Effect of mass flux

For diabatic flow, that is, one-component flow with subcooled and saturated nucleate boiling, bubbles may exist at the wall of the tube and in the liquid boundary layer. In an investigation of steam-water flow characteristics at high pressures, Kirillov et al. (1978) showed the effects of mass flux and heat flux on the dependence of wave crest amplitude, 8f, on the steam quality, X (Fig. 3.46). The effects of mass and heat fluxes on the relative frictional pressure losses are shown in Figure 3.47. These experimental data agree quite satisfactorily with Tarasova s recommendation (Sec. 3.5.3). 

Figure 5.38 Effect of mass flux on the CHF of potassium and water in a seven-rod bundle. (From Jones and Hoffman, 1970. Copyright 1970 by American Society of Mechanical Engineers, New York. Reprinted with permission.)...

Collins and Gacesa (1969) tested the effects of mass flux and power on flow oscillation frequency in a 19-rod bundle with steam-water flow at 800 psia. (5.5 MPa) They found that the oscillation frequency increases with mass flux as well as power input to the channel. Within the mass flux range 0.14-1.0 X 106 lb/hr ft2 (189-1,350 kg/m2 s), the frequency / can be expressed as... 

Figure 12. Effect of mass flux and bed diameter on solid concentration. (From Hartge, Li and Wether, 1986.)...

This equation, which is analogous in form 10 Eq. (2.4-8) fur the effect of mass flux on mass transfer coefficient, is known as the Ackermann correction factor7 for the effect of mass transfer on hent transfer. Note that the tmal flux of enthalpy to the vapor-liquid interface is ihe sum of the condnetiva flux and the enthalpy carried by the tmasferring molecules... 

Although the film theory js simple, conceptually useful, and snccessfiil in demonstrating effects of reaction on mass transfer12 aed tha effects of mass flux on heat transfer rates. it is based on physically unrealistic assumptions. Additional models that relax some of the film theory assumptions have therefore been developed. 

Effect of Mass Flux. Typical results calculated from the Bowring [293] correlation for the effect of mass flux are shown in Fig. 15.118. At low mass fluxes, the critical heat flux increases rapidly with increasing mass flux and tends to approach a constant value. 

FIGURE 15.118 Effect of mass flux on critical heat flux in upward water flow in a vertical tube (calculated from the Bowring [293] correlation for a tube length of 1 m, a tube diameter of 0.01 m, and zero inlet subcooling) (from Hewitt [291], with permission from The McGraw-Hill Companies). 

Condensation in Microchanneis, Figure 4 Effects of mass flux on the dimensionless distance Z/L at different Co in microchanneis having a hydraulic diameter of 136 xm [7]... 

Krasyakova et al. (1967) found that in a horizontal tube, in addition to the effects of nonisothermal flow that is relevant to a vertical tube, the effect of gravitational forces is important. The latter effect leads to the appearance of temperature differences between the lower and upper parts of the tube. These temperature differences depend on flow enthalpy, mass flux, and heat flux. A temperature difference in a tube cross section was found at G = 300—1000 kg/m s and within the investigated range of enthalpies (H = 840—2520 kJ/kg). The temperature difference was directly proportional to increases in heat flux values. The effect of mass flux on the temperature difference is the opposite, ie, with an increase in mass flux, the temperature difference decreases. DHT was also observed in a horizontal tube. However, the temperature profile for a horizontal tube at locations of DHT differs from that for a vertical tube, being smoother for a horizontal tube compared to that of a vertical tube with a higher temperature increase on the upper part of the tube than on the lower part. 

The main characteristics of the effect of mass velocity are shown in Fig. 28. One interesting feature, curve (2), is a rapid rise of burn-out flux in the low-velocity regime to a value which thereafter remains practically independent of mass velocity. The primary condition which tends to induce this effect is a low value of Ah, but the pressure and Ljd ratio are also important. At 1000 psia, for example, the Ljd ratio must be less than about 100. The influence of the Ljd ratio was shown in Fig. 26. 

The quantity G of the effective mixing mass flux is determined by the turbulent velocity fluctuations at the bubble-layer edge. The distance of the edge of the bubble layer from the wall is taken as the distance at which the size of the turbulent eddies is k times the average bubble diameter. Weisman and Pei have determined empirically that k equals 2.28. Only a fraction of the turbulent velocity fluctuations produced are assumed to be effective in reaching the wall. The effective velocity fluctuations are those in which the velocity exceeds the average velocity away from the wall produced by evaporation heat flux q"b. At the bubble layer-core interface, the effective mass flux to the wall is computed as... 

Dwyer, O. E., G. Strickland, S. Kalish, and P. J. Schoen, 1973a, Incipient-Boiling Superheat for Sodium in Turbulent Channel Flow Effects of Heat Flux and Flow Rate, Int. Heat Mass Transfer 16 911-984. (4)... 

The mass flux vector is also the sum of four components j (l), the mass flux due to a concentration gradient (ordinary diffusion) jYp), the mass flux associated with a gradient in the pressure (pressure diffusion) ji(F), the mass flux associated with differences in external forces (forced diffusion) and j,-(r), the mass flux due to a temperature gradient (the thermal diffusion effect or the Soret effect). The mass flux contributions may then be summarized ... 

Equation 28 and its liquid-pliase equivalent aie very general and valid in all situations. Similarly, llie overall mass transfer coefficients may be made independent of I lie effect of bulk flux flirougli die films and tlius nearly concentration independent for straiglit equilibrium lines ... 

The inverse of the Dufour effect is the production of mass fluxes due to temperature gradients this is referred to as thermal diffusion or the Soret effect. To account for this effect, we need to augment the generalized Maxwell-Stefan diffusion equations in the following manner ... 

If there were no mass transfer, the heat flux would be almost 10% higher. The effect of mass transfer on heat transfer, although not all that large here, is clearly too large to ignore altogether. ... 

Averaging the product of the absolute value of the gradient and the fluxes gives as the result the average contributory effect of mass and molecular fluxes at the interfaces over the whole domain of integration [67]. Drew [54] defined the averaged interfacial area per unit volume by ... 

The model for aggregation and sedimentation in lakes (Eq. 6) has a conceptual basis and is consistent with some field observations. It is used here to make predictions about the kinetics and effects of coagulation and sedimentation in Lake Zurich. The responses of a lake to coagulation and sedimentation can be represented as mass flux distributions (O Melia and Bowman, 1984). Simulations of mass fluxes by river flow, net production in the epilimnion, coagulation, and sedimentation for Lake Zurich are presented in Figure 6. The particle mass flux distributions, AJ/(A log dp), are plotted as functions of particle size (log scale) for mass fluxes by these processes in the epilimnion. A positive sign indicates a flux of mass into a given size class. 

The effect of mass and heat transfer associated with the problem of the bubble evolution is also very interesting. In the case of mass transport, we can assume that at a given current density, or flux, N number of the adsorbed bubbles can be formed. At a given time tR, the diameter reaches a critical value rh after which it breaks off. We assume that the fresh electrolyte arrives at a similar concentration of that of the bulk, especially when the convective flux is large enough. We also consider that the mass transport is rate determining, so when the new electrolyte arrives it rapidly converts into the product. Under this consideration, it follows the second Fick s law ... 

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