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Applied Thermal Engineering 30 (2010) 1333e1340

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Applied Thermal Engineering

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Experimental study of boiling incipience in a closed loop verticalannular thermosiphon

M. Altamush Siddiqui a,1, M. Kamil b,*, M. Asif a,1, A.M. Jairajpuri a,1

aDepartment of Mechanical Engineering, Aligarh Muslim University, Aligarh 202002, IndiabDepartment of Petroleum Studies, Aligarh Muslim University, Aligarh 202002, India

a r t i c l e i n f o

Article history:Received 28 June 2008Accepted 20 February 2010Available online 6 March 2010

Keywords:Thermosiphonic flowVertical annulusBoiling incipienceSub-cooled boilingWall superheat

* Corresponding author. Tel.: þ91 571 2501887/þ9þ91 571 2700528.

E-mail addresses: altamushsiddiqui@yahoo.co.inrediffmail.com (M. Kamil).

1 Mobile: þ91 9411979711.

1359-4311/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.applthermaleng.2010.02.020

a b s t r a c t

The present study aims to identify the conditions of boiling incipience experimentally and relate them tothe important relevant parameters such as heat flux, liquid submergence level and physical propertiesduring boiling of liquids in an internally heated vertical annulus. The heating surface and liquidtemperature distributions were therefore obtained with distilled water as a test fluid in the annulus. Thetest section is an annulus made of two concentric tubes, the inner made of stainless steel while the outerof corning glass through which flow during the boiling and non-boiling phenomenon along the annuluscan be visualized. The maximum wall superheat, attained around boiling incipience, was taken from thewall temperature distributions. The computed values of (d�/rc), which is ratio of the superheated layer tothe radius of cavity on the heating surface, come out to be in the range of 8e18, which is quitecomparable to the reported values in the literature. Correlations have been proposed in terms of the heatflux, physical properties of water and liquid submergence level.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

In the natural circulation systems, the flow is thermally inducedwhere the working fluid may remain as a single phase liquid orchange phase to boil, depending upon the heating conditions. Thebuoyancy induced flow, occurs in atmospheric and geophysicalprocesses and is made use of in the cooling of electronic equip-ments and nuclear reactor-fuel elements during shut off periods.They may also be useful in solar heating and ventilating applica-tions for domestic purposes. The boiling heat transfer, on the otherhand, plays an important role in the design of vaporizers, evapo-rators, re-boilers and similar equipments employed in processindustry, power plants, refrigeration systems and many others.In refrigeration engineering, tubular and tube in shell evaporatorsare used.

Generally, a sub-cooled liquid entering the annulus, receives thesensible heat and its temperature rises as it moves upward.Depending upon the wall temperature, sub-cooled boiling may setin at the surface. When the liquid temperature attains saturationvalue, boiling begins with the existence of net vapor which

1 9359500486(mobile); fax:

(M.A. Siddiqui), sm_kamil@

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increases resulting in two-phase flow along the length. The instantat which two-phase flow begins is known as incipient point ofboiling, which corresponds to the conditions of minimum degree ofsuperheat or heat flux required for the formation and detachmentof the first vapor bubble from the heating surface. The prediction ofwall superheat is important in the design of various heat transferequipments. The point of onset of nucleation along the test sectionlength and its required superheat depends upon a number ofoperating parameters. Most of the studies reported in the literaturehave been conducted for boiling of liquids in vertical tube.However, the data on closed loop thermosiphonic flow boiling inannuli seems to be scarce.

Various studies to this effect on predicting wall superheatthrough semi-empirical approach for forced convection boiling intubes have been reported in literature. These studies made byHodgson [1], Collier [2], Murphey and Bergles [3] and Yin andAbdelmessih [4,5] include the effects of various physical parame-ters, the size and geometry of nucleation sites, surface roughness,role of surface tension and wettability. The widely acceptedapproach for the prediction of incipient boiling is based on theGibb's equilibrium theory of bubble in the uniformly superheatedliquid and the one-dimensional steady or transient heat conductionequation. It was postulated that in the liquid film adjacent to theheating surface, the superheated layer d� must attain a thresholdvalue so that the critical bubble nuclei with radius rc can furthergrow to the point of detachment. Zuber [6] was probably the first to

Nomenclature

a,b,c ConstantsCl Heat capacity of liquid, J/kg Khfg Latent heat of vaporization, J/kgk Thermal conductivity, W/m KKsub Sub-cooling number [1þ(r1/rv)(DTsub/Ts)]L Total heated length, mMAD Mean absolute deviationN Number of experimental data pointsPs Saturation Pressure, N/m2

Peb Peclet number for boiling [(qr1C1)/k1rvhfg)][s/{g(r1�rv)}]0.5

q Heat flux, W/m2

R Universal Gas Constant, kJ/(kmol)KS Submergence, Percent (%)rc Radius of the active cavity, mT Temperature, �CDTsup Degree of superheat (Tw�Ts), �CDTsub Degree of sub-cooling (Ts�Ti), �Cy Distance of bubbleeliquid interface from the heated

wall surface, m

Z Distance along the test section height, m

Greek symbolsd* Superheated layer thickness, mr Density, kg/m3

s Surface tension, N/mv Kinematic viscosity, m2/sd*/rc Liquid-bubble film ratio for wall super heat

Subscriptsb BoilingExp Experimentali Inletl LiquidONB Onset of boilingPred Predicteds Saturationv Vaporw Wall

Superscriptn Exponent

M.A. Siddiqui et al. / Applied Thermal Engineering 30 (2010) 1333e13401334

analyze the inter-relationship between the local heat flux, thesuperheated layer and diameter of the surface cavity. He employedthe data of Clark et al. [7] as well as Griffith and Wallis [8] fora series of calculations and found that the superheated layerthickness is approximately equal to the diameter of the activecavity, i.e. d*/rc ¼ 2. Hsu [9] developed an analytical expression forthe size range of active nucleation sites for constant heat flux at thewall. For water at atmospheric pressure, the degree of superheatcorresponding to the cavity satisfying the condition of tangencyd* ¼ 2rc is around 1 �C, though in practice, some 10e15 �C ofsuperheat is normally required to initiate the boiling [2]. Han andGriffith [10] proposed an analysis similar to Hsu [9]. Unal [11]considered the effect of pressure on the boiling incipience undersub-cooled flow boiling of water in a vertical tube. Yin and Abdel-messih [5] investigated the phenomenon of liquid superheat duringincipient boiling in a uniformly heated forced convection channel.Butterworth and Shock [12] found that the Davis and Anderson [13]equation did not predict the sub-cooled boiling incipience satis-factorily for higher value of rc for some fluids and conditions. Kamil[14], Kamil et al. [15], Kamil and Hakim [16] and Shamsuzzoha et al.[17] experimentally obtained the boiling and non-boiling zones forheating surface and wall superheat for incipient boiling fordifferent liquids in a vertical tube thermosiphon reboiler with wideranges of submergence. They [14e17] proposed a correlation forwall superheat, relating the heat flux with thermo-physical prop-erties of the test liquids. Kamil et al. [18,19] developed a correlationto predict wall superheat by including the effect of submergence forthe vertical tube thermosiphon reboiler among others [20].

There are two different criteria for predicting the incipient pointof boiling; one is (rtan) and the other is (rmax). The incipience inforced convection systems has been studied extensively bya number of workers [4,5,13,21] who predicted incipience based onthe point of tangency (rtan). The validity of this criterionwas provenin many practical applications. There are a few other researchers[14e20] who predicted incipience also for the natural convectionsystem based on the (rtan) criterion. Hino and Ueda [22] and Sudoet al. [23] predicted incipience based on themaximum cavity radius(rmax) available for nucleation on the heated surface. Thus, from theavailable literature, it is evident that only a few studies on hori-zontal annulus [21], vertical annulus [22,25,26] and vertical

channels [23,24,27] for predicting the incipient point of boiling arereported. Pradeep et al. [28] have carried out an experimental andnumerical investigation on a two-phase natural circulation system.However, effect of submergence which is an important parameterin the prediction of wall superheat was not considered in theannulus by any of these investigators. Therefore in the presentstudy an effort has been made to identify the conditions of boilingincipience on an internally heated vertical annulus and relate themto the important relevant parameters such as heat flux, liquidsubmergence level and physical properties of water.

2. Experimentation

2.1. Experimental apparatus and procedure

The experimental set up consists of a vertical annular testsection, a separator, a condenser, a down flow pipe and a preheaterarranged to form a closed loop as shown in Fig. 1. The test sectionis an annulus made of two concentric tubes, the inner made ofstainless steel while the outer of corning glass through which flowduring the boiling and non-boiling phenomenon along theannulus can be visualized. The glass tube has dimensions of45 mm inner and 50 mm outer diameters, with length equal to1175 mm. The inner tube is of 32 mm I.D. and 38 mm O.D.(ds);with effective length equal to 1000 mm and annular gap of around3.5 mm which is electrically heated by supplying stabilized powerthrough a 30 kVA low voltage high current transformer which wasadjusted by means of a variable auto-transformer of suitablecapacity. For the impressed values of heat flux on the testsection used, the power supply readings were 1.8 V and 344 A for5.5 kW/m2 while, 4.3 V and 700 A for 25 kW/m2. The inner tube iselongated at both ends by joining same diameter copper pipeswhich pass through stainless steel seats located at the top andbottom ends of the test section. For the purpose of electricalconnections, copper clamps with negligible contact resistance arealso provided at the ends of the inner tube. The test section iselectrically isolated from rest of the set up by means of teflon-flanges, fitted at the lower and the upper ends of the test section.Lagging with asbestos rope has been provided on the partswherever heat loss was to be reduced.

Fig. 1. Schematic view of the experimental set up.

M.A. Siddiqui et al. / Applied Thermal Engineering 30 (2010) 1333e1340 1335

The experimental measurement consists of temperatures of thesteel tube-wall surface along the length and of the working fluid atthe inlets and outlets of the test section (tube), separator and thecondenser. The rate of liquid circulation caused by buoyancyinduced flow through the annular test section was measured bymeans of an IE Badger electromagnetic type flow meter. Mass flowrates and temperatures of the cooling water in the condenser werealso measured. In order to monitor the heat transfer surfacetemperatures along the tube length, twelve copper-constantanthermocouples are held at suitable distances on inside of the innertube by means of leaf springs fixed on a wooden rod, which passesthrough the tube. Temperatures of the fluid at the inlet and theoutlet of the test section are measured by inserting thermocouplesin the flow line. The exit end of the test section is connected to thedown flow pipe via a separator followed by a condenser to

condense traces of vapor if generated. The down flow pipe isjacketedwith cooling water to regulate the inlet temperature of theliquid entering the test section. The inlet temperature of the liquidat the test section was also regulated by preheating, wheneverrequired, through a 1 kW nichrome tape-heater wounded on thehorizontal pipe connecting the cold leg to the inlet of the testsection, as shown in Fig.1. Thus, desired temperature of the liquid atinlet of the test section was maintained depending upon the rangeof heat flux impressed. The down flow pipe is also provided witha level indicator of glass tube to view the liquid level in the testsection. The temperatures were measured by means of a 36-channel temperature scanner. The experiment was conductedunder different heat fluxes impressed over the steel tube. The liquidwater was filled up to the heated test section and desired heat fluxwas impressed. The maximum liquid head, used in the present

M.A. Siddiqui et al. / Applied Thermal Engineering 30 (2010) 1333e13401336

work, corresponded to the liquid level equal to the top end of theheated test section in the annulus. This condition is termed as 100%submergence. Thus, the data were generated at different levels ofsubmergence and heat flux.

2.2. Experimental uncertainty

The measurements involved in the present work includevoltage, current, temperature and tube dimensions. Themeasured values are subjected to some uncertainties due to theerror of measurement. Taking into account the least count andaccuracy of each instrument employed, uncertainty analysis hasbeen carried out using the method suggested by Kline andMcClintock [29]. A numerical estimate of the uncertainty in heatflux, ranging from 5 kW/m2 to 25 kW/m2, turns out to be �2.12%,while in the degree of superheat it is �2.2% and �5%, whenDT ¼ 16 �C and DT ¼ 7 �C, respectively. The uncertainty in themeasurement of the test section length were estimated as �0.3%at 0.8 m and �2.5% at 0.5 m submergence of the water from theinlet at the bottom end.

3. Boiling incipience model

Various boiling incipience models are reported in the literaturefor flow boiling in the tube with a few in the annuli. The incipienceof nucleate boiling depends on the existence of active cavities aswell as a temperature profile that can satisfy the superheatrequirement. If a sufficiently wide range of cavity size is involved,the first cavities to become active will be those corresponding tothe point of tangency of the superheat (Equilibrium bubble) curveand the temperature profile curve as shown in Fig. 2. As the surfaceheat flux increases, the wall temperature exceeds the saturationtemperature of the liquid subjected to boiling. In Fig. 2, is showna conical active nucleation site with a hemispherical vapor nucleus,of radius rc corresponding to a contact angle of 90�, sitting at themouth of the cavity. The liquid temperature profiles with increasingwall temperature are also shown in the diagram. They are assumedto be essentially linear through the liquid film forming a thermal

Fig. 2. Bubble formation in the superheated liquid film over a heated wall.

boundary layer of thickness, d*. According to Hsu’ [9] postulate, thecriterion for nucleation from this site is that the temperature of theliquid surrounding top of the bubble, should exceed that necessaryfor the nucleation to remain in equilibrium. If the line representingthe liquid temperature profile intersects the equilibrium bubblecurve, then nucleation occurs. Thus, the first nucleation site to beactivated (when y ¼ rc) corresponds to the point of tangency atpoint B between the equilibrium bubble curve and the liquidtemperature profile (TL)ONB, shown in Fig. 2. The wall temperaturecorresponding to this condition will be(Tw)ONB. If an active site ofsize, rc does not exist on the heating surface, then the walltemperature must be increased until the liquid temperature profileintersect the equilibrium bubble curve at points where activecavities do exist. Referring to Fig. 2, the liquid temperature profile(TL0)ONB, for the increased wall temperature (Tw0)ONB, will thereforeintersect the equilibrium bubble curve at points A and C thatcorrespond to the cavities at y ¼ rmin and y ¼ rmax, now activatingfor nucleation. However, only a small additional increase in walltemperature is necessary to activate a considerable angle of cavitysizes.

The detailed description of the submergence effect on theinduced flow has been discussed earlier by a number of investi-gators [14e20,30] making clear that submergence has an importanteffect on boiling incipience in the case of natural circulation system.Yin and Abdelmessih [4] also investigated the effect of velocity ond*/rc. Thus, after including the effect of submergence in theprediction of degree of wall superheat, Kamil et al. [18] proposeda modified equation of the following form:

ðTw�TsÞ ¼

264 8sTsq

klrvhfg�1þ 2s

rcPs

�h1� RTs

hfgln�1þ 2s

rcPs

�i23750:5

ðSÞn (1)

It is interesting to see that the equation (1) involves only thewall superheat which is easy to measure directly. Whereas, righthand side of the above equation, can as a whole, be evaluated withreasonable accuracy from themeasurable quantities. For systems oflow surface tension or high pressure, a justified simplification:1 >> (2s/rcPs) in equation (1), reduces to the results of differentinvestigator's [4,10,13,15e20,24].

4. Results and discussion

4.1. Wall and liquid temperature profiles along the heated testsection

The heat transfer surface temperature distribution along thelength of the tube is obtained from the wall thermocouple readingsafter correction for the temperature difference across the wallthickness. In order to obtain the variation of test liquid temperaturealong the annulus height it was necessary to predict the non-boiling and boiling zones in the test section. The effective non-boiling zone, which is also the incipient point of boiling termed asonset of boiling, was determined by performing energy balance onthe non-boiling zone of the test section, from the followingequation:

ZONB ¼ mlClðTs � TiÞ=ðpdsqÞ (2)

and the boiling zone,

Zb ¼ L� ZONB (3)

The liquid temperature distribution in the non-boiling zones ofthe test section was calculated from the following linearrelationship,

120

M.A. Siddiqui et al. / Applied Thermal Engineering 30 (2010) 1333e1340 1337

Tl ¼ Ti þ ðTs � TiÞZ=ZONB (4)

30

40

50

60

70

80

90

100

110

0 0.2 0.4 0.6 0.8 1Test section height in m

Te

mp

era

tu

re

s in

°C

Twall(q=14.5)Twall(q=10.0)Twall(q=5.5)Tliquid(q=14.5)Tliquid(q=10.0)Tliquid(q=5.5)

at S=100% , q in kW/m2

Fig. 4. Wall and liquid temperatures along the test section at 100% submergence andhigh sub-cooled temperature.

where, Z � ZONBThe length of non-boiling zone, computed using equation (2)

was almost the same as visualized experimentally through theglass tube. This is evident from the Photographs shown in Fig. 3 forthe flow boiling of water in the annulus, at 100% submergence andtwo temperature levels of sub-cooling.

The effect of heat flux and liquid submergence on the temper-ature distribution has been studied in detail. Figs. 4 and 5 show thetemperature distributions for water at submergence of 100% and85%, respectively. The nature of the curves is almost similar at allthe heat fluxes. The general characteristic behavior of the curvesmay be observed as follows:

(i) The wall temperature, Tw rises at a fast rate with Z from itsinlet up to a point beyond which a steep fall sets in (near theposition of incipient point) followed by a gradual decrease andbecomes nearly constant in the down stream region ofnucleate boiling. The shape of the curve, at approximately thesame inlet liquid sub-cooling, is almost similar for all heatfluxes. However, the curves at higher heat fluxes get shifted tohigh wall temperatures. Similar plots were also shown by Yinand Abdelmessih [4] and Hino and Ueda [22] at the onset ofnucleate boiling for their fluorocarbon and R-113 forcedconvection data, respectively.

(ii) The peak (maximum) value of wall temperature and its loca-tion at a fixed value of q, almost at the same degree of sub-cooling, are strongly influenced by the submergence level S.The location of the peak values of Tw get shifted towards thetube inlet and the curve moves to lower values of Tw as thesubmergence is reduced from 100% to 70%.

The liquid temperature increases linearly with the distancealong the tube length till it attains the saturation value. The typicalvariation of wall and liquid temperatures as observed indicates thatthere exist different regimes of heat transfer in the annulus. Thelinear rise in the liquid temperature, as it moves upwards throughthe annulus along the heated test section, results from sensibleheating under uniform heat flux. When the system attains therequired minimum wall superheat, the bubbles start nucleating atthe surface, but collapse there due to presence of the sub-cooledliquid core. The onset of sub-cooled boiling thus creates additional

Fig. 3. Photographic views showing incipience of the boiling water siphoned through the asubmergence level of S ¼ 100%.

turbulence at the surface. Once the bulk liquid temperature attainssaturation value, the bubbles generated at the surface grow to theirmaximum size and get detached, resulting in the existence of vaporphase in the annulus. The two phases of the fluid, flow upwardswith increasing quantity of vapor and hence, changing flowpatterns as shown in Fig. 3. This corresponds to the saturatedboiling of liquid during which the liquid temperature remainsconstant while the wall temperature of the heated surfacedecreases slowly.

The induced flow rate is established due to the differential headexisting between the cold and hot legs. The hydrostatic head in thecold leg (down flow pipe) of a thermosiphon system depends uponthe liquid submergence, the maximumvalue of which equals to theliquid level corresponding to the top end of the test section, termedas 100 percent submergence (S ¼ 100%). The rate of circulation,therefore, depends upon liquid submergence, heat flux, inlet liquid

nnulus when subjected to different heat fluxes at a high sub-cooled temperature and

30

40

50

60

70

80

90

100

110

120

0 0.2 0.4 0.6 0.8 1

Twall(q=24.5)Twall(q=19.0)Twall(q=14.5)Tliquid(q=24.5)Tliquid(q=19.0)Tliquid(q=14.5)

Te

mp

era

tu

re

s in

°C

Test section height in m

S=85% q in kW/m2

Fig. 5. Wall and liquid temperatures along the test section at 85% submergence andlow sub-cooled temperature.

0

5000

10000

15000

20000

25000

30000

35000

6 8 10 12 14 16 18Wall Super heat (Tw-Ts) in

oC

He

at flu

x in

W

/m

2

S=100S=85S=70

qs=100 = 3303.9(Tw-Ts) - 31864qs=85 = 4964.3(Tw-Ts) - 41982qs=70 = 5325.1(Tw-Ts) - 32502

Fig. 6. Variation of heat flux with wall superheat for different submergence levels.

Table 1Values of the constants for equations (5) and (7).

S. No. Submergence Constants for

Equation (5) Equation (7)

S ao bo a1 b1

1 70% 5325.1 32 502 14.319 0.00022 85% 4964.3 41 982 18.97 0.00033 100% 3303.9 31 864 21.901 0.0003

M.A. Siddiqui et al. / Applied Thermal Engineering 30 (2010) 1333e13401338

sub-cooling, vapor fraction and frictional resistance. At a givensubmergence, the liquid head in the cold leg remains unchangedwhile increase in heat flux shift the point of boiling incipiencetowards tube inlet. As the submergence is lowered, the liquid headgets decreased while the vapor fraction increases due to theenhanced effect of saturated boiling in the tube. However, thedifferential head causing circulation becomes smaller than that athigher value of submergence. The detailed description of the effectof submergence on induced flow has been discussed earlier[14e20]. Thus, it is clear that submergence has an important effecton boiling incipience in the case of natural circulation systems.Therefore, it becomes essential to include the effect of submergencein the prediction of degree of wall superheat.

4.2. Boiling incipience

The mathematical analysis established for the prediction ofboiling incipience as reported in the literature is based on widelyused Gibb's equilibrium theory. In the present study it is assumedthat nucleation should occur at the heat flux which brings the twocurves tangent to each other. Fig. 6 shows the heat flux versus wallsuper heat curves for water at submergence of 100, 85, and 70percent, respectively. (Tw�Ts) was taken corresponding to the peakvalues of wall temperature at a given heat flux q. As the heat fluxincreases, the super heat also increases at a fixed submergence;shifting towards higher values of wall super heat at high submer-gence. Different lines are shown for different submergence levelswhich are almost parallel to each other. They vary linearly asfollows:

q ¼ aoðTw � TsÞ � bo (5)

where, the constant ao and bo for different submergence are givenin Table 1.

In Fig. 7, are shown plots of the wall super heat with submer-gence level for water. It is seen that the super heat increases linearlywith increase in S for a given heat flux. As the value of heat flux isdecreased, the lines shift to lower values of the wall superheat. It istherefore quite clear that the submergence has a strong influence

on onset of nucleate boiling. The different lines corresponding todifferent heat flux values are almost parallel to each other whichget correlated in terms of submergence as given in the figure itself.

The minimum degree of wall superheat required for the onset offully developed boiling of liquids, measured experimentally, wererelated to the physical properties of the test liquid and liquidsubmergence as suggested by Kamil et al. [18]. The analyticallyderived expression is reproduced as follows:

d�

rc

!2

¼ ðTw � TsÞ2klhfgrv2sqTs

(6)

The computed values of (d�/rc), which is ratio of the superheatedlayer to the radius of cavity on the heating surface, have beenplotted as a function of q for all the heat fluxes and submergences inFig. 8. The slight scatter of data points in this figure is mainly due tohighly unstable point of maxima (Peak) followed by a steep fall inthe wall temperature distribution-curves from which the values of(Tw�Ts) are taken. In the present study the values of (d�/rc)come outto be in the range of 8e18, which is quite comparable to thereported values by Collier [2], Kamil [14] among others. The datashown in Fig. 8 may be represented by a family of straight lines inthe following form: d�

rc

!¼ a1 � b1q (7)

where, the constants a1 and b1 for different submergence are givenin Table 1.

(Tw-Ts)q=24.5 = 0.2S - 3.9333 (Tw-Ts)q=19.0 = 0.1767S - 2.55

(Tw-Ts)q=14.5 = 0.1767S - 3.3167(Tw-Ts)q=10.0 = 0.15S - 2.45(Tw-Ts)q=5.5 = 0.14S - 2.7

6

8

10

12

14

16

18

65 70 75 80 85 90 95 100 105Submergence level, S in %age

T(

t

ae

h

re

pu

S

ll

aW

wT

-s

n

i

)o

C

q=24.5q=19.0q=14.5q=10.0q=5.5

Fig. 7. Variation of wall superheat with submergence level at different heat flux.

M.A. Siddiqui et al. / Applied Thermal Engineering 30 (2010) 1333e1340 1339

The equation (7) can be written in a general form as: d�

rc

!¼ ða� bqÞ Sn (8)

where a and b are constants, characteristics to the liquid.Correlating equations (6) and (8) we get the following relation:

ðTw � TsÞ ¼ ða� bqÞ Sn"2sqTsklhfgrv

#0:5(9)

Fig. 8. Plots for the ratio of the superheated layer thickness to radius of the activecavity against heat flux.

Equation (9) may be used to predict the degree of superheat,required for onset of boiling at a given heat flux and submergence,using the physical properties of the test liquid. The constants a andb along with the exponent n, were determined through regressionanalysis of the experimental data. The equation (9) thus, becomes:

ðTw � TsÞ ¼�2:0436� 3:0� 10�5q

� " 2sqTsklhfgrv

S

#0:5(10)

Fig. 9 shows comparison of the experimental wall superheatwith those predicted from equation (10) for water. The majority ofdata points lie within the permissible error limit, having meanabsolute deviation of 6.318%. The maximum error found at 85%and 100% submergence was �15%, while at the 70% submergence,it was �25%.

4.3. Prediction of the heated tube length

Depending upon the set of governing parameters for a liquid,the location of the condition of onset of boiling varies along thetube length, as reported [14e19]. The length of the heated tuberequired for onset of boiling depends on heat flux, submergencelevel, inlet liquid sub-cooling and properties of the fluids. A func-tional relationship, as suggested by earlier investigators betweenZONB/L and the influencing variables in their dimensionless forms,will be as follows:

ZONBL

� 100 ¼ cðPebÞn1ðKsubÞn2ðSÞn3

�ylyv

�n4

(11)

After determining the values of constant c and indices n1, n2, n3and n4 the above equation becomes as:

ZONBL

�100¼ 0:5465ðPebÞ�0:027158ðKsubÞ0:059274ðSÞ1:3�ylyv

�0:33468

(12)

It is observed that almost all the data points lie withina maximum error of �6%, having mean absolute deviation of 3.02%.

8

10

12

14

16

18

20

22

24

8 10 12 14 16 18 20 22 24Experimental Wall Superheat (T

w-T

s) in °C

Pred

icted

W

all S

up

erh

eat (T

w-T

s) in

°C

S=100S=85S=70

S is in percentage and q in W/m2

+15%

-15%

+25%

Fig. 9. Comparison of the predicted values of the degree of wall superheat with thoseof the experimental values.

M.A. Siddiqui et al. / Applied Thermal Engineering 30 (2010) 1333e13401340

The properties used in the correlation were taken at their satura-tion temperature of the test liquid.

The ranges of dimensionless groups are: 60 � (Peb) � 290;700 � (Ksub) � 1142.

The average mean deviation was calculated using the followingequation:

MAD ¼"1N

Xni¼1

�����DTPred � DTExpDTExp

������ 100

#(13)

5. Conclusions

(i) The wall temperature distribution along the tube-length,clearly revealed existence of the non-boiling and boilingregions with a point of boiling incipience in between.

(ii) The computed values of (d�/rc), which is ratio of the super-heated layer to the radius of cavity on the heating surface,come out to be in the range of 8e18, which is quite comparableto the reported values in the literature.

(iii) It has been established that the liquid submergence plays animportant role on boiling incipience also in an internallyheated vertical annulus forming a closed loop thermosiphon.

(iv) Correlations have been proposed in terms of the heat flux,physical properties of water and liquid submergence level. Theform of the equations are fairly general and may be used forother systems.

References

[1] A.S. Hodgson, Hysteresis effects in surface boiling of water. J. Heat Transfer 91(1969) 160e162.

[2] J.G. Collier, Convective Boiling and Condensation. McGraw-Hill, New York, U.S.A., 1972.

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