for the fluids with different rheological behaviors have been well reviewed by Skelland (1967). Here, a few equations containing dimensionless groups are given to illustrate such relationships. 

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. ... 

Knowledge of the temperature field in the fluid is a prerequisite for the calculation of the heat transfer coefficient using (1.25). This, in turn, can only be determined when the velocity field is known. Only in relatively simple cases, exact values for the heat transfer coefficient can be found by solving the fundamental partial differential equations for the temperature and velocity. Examples of this include heat transfer in fully developed, laminar flow in tubes and parallel flow over a flat plate with a laminar boundary layer. Simplified models are required for turbulent... 

Boundary Layer Theory. The Reynolds number for flow-through hollow fibers during our experiments was at most about 0.02 cm (diameter) x 4 cm/sec (velocity) x 1.0 g/cm (density)/ 0.007 poise (viscosity) 11 therefore, a boundary layer theory is needed for laminar flow in tubes. Because of its simplicity, the most attractive available theory is an approximate result of thln-film theory. This theory is restricted to a description of boundary layers that are thin in comparison to the tube radius. Furthermore, the ultrafiltrate velocity, J, must not vary along the tube length (uniform-wall-flux theory). At the centerline or axis of the fiber, the impermeable solute concentration C = C... 

The heat-transfer coefficient, k, for laminar flow in tubes can be enhanced by a factor of two- to sixfold using static mixer elements in the heat-exchanger tubes. The heat-transfer coefficient is correlated using the Nusselt, Prandtl, and Reynolds numbers. Table 9.21 gives constants for Koch SMX and SMXL mixers for... 

Values of the drag coefficients for laminar flow in tubes of various shape... 

This is the Hagen-Poiseuille law for laminar flow in tubes. Its conversion to a form applicable to experimental measurements will be given later. For the present we note that the quantities R, aP and I can all be obtained by direct measurement and Eqn 4-8 therefore can be used in the absolute experimental method for the determination of the viscosity of a liquid in any physically rational system of units. When the... 

Heat transfer for laminar flow in tubes with a parabolic velocity profile. (Does not include effects of natural convection or viscosity gradients.)... 

V. Gnielinski, Heat-transfer on laminar-flow in tubes and constant wall temperature. Chemie Ingenieur Technik, 1989, 61, 160-161. 

Laminar flow in tubes. A large portion of the experimental investigations have been concerned with heat transfer of non-Newtonian fluids in laminar flow through cylindrical tubes. The physical properties that are needed for heat transfer coefficients are density, heat capacity, thermal conductivity, and the rheological constants K and n or K and n. 

Figure 3.6 shows other data for overall enhancement factors (taking into account both Nusselt number improvement and possible degradation in friction factor) for laminar flow in tubes using various twisted tape and wire coil tube inserts. The data are compared with that of a plain tube (Wang et al., 2002). The authors found that... 

Axiai Dispersion Modei for Laminar Fiow in Round Tubes The exact two-dimensional equation for laminar flow in tubes is given by Eqs. (4.10.27) and (4.10.28) ... 

For laminar flow in tubes the concept of axial mixing can be used to describe the combined effect of the velocity profile and radial diffusion. The following relation was derived from a theoretical basis by Taylor (1953) ... 

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