Growth Reynolds number

Friction loss The pressure energy loss that takes place in duct or pipe flow. It is related to the Reynolds number, boundary layer growth, and the velocity distribution. 

Figure 5.7 Effect of solution velocity on crystal growth rates after Miillin and Garside, 1967) number Sh = IcLjD, the partiele Reynolds number...

M. Amon and C. D. Denson [33-34] attempted a theoretical and experimental examination of molding a thin plate from foamed thermoplastic. In the first part of the series [33] the authors examined bubble growth, and in the second [34] — used the obtained data to describe how the thin plate could be molded with reference to the complex situation characterized in our third note. Here, we are primarily interested in the model of bubble growth per se, and, of course, the appropriate simplification proposals [33]. Besides the conditions usual for such situations ideal gets, adherence to Henry s law, negligible mass of gas as compared to mass of liquid, absence of inertia, small Reynolds numbers, incompressibility of liquid, the authors postulated [33] several things that require discussion ... 

Laminar flow ceases to be stable when a small perturbation or disturbance in the flow tends to increase in magnitude rather than decay. For flow in a pipe of circular cross-section, the critical condition occurs at a Reynolds number of about 2100. Thus although laminar flow can take place at much higher values of Reynolds number, that flow is no longer stable and a small disturbance to the flow will lead to the growth of the disturbance and the onset of turbulence. Similarly, if turbulence is artificially promoted at a Reynolds number of less than 2100 the flow will ultimately revert to a laminar condition in the absence of any further disturbance. 

Reynolds number. It should be stressed that the heat transfer coefficient depends on the character of the wall temperature and the bulk fluid temperature variation along the heated tube wall. It is well known that under certain conditions the use of mean wall and fluid temperatures to calculate the heat transfer coefficient may lead to peculiar behavior of the Nusselt number (see Eckert and Weise 1941 Petukhov 1967 Kays and Crawford 1993). The experimental results of Hetsroni et al. (2004) showed that the use of the heat transfer model based on the assumption of constant heat flux, and linear variation of the bulk temperature of the fluid at low Reynolds number, yield an apparent growth of the Nusselt number with an increase in the Reynolds number, as well as underestimation of this number. 

Winant, D., and F. K. Browand. 1974. Vortex pairing, the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mechanics 63 237-55. 

Examples of dimensionless groups that specify ratios of transport mechanisms are listed next in Table II and depend on the size and shape of the domain. The Peclet numbers for heat (Pet) and solute (Pes) and momentum (Re) transport are ratios of scales for convective to diffusive transport and depend on the magnitudes of the velocity field and the length scale for the diffusion gradient. Boundary layers form at large Peclet numbers (Pet or Pes) or Reynolds numbers (Re). The fonnation of a boundary layer at a large Re is particularly important in crystal growth from the melt, because the low... 

Figure 2.2 Contour plots of asymptotic growth rate in Reynolds number- circular frequency plane...

First, we obtained the neutral curve for the case of K = 0, as shown in Fig. 6.3. From the figure, it is noted that the critical Reynolds number is given by Rccr = 519.018 and the corresponding critical circular frequency is uJcr = 0.12- values that are exactly the same for the Blasius profile. We also report such data in Table 6.4 for all the different values of K considered in the present study. Maximum growth rate for spatially growing waves are in the range of kimag —0.0074 for the case of Fig. 6.3. 

The relationship between increasing flow rate and decreasing short crack growth rate is consistent with the concept of flow-induced rinsing of the crack enclave. Assuming an aspect ratio of 10, a crack opening of 10 pm is indicated, which would seem to be a reasonable value. While the studies of Choi et al. [102] were carried out under some conditions that closely resemble those that exist in BWR primary circuits and in PWR secondary circuits, the flow rates and Reynolds numbers... 

Problem 9-25. Mass Transfer From a Gas Bubble in a Bioreactor. Gas bubbles are injected through a sparger into a bioreactor to oxygenate a liquid growth medium. The liquid is sufficiently viscous that the bubbles flow at low Reynolds number. You have been asked to model the mass transfer of oxygen in the reactor. 

A compilation of optimum physical properties of CVD-derived Nb3Ge films (i.e., T, 7c, and //c2 values of 22.5 K, 1.8 x 10 Acm " and 27.3 T) is listed in Table 2-4. Evaluated variables for Nb3Ge film growth include substrate temperature, the gaseous metal chloride hydrogen mole ratio in the carrier gas stream, NbCU (g) to GeCb (g) mole ratio, and the reactor viscosity (Reynolds number). 

Fig. 12.15 shows a remarkable increase in biofilm thickness for only 5°C temperature change. These data were obtained for Escherichia coli in an experimental apparatus with flow Reynolds number of 6.3 x 10, i.e. turbulent [Bott and Pinheiro 1977]. The optimum temperature for maximum growth for this species is around 35 - 40°C. Work by Harty [1980] using the same species (Escherichia coli) demonstrated similar effects. Fig. 12.16 also shows that as velocity is increased (i.e. increased shear at the surface) in the particular system studied, the effect of temperature becomes less. It would be expected that the effects of shear are likely to be more pronounced than the effects of temperature on growth. 

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