AIChE Journal Vol 53 No 1

Analysis of Incipience of NucleateBoiling in a Reboiler Tube

M. Kamil and M. ShamsuzzohaDept. of Petroleum Studies, Aligarh Muslim Univ., Aligarh-202002 (U.P) India

M. Abdul HakeemDept. of Chemical Engineering, Aligarh Muslim Univ., Aligarh-202002 (U.P) India

DOI 10.1002/aic.11058Published online November 22, 2006 in Wiley InterScience (www.interscience.wiley.com).

An analysis has been carried out to predict the boiling incipience with natural circu-lation ow in a reboiler tube. An equation has been proposed to estimate the wallsuperheat for different types of liquids covering a wide range of thermo physical prop-erties. Incipience in liquid lms is inuenced both by turbulent eddies and liquid sub-mergence. This approach utilizes physical parameters of commonly accepted incipiencemodels and takes into account the effects of turbulent eddies and submergence. Theresults predicted from the theoretical analysis were found to be consistent with theexperimental data, having average absolute relative error of 15.42 percent. 2006American Institute of Chemical Engineers AIChE J, 53: 3950, 2007

Keywords: nucleation, natural circulation ow, turbulence, submergence, thermosiphonreboiler

Introduction

Nucleate boiling of liquids in vertical tube closed loopthermosiphon reboilers with natural circulation is of com-mon occurrence in a variety of process equipments such asreboilers, vaporizers, and evaporators used in processindustries. In most of these applications, it is important topredict the operating conditions that trigger nucleate boil-ing at the wall. Generally, a subcooled liquid entering thetube gets heated by single phase convection and movesupwards. Depending upon wall temperature conditions,subcooled boiling may set in at the surface. When the liq-uid temperature attains saturation value, saturated boilingbegins with generation of vapor, which increases along thetube length, resulting in bubbly to mist ow. Thus, theheat transfer to liquids in the reboiler tube generates achanging two-phase ow with various ow regimes spreadalong the tube length. The point at which the two-phase

begins is known as the incipient point of boiling (IPB). Itcorresponds to the conditions of minimum degree of super-heat or heat ux required for the formation and detach-ment of the rst vapor bubble from the heated surface.Since IBP divides the tube in two distinct regions, non-boiling single phase and boiling two phases with entirelydifferent modes of heat transfer, its prediction is very im-portant in the design of two phase heat transfer equipment.Incipience in forced convection systems has been studied

extensively by a number of investigators, such as Collier,1

Hsu,2 Bergles and Rohsenow,3 Sato and Matsmura,4 Davisand Anderson,5 Frost and Dzakowic,6 Unal,7 Yin andAbdelmessih,8 Sudo et al.,9 and Hino and Ueda,10 amongothers. The predicted incipience is either based on the pointof tangency between the liquid temperature prole in the vi-cinity of the heated surface and the superheat temperatureprole required for mechanical equilibrium of a vapor bub-ble growing at a surface cavity or based on the maximumcavity radius available for nucleation on the heated surface.Han and Grifth11 proposed an analysis similar to Hsu2 forthe nucleate pool boiling. Unal7 considered the effect ofpressure on the boiling incipience under subcooled owboiling of water in a vertical tube. Celata et al.12 carried

Correspondence concerning this article should be addressed to M. Kamil [email protected] or [email protected].

2006 American Institute of Chemical Engineers

AIChE Journal January 2007 Vol. 53, No. 1 39

out an experimental work to determine the ow pattern mapin vertical heated pipes under steady state and transient con-ditions using Freon-12 in forced convective ow. From theanalysis of the experimental measurements, they obtained amap for annular and intermittent ow regimes. Chen, Klaus-ner, and Mei13 proposed a simplied model for predictingvapor bubble growth in heterogeneous boiling. Wanget al.14 studied a new type of dynamic instability in a forcedconvection up ow boiling system at the boiling onset oscil-lation. Rashidnia15 studied bubble dynamics on a heatedsurface. Reed and Mudawar16 examined the effectiveness ofthe zero-angle cavities created by curved contact with a atsurface in promoting vapor embryo capture, low tempera-ture boiling incipience, and reduction or elimination of theincipience temperature overshoot with highly wettingliquids. Agarwal,17 Ali and Alam,18 Kamil,19 and Kamilet al.20,21 experimentally determined the boiling and non-boiling zones for the heating surface and superheat for in-cipient boiling in a vertical tube thermosiphon reboiler withwide ranges of submergence. A dimensionless correlationrelating the values of heat ux, inlet liquid subcooling, andsubmergence was proposed for predicting ZOB/L and wallsuperheat relating the heat ux with thermophysical proper-ties of test liquids as given in Table 1. Shim et al.22 devel-oped an analytical model for fully developed turbulent owand heat transfer in nned annuli using a modied mixing-length turbulence model. They had extended the model topredict the conditions at the onset of nucleate boiling usingthe criterion of Davis and Anderson.5 Again, these predic-tions agreed well in magnitude and trend with experimentaldata. Recently, Kamil et al.23 investigated the effect of liq-uid submergence on incipience of nucleate boiling in a ver-tical thermosiphon reboiler.There are two different criteria for the incipient point of

boilingone is rtan, and the other is rmax. The incipience inforced convection systems was studied extensively by anumber of workers as given in Table 1, and they predictedincipience based on the point of tangency (rtan). The valid-ity of the criterion was proven in many practical applica-tions. Incipience based on rtan criteria for natural convectionsystem was studied by Agarwal,17 Ali and Alam,18 Kamil,19

and Kamil et al.2024 Sudo et al.9 and Hino and Ueda10

used a different hypothesis in their forced convection study.They predicted incipience based on the maximum cavityradius (rmax) available for nucleation on the heated surface.Thus, it is evident from the literature that in the region ofincipient boiling, the thickness of the superheated layerchanges wavily and the heat is not transferred by pure heatconduction alone.Therefore, the present study focuses on the prediction of

boiling incipience in a vertical thermosiphon reboilerincluding the effect of submergence and turbulent eddies. Inthe present work, experimental data of Agarwal,17 Ali andAlam,18 and Kamil19 are compared with the predicted val-ues from existing incipience models, to evaluate theirapplicability to a vertical thermosiphon reboiler. A semi-empirical model has been developed including the effect ofsubmergence and turbulent eddies to predict the onset ofnucleate boiling for the systems, namely, acetone, methanol,ethyl acetate, ethanol, benzene, propanol, distilled water,toluene, and ethylene glycol.

Experimentation

The experimental rig was in the form of a U-shaped cir-culation system made of two long vertical stainless steeltubes whose lower ends were connected by a small horizon-tal tube, while a vapor liquid separator and condenser vesselwere tted to the upper end, as shown in Figure 1. Thestainless steel tube, which served as the test section, was25.56 mm I.D. and 28.55 mm O.D. Out of a total length of2100 mm, a section of 1900 mm was tapped between twothick copper clamps, which were designed to provide elec-trical connection to the tube with almost negligible contactresistance. In order to monitor the heat transfer surface tem-perature along the tube length, 21 copper-constantan ther-mocouples were spot welded on the outer surface of thetube at intervals of 50 mm up to a length of 200 mm fromthe bottom end and 100 mm intervals over the remaininglength. A copper-constantan thermocouple was used to mea-sure the inlet liquid temperature. The temperature of theboiling liquid, before entry to the vapor liquid separator,was measured by another traversing thermocouple probe.The condensed liquid was drained from the bottom of thecondenser vessel through a vertical tube 50 mm I.D. and300 mm long. A level indicator was attached with this tubeto indicate the liquid level in it. The cooling water to thecondensers was circulated by means of a centrifugal pumpfrom a small storage tank to which freshwater supply wasmaintained. The entire set-up was thoroughly lagged tomake the heat losses negligible, less than 62.5%. The max-imum liquid head used in the present study corresponded tothe liquid level equal to the top end of the reboiler tube.This condition has been termed as 100% submergence. Thecold liquid head (submergence) could be varied independ-ently at 75, 50, and 30%. The experimental data were gen-erated by varying the heat uxes at atmospheric pressure.The range of parameters covered is given in Table 2 for allthe systems. Other details of the reboiler and cooling sys-tem, along with its operating procedure, are described indetail elsewhere in the literature.1921

Analysis and the Wall Superheat Equation

The basic assumptions made in the present theoreticalanalysis are: The potentially active cavities are of conical shape, and

the bubble nucleus that forms at such a surface has the shapeof a truncated sphere. Bubbles grow and detach from the nucleation sites only

when the superheated liquid layer is thick enough so that anet heat ux into the developing bubble is realized. The equation for the superheated vapor temperature pro-

le Tb can be obtained from the most extensively used Clau-sius-Clapeyron relation. Assuming a constant value for T/hfgrv within the wall superheat range associated with incipi-ence, gives the following relationship:

Tb Ts 2sTshfg rv rb

(1)

The liquid temperature within the thermal layer has aturbulent lm temperature prole.

40 DOI 10.1002/aic Published on behalf of the AIChE January 2007 Vol. 53, No. 1 AIChE Journal

Table 1. Summary of Important Boiling Incipience Investigations

Authors(year)

FlowGeometry

HeaterMaterial Fluid

MeanVelocity(m s1)

Pressure[bar(psia)]

Subcooling(8C)

IncipienceFormula

Sato andMatsumura(1964)

Verticalchannel

Stainlesssteel

Water 0.64.1 1.0 (14.7) 370 Tangency criterion,r kL (TwTs)/2q

q kL rvhfg8s Ts

Tw Ts 2

Bergles andRohsenow(1964)

Horizontalannutus

Stainlesssteel

Water 3.317.4 Up to 2.6(38.0)

3290 q 15.60 P1.156 (TwTs)230/P0.023(P in psia)

Graphical solution for waterover a pressure range of 15-2000psia based on tangency criterion

Han andGrifth(1965)

Pool boilingon horizontalsurface

Gold nishedwith 600 gritemery paper

Water 1.0 (14.7) 7q kL rvhfg

12s TsTw Ts 2

Tangency criterion,y 1.5r at the point of tangency

Davis andAnderson(1966)

Authors performed analysis using experimental data from prior studies.q kL rvhfg

8C1s TsTw Ts 2

Tangency criterion,y r at the point of tangency

C1 1 for hemisphericalbubble nucleus

Frost andDzakowic(1967)

Authors performed analysis using experimental data from prior studies.q kLrvhfg

8s TsTw Ts 2 1

Pr2L

Tangency criterion,y Pr

L2r at the point of tangency.

Yin andAbdel-messih(1977)

Verticaltube

Stainle-ss steel

Freon-11 0.080.4 Up to2.0 (30.0)

1.20 For increasing heat ux:

q 17 q

6500

2 kLrvhfg2sTs

Tw Ts2

For decreasing heat ux:

q kLrvhfg5sTs

Tw Ts2

Tangency criterion, y/r atthe point of tangencycorrelated empirically.

Hino andUeda(1985)

Verticalannulus

S.S nishedwith 4/0emery cloth

Freon-113 0.11.0 1.47(22.0)

1030 For rtan < rmax:

q kLrvhfg8sTs

Tw Ts 2

For rtan > rmax:

q kLrmax

Tw Ts 2s TskLrvhfgr2max(continued)

AIChE Journal January 2007 Vol. 53, No. 1 Published on behalf of the AIChE DOI 10.1002/aic 41

Assuming a constant wall ux, the temperature gradientand mean liquid temperature in the turbulent boundary layeras given by Collier1 can be written as:

dTLdy

qrCpa eH (2)

Thus, nally, after simplication, we get:

dTLdy

qkL

1

1 PrLemPrtvLh i (3)

After integrating Eq. 3, it is possible to evaluate TL asgiven below:

TL Tw qkL

Z y0

1

1 PrLemPrtvLh i dy (4)

The radius of the rst cavity at which boiling occurs canbe determined by equating the slopes of TL and Tb, as sug-gested by Bergles and Rohsenow3:

dTbdrb

dTLdy

(5)

Taking the rst derivative of Eq. 1:

dTbdrb

2sTshfg rv rb2

(6)

according to Davis and Anderson,5 the tangency radius is:

rtan 2sTskLq hfg rv

1=2(7)

Equating Eq. 3 and Eq. 6, we get:

qkL

1

1 PrL emPrt vLh i 2sTs

hfg rv r2tan(8)

Thus, after simplication and using the tangency criterion,we get:

rtan 2sTskLq hfg rv

1=21 PrLem

PrtvL

rtan

" #1=2(9)

Equation 9 for the tangency radius is similar to Eq. 7except for the turbulent eddy diffusivity term. Thus, fromEq. 9, it is clear that rtan will be greater for turbulent lmsthan predicted by Eq. 7 as reported in the literature. Because

1 PrL emPrt vL

rtan

" #1=2 1 (10)

at the point of tangency, the temperature Tb and TL, in addi-tion to their slopes, must be equal. Thus, equating Eqs. 1

Table 1. (Continued)

Authors(year)

FlowGeometry

HeaterMaterial Fluid

MeanVelocity(m s1)

Pressure[bar(psla)]

Subcooling(8C)

IncipienceFormula

Sudo et al.(1986)

Verticalchannel

Inconel600

Water 0.71.5 1.2 (17.0) 2835 For rtan < rmax:

q kLrvhfg8sTs

Tw Ts2

For rtan > rmax:

q kLrmax

Tw Ts 2sTskLrvhfgr2maxKamil,Shamsuzzoha,and Alam (2005)

Authors performed analysis using experimental data from prior studies

Tw Ts

8s TsqkL rvhfg1 2srcPs1

RTshfg

ln1 2srcPs2

24

351=2

x S0.67079Kamil, Hakeem,and Shamsuzzoha

Authors performed analysis using experimental data from priorstudies for acetone, methanol, ethyl acetate, ethanol, benzene,propanol, water, toluene, and ethylene glycol. Tw Ts 1:1043 8sTsq

kLrvhf g

1=2S0:59867(Present Study)


and 4, we get:

Tw qkL

Z y0

1

1 PrLemPrtvLh i dy Ts 2sTs

hfg rv rtan; (11)

or

Tw Ts q rtankL

Z 10

1

1 PrLemPrtvLh i d y

rtan

8>: 9>; 2sTshfg rv rtan

(12)

Substituting Eq. 9 for rtan in Eq. 12 yields

TwTs 8sTs ahfg rv kL

1=2

1212

Z 10

1PrLemt vLrtan

" #

1PrL emPrt vLh i d y

rtan

8>: 9>;266664

377775

1PrL emPrt vL

rtan

" #1=22435

13or

Figure 1. Experimental setup.


TwTs 8sTsqhfg rv kL

1=2c1 (14)

where the turbulent boundary layer prole multiplier Ct isdened as:

c1

12 12

Z 10

1 PrL emPrt vLrtan

" #

1 PrL emPrt vLh i d y

rtan

8>: 9>;266664

377775

1 PrL emPrt vL

rtan

" #1=22435

15

Thus, Eq. 14 is a general expression for incipience in tur-bulent boundary layers including ow in closed channels.The above equation assumes bubble growth based on themean liquid temperature within the thermal boundary layer.Due to subcooled liquid continuously moved from the lm tothe wall, turbulent eddies may suppress the growth of bub-bles at potential nucleation sites. This may happen despitethe high mean liquid superheat available at the wall. Thesetransient phenomena create a quenching effect on the nuclea-tion process, which is further complicated by liquid submer-gence. A few workers, such as Agarwal,17 Ali and Alam,18

Figure 2. Wall temperature proles along the test sectionwith heat ux as a parameter for methanol.

Figure 3. Wall temperature proles along the test sectionwith submergence as a parameter for propanol.

Table 2. Range of Experimental Parameters

SystemsSubmergence(Percent) DTsub (8C)

Heat Flux(W/m2)

Acetone 44100 0.926.7 354814500Methanol 30100 1.03.7 410521305Ethyl acetate 2897 2.544.5 354818800Ethanol 30100 1.121.6 380021884Benzene 30100 0.73.6 410629225Propanol 39100 1.254.2 334221765Water 30100 0.54.6 573043373Toluene 30100 1.98.7 410632085Ethylene glycol 30100 3.2515.8 1511533654

Figure 4. Heat ux versus degree of superheat at boil-ing incipience for benzene.


Kamil,19 and Kamil et al.,1921 have investigated the effectof inlet liquid subcooling and submergence on heat transfer,circulation rate, and boiling incipience in a vertical thermosi-phon reboiler. In a natural circulation reboiler, the inducedow is established due to the differential head between thecold and hot legs. The hydrostatic head in the cold leg(down ow pipe) of a thermosiphon reboiler depends uponthe liquid submergence. Therefore, the rate of circulationdepends upon liquid submergence, heat ux, inlet liquid sub-cooling, and frictional resistance. At a given submergence,the liquid head in the cold leg remains unchanged, whileincrease in the heat ux shifts the boiling incipience towardsthe tube inlet. As the submergence is lowered, the liquidhead gets decreased while the vapor fraction increases due tothe enhanced effect of saturated boiling in the tube. How-ever, the differential head causing circulation becomessmaller than that of higher submergence value. The detaileddescription of the effect of submergence on induced ow hasbeen discussed earlier by Kamil19 and Kamil et al.,25 amongothers. Yin and Abdelmessih8 have also investigated theeffect of velocity on d*/rc. Thus, the submergence has animportant effect on boiling incipience in the case of a nat-

Figure 5. Heat ux vs. degree of superheat at boilingincipience for water.

Figure 6. Heat ux versus degree of superheat at boiling incipience for ethylene glycol.


ural circulation reboiler. Hence, after incorporating theeffect of submergence as suggested by Kamil et al.,23 theabove equation was modied as:

Tw Ts c18sTsq

kL hfg rv

1=2Sn (16)

Equation 16 is the general expression for boiling incipi-ence in the turbulent boundary layer for a vertical thermosi-phon reboiler. The above equation involves only the super-heat that is easy to measure directly, and the right-hand sideas a whole can be evaluated with reasonable accuracy fromthe measurable quantities.

Results and Discussion

Wall and liquid temperature proles along theheated test section

Figure 2 shows the variation for wall temperature prolesalong the test section with heat ux as a parameter for meth-anol using data from the literature.19 The typical behavior, asobserved in the above gure, remains the same for other testliquids. However, the values of wall temperature, location ofpeak values, and the lengths of various zones are different.The variation of liquid temperature along the tube length hasbeen shown corresponding to the lowermost heat ux. Theliquid temperature increases linearly with distance along the

Figure 7. Heat ux versus degree of superheat at boil-ing incipience for acetone.

Figure 8. Heat ux versus degree of superheat at boil-ing incipience for propanol.

Figure 9. Heat ux versus degree of superheat at boil-ing incipience for ethyl acetate.

Figure 10. Degree of superheat versus submergence forwater.


tube length until it attains the saturation value, which itselfdecreases linearly as the liquid moves upwards due to thereduction of the hydrostatic head.The plots of wall temperature versus tube length with liq-

uid submergence as a parameter have been shown in Figure 3.The location of wall temperature peaks gets shifted towardsthe tube inlet and the curves move to lower values of Tw asthe liquid submergence is reduced from high to low values.The typical variation of wall and liquid temperatures asobserved indicates that there exist different regimes of heattransfer in a reboiler tube. The linear rise in the temperatureof liquid as it moves upwards through the tube results fromsensible heating under uniform heat ux. When the minimumwall superheat required is attained, the bubbles start nucleat-ing at the surface but collapse there due to the presence of asubcooled liquid core. The onset of subcooled boiling, thus,creates additional turbulence at the surface. This explainswhy the linearly increasing wall temperature correspondingto convective heat transfer, starts varying at decreasing rate,eventually becoming zero at peak values (Figures 2 and 3).Once the bulk liquid temperature attains saturation value, thebubbles generated at the surface grow to their maximum sizeand get detached, resulting in the existence of the vaporphase in the tube. All the heat supplied gets absorbed aslatent heat of vaporization, converting the liquid to vapor.The two-phase ow moves upwards through the tube withincreasing quantity of vapor and, hence, changing ow pat-terns. This corresponds to the saturated boiling regime asexhibited by the slowly decreasing wall and liquid tempera-ture proles. Further details are given elsewhere by Kamil19

and Kamil et al.20,21

Boiling incipience in a vertical thermosiphon reboiler

From the wall and liquid temperature distributions as dis-cussed earlier, it is observed that there exists a point at whichthe bubbles start appearing at the surface, though the liquidis still below its saturation value. This may be the onset of

subcooled/surface boiling, and its effect is exhibited in devia-tion of wall temperature curves from straight-line behavior,characteristic of single-phase convection. In fact, the nuclea-tion of bubbles must have started on attainment of therequired minimum superheat even before the point mentionedabove has been reached. As the liquid moves upward, itstemperature rises and the boiling process becomes increas-ingly effective with additional turbulence at the wall. Thewall temperature increases with diminished rate, which even-tually becomes zero, showing a maximum wall superheatfollowed by a severe fall in its value. This is observed tohappen when the liquid temperature has attained its satura-tion value, enabling bubble growth to the maximum size.This marks the onset of saturated boiling (OB). The effect ofheat ux and liquid submergence on the general nature ofwall temperature distribution and onset of boiling is essen-tially similar for all the test liquids. However, the maximumvalues of wall superheat and locations of boiling incipiencefor different systems, even under identical conditions, werenot the same. The superheat for boiling incipience was calcu-lated corresponding to the maximum values of wall tempera-tures attained for a particular run.Figure 4 shows the heat ux versus wall superheat plot for

benzene at a submergence of 100%. The scatter of datapoints is mainly due to highly unstable points of maxima fol-lowed by a steep fall in the wall temperature from which thevalues of (Tw Ts) are taken. In the same plot, the experi-mental data of Backhurst26 are also shown. Figure 5 showsthe heat ux versus wall superheat plot for water at a sub-mergence of 100%. In the above gure, data of Sato andMatsumura,4 Sudo et al.,9 and Mantzouranis27 for water havebeen plotted. Similar variation has been shown in Figure 6for ethylene glycol. For these systems at 100% submergence,around 97% of the data points lie within 618% of the corre-lation line, as shown in Figures 4 and 5, respectively. Thesegures clearly indicate that natural convection data andforced convection incipient boiling data are not in agreement.

Figure 11. Comparison between experimental and pre-dicted values of superheat for methanol.

Figure 12. Comparison between experimental and pre-dicted values of superheat for ethanol.


The incipient boiling superheat was also calculated from thecorrelations of other investigators, and the same is plotted inthe above gures. An almost similar trend was observed forother test liquids. At a particular submergence, as the heatux increases, the wall superheat also increases. At low heatux, the submergence has less inuence on incipient boilingin comparison to high heat ux. Thus, from the above, it isevident that none of the correlations predict the data well,and generally most of the correlations under predict thesuperheat values for different systems. But the correlations ofSudo et al.9 and Hino and Ueda10 for rtan > rmax criteria overpredicts the superheat value for water and ethylene glycol atdifferent submergences.Figures 7 and 8 show the plots of heat ux versus wall

superheat with submergence as a parameter for acetone andpropanol, respectively. These gures also show that at differ-ent submergences there are different predicted lines. From theplots, it is clear that the superheat increases almost linearlywith increase in submergence for a constant heat ux. Theselines are almost parallel to each other. As the value of heat

ux is decreased, the lines shift to a lower level, as exhibitedin the above gures. It is, therefore, clear that submergencestrongly inuences the condition of the onset of nucleate boil-ing. Figures 9 and 10 show the plots of degree of superheatversus submergence with heat ux as a parameter for ethyl ac-etate and water, respectively. These gures also show that atdifferent heat uxes there are different predicted lines. In theabove gures, the predicted results agree well with experimen-tal data. Figures 1114 show the comparison of the experi-mental wall superheat with predicted superheat (Eq. 16) formethanol, ethanol, water, and toluene, respectively. The ma-jority of data points lie within considerable error limits. Thevalues of exponent n and Ct in Eq. 16 with maximum errorare given in Table 3 for all the systems.An effort was also made to obtain a unied correlation for

the data of all systems with widely varying thermophysicalproperties. The correlation for the incipient boiling superheatwas obtained by regression as:

Tw Ts 1:1043 8sTsqkL rv hfg

1=2S0:59867 (17)

Figure 15 shows the plot of the comparison of the experi-mental wall superheat data with those predicted by the pro-posed correlation (Eq. 17). It was observed that the majorityof data points lie within the maximum error of 618 % andan average absolute relative error of 15.42%.

Experimental uncertainty

In the present study, the measured variables are the walltemperatures, liquid temperatures, and electrical input to thetest section. The measurements involved include voltage, cur-rent, temperature, and tube dimensions. The measured valuesare subjected to some uncertainties due to the error of mea-surement. Taking into account the least count and accuracy ofeach instrument employed, uncertainty analysis has been car-ried out using the method suggested by Schultz and Cole.28

The resolution in the measurement of temperature was 0.18Cover the temperature encountered; the average uncertainty inthe measurement of temperature is 0.2 %. Hence, the uncer-tainty in estimating wall superheat is 60.4%.

Conclusions

Based on the theoretical analysis, a new semi empiricalmodel has been proposed to predict the wall superheat

Table 3. Values of Exponent, Turbulent Boundary LayerProle Multiplier, and Maximum Percent Errors for

Different Systems

SystemsExponent n

Eq. 16MaximumError (%) Ct

Acetone 0.78265 618 0.9498Methanol 0.50659 616 3.0798Ethyl acetate 1.0053 612 0.2125Ethanol 0.70808 611 1.0078Benzene 0.52619 617 1.5517Propanol 0.45699 614 2.2095Water 0.60331 615 1.0308Toluene 0.56017 614 1.1889Ethylene glycol 0.62556 618 0.7771

Figure 14. Comparison between experimental and pre-dicted values of superheat for toluene.

Figure 13. Comparison between experimental and pre-dicted values of superheat for water.


required for onset of boiling in a vertical thermosiphonreboiler. A correlation for the minimum degree of wallsuperheat for a given liquid and heat transfer surface wasdeveloped in terms of the thermophysical properties of theliquid, liquid submergence, and turbulent eddies. At constantsubmergence, as the heat ux increases, the superheatrequired for incipient boiling increases. The superheat alsoincreases with submergence for a constant heat ux. Thus,incipience is strongly inuenced by turbulent eddies and sub-mergence, which together suppress nucleation from surfacecavities, requiring higher wall superheat for incipience com-pared to other forced convection systems.

Notation

CP heat capacity, J/kg Khfg latent heat of vaporization, J/kgk thermal conductivity, W/m Kn exponent used in Eq. 16

Pr Prandtl numberPrt turbulent Prandtl numberq heat ux, W/m2r radius, mR gas constant, Nm/kg K

rmax maximum cavity radius, mrtan cavity radius based on the tangency criterion, mS submergence, percent (%)T temperature, 8C (K)

DTs degree of superheat (Tw Ts), KDTsub degree of subcooling (Ts TL), K

y distance perpendicular to the heated wall, mZ distance along the test section, m

Greek letters

d* superheated layer thickness, mr density, kg/m3s surface tension, N/meH eddy heat diffusivity, m2/sem eddy momentum diffusivity, m2/s

Ct turbulent boundary layer prole multipliera thermal diffusivity of liquid (kL/rCP), m2/s)m dynamic viscosity, kg/m sn kinematic viscosity, m2/s

Subscripts

B boilingb bubblec cavity, critical conditionL liquid

OB onset of boilings saturation

sub subcoolingv vaporw wall

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Figure 15. Comparison of experimental with predicteddegree of superheat by proposed correla-tion (Eq. 17) for all test liquids.


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AIChE Symp Ser. 1979;75:3239.

Manuscript received Apr. 25, 2006, and revision received Oct. 16, 2006.


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AIChE Journal Vol 53 No 1

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