John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 70
Текст из файла (страница 70)
(9.25):20.0006R = 4=0.04σ /g(ρf − ρg )V /A9.8(958)= 6.00.0589This is larger than the specified lower bound of about 4.485486Heat transfer in boiling and other phase-change configurations9.4§9.4Film boilingFilm boiling bears an uncanny similarity to film condensation. The similarity is so great that in 1950, Bromley [9.24] was able to use the eqn.
(8.64)for condensation on cylinders—almost directly—to predict film boilingfrom cylinders. He observed that the boundary condition (∂u/∂y)y=δ =0 at the liquid–vapor interface in film condensation would have to changeto something in between (∂u/∂y)y=δ = 0 and u(y = δ) = 0 during filmboiling. The reason is that the external liquid is not so easily set intomotion. He then redid the film condensation analysis, merely changingk and ν from liquid to vapor properties.
The change of boundary conditions gave eqn. (8.64) with the constant changed from 0.729 to 0.512and with k and ν changed to vapor values. By comparing the equationwith experimental data, he fixed the constant at the intermediate valueof 0.62. Thus, NuD based on kg became⎡NuD = 0.62 ⎣(ρf − ρg )ghfg D 3νg kg (Tw − Tsat )⎤1/4⎦(9.28)where vapor and liquid properties should be evaluated at Tsat + ∆T /2and at Tsat , respectively. The latent heat correction in this case is similarin form to that for film condensation, but with different constants in it.Sadasivan and Lienhard [9.25] have shown it to be(9.29)hfg = hfg 1 + 0.968 − 0.163 Prg Jagfor Prg ≥ 0.6, where Jag = cpg (Tw − Tsat ) hfg .Dhir and Lienhard [9.26] did the same thing for spheres, as Bromleydid for cylinders, 20 years later.
Their result [cf. eqn. (8.65)] was⎡NuD = 0.67 ⎣(ρf − ρg )ghfg D 3νg kg (Tw − Tsat )⎤1/4⎦(9.30)The preceding expressions are based on heat transfer by convectionthrough the vapor film, alone. However, when film boiling occurs muchbeyond qmin in water, the heater glows dull cherry-red to white-hot. Radiation in such cases can be enormous.
One’s first temptation mightFilm boiling§9.4487be simply to add a radiation heat transfer coefficient, hrad to hboiling asobtained from eqn. (9.28) or (9.30), where4 − T4εσ Twsatqradhrad ==Tw − TsatTw − Tsatand where ε is a surface radiation property of the heater called the emittance (see Section 10.1).Unfortunately, such addition is not correct, because the additionalradiative heat transfer will increase the vapor blanket thickness, reducingthe convective contribution.
Bromley [9.24] suggested for cylinders theapproximate relationhtotal = hboiling +34hrad ,hrad < hboiling(9.31)More accurate corrections that have subsequently been offered are considerably more complex than this [9.10]. One of the most comprehensiveis that of Pitschmann and Grigull [9.27]. Their correlation, which is fairlyintricate, brings together an enormous range of heat transfer data forcylinders, within 20%. It is worth noting that radiation is seldom important when the heater temperature is less than 300◦ C.The use of the analogy between film condensation and film boiling issomewhat questionable during film boiling on a vertical surface.
In thiscase, the liquid–vapor interface becomes Helmholtz-unstable at a shortdistance from the leading edge.√ However, Leonard, Sun, and Dix [9.28]have shown that by using λd1 3 in place of D in eqn. (9.28), one obtainsa very satisfactory prediction of h for rather tall vertical plates.The analogy between film condensation and film boiling also deteriorates when it is applied to small curved bodies.
The reason is that thethickness of the vapor film in boiling is far greater than the liquid filmduring condensation. Consequently, a curvature correction, which couldbe ignored in film condensation, must be included during film boilingfrom small cylinders, spheres, and other curved bodies. The first curvature correction to be made was an empirical one given by Westwater andBreen [9.29] in 1962. They showed that the equationNuD =0.715 +0.263 RR1/4NuDBromley(9.32)applies when R < 1.86. Otherwise, Bromley’s equation should be useddirectly.488Heat transfer in boiling and other phase-change configurations9.5§9.5Minimum heat fluxZuber [9.17] also provided a prediction of the minimum heat flux, qmin ,along with his prediction of qmax .
He assumed that as Tw − Tsat is reduced in the film boiling regime, the rate of vapor generation eventuallybecomes too small to sustain the Taylor wave action that characterizesfilm boiling. Zuber’s qmin prediction, based on this assumption, has toinclude an arbitrary constant. The result for flat horizontal heaters is>??σ g(ρf − ρg )4(9.33)qmin = C ρg hfg @(ρf + ρg )2Zuber guessed a value of C which Berenson [9.30] subsequently correctedon the basis of experimental data.
Berenson used measured values ofqmin on horizontal heaters to getqminBerenson = 0.09 ρg hfg>??σ g(ρf − ρg )4@(ρf + ρg )2(9.34)Lienhard and Wong [9.31] did the parallel prediction for horizontal wiresand found thatqmin18= 0.5152R (2R 2 + 1)1/4qmin Berenson(9.35)The problem with all of these expressions is that some contact frequently occurs between the liquid and the heater wall at film boiling heatfluxes higher than the minimum. When this happens, the boiling curvedeviates above the film boiling curve and finds a higher minimum thanthose reported above. The values of the constants shown above shouldtherefore be viewed as practical lower limits of qmin .
We return to thismatter subsequently.Example 9.8Check the value of qmin shown in Fig. 9.2.Solution. The heater is a flat surface, so we use eqn. (9.34) and thephysical properties given in Example 9.5.24 9.8(0.0589)(958)qmin = 0.09(0.597)(2, 257, 000)(959)2§9.6Transition boiling and system influencesorqmin = 18, 990 W/m2From Fig.
9.2 we read 20,000 W/m2 , which is the same, within theaccuracy of the graph.9.6Transition boiling and system influencesMany system features influence the pool boiling behavior we have discussed thus far. These include forced convection, subcooling, gravity,surface roughness and surface chemistry, and the heater configuration,among others.
To understand one of the most serious of these—the influence of surface roughness and surface chemistry—we begin by thinkingabout transition boiling, which is extremely sensitive to both.Surface condition and transition boilingLess is known about transition boiling than about any other mode ofboiling. Data are limited, and there is no comprehensive body of theory.The first systematic sets of accurate measurements of transition boilingwere reported by Berenson [9.30] in 1960. Figure 9.14 shows two sets ofhis data.The upper set of curves shows the typical influence of surface chemistry on transition boiling. It makes it clear that a change in the surfacechemistry has little effect on the boiling curve except in the transitionboiling region and the low heat flux film boiling region.
The oxidation ofthe surface has the effect of changing the contact angle dramatically—making it far easier for the liquid to wet the surface when it touches it.Transition boiling is more susceptible than any other mode to such achange.The bottom set of curves shows the influence of surface roughness onboiling. In this case, nucleate boiling is far more susceptible to roughnessthan any other mode of boiling except, perhaps, the very lowest end of thefilm boiling range.
That is because as roughness increases the numberof active nucleation sites, the heat transfer rises in accordance with theYamagata relation, eqn. (9.3).It is important to recognize that neither roughness nor surface chemistry affects film boiling, because the liquid does not touch the heater.489Figure 9.14 Typical data from Berenson’s [9.30] study of theinfluence of surface condition on the boiling curve.490§9.6Transition boiling and system influencesFigure 9.15 The transition boiling regime.The fact that both effects appear to influence the lower film boiling rangemeans that they actually cause film boiling to break down by initiatingliquid–solid contact at low heat fluxes.Figure 9.15 shows what an actual boiling curve looks like under theinfluence of a wetting (or even slightly wetting) contact angle. This figureis based on the work of Witte and Lienhard ([9.32] and [9.33]).
On it areidentified a nucleate-transition and a film-transition boiling region. Theseare continuations of nucleate boiling behavior with decreasing liquid–solid contact (as shown in Fig. 9.3c) and of film boiling behavior withincreasing liquid–solid contact, respectively.These two regions of transition boiling are often connected by abruptjumps. However, no one has yet seen how to predict where such jumpstake place. Reference [9.33] is a full discussion of the hydrodynamictheory of boiling, which includes an extended discussion of the transitionboiling problem and a correlation for the transition-film boiling heat fluxby Ramilison and Lienhard [9.34].491492Heat transfer in boiling and other phase-change configurations§9.6Figure 9.14 also indicates fairly accurately the influence of roughnessand surface chemistry on qmax .
It suggests that these influences normally can cause significant variations in qmax that are not predicted inthe hydrodynamic theory. Ramilison et al. [9.35] correlated these effectsfor large flat-plate heaters using the rms surface roughness, r in µm,and the receding contact angle for the liquid on the heater material, βrin radians:qmax= 0.0336 (π − βr )3.0 r 0.0125qmaxZ(9.36)This correlation collapses the data to ±6%. Uncorrected, variations fromthe predictions of hydrodynamic theory reached 40% as a result of roughness and finish. Equivalent results are needed for other geometries.SubcoolingA stationary pool will normally not remain below its saturation temperature over an extended period of time. When heat is transferred to thepool, the liquid soon becomes saturated—as it does in a teakettle (recallExperiment 9.1).
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
