Length to hydraulic diameter ratio

Figure 10.38. Effect of length to hydraulic diameter ratio on backmixing through a center draft tube with 6BD Impellers.

Figure 1.142 A kind of flow-pattern map for zig-zag micro mixers of various dimensions correlating their Reynolds numbers with their hydrodynamic regimes as a function of their ratio of bend length to hydraulic diameter [151]...

Based on these experiments, a kind of flow-pattern map was proposed describing a region of laminar flow where viscous losses dominate, an intermediate region with secondary flow where inertial losses dominate (albeit still not turbulent) and a region of fully developed turbulent flow (see Figure 1.142) [151]. The transitional Reynolds number from the pure laminar to the secondary-flow regime increases with the ratio of bend length to hydraulic diameter. 

Numerical solutions to predict EO flows for all relevant length scales in complex geometries with arbitrary cross-sections are difficult for Debye lengths much smaller than the characteristic dimensions of the channels (e.g., the hydraulic diameter). Indeed, this is the case for typical microfluidic elec-trokinetic systems, which have Debye length-to-charmel-diameter ratios of order 10 or less. For these cases, thin double-layer assumptions are often appropriate as approximations of EO flow solutions in complex geometries. For the case of thin double layers, the electric potential throughout most of the cross-sectional area of a microcharmel is zero, and the previous equation, for the case of zero pressure gradients, reduces to ... 

Determine the surface geometrical properties on each fluid side. This includes the minimum free flow area A , heat transfer surface area A (both primary and secondary), flow lengths L, hydraulic diameter Dh, heat transfer surface area density P, the ratio of minimum free flow area to frontal area o, fin length and fin thickness for fin efficiency determination, and any specialized dimensions used for heat transfer and pressure drop correlations. 

For other length-to-diameter ratio, refer to Ref. [27]. For cross sections other than circular or square, use the hydraulic diameter ... 

Equations (3.11) and (3.12) show that the friction factor of a rectangular micro-channel is determined by two dimensionless groups (1) the Reynolds number that is defined by channel depth, and (2) the channel aspect ratio. It is essential that the introduction of a hydraulic diameter as the characteristic length scale does not allow for the reduction of the number of dimensionless groups to one. We obtain... 

Warrier et al. (2002) conducted experiments of forced convection in small rectangular channels using FC-84 as the test fluid. The test section consisted of five parallel channels with hydraulic diameter = 0.75 mm and length-to-diameter ratio Lh/r/h = 433.5 (Fig. 4.5d and Table 4.4). The experiments were performed with uniform heat fluxes applied to the top and bottom surfaces. The wall heat flux was calculated using the total surface area of the flow channels. Variation of single-phase Nusselt number with dimensionless axial distance is shown in Fig. 4.6b. The numerical results presented by Kays and Crawford (1993) are also shown in Fig. 4.6b. The measured values agree quite well with the numerical results. 

Available data sets for flow boiling critical heat flux (CHF) of water in small-diameter tubes are shown in Table 6.9. There are 13 collected data sets in all. Only taking data for tube diameters less than 6.22 mm, and then eliminating duplicate data and those not meeting the heat balance calculation, the collected database included a total of 3,837 data points (2,539 points for saturated CHF, and 1,298 points for subcooled CHF), covering a wide range of parameters, such as outlet pressures from 0.101 to 19.0 MPa, mass fluxes from 5.33 to 1.34 x lO kg/m s, critical heat fluxes from 0.094 to 276 MW/m, hydraulic diameters of channels from 0.330 to 6.22 mm, length-to-diameter ratios from 1.00 to 975, inlet qualities from —2.35 to 0, and outlet thermal equilibrium qualities from -1.75 to 1.00. 

This equation shows that for fixed relative losses, frequency has no effect on the volume, length or hydraulie diameter, but an increase in the average pressure for the same pressure ratio has a significant effect in decreasing the volume and a smaller effect on the hydraulic diameter. We can relate the mass flow rate to the total mass m/(peak to peak) of gas that flows through the regenerator and out the ends... 

It is easy to demonstrate that for a rectangular cross section the hydraulic diameter Dh, the aspect ratio jS, and the length of the sides (a, h) are correlated ... 

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