Critical flux

The maximum heat flux achievable with nucleate boiling is known as the critical heat flux. In a system where the surface temperature is not self-limiting, such as a nuclear reactor fuel element, operation above the critical flux will result in a rapid increase in the surface temperature, and in the extreme situation the surface will melt. This phenomenon is known as burn-out . The heating media used for process plant are normally self-limiting for example, with steam the surface temperature can never exceed the saturation temperature. Care must be taken in the design of electrically heated vaporisers to ensure that the critical flux can never be exceeded. 

The critical flux is reached at surprisingly low temperature differences around 20 to 30°C for water, and 20 to 50°C for light organics. 

It is important to check that the design, and operating, heat flux is well below the critical flux. Several correlations are available for predicting the critical flux. That given by Zuber et al. (1961) has been found to give satisfactory predictions for use in reboiler and vaporiser design. In SI units, Zuber s equation can be written as ... 

Estimate the heat-transfer coefficient for the pool boiling of water at 2.1 bar, from a surface at 125°C. Check that the critical flux is not exceeded. 

The critical flux in forced-convection boiling is difficult to predict. Kern (1950) recommends that for commercial reboiler designs the heat flux should not exceed 63,000 W/m2 (20,000 Btu/ft2h) for organics and 95,000 W/m2 (30,000 Btu/ft2h) for water and dilute aqueous solutions. These values are now generally considered to be too pessimistic. 

By further simplification, Chang (1961) obtained the critical flux for vertical surfaces,... 

Kutateladze s data on various surface conditions of horizontal wires and disks indicate that the average value of Km is 0.16, in a range from 0.13 to 0.19. This equation agrees well with the pool boiling critical fluxes obtained by Cichelli and Bonilla (1945) for a number of organic liquids. 

Ivey and Morris (1962) reported the ratio of subcooled critical flux to saturated critical flux of pool boiling in water, ethyl alcohol, ammonia, carbon tetrachloride, and isooctane for pressures from 4.5 to 500 psia (0.3 to 34 X 105 Pa) as... 

Bernath (1960) also studied the orientation effect on the CHF and found that the critical flux from a vertical heater is only about 75% of that of a horizontal heater under the same conditions. Further discussion of the latter effect is given in the section on the related effect of acceleration. 

In a uniform heat flux test section, the CHF cannot vary by one variable without affecting another accompanying variable. Figure 5.40 is reproduced from an article by Aladyev et al. (1961). This figure actually indicates the combined effects of pressure and inlet subcooling at a constant exit quality. The CHF occurs at the exit, and the exit enthalpy is kept at saturation. Because the critical flux varies with pressure, the inlet temperature must also vary. Hence the high CHF at low pressure is achieved by means of a low inlet temperature and the favorable physical properties of water and steam under low pressures also help the heat transfer at the corebubble layer interface. 

The effect of local enthalpy at CHF is due primarily to the wall voidage, which impairs the critical flux, and secondarily to the bulk voidage, which affects the flow pattern. The coupled effects of local subcooling and flow velocity in a subcooled bubbly flow were first reported by Griff el and Bonilla (1965), neglecting the pressure effect ... 

Table 7.1 lists heat flux levels commonly encountered in fire and contrasts them with perceptible levels. It is typically found for common materials that the lowest heat fluxes to cause piloted ignition are about 10 kW/m2 for thin materials and 20 kW/m2 for thick materials. The time for ignition at these critical fluxes is theoretically infinite, but practically can be (9(1 min) (order of magnitude of a minute). Hashover, or more precisely the onset to a fully involved compartment fire, is sometimes associated with a heat flux of 20 kW/m2 to the floor. This flow heat flux can be associated with typical... 

For long heating times, eventually at t —> oo, the temperature just reaches Tig. Thus for any heat flux below this critical heat flux for ignition, gig crit, no ignition is possible by the conduction model. The critical flux is given by the steady state condition for Equation... 

As in the thermally thin case, as > oo, the critical flux for ignition is... 

Table 7.4 Estimated ignition temperatures and critical flux for redwood...

Heating along grain (°C) Heating across grain (°C) Critical flux (kW/m2)... 

Calculate the time to ignite (piloted) for the materials listed below if the irradiance is 30 kW/ m2 and the initial temperature is 25 °C. The materials are thick and the convective heat transfer coefficient is 15 W/m2 K. Compute the critical flux for ignition as well. 

Examine data taken under a natural convection lateral vertical surface spread for a particle board as shown in Figures 8.12(a) and (b) [17]. The correlation of these data based on Equation (8.29) suggests that the critical flux for ignition is... 

The entanglement time and area depend on the thickness of nonhnear crystal, the type of nonlinear interaction, and piunping conditions. Their chosen values are close to those used in [73]. Together, they yield the critical flux density of 0c = 3 x 10 cm. This results in the entangled photon absorption cross-section = 2.95 x 10 cm. The latter estimate falls between the values obtained earlier from quantum-mechanical calculations for Na (6.0 X 10-3° K2CsSb (2.6 x lO cm ) [73]. 

Dependencies of the absorption rates on the irradiation area at a constant pair arrival rate of 10 MHz are shown in Fig. 18. Here R2 and Re exhibit different slopes. For areas larger than a certain critical value (which corresponds to the critical flux density, and in this case is very close to the area with diameter of 0.8 pm), the entangled photon TPA dominates the classical TPA. However,... 

Figure 7.17 Experiments showing the rate of fouling of 0.22-p.m microfiltration membranes used to treat dilute biomass solutions. The membranes were operated at the fluxes shown, by increasing transmembrane pressure over time to maintain this flux as the membranes fouled [12]. Reprinted from J. Membr. Sci. 209, B.D. Cho and A.G. Fane, Fouling Transients in Nominally Sub-critical Flux Operation of a Membrane Bioreactor, p. 391, Copyright 2002, with permission from Elsevier...

The concept of critical flux ( Jcrit) was introduced by Field et al. [3] and is based on the notion that foulants experience convection and back-transport mechanisms and that there is a flux below which the net transport to the membrane, and the fouling, is negligible. As the back transport depends on particle size and crossflow conditions the Jcrit is species and operation dependent. It is a useful concept as it highlights the... 

The concept of critical flux was introduced during the mid-1990s and defined as a flux below which fouling is absent or negligible. The basis of this concept is that for a... 

Figure 16.7 Determination of critical flux in MBRs (a) method, (b) applied.

Cho, B.D. and Fane, A.G. (2002) Fouling transients in nominally cub-critical flux operation of a membrane bioreactor. Journal of Membrane Science, 209 (2), 391 103. 

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