Heat Transfer Engineering, 22:41–55, 2001Copyright C°° 2001 Taylor & Francis0145–7632/01 $12.00 + .00

Performance ofEvaporative Condensers

HISHAM M. ETTOUNEY, HISHAM T. EL-DESSOUKY,WALID BOUHAMRA, and BADER AL-AZMIDepartment of Chemical Engineering, College of Engineering and Petroleum,Kuwait University, Safat, Kuwait

Experimental investigation is conducted to study the performance of evaporativecondensers/coolers. The analysis includes development of correlations for the external heat transfercoef� cient and the system ef� ciency. The evaporative condenser includes two � nned-tube heatexchangers. The system is designed to allow for operation of a single condenser, two condensers inparallel, and two condensers in series. The analysis is performed as a function of the water-to-airmass � ow rate ratio (L/G) and the steam temperature. Also, comparison is made between theperformance of the evaporative condenser and same device as an air-cooled condenser. Analysis ofthe collected data shows that the system ef�ciency increases at lower L/G ratios and higher steamtemperatures. The system ef� ciency for various con� gurations for the evaporative condenser variesbetween 97% and 99%. Lower ef�ciencies are obtained for the air-cooled condenser, with valuesbetween 88% and 92%. The highest ef� ciency is found for the two condensers in series, followed bytwo condensers in parallel and then the single condenser. The parallel condenser con� guration canhandle a larger amount of inlet steam and can provide the required system ef� ciency and degree ofsubcooling. The correlation for the system ef� ciency gives a simple tool for preliminary systemdesign. The correlation developed for the external heat transfer coef�cient is found to be consistentwith the available literature data.

Condensers are found in a wide range of applications,such as petroleum re� neries, petrochemical plants,power-generation stations, chemical process industries,and air-conditioning units. The cooling � uid in conven-tional condensers is commonly fresh water, which canbe costly or not readily accessible. However, demandsfor conservation of the limited fresh-water resourceson a global scale necessitates the use of abundant cool-ing media, which includes seawater or ambient air. Useof seawater as the cooling medium is limited to lowcondensation temperatures to avoid scale and foulingby the seawater at temperatures above 60±C. Moreover,

Address correspondence to Hisham Ettouney, Chemical EngineeringDepartment, College of Engineering and Petroleum, Kuwait University, P.O.Box 5969, Safat 13060, Kuwait. E-mail: hisham@kuc01.kuniv.edu.kw

the feed seawater must be treated to remove particulatematter and chemically treated to control scale forma-tion, fouling, and corrosion. The rejected seawater hasan adverse effect on the environment, due to the ther-mal pollution caused in the locality of the dischargearea. Applications of air-cooled condensers are foundin conventional air-conditioning units, where ambientair is used as a heat sink to condense the refrigerant va-por. On an industrial scale, air condensers are also usedin power plants, where fresh water may be inaccessibleand expensive.

Use of evaporative cooling improves the perform-ance of air-cooled condensers. The evaporative effectcools the condensate to a temperature lower than theair ambient temperature. This increases the thermalcapacity of the air stream and as a result makes it

41

possible to use a lower air � ow rate and consequentlythe fan capacity and its power consumption are reduced.Further, the heat transfer coef� cient for the evaporativesystem is higher than for air-cooled condensers. Thisenhances the heat transfer rate and increases the valueof the overall heat transfer coef� cient. As a result, asmaller heat transfer area is used to remove the samethermal load in air-cooled condensers. Use of evapora-tive condensers eliminates the shell cover for the heatexchange tubes, which is an expensive element in con-ventional condenser units that combines a cooling towerand an external heat exchanger. Also, placement of theevaporative unit inside the cooling tower reduces thespace requirements for piping connections and valvesused in conventional units.

LITERATURE REVIEW

Literature studies for modeling and analysis of evap-orative condensers are limited in number. On the otherhand, the major fraction of the literature studies on air–

water evaporative systems focuses on performance andanalysis of cooling towers and the indirect evaporativecooling systems. The latter have a number of similaritieswith the evaporative condenser, especially when con-sidering heat and mass transfer in the air–water systemoutside the heat exchanger tubes. Therefore, analysis ofliterature studies for indirect evaporative coolers as wellas evaporative condensers is considered in the follow-ing discussion. Differences in modeling these systemsare caused primarily by variations in the driving forcebetween the � uid inside the tubes of the heat exchangerand the water/air streams � owing outside the heat ex-changer tubes, and the heat transfer mechanisms insidethe tubes. The driving force in evaporative condensers isprimarily equal to the difference of the condensing va-por temperature and the external temperature betweenthe surface and the air–water mixture. The condensationprocess also includes vapor desuperheating and conden-sate subcooling. Either process is similar to � uid coolinginside the heat exchanger tubes in indirect evaporativecoolers.

The main focus of the literature studies on indirectevaporative coolers is the development of more energy-ef� cient air-conditioning systems. This is achieved byvarious combinations of cooling towers, indirect anddirect evaporative coolers, and conventional mechani-cal vapor compression units [1]. Webb [2] presented auni� ed theory for modeling of cooling towers, evap-orative condensers, and evaporative coolers. Variouscorrelations are adopted to de� ne the water � lm heattransfer coef� cient and the mass transfer coef� cient forwater transport from the water � lm to the air stream.In modeling the condenser and cooler units, additional

correlations are used to de� ne the heat transfer coef� -cient for the � uid inside the tubes of the heat exchanger.The heat transfer coef� cient for the water � lm used byWebb [2] corresponds to a water � lm � owing undergravity conditions and in the absence of the air stream.Subsequently, three algorithms and computer modelsare presented by Webb and Villacres [3] for analysisof cooling towers, � uid coolers, and evaporative con-densers. The algorithms are found to predict accuratelythe duty of the three systems, within 3% of the man-ufacturer’s rating data. Models of indirect evaporativecooling towers are developed by Maclaine-Cross andBanks [4], Kettleborough and Hsieh [5], Chen et al. [6].These models are found to give reasonable agreementfor outdoor air applications. However, the models over-predict the cooling effectiveness of the system duringcertain operations, which include mixed or exhaust-airapplications. This motivated Peterson [7] to develop amathematical model for analysis of indirect evaporativecoolers.

Predictions of the mathematical model are validatedagainst experimental data. This comparison shows thelimitations of the model in accurate predictions of en-ergy savings or performance at some operating con-ditions. At such conditions, Peterson [7] recommendsthe use of correlations generated from experimentaldata to obtain necessary design or performance data.Kettleborough [8] presented a numerical model for eval-uation of the effectiveness of indirect evaporative cool-ers. The numerical model evaluates the temperaturesof the plate, secondary air, and primary air. Also, themodel calculates the humidity of the outlet secondaryair stream. Since the model equations are coupled andnonlinear, an iterative and numerical solution is foundnecessary to determine the system effectiveness, whichis de� ned as the ratio between the drop in the primaryair temperature and the wet-bulb depression (de� ned asthe difference of the dry- and wet-bulb temperatures)of the inlet primary air with respect to the secondaryair stream. Experimental evaluation of indirect evapo-rative coolers, when combined with conventional air-conditioning systems, are presented by Peterson andHunn [9] for a small of� ce building in Dallas, Texas.Analysis of the data shows a system ef� ciency higherby 70% than conventional air-conditioning units. Thisallows for a 12% reduction in the capacity of the air-conditioning system. Further evaluation of the evapo-rative air precooling system shows that the water pumpis the largest energy-using component, rather than theair fan. Erens and Dreyer [10] tested the performanceof three mathematical models for simulation of evap-orative coolers. The mathematical development of themodels is based on either dividing the cooler into dif-ferential elements or by considering the cooler as one

42 heat transfer engineering vol. 22 no. 4 2001

element. The � rst and second models are differential,where the � rst model evaluates the Lewis number andthe second model assumes the Lewis number is equalto one. The third model assumes unit Lewis number,constant water temperature, and negligible thermal re-sistance in the water � lm. Results show that the simpli-� ed model gives accurate results for evaluation of smallunits, and it is useful to obtain preliminary design andrating data. On the other hand, the detailed models aresuitable for more accurate performance predictions.

Effect of tube arrangement in indirect evaporativecooling is analyzed by Erens [11]. Results show thatthe performance of bare tubes is enhanced through theuse of plastic � ll, which can be integrated with the tubesor placed below the tubes. The improved performanceis caused by the increase of the water residence timein the � ll material, which generates higher rates of heatand mass transfer between the air and water streams.A similar effect on enhancement of the performanceof cooling towers is reported by El-Dessouky [12] onthe use of rough surface packing material. Goswamiet al. [13] studied performance enhancement of smallto medium-size air-conditioning units by evaporativecooling of the ambient air used to condense the refriger-ant � uid. The study follows a similar approach adoptedin air-conditioning units for large facilities and build-ings. Evaporative cooling of the air is found to increasethe temperature driving force for the condensation pro-cess. In turn, energy savings up to 20% are reported forthe evaporatively cooled air against system operationwithout the evaporative cooler.

Simulation of cooling towers includes analyticalmodels, i.e., the model by Merkel [14], and numeri-cal models, i.e., the models by Nahavandi et al. [15]and Sutherland [16]. Comparison of both models showssmall differences of 5–12% in their predictions.El-Dessouky et al. [17] developed a modi� ed model foranalysis and rating of cooling towers. The model prese-nts new de� nitions for the number of transfer units andthe effectiveness of the cooling tower. The number oftransfer units is expressed in terms of the air and waterheat capacity, and the effectiveness is expressed as afunction of the tower cooling range and the approachto equilibrium. The model also considers the nonlin-ear dependence of the air/water vapor enthalpy on thetemperature.

Early models of evaporative condensers by Goodman[18] and Thomsen [19] assumed constant temperaturefor the water stream. This assumption is found to gen-erate poor predictive results for the system and waseliminated in the study by Parker and Treybal [20]. Intheir model, they assumed a Lewis number of unity,linear dependence of the air enthalpy on temperature,and negligible change in the water � ow rate. The model

by Parker and Treybal [20] does not require numericalsolution and can be solved using a simple analyticalprocedure. A more detailed numerical model is devel-oped by Leidenfrost and Korenic [21], in which thethree assumptions in the Parker and Treybal model areeliminated. However, a number of inconsistencies inthe model were later cited by Peterson et al. [22], whomodi� ed the Parker and Treybal model and validatedtheir results against experimental data. Their analysisshows that the value for the water-side heat transfer co-ef� cient of the water– tube interface proposed by Parkerand Treybal is low, since the model underpredicts thecondenser load by 30%.

From the above survey it can be concluded that alimited number of studies are found on performance ofevaporative condensers. The survey shows the need forexecution of the following.

Experimental measurements of the temperature pro� lein the evaporative condenser are necessary for bet-ter understanding of the system performance and indevelopment of accurate models for the system.

Evaluation of the evaporative condenser ef� ciency atdifferent operating conditions.

Development of correlations for the heat transfer coef-� cient of the air/water side.

Development of accurate mathematical models for theevaporative condenser and validation against exper-imental data. This will be executed in a subsequentstudy.

Accordingly, the main objective of this study is to de-termine experimentally the performance of evaporativecondensers as a function of the � ow rate ratio of waterto air and the thermal load. This involves measurementsof the axial temperature distribution and calculating thesystem ef� ciency and the heat transfer coef� cient. Thestudy also compares the performance of evaporativecondensers versus air condensers. Results and analysisgives better understanding in the performance of evap-orative condensers, which is necessary to develop anddesign more ef� cient systems.

EXPERIMENTAL APPARATUSAND PROCEDURE

Figure 1 shows a schematic for the evaporative con-denser system. As is shown, the system is made of ametal frame and includes a water basin, a water circula-tion pump, an air fan, packing material, two evaporativecondenser units, water spray nozzles, siding sheets ofPlexiglas, connection tubes, and valves. The measur-ing devices include water � ow meters and temperature

heat transfer engineering vol. 22 no. 4 2001 43

Figure 1 Schematic of the evaporative condenser.

thermocouples. The sides of the apparatus are tightlysealed with the Plexiglas sheets, which is necessary toprevent air leakage to or from the system. The systemdimensions are 0.83 £ 0.6 £ 2 m in width, length, andheight, respectively. The water basin has dimensions of0.83 £ 0.6 £ 0.32 m in width, length, and height. The� oat control in the water basin is adjusted to a height of0.3 m, which allows for accumulation of 0.1494 m3 ofwater in the basin. This volume is necessary to main-tain a nearly constant water temperature in the system.The water circulates from the water basin to the spraynozzles via the water circulation pump and the � owmeter. The circulation pump has a maximum power of0.278 kW and provides a maximum � ow rate of 2 kg/s.The spray nozzle system breaks the water stream into a� ne mist, with an average drop diameter of 5 £ 10¡4 m,which is evenly distributed over the packing material.Therefore, the water � ows from the top of the columntoward the basin in a countercurrent direction to theair stream. The suction fan has an input/output power

rating of 440/350 W. The fan moves the air stream fromthe side openings near the water basin to the top of thecolumn. The suction fan has a constant speed and movesthe air at an average � ow rate of 2.767 m3 (STP)/s or2.68 kg/s.

As is shown in Figure 1, structured packing mate-rial is used and is divided into three layers. As reportedby El-Dessouky et al. [23], this type of packing giveshigher system ef� ciency than Sheathy leaf or natural� ber. Each layer has the same cross-sectional area asthe metal frame (0.83 £ 0.6 m). This prevents bypassof the air or water streams, which would result in re-duction of the contact area between the two streams andconsequently decrease in the cooling ef� ciency. Eachlayer has a thickness of 0.1 m, which gives suf� cientinternal surface area for air and water contact. Use ofthe three packing layers maintains proper water distri-bution and suf� cient contact area between the air andwater streams. The two condenser units have properpiping that allow operation of a single condenser or the

44 heattransfer engineering vol. 22 no. 4 2001

two condensers in series or parallel. The two condensersare identical, and each has a single path and dimensionsof 0.83 £ 0.6 £ 0.02 m in length, width, and thickness,respectively. Each condenser contains a single row of18 tubes with an outer diameter of 0.011 m and an innerdiameter of 0.008 m. Thin � at sheet � ns hold the tubebundle together, and each � n has dimensions of 0.02 £0.6 £ 0.0015 m in height, length, and thickness. Thenumber of � ns in a 1-m length is 394. This arrangementgives a total heat transfer area of 3.672 m2, which in-cludes a heat transfer area of 0.312 m2 for the tubes and3.36 m2 for the � ns.

The measuring devices are used to determine the � owrates of circulating water and condensing steam as wellas the dry- and wet-bulb temperatures of the ambient air,the water temperature inside the column, and the steaminlet and condensate temperatures. Locations for thethermocouple measurements are shown in Figure 1. Ac-curacy of the temperature-measuring device is §0.1±Cand for water � ow is §1% of the full scale.

Experimental Procedure

Operation of the evaporative condenser requires � ll-ing the water basin prior to operating the water pumpand opening the steam valve. The system operating con-ditions are determined by adjusting the water � ow rate,setting the steam pressure, and selecting the condensercon� guration (single, two in series, or two in parallel).At the start of operation, the system is monitored for aperiod of 1 h before commencing data collection. Alltemperature measurements are stored in a data loggerat an interval of 5 min. Other data, which includes the� ow rate of the steam condensate and the circulatingwater, are measured repeatedly on hourly basis over aperiod of 12 h. Temperature measurements include thewater temperature pro� le inside the column as well asthe temperatures of the ambient air, inlet steam, andcondensate. In all experiments, the air � ow rate is keptconstant at 9,660 m3 (STP)/h or 2.68 kg/s, and the wa-ter � ow rate is varied and maintained at values of 0.44,0.63, 0.82, and 0.95 kg/s. These values give water-to-air � ow rate ratios (L /G ) of 0.164, 0.235, 0.306, and0.354. The steam inlet temperatures used in the experi-ments are 111.9 and 120.8±C, which correspond to sat-uration pressures of 1.5 and 2 bar. In all experiments,which include the evaporative and air condensers, com-plete condensation of the inlet steam is achieved. Thecondensate � ow rate varies over a range of 0.014 to0.012 kg/s.

Operation of the system as an air condenser is donesimply by keeping the packing and the water basindry and turning off the water pump. Other operatingprocedures and conditions, which include the air � ow

rate, steam pressures, and condenser con� gurations, areidentical to those of the evaporative con� guration.

EXPERIMENTAL RESULTS AND DISCUSSION

The collected data are used to analyze the perfor-mance of the evaporative condenser and the air con-denser. This includes analysis of the axial temperaturepro� les for the water stream and calculations of the ef� -ciency, e , which is de� ned as the ratio of the actual to themaximum possible amounts of heat that can be removedfrom the condenser. The maximum amount of heat re-moved from the condenser occurs as the condensatesteam temperature cools to the wet-bulb temperature ofthe air � owing to the column. That is,

e DMs(H 00

s ¡Hu )

Ms(H 00s ¡Hw )

DMs[ k C C p(Ts¡Tu )]

Ms[ k C C p(Ts¡Tw )](1)

where H 00s is the saturated steam enthalpy, k is the latent

heat, Ms is the steam mass � ow rate, T is the tempera-ture, C p is the speci� c heat at constant pressure, H is thecondensate enthalpy, and the subscripts s; u, and w de-� nes the saturated steam or condensate, the subcooledcondensate, and the wet-bulb condition of the ambientair. It should be emphasized that the steam condensedin the evaporator is in the saturation state.

The axial temperature pro� les for the water stream inthe evaporative condensers are shown in Figure 2 for thetwo condensers in series. Results are obtained for steamtemperatures of 111.9 and 120.8±C and L /G values of0.235 and 0.353. As is shown, the lowest water temper-ature is found in the water basin, and its value is abovethe wet-bulb temperature of the ambient air. The watertemperature increases as it � ows from the spray noz-zles through the tower. The maximum water tempera-ture occurs below the second heat exchanger. The watertemperature and the condensate temperature increasesat higher steam temperatures and as L /G increases. Itshould be noted that the effect of the wet-bulb tempera-ture is consistent with the measured results. With regardto this, an increase in the wet-bulb temperature resultsin an increase of the condensate and water temperaturein the system. This is caused by the small difference ofthe humidity for the dry and wet air. Therefore, at highwet-bulb temperatures the amount of water evaporatedper unit � ow rate of the water stream is reduced.

The measured data for the temperature pro� le of thewater stream in the evaporative condenser tower arevery important in modeling the system characteristics.This pro� le can be used to de� ne the driving forcefor heat transfer, which is necessary for heat trans-fer calculations. In literature studies, it is common to

heat transfer engineering vol. 22 no. 4 2001 45

Figure 2 Variation in the water axial temperature pro� le as a function of measuring hour, steam temperature, and L /G for two condensersin series.

assume constant water temperature throughout the col-umn, which is equal to the wet-bulb temperature [2].This assumption is not consistent with the above mea-surements, and its adoption may lead to inaccuracies inthe model predictions.

Hourly variations in the ef� ciency of the evaporativecondenser and the air condenser are shown in Figure 3for the single condenser, two condensers in parallel,and two condensers in series. The evaporative effect in-creases the system ef� ciency from values of below 92%to values above 99%. Inspection of the ef� ciency varia-tions shows the decrease in the ef� ciency of all systemsduring the daytime. The lowest ef� ciency is found atnoontime, and the highest ef� ciency is measured dur-ing the early morning and the evening hours. This in-crease is associated with the decrease in the wet-bulbtemperature of the ambient air � owing to the column.

Effects of the steam temperature and L /G on theef� ciency of the evaporative condenser are shown inFigures 4–6. As is shown, the ef� ciency averages are97.7%, 98.1%, and 98.9% for the single condenser, twocondensers in parallel, and two condensers in series.The higher ef� ciency of the two condensers in seriesis caused by the larger heat transfer area, which allows

for additional subcooling of the condensate. Increasein L /G results in decrease of the ef� ciency for all sys-tems. This is because the wet-bulb temperature of theambient air sets the amount of water evaporated in-side the tower. Therefore, increase in the � ow rate of

Figure 3 Variation in the system ef� ciency as a function con-denser con� guration and measuring time.

46 heat transfer engineering vol. 22 no. 4 2001

Figure 4 Variation in the ef� ciency of the single condenseras a function of the water-to-air � ow-rate ratio and the steamtemperature.

the cooling water results in reduction of the amount ofwater evaporated per unit mass � ow rate of cooling wa-ter. Therefore, at higher L /G ratios an increase occursin the cooling-water temperature and consequently thecondensate temperature increases and the system ef� -ciency decreases. Effects of the steam temperature arenot discernable; however, at higher steam temperatures,a higher ef� ciency is expected because of the increasein the heat transfer driving force.

Comparison of the condensate temperature for theevaporative condenser (wet) and the air condenser (wet)is shown in Figure 7 for the single condenser, two con-densers in parallel, and two condensers in series. As isshown, the averages for the condensate temperature forthe air system are 76.9, 86.5, and 97.2±C for the twocondensers in series, two condensers in parallel, and

Figure 5 Variation in the ef� ciency of two condensers in paral-lel as a function of the water-to-air � ow-rate ratio and the steamtemperature.

the single condenser, respectively. Lower condensatetemperatures are obtained for the evaporative system,with values of 30.3, 35.6, and 37.8±C for the two con-densers in series, two condensers in parallel, and the sin-gle condenser, respectively. Comparison of these resultsshows that the evaporative system is capable of remov-ing larger amounts of heat than the air system, whichresults in a higher degree of subcooling. The above re-sults show that the degree of condensate subcooling islarge, with values between 73.3 and 90±C. As is shown,the largest subcooling is obtained for the two condensersin series. Comparison of the energy release accompa-nied with the subcooling process and the latent heat forthe same amount of condensate show that the subcool-ing energy is less than 15% of the condensation energy.However, the subcooling heat transfer area is compa-rable to the heat transfer area required for condensa-tion. This is because the low thermal energy of subcool-ing is also associated with a low overall heat transfer

heat transfer engineering vol. 22 no. 4 2001 47

Figure 6 Variation in the ef� ciency of two condensers in se-ries as a function of the water-to-air � ow-rate ratio and the steamtemperature.

coef� cient. The opposite is true for the condensationprocess, where the overall heat transfer coef� cient ishigh, as well as the thermal energy for condensation.

CALCULATIONS OF THE HEAT TRANSFERCOEFFICIENTS

The following assumptions are made to calculate theheat transfer coef� cients:

Steady-state operation.The surfaces are clean or fouling resistant is zero.The condenser surface is clean or the fouling resistance

is zero.Uniform distribution of the air and water stream in the

column and on the outside surface of the condenser.Water losses in the column are negligible.

Figure 7 Variation in condensate temperature as a function con-denser con� guration and measuring time.

The steam stream entering the condenser unit is satu-rated.

Condensate subcooling follows steam condensation.The thermophysical properties of air and water in the

heat transfer coef� cient, which include the speci� cheat at constant pressure, the density, the viscos-ity, and the thermal conductivity, are obtained at themean temperature of the stream.

Operation of the coil heat exchangers in series allowsfor simple calculations of the heat transfer coef� cientfor the two cases of condensation with two-phase � owand subcooling with a single phase. In this case the� rst heat exchanger performs the condensation step, andit includes steam and its condensate; the second heatexchanger includes only the condensate. The followingtwo sections give the analysis for each heat exchanger.Figure 8 shows a schematic for the temperature pro� lesin the two heat exchangers and in the air/water systemoutside the heat exchanger tubes.

Heat Transfer Coef� cient with Two Phases

As is shown in Figure 8, the steam condenses insidethe heat exchanger tubes at the saturation temperature,Tc, and then is subcooled to a lower temperature, Tu .On the outside of the heat exchanger tubes, the watertemperature increases from T1 to T2 during steam con-densation and then from T2 to T3 during subcooling.The thermal load for condensation is then de� ned by

q D qc C qu (2)

48 heat transfer engineering vol. 22 no. 4 2001

Figure 8 Schematic of the temperature pro� les inside the heat exchangers in the air/water stream on the outside.

where

qc D Ms k (3)

and

qu D MsC p(Tc ¡ Tu ) (4)

In the above equations, qc and qu are the thermal loadsdue to condensation and subcooling, respectively, Ms isthe steam � ow rate, and Tc and Tu are the condensationand subcooling temperatures. The two thermal loadsare then used to de� ne the corresponding overall heattransfer coef� cients:

qc D Ms k D Uc Ac LMTDc (5)

qu D MsC p(Tc ¡ Tu ) D Uu Au LMTDu (6)

where Ac and Au are the heat transfer areas required forcondensation and subcooling, respectively. The sum ofthe two areas is equal to the total heat transfer area, At ,or

At D Ac C Au (7)

In Eqs. (5) and (6) the values of LMTD are de� ned by

LMTDc D(T2 ¡ T1)

ln[(Tc ¡ T1)=(Tc ¡ T2 )](8)

LMTDu D(T3 ¡ T2)

lnfR=[R C ln(1 ¡ RP)]g(9)

where (T2 ¡ T1 ) is the difference of the water � lm tem-perature due to steam condensation and (T3 ¡ T2 ) is dif-ference of the water � lm temperature during condensatesteam. The two terms R and P in Eq. (9) are given by

R DTc ¡ Tu

T3 ¡ T2

P DT3 ¡ T2

Tc ¡ T2

The expression for LMTDu given in Eq. (9) is obtainedfrom the work by Threlkeld [24]. In Eqs. (5) and (6) theoverall heat transfer coef� cients, Uc and Uu , are de� nedby

1

UcD

1

hc

Ao

A p;iC

Ao d p

A p;mkC

1

ho

³1 C

1 ¡ u

Ap;o=AF C Á

´

(10)

1

UuD

1

hu

Ao

A p;iC

Ao d p

A p;mkC

1

ho

³1 C

1 ¡ u

Ap;o=AF C u

´

(11)

where ho is the external heat transfer coef� cient, u isthe � n ef� ciency, and k is the thermal conductivity of

heat transfer engineering vol. 22 no. 4 2001 49

the tube wall. The surface areas in Eqs. (10) and (11)are given by

The tube inner surface area,

Ap;i D n p Di Z p

The tube outer surface area,

Ap;o D n( p Do Z p ¡ m p Dod )

The � n surface area,

AF D m

³BW ¡

n p D2i

4

´

The � n and tube outer surface area,

Ao D AF C Ap;o

In the above relations, n is the number of tubes, m isthe number � ns, Do and Di are the tube outer and innerdiameters, Z p is the tube length, B is the � n height,and W is the � n width. In Eq. (10) the internal heattransfer coef� cient for condensation, hc, is de� ned bythe correlation of Shah [25]. This relation is given by

hc

h loD 1 C

³3:8

z 0:95

´(12)

The parameter z is de� ned by

z D³

1v

¡ 1

´0:8

P0:4 (13)

where P is the reduced pressure, and v is the vapor massfraction. The local super� cial heat transfer coef� cienth lo is calculated using the relation

h lo D hu(1 ¡ v )0:8 (14)

where hu is the heat transfer coef� cient, assuming all� owing mass as liquid, and is calculated by the well-known Dittus-Bolter equation:

hu D 0:023(Re)0:8(Pr)0:4³

k`

Di

´(15)

The ranges of data over which the equation by Shah canbe used are

2:8 · Di · 40 mm

21 · Ts · 355±C

0:01 · v · 0:99

158 · q · 1:6 £ 106 W=m2

11 · G · 4;000 kg=m2 s

7 · P · 18;000 kPa

0:0019 · Pr · 0:82

350 · Re · 100;000

The average heat transfer coef� cient is obtained by con-sidering an average value of 0.5 for complete conden-sation of steam. The correlation for heat transfer duringsubcooling, hu , is given by the Dittus and Bolter relation[Eq. (15)].

Theabove system of equations (2)–(15) is used to cal-culate qc; qu; hu; hc; Uc; Uu ; T2; Ac; and Au . How-ever, determination of these requires calculations of theoutside heat transfer coef� cient, ho. This coef� cient isobtained from the analysis of heat transfer in the secondheat exchanger, which is described in the next section.

Heat Transfer Coef� cient with Single Phase

As is shown in Figure 8, the subccoled condensateleaves the � rst heat exchanger at temperature Tu and iscooled further in the second heat exchanger to a lowertemperature, Tv . On the outside of the heat exchangertubes, the water temperature increases from T3 to T4.The thermal load for the second heat exchanger is givenby

q D MC p(Tu ¡ Tv )D Uu A LMTD (16)

In Eq. (16), q; M , and C p de� ne the thermal load, the� ow rate, and the speci� c heat at constant pressure ofthe � uid � owing inside the heat exchanger tubes. Also,Tu and Tv de� ne the inlet and outlet temperatures of the� uid inside the heat exchanger tubes. The LMTD valuein Eq. (16) is given by

LMTD D(T4 ¡ T3 )

lnfR=[R C ln(1 ¡ RP)]g(17)

where

R DTu ¡ Tv

T4 ¡ T3

P DT4 ¡ T3

Tu ¡ T3

50 heat transfer engineering vol. 22 no. 4 2001

Figure 9 Variation in outside heat transfer coef� cient as a func-tion of water-to-air � ow-rate ratio and steam temperature.

where (T4 ¡ T3) is the difference in the water � lm tem-perature. The overall heat transfer coef� cient in Eq. (16)is given by Eq. (11). As discussed before, the Dittus andBolter relation given by Eq. (15) is used to calculatethe internal heat transfer coef� cient, hu . Therefore,Eqs. (11), (16), and (17) are used to determine the ex-ternal heat transfer coef� cient, ho.

The outside heat transfer coef� cient is determinedas a function of the air-to-water � ow rate ratio and thetemperature of the inlet steam. As is shown in Figure 9,the heat transfer coef� cient varies over a range of 150to 230 W/m2 ±C. The two sets of data given in Figure 9show that the outside heat transfer coef� cient increasesat higher inlet steam temperatures. This is caused by theincrease in the driving force for heat transfer rate acrossthe surface area of the heat exchanger at higher temper-atures. This enhancement is caused by reduction in thewater viscosity and increase in the thermal conductivityof the air and water at higher temperatures. Regardlessof this, the thermal resistance on the water/air side in-creases at higher L /G values. This is because of theincrease in the water � lm thickness. Evidently, this ef-fect is masked by the enhancement caused by the highsteam temperature and the increase in the water tem-perature at higher L /G values.

For a zero � ow rate of the water stream, the systemis reduced to an air condenser. At this condition theheat transfer coef� cient is calculated using the sameprocedure as for the evaporative condenser. The resultsgive a dry heat transfer coef� cient that varies over arange of 150–165 W/m2 ±C.

Comparison of the measured values of the wet heattransfer coef� cient is made against literature data. Thisrequired measurements of the air velocity inside the

column and in the void space of the heat exchanger.The measured averages are 5.39 and 7.85 m/s for theair velocity in the column and the heat exchanger voidspace, respectively. The former value gives a free � owarea of 68.6% of the face area of the heat exchanger.The correlation by Myers [26] is used to calculate thewet heat transfer coef� cient. This correlation relates thewet and dry heat transfer coef� cients, or

hw D hd (1:07)V 0:101a (18)

where Va is the air velocity in m/s. Substituting the val-ues for the dry heat transfer coef� cient, with an averageof 157.5 W/m2 ±C, and the void space air velocity givesa wet heat transfer coef� cient of 206.9 W/m2 ±C, whichis consistent with the data shown in Figure 9.

HEAT TRANSFER AREA FOR CONDENSATIONAND SUBCOOLING

Variations in the heat transfer area for condensationand subcooling are shown in Figure 10 as a functionof the water-to-air � ow ratio. The data are shown forinlet steam temperature of 120.8±C. The higher con-densation area is a result of higher thermal load forcondensation than subcooling. Also, the decrease in thecondensation area at higher values for L /G is caused bythe increase in the heat transfer coef� cient as shown inFigure 9. On the other hand, the increase in the subcool-ing area upon the increase in the L /G ratio is caused bythe constraint imposed on the total heat transfer area.Since the total area of the condenser is constant, it isequal to the summation of the condensation and sub-cooling heat transfer areas.

Figure 10 Variation in the condensation and subcooling heattransfer area as a function of water-to-air � ow-rate ratio.

heat transfer engineering vol. 22 no. 4 2001 51

CORRELATIONS OF EXPERIMENTAL RESULTS

The ef� ciency data for the evaporative condenser andair condenser are correlated as a function of the steamtemperature (Ts ), the wet-bulb temperature (Tw ), theheat transfer area (A), and the water-to-air � ow rate ratio(L /G ). The heat transfer area for the two condensers inparallel is set equal to the area of the single condenser.The resulting ef� ciency correlation for the evaporativecondenser is given by

e e D 98:57 ¡ 1:76(L /G ) ¡ 2:09 £ 10¡2(Ts )

C 0:27A C 4:83 £ 10¡2(Tw ) (19)

with an R2 value of 0.89, average deviation of0.15%, and maximum deviation of 0.39%. The above

Figure 11 Variation in measured and calculated systemef� ciency.

correlations are limited to the ranges 0:164 · L /G ·0:352; 23:1 · Tw · 26; 111:9 · Ts · 120:8, and3:68 · A · 7:36, where the temperatures are in ±Cand the area is in m2. Similarly, the ef� ciency correla-tion for the air condenser is given by

e a D 223:03 C 1:81 £ 10¡2(Ts )¡ 0:31A ¡ 5:29(Tw )

(20)

with an R2 value of 0.97, average deviation of 0.28%,and maximum deviation of 1.18%. The results for thetwo correlations are shown in Figure 11. The abovecorrelations are limited to the ranges 24:52 · Tw ·26; 111:9 · Ts · 120:7, and 3:68 · A · 7:36, wherethe temperatures are in ±C and the area is in m2.

The wet heat transfer coef� cient data are correlatedas a function of the water-to-air � ow rate ratio and thesteam temperature. The resulting correlation is given by

ho D 0:16(L /G )0:23(Ts )2:13 (21)

The above correlations are limited to the ranges 0:164· L/G · 0:352 and 111:9 · Ts · 120:8, where thetemperature is in ±C. The R2 value for the above corre-lation is 0.94, with an average deviation of 1.7%, andmaximum deviation of 5.8%. The correlation results areshown in Figure 12.

ERROR ANALYSIS

Error analysis in calculating the dimensionless gro-ups presented in this article is performed by the Kline-McClintock procedure [27]. The uncertainty inmeasurements is de� ned as the root sum square of the

Figure 12 Variation in measured and calculated heat transfercoef� cient.

52 heat transfer engineering vol. 22 no. 4 2001

� xed error by the instrumentation and the random er-ror observed during different measurements. The erroranalysis includes measured temperature and � ow rate.The calculated errors are 3.1% of the full scale for thetemperature measurement and 2.45% of the full scalefor the � ow-rate measurements. Accordingly, devia-tions in the calculated heat transfer coef� cient and sys-tem ef� ciency are 5.3% and 6.59%, respectively, fromthe true value.

CONCLUSIONS

An experimental investigation is conducted to studythe performance of evaporative condensers. In the lightof results and analysis, the following conclusions aremade.

The evaporative condenser ef� ciency increases at lowerL /G ratios and higher inlet steam temperatures.

The system performance shows that the parallel con-denser arrangement allows for processing the maxi-mum amount of inlet steam. On the other hand, theseries con� guration provides the maximum degreeof subcooling.

Performance of the single condenser unit is similar tothat of the two condensers in parallel. However, forthe same amount of steam load, the single condenserresults in a higher water temperature inside the col-umn and a lower degree of subcooling.

Proper design of the evaporative condenser and ef� -cient use of the heat transfer area for condensationrather than subcooling, would allow the evaporativecondenser to handle a thermal load 60% higher thanthat of the air condenser. In other words, for the sameamount of inlet steam, the higher thermal capacity ofthe evaporative condenser allows for use of a smallerheat transfer surface area and fan power than the aircondenser.

The ef� ciency correlation is expressed in terms of thesteam temperature, the heat transfer area, L /G , andthe ambient air wet-bulb temperature. The correla-tion is simple and can provide preliminary designdata.

The correlation for the water/air heat transfer coef� cientis expressed as a function of the steam temperatureand L /G . The correlation predictions are consistentwith literature studies.

NOMENCLATURE

A heat transfer area, m2

B � n height, m

C p speci� c heat at constant pressure, J/kg ±Cd � n thickness, mD tube diameter, mG air � ow rate, kg/sG steam mass � ux, kg/m2 sh heat transfer coef� cient, W/m2 ±CH liquid enthalpy, J/kgH 00 vapor enthalpy, J/kgk thermal conductivity, W/m ±CL liquid � ow rate, kg/sm number of � nsM mass � ow rate of condensate vapor, kg/sn number of tubesP pressure, kPaP reduced pressure, � uid pressure/critical pressure,

dimensionlessPr Prandtl number (D Cp l =k )q thermal load, Wq heat � ux, W/m2

Re Reynolds number (D q VD=l )T temperature, ±CU overall heat transfer coef� cient, W/m2 ±CV velocity, m/sW � n width, mZ length, md thickness of tube wall, me system ef� ciency [D (Ts ¡ Te )=(Ts ¡ Tw )]k latent heat, J/kgl dynamic viscosity, kg/m su � n ef� ciencyq density, kg/m3

v vapor mass fraction

Subscripts

a air stream or air condenserc condensate or condensation aread dry-bulb or dry heat transfer coef� ciente evaporative condenserF � ni inner tube` liquid waterlo local heat transfer coef� cient of liquid waterm meano outer tubep tubes heating steamt total heat transfer areau subcooled condensate leaving � rst heat exchangerv subcooled condensate leaving second heat ex-

changerw wet-bulb or wet heat transfer coef� cient

heat transfer engineering vol. 22 no. 4 2001 53

REFERENCES

[1] Al-Juwayhel, F. I., Al-Haddad, A. A., Shaban, H. I., andEl-Dessouky, H. T. A., Experimental Investigation of the Per-formance of Two-Stage Evaporative Cooler, Heat TransferEng., vol. 18, no. 2, pp. 21–33, 1997.

[2] Webb, R. L., A Uni� ed Theoretical Treatment of ThermalAnalysis of Cooling Towers, Evaporative Condensers, andFluid Coolers, ASHRAE Trans., vol. 90, pp. 398–415, 1984.

[3] Webb, R. L., and Villacres, A., Algorithms for PerformanceSimulation of Cooling Towers, Evaporative Condensers, andFluid Coolers, ASHRAE Trans., vol. 90, pp. 416–458, 1984.

[4] Maclain-Cross,I. L., and Banks, P. J.,A General Theory of WetSurface Heat Exchangers and Its Application to RegenerativeEvaporative Cooling, J. Heat Transfer, vol. 103, pp. 579–584,1981.

[5] Kettleborough, C. F., and Hsieh, C. S., The Thermal Perfor-mance of the Wet Surface Plastic Plate Heat Exchanger Usedas an Indirect Evaporative Cooler, ASME J. Heat Transfer, vol.105, pp. 366–373, 1983.

[6] Chen, P., Qin, H., Huang, Y. J., and Wu, H., A Heat and MassTransfer Model for Thermal and Hydraulic Calculations ofIndirect Evaporative Cooler Performance, ASHRAE Trans.,vol. 97, Part 2, pp. 852–865, 1991.

[7] Peterson, J. L., An Effectiveness Model for Indirect Evapora-tive Coolers, ASHRAE Trans., vol. 99, pp. 392–399, 1993.

[8] Kettleborough, C. F., The Thermal Performance of Cross-FlowIndirect Evaporative Cooler, Proc. ASME-JSME Thermal En-gineering Joint Conf., vol. 3, pp. 195–201, 1987.

[9] Peterson, J. L., and Hunn, B. D., Experimental Performanceof an Indirect Evaporative Cooler, ASHRAE Trans., vol. 98,pp. 15–23, 1992.

[10] Erens, P. J., and Dreyer, A. A., Modelling of Indirect Evapora-tive Air Coolers, Int. J. Heat Mass Transfer, vol. 36, pp. 17–26,1993.

[11] Erens, P. J., Comparison of Some Design Choices for Evapora-tive Cooler Cores, Heat Transfer Eng., vol. 9, no. 2, pp. 29–35,1988.

[12] El-Dessouky, H., Enhancement of the Thermal Performanceof a Wet Cooling Tower, Can. J. Chem. Eng., vol. 71, no. 3,pp. 1–8, 1996.

[13] Goswami, D. Y., Mathur, G. D., and Kulkarni, S. M., Experi-mental Investigation of Performance of a Residential Air Con-ditioning System with an Evaporatively Cooled Condenser,J. Solar Energy Eng., vol. 115, no. 4, pp. 206–211, 1993.

[14] Merkel, F., Verdunstungshuhlung, Z.Ver. Deutsch. Ing. (V.D.I.),vol. 70, pp. 123–128, 1925.

[15] Nahavandi, A. N., Kershah, R. M., and Serico, B. J., The Effectof Evaporation Losses in the Analysis of Counter Flow CoolingTowers, J. Nuclear Eng. Design, vol. 32, pp. 29–36, 1975.

[16] Sutherland, J. W., Analysis of Mechanical-Draught CounterFlow Air/Water Cooling Towers, J. Heat Transfer, vol. 105,pp. 576–583, 1983.

[17] El-Dessouky, H. T. A., Al-Haddad, A., and Al-Juwayhel, F.,A Modi� ed Analysis of Counter Flow Wet Cooling Towers,ASME J. Heat Transfer, vol. 119, no. 3, pp. 617–626, 1997.

[18] Goodman, W., The Evaporative Condenser, Heating, Piping,and Air Conditioning, vol. 10, pp. 165–328, 1938.

[19] Thomsen, E. G., Heat Transfer in an Evaporative Condenser,Refrig. Eng., vol. 51, pp. 425–431, 1946.

[20] Parker, R. O., and Treybal, R. E., The Heat, Mass Trans-fer Characteristics of Evaporative Coolers, Chem. Eng. Prog.Symp. Ser., vol. 57, pp. 138–149, 1961.

[21] Leidenfrost, W., and Korenic, B., Evaporative Cooling andHeat Transfer Augmentation Related to Reduced CondenserTemperature, Heat Transfer Eng., vol. 3, no. 3–4, pp. 38–59,1982.

[22] Peterson, D., Glasser,D., and Williams,D., Predicting the Per-formance of an Evaporative Condenser, ASME Trans., J. HeatTransfer, vol. 110, no. 3, pp. 748–753, 1988.

[23] El-Dessouky, H. T., Al-Haddad, A. A., and Al-Juwayhel, F.I., Thermal and Hydraulic Performance of a Modi� ed Two-Stage Evaporative Cooler, J. Renewable Energy, vol. 7, no. 2,pp. 165–176, 1996.

[24] Threlkeld, J., Thermal Environmental Engineering, 2d ed.,pp. 235–275, Prentice-Hall, Englewood Cliff, NJ, 1970.

[25] Shah, M. M., General Correlation for Heat Transfer duringFilm Condensation inside Pipes, Int. J. Heat Mass Transfer,vol. 22, no. 4, pp. 547–556, 1979.

[26] Myers, R. J., The Effect of Dehumidi� cation on the Air SideHeat Transfer Coef� cient for a Finned-Tube Coil, M.Sc. thesis,University of Minnesota, 1967.

[27] Kline, S. J., and McClintock, F. A., Describing Uncertainitiesin Single Sample Experiments, in Mech. Eng. ASME, NewYork, 1953.

Hisham Ettouney has been Professor of Chemi-cal Engineering at Kuwait University since 1988.Previously, he was a faculty member at the KingSaud University, Saudi Arabi, and University ofNew Hampshire, USA. He received his Ph.D. inChemical Engineering from MIT, USA, in 1983.Also, he received his B.Sc. in Chemical Engineer-ing from Cairo University, Egypt, in 1975. He has

more than 100 research publications and conference presentations in desali-nation, evaporative cooling, energy storage, and membrane separation.

Hisham El-Dessouky has been Professor ofChemical Engineering at Kuwait University since1991. Previously, he was a faculty member atQatar University, Qatar, and Zagazzig University,Egypt. He received his Ph.D. in Chemical Engi-neering from the University of Hannover, WestGermany, in 1981. Also, he received his M.Sc.and B.Sc. in Chemical Engineering from Cairo

University, Egypt, in 1976 and 1971, respectively. He is an Associate Edi-tor of Heat Transfer Engineering and Desalination. He has more than 100research publications and conference presentations in desalination, evapo-rative cooling, energy storage, and membrane separation.

Waleed S. Bouhamra is Professor of ChemicalEngineering at Kuwait University since 1999. Hereceived his Ph.D. and M.Sc. in Chemical Engi-neering from Oklahoma State University in 1988and 1985. His B.Sc. in Chemical Engineering wasreceived from Kuwait University in 1981. He hasheld a number of academic positions at KuwaitUniversity, which includes Assistant Vice Rectorfor Scienti� c Affairs, Director for the Center ofEvaluation and Measurement, Vice Dean for Re-

search and Academic Affairs at the College of Engineering and Petroleum,and currently he is the Vice Rector for Academic Support and Services. Hisresearch interests include environmental and indoor air pollution, reactordesign, and energy. He has published and presented more than 50 researcharticles in refereed journals and international conferences.

54 heat transfer engineering vol. 22 no. 4 2001

Bader Al-Azmi has been an Instructor ofChemical Engineering at Kuwait University since1994. He received his M.Sc. and B.Sc. in Chem-ical Engineering from Kuwait University in 1998and 1994, respectively. Currently, he is pursuinghis Ph.D. studies in heat transfer.

heat transfer engineering vol. 22 no. 4 2001 55