performance characteristics of counter flow wet cooling towers

Performance characteristics of counter flow wet cooling towers

Jameel-Ur-Rehman Khan, M. Yaqub, Syed M. Zubair *

Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Mail Box 1474,

Dhahran 31261, Saudi Arabia

Received 16 June 2002; accepted 23 September 2002

Abstract

Cooling towers are one of the biggest heat and mass transfer devices that are in widespread use. In this

paper, we use a detailed model of counter flow wet cooling towers in investigating the performance

characteristics. The validity of the model is checked by experimental data reported in the literature. The

thermal performance of the cooling towers is clearly explained in terms of varying air and water tempera-

tures, as well as the driving potential for convection and evaporation heat transfer, along the height of the

tower. The relative contribution of each mode of heat transfer rate to the total heat transfer rate in thecooling tower is established. It is demonstrated with an example problem that the predominant mode of

heat transfer is evaporation. For example, evaporation contributes about 62.5% of the total rate of heat

transfer at the bottom of the tower and almost 90% at the top of the tower. The variation of air and water

temperatures along the height of the tower (process line) is explained on psychometric charts.

� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Cooling towers; Model; Performance evaluation

1. Introduction

Cooling towers, as shown schematically in Fig. 1, consist of large chambers loosely filled withtrays or decks of wooden boards as slats or of PVC material. The water to be cooled is pumped tothe top of the tower, where it is distributed over the top deck by sprays or distributor troughsmade of wood or PVC material. It then falls and splashes from deck-to-deck down through thetower. Air is permitted to pass through the tower horizontally due to wind currents (cross flow) orvertically upward (counter current) to the falling water droplets. In the case of counter current

Energy Conversion and Management 44 (2003) 2073–2091www.elsevier.com/locate/enconman

*Corresponding author. Tel.: +966-3-860-3135; fax: +966-3-860-2949.

E-mail address: [email protected] (S.M. Zubair).

0196-8904/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0196-8904(02)00231-5

mail to: [email protected]

Nomenclature

AV surface area of water droplets per unit volume of tower, m2/m3

cpa specific heat at constant pressure of moist air, kJ/kga Kcw specific heat of water, kJ/kgw KE slope of the ‘‘tie’’ line, kJ/kgw Kh enthalpy of moist air, kJ/kgahc convective heat transfer coefficient of air, kW/m2 Khc;w convective heat transfer coefficient of water, kW/m2 KhD convective mass transfer coefficient, kgw/m

2 shf specific enthalpy of saturated liquid water, kJ/kgwhf;w specific enthalpy of water evaluated at tw, kJ/kgwhg specific enthalpy of saturated water vapor, kJ/kgwh0g specific enthalpy of saturated water vapor evaluated at 0 �C, kJ/kgwhfg;w change of phase enthalpy ðhfg;w ¼ hg;w � hf ;wÞ, kJ/kgwhs;w enthalpy of saturated moist air evaluated at tw, kJ/kgahs;int enthalpy of saturated moist air evaluated at tint, kJ/kgaLe Lewis number ðLe ¼ hc=hDcp;aÞ_mma mass flow rate of dry air, kga/s_mmw mass flow rate of water, kgw/sNTU number of transfer unitsPQ percentage heat rate(Q=Qtot)Pr Prandtl numberSc Schmidt numbert dry bulb temperature of moist air, �Ctint air–water interface temperature, �Ctw water temperature, �CV volume of tower, m3

W humidity ratio of moist air, kgw/kgaWs;w humidity ratio of saturated moist air evaluated at tw, kgw/kgae effectiveness

Subscripts

a moist airdb dry bulbem empiricalg,w vapor at water temperaturei inletint air–water interfacemax maximumo outlets,w saturated moist air at water temperaturew water

2074 J.-U.-R. Khan et al. / Energy Conversion and Management 44 (2003) 2073–2091

towers, the air motion is due to the natural chimney effect of the warm moist air in the tower ormay be caused by fans at the bottom (forced draft) or at the top (induced draft) of the tower.Walker et al. [1] was the first to propose a basic theory of cooling tower operation. The

practical use of basic differential equations, however, was first presented by Merkel [2], in whichhe combined the equations for heat and water vapor transfer. He showed the utility of total heator enthalpy difference as a driving force to allow for both sensible and latent heats. The basicpostulations and approximations that are inherent in Merkel�s theory are:

• the resistance for heat transfer in the liquid film is negligible;• the mass flow rate of water per unit cross sectional area of the tower is constant, i.e. there is noloss of water due to evaporation;

w,i water inletw,o water outletwb,i wet bulb inletwb,o wet bulb outlet

Superscriptscal calculatedexp experimental

Fig. 1. Schematic of a wet counter flow cooling tower.

J.-U.-R. Khan et al. / Energy Conversion and Management 44 (2003) 2073–2091 2075

• the specific heat of the air–steam mixture at constant pressure is the same as that of dry air;• the Lewis number for humid air is unity.

It should be noted that the formulation and implementation of Merkel�s theory in coolingtower design and performance evaluation is presented and discussed in most unit operations andprocess heat transfer textbooks.

2. Literature review

Webb [3] performed a unified theoretical treatment for thermal analysis of cooling towers,evaporative condensers and evaporative fluid coolers. In this paper, specific calculation proce-dures are explained for sizing and rating each type of evaporative exchanger. In another paper,Webb and Villacres [4] described three computer algorithms that have been developed to performrating calculations of three evaporatively cooled heat exchangers. The algorithms are particularlyuseful for rating commercially available heat exchangers at part load conditions. The heat andmass transfer ‘‘characteristic equation’’ of one of the heat exchangers is derived from the manu-facturer�s rating data at the design point.Jaber and Webb [5] presented an analysis that shows how the theory of heat exchanger design

may be applied to cooling towers. They demonstrated that the effectiveness ðeÞ and NTUs defi-nitions are in very good agreement with those used for heat exchanger design and are applicable toall cooling tower operating conditions. It is important to note that they did not consider heattransfer resistance in the air–water interface and the effect of water evaporation on the air processstates along the vertical length of the tower. The results are only applicable for Lewis numberequal to one. Furthermore, they used Merkel�s approximation of replacing the sum of the singlephase heat transfer from the water–air interface to the air and the mass transfer (evaporation ofwater) at the interface with the enthalpy as a driving potential.Braun et al. [6] presented effectiveness models for cooling towers and cooling coils. The models

utilize existing thermal effectiveness relationships developed for sensible heat exchangers withmodified definitions for the number of transfer units and the fluid capacitance rate ratio. Theresults of the models were compared with those of more detailed numerical solutions to the basicheat and mass transfer equations and experimental data. They also did not consider the effect ofair–water interface temperature, however, they did consider the effect of water evaporation on theair process states along the vertical length of the tower. The results are only presented for a Lewisnumber equal to unity.Dessouky et al. [7] presented a solution for the steady state counter flow wet cooling tower with

new definitions of tower effectiveness and number of transfer units. Their model is essentially amodified version of Jaber and Webb�s model with the inclusion of Lewis number, which appearsas a multiplication factor to the enthalpy driving potential. They did consider the effect of in-terface temperature and Lewis number, however, the effect of water evaporation on the air processstates along the vertical length is not considered. Furthermore, they used an approximate equa-tion for calculating the moist air enthalpy, which was obtained by curve fitting the tabu-lated thermodynamic properties of saturated air–water vapor mixtures. It is important to notethat the calculation of moist air properties should be accurate to obtain reliable results. Jorge and


Armando [8] tested a new closed wet cooling tower for use in chilled ceilings in buildings. Theyalso obtained experimental correlations for the heat and mass transfer coefficients and concludedthat existing thermal models were found to predict reliably the thermal performance of coolingtowers. Bernier [9,10] explained the performance of a cooling tower by examining the heat andmass transfer mechanism from a single water droplet to the ambient air. He did not consider theeffect of air temperature as it moved from the bottom to the top of the tower. Nimr [11] presenteda mathematical model to describe the thermal behavior of cooling towers that contain packingmaterials. The model takes into account both sensible and latent effects on the tower performance.A closed form solution was obtained for both the transient and steady temperature distribution ina cooling tower. Jose [12] defined a new parameter ‘‘thermo fluid dynamic efficiency’’, to quantifythe performances of cooling tower fills and concluded that it is independent of the cooling towerheight.The objective of this paper is to investigate the heat and mass transfer mechanisms from a water

droplet in a cooling tower as the air moves in the vertical direction. In this regard, for the sake ofcompleteness, we first discuss briefly the model of the tower, in which we have used reliable air–water thermodynamic property equations that are formulated by Hyland and Wexler [13,14]. It isthen followed by results and discussions related to the heat and mass transfer mechanisms of awater droplet as it travels from the top to the bottom of the tower.

3. Analysis of a cooling tower

A schematic of a counter flow cooling tower, showing the important states, is presented inFig. 2. The major assumptions that are used to derive the basic modeling equations may besummarized as [15,16]:

• heat and mass transfer is in a direction normal to the flows only;• negligible heat and mass transfer through the tower walls to the environment;• negligible heat transfer from the tower fans to the air or water streams;• constant water and dry air specific heats;• constant heat and mass transfer coefficients throughout the tower;• constant value of Lewis number throughout the tower;• water lost by drift is negligible;• uniform temperature throughout the water stream at each cross section; and• uniform cross sectional area of the tower.

From the steady state energy and mass balances on an incremental volume (refer to Fig. 2), thefollowing equation may be written [16]

_mma dh ¼ _mmw dhf;w þ _mma dW hf;w ð1Þ

We may also write the water energy balance in terms of the heat and mass transfer coefficients, hcand hD, respectively, as

_mmw dhf;w ¼ hcAV dV ðtw � tÞ þ hDAV dV ðWs;w � W Þhfg;w ð2Þ


and the air side water vapor mass balance as

_mma dW ¼ hDAV dV ðWs;w � W Þ ð3Þ

By substitution of the Lewis number as Le ¼ hc=hDcpa in Eq. (2), we get, after simplification,

_mmw dhf ;w ¼ hDAV dV ½Lecpaðtw � tÞ þ ðWs;w � W Þhfg;w� ð4Þ

Notice that we have defined Lewis number in Eq. (4) similar to the definition that is used byBraun et al. [6] and Kuehn et al. [15], however, Jaber and Webb [5] and El-Dessouky et al. [7] haveused Le ¼ Sc=Pr, commonly used in heat and mass transfer literature. In this regard, we prefer tostick to the notation of Kuehn et al. [15] that is considered as one of the standard references incooling tower literature. Combining Eqs. (1)–(4), we get, after some simplification [16],

dhdW

¼ Leðhs;w � hÞðWs;w � W Þ þ ðhg;w � h0gLeÞ ð5Þ

It should be noted that Eq. (5) describes the condition line on the psychometric chart for thechanges in state for moist air passing through the tower. For given water temperatures ðtw;i; tw;oÞ,Lewis number (Le), inlet condition of air and mass flow rates, Eqs. (1) and (5) may be solvednumerically for the exit conditions of both the air and water stream. The solution is iterative withrespect to the air humidity ratio and temperatures (W , t and tw). At each iteration, Eqs. (1)–(5) can

Fig. 2. Mass and energy balance of a wet counter flow cooling tower [15,16].


be integrated numerically over the entire tower volume from air inlet to outlet by a proceduresimilar to that described in Kuehn et al. [15] and Khan and Zubair [16].In deriving Eqs. (1)–(5), it was assumed that there is no resistance to heat flow in the interface

between the air and water. In other words, the interface temperature was assumed to be equal tothe bulk water temperature. However, for heat transfer to take place between the air and water,the temperature of the interface film must be less than the bulk water temperature, as shown inFig. 3. In that case, all the terms in Eqs. (1)–(5) with the subscripts (s, w) will be replaced bysubscript (s, int). Webb [5] assumed that tw is nearly equal to ðtint þ 0:5Þ.Fig. 3 shows both the enthalpies of the saturated air–water vapor mixture and tower operating

line as a function of water temperature. Considering the short distance between hs;w and hs;int onthe saturation curve as a straight line, the following simple relationship can be easily deduced [7],

hs;w � h ¼ hs;w � hs;int þ Eðtw � tintÞ ð6Þwhere E is the slope of the tie line and is constant for a given cooling tower. This slope is given by

E ¼ �hc;w=hD ð7ÞThe above equation can be used for obtaining the interface temperature. However, for largevalues of E, the interface and bulk water temperatures are almost equal.A computer program written by Khan and Zubair [16] is used for solving Eqs. (1)–(5) nu-

merically, and the flow chart of the program is shown in Fig. 4. In this program, the properties ofthe air–water vapor mixture and moist air are needed at each step of the numerical calculation.These properties are obtained from the property equations given in Hyland and Wexler [13,14],which are also used by ASHRAE [17] in computing air–water vapor thermodynamic properties.The program gives the dry bulb temperature, wet bulb temperature of air, water temperature andhumidity ratio of air at each step of the numerical calculation starting from the air inlet to the airoutlet values. If the value of ðhDAV Þ is known, the required tower volume may be obtained byusing [16]:

Ent

halp

y kJ

/kg

dry

air

0

100

200

Saturated Air

air operating line

10 50

hs,int

hs,w

hE=

-

E=

h s,w

h-

hs,

int

h-

Water Temperature Co

Ta

Tint

Tw

Tw > >Tint Ta

Dhc,wh

Fig. 3. Water operating line on enthalpy–temperature diagram indicating the effect of tie line ðE ¼ �hc;w=hDÞ on

saturated moist air enthalpy [16].


Fig. 4. Flow chart of the computer model.


V ¼ _mma

hDAV

Z Wo

Wi

dWWs;w � W

ð8Þ

The integral in the above equation is solved numerically. The number of transfer units of thetower is calculated by

NTU ¼ hDAV V = _mma ¼Z Wo

Wi

dWWs;w � W

ð9Þ

The cooling tower effectiveness ðeÞ is defined as the ratio of the actual energy transfer to themaximum possible energy transfer

e ¼ ho � hihs;w;i � hi

ð10Þ

Correlations for the heat and mass transfer of cooling towers in terms of physical parameters donot exist. It is usually necessary to correlate the tower performance data for specific tower designs.Mass transfer data are typically correlated in the form [18]:

hDAV V_mmw

¼ c_mmw

_mma

!n

ð11Þ

where c and n are empirical constants specific to a particular tower design. Multiplying both sidesof the above equation by ð _mmw= _mmaÞ and considering the definition for NTU (refer to Eq. (9)) givesthe empirical value of NTU as

NTUem ¼ c_mmw

_mma

!nþ1

ð12Þ

The coefficients c and n of the above equation were fit to the measurements of Simpson andSherwood [19] for four different tower designs over a range of performance conditions by Braunet al. [6]. Their experimental values were also compared with the values obtained by our model,and the results are discussed in Khan and Zubair [16]. It was shown that the calculated andempirical values of NTU are well within acceptable limits. Also, the wet bulb temperature of theoutlet air ðtwb;oÞ calculated from the present model is compared with the experimental valuesreported in Simpson and Sherwood [19], and the two values are very close to each other (within�0.6%).

4. Performance characteristics

It is commonly believed that the evaporation heat transfer rate inside the cooling tower is muchgreater than the convective heat transfer rate. To investigate the contribution of evaporation heattransfer in a cooling tower, a study is conducted on a water droplet as it moves from the top to thebottom of the tower, whereas the air that is used to cool the water is forced from the bottom of thetower in a counter flow arrangement. In this regard, the heat transfer rates from a single waterdroplet (of 3 mm diameter) inside the cooling tower due to convection and evaporation wereexpressed, respectively, as


_QQconv ¼ hcAV ðtw � tdbÞ ð13Þ

_QQevap ¼ hDAV ðWs;w � WaÞhfg;w ð14ÞThe computer program for simulating the performance of the cooling tower, explained in theprevious section, was used for analyzing the heat transfer rates for the following set of input data:tdb;i ¼ 29:0 �C, twb;i ¼ 21:11 �C, tw;i ¼ 28:72 �C, tw;o ¼ 24:22 �C, hDAV ¼ 3:025 kg/sm3, Le ¼ 0:9and _mma ¼ 1:187 kg/s. At each incremental control volume, measured from the top of the tower, theprogram calculates the thermodynamic properties of the air–water mixture that are then used tocalculate the heat transfer rates from the water droplet by using Eqs. (13) and (14). The resultsfrom the program are plotted in Figs. 5–19. In these figures, the effects of water to air mass flowrate ratios on the air–water temperatures, as well as the driving potential for convective–evapo-rative heat transfer rates are investigated. In this regard, the ratio of mass flow rate of water tomass flow rate of air, _mmw= _mma, is varied from 0.5 to 1.5 at an interval of 0.5.Fig. 5 is a plot of the air and water temperatures versus volume of tower. The water falls from

the top and its temperature, tw, decreases continuously as it approaches the bottom of the tower.This is generally expected in a cooling tower because the water loses heat both by convection andevaporation. It is interesting to see that the air, which enters from the bottom of the tower withinitial dry bulb temperature, tdb, decreases in temperature and then increases before leaving fromthe top of the tower. This can be explained from the fact that the water, which enters from the topof the tower, when it reaches the lower part, is cooled because of a predominantly evaporationmechanism. In this region, the water temperature, tw, is much lower than the entering air dry bulbtemperature, tdb, however, as we note from Fig. 5, when the tower volume from the top reaches

0 0.2 0.4 0.6 0.820

22

24

26

28

30

tdb

tw

twb

Tem

pera

ture

(°C

)

Volume of Tower "V" m3

Fig. 5. Variation of dry and wet bulb temperature of air and water temperature with volume of tower for _mmw= _mma ¼0:50.


above 0.15 m3, the water temperature is less than tdb. This results in heat transfer from the air tothe water (i.e. negative convection). The intersection point of the tdb and tw curves indicates no

20

22

24

26

28

30

tdb

tw

twb

0 0.2 0.4 0.6 0.8

Tem

pera

ture

(°C

)


Fig. 6. Variation of dry and wet bulb temperature of air and water temperature with volume of tower for

_mmw= _mma ¼ 1:00.

20

22

24

26

28

30

tdb

tw

twb

0 0.2 0.4 0.6 0.8

Tem

pera

ture

(°C

)


Fig. 7. Variation of dry and wet bulb temperature of air and water temperature with volume of tower for

_mmw= _mma ¼ 1:50.


temperature difference. At this point, there is no convection heat exchange between the water andthe air. Furthermore, below this point tdb is less than tw, which results in heat transfer from thewater to the air (i.e. positive convection). As expected, the wet bulb temperature of the air twb

Fig. 8. Variation of driving potential for convection and evaporation heat transfer with volume of tower for

_mmw= _mma ¼ 0:50.


_mmw= _mma ¼ 1:00.


decreases continuously in the tower from the top to the bottom. It approaches the water outlettemperature at the bottom of the tower.


_mmw= _mma ¼ 1:50.

-1

0

1

2

3

Qevap

Qtotal

Qconv

0 0.2 0.4 0.6 0.8

Hea

t Rat

es "Q

" (W

atts

)


Fig. 11. Variation of heat rates with volume of tower for _mmw= _mma ¼ 0:50.


The effect of mass flow rate ratio _mmw= _mma is investigated by varying the mass flow rate of water,_mmw, while keeping the air flow rate, _mma, constant. The results are shown in Figs. 5–7. We note that

Qevap

Qtotal

Qconv

-1

0

1

2

3

0 0.2 0.4 0.6 0.8

Hea

t Rat

es "Q

" (W

atts

)



Qevap

Qtotal

Qconv

-1

0

1

2

3

0 0.2 0.4 0.6 0.8

Hea

t Rat

es "Q

" (W

atts

)




with the increase in water mass flow rate, the dry bulb temperature of the air decreases over arelatively small height of the tower, and also the temperature drop of water is less with the in-crease in _mmw. This can be explained from the fact that with an increase in mass flow rate ratio,more water is to be cooled for a given tower volume. Therefore, one would expect that the surface

Fig. 14. Variation of percent heat rates with volume of tower for _mmw= _mma ¼ 0:50.



area required both for convection and evaporation will be reduced, resulting in higher water outlettemperatures and reduced heat transfer rates.The driving potentials for evaporative heat transfer ðWs;w � WaÞ and convective heat transfer

ðtw � tdbÞ versus tower volume are presented in Figs. 8–10 for _mmw= _mma varying from 0.5 to 1.5 at aninterval of 0.5. We note that the humidity ratio of saturated moist air, Ws;w decreases with towervolume measured from the top because the water temperature decreases as it moves down, while


75

50

0

0.04

0.01

0.03

0.02

50

75

100

125

25 30

100

125

150

175

200

225

250

275

Enthalp

y (kJ/

kg of

dry a

ir)

RH = 20%

0.08

0.06

0.04

0.02

0

Dry Bulb Temperature (°C)10 20 30 40 50 60

Hum

idity

Rat

io (k

g of

moi

stur

e/kg

of d

ry a

ir)

Fig. 17. Process line of water cooling in cooling tower for _mmw= _mma ¼ 0:50.


the humidity ratio of moist air, Wa increases with tower volume measured from the bottom becausethe air absorbs moisture as it move upwards. These figures show that the potential for evaporationdecreases first and then increases with the tower volume, particularly for _mmw= _mma ¼ 0:5. However,for _mmw= _mma P 1:0, the potential increases with tower volume. On the other hand, the driving po-tential for convection heat transfer ðtw � tdbÞ decreases with tower volume, and it becomes negativeafter reaching some height of the tower. It, therefore, results in a negative convective heat transferin the tower (from water to air). As explained above, the negative convection in the tower occurswhen the water temperature is lower than the air dry bulb temperature.

75

50

0

0.04

0.01

0.03

0.02

50

75

100

125

25 30

100

125

150

175

200

225

250

275

Enthalp

y (kJ/

kg of

dry a

ir)

RH = 20%

0.08

0.06

0.04

0.02

0


Hum

idity

Rat

io (k

g of

moi

stur

e/kg

of d

ry a

ir)


75

50

0

0.04

0.01

0.03

0.02

50

75

100

125

25 30

100

125

150

175

200

225

250

275

Enthalp

y (kJ/

kg of

dry a

ir)

RH = 20%

0.08

0.06

0.04

0.02

0


Hum

idity

Rat

io (k

g of

moi

stur

e/kg

of d

ry a

ir)



The convection and evaporation heat transfer rates _QQconv, _QQevap and _QQtotalð¼ _QQconv þ _QQevapÞ areplotted as a function of tower volume measured from the top of the tower in Figs. 11–13. Thesefigures show that the heat transfer rates are high in the top portions of the tower and decrease asthe water moves from the top to the bottom of the tower, particularly for _mmw= _mma6 1. Thesefigures, however, indicate that the total heat rate increases for _mmw= _mma P 1 and is mainly controlledby the evaporation mechanism. In the region where the heat transfer is taking place from air towater; i.e. negative convection, the evaporation heat rates are generally high. These figures clearlyshow that evaporation is basically controlling the total heat flow in a cooling tower.The percentage heat rates due to convection and evaporation PQconv and PQevap, are plotted

in Figs. 14–16 as a function of tower volume for different mass flow rate ratios, _mmw= _mma. Asdiscussed above, _QQconv decreases with _mmw= _mma. Therefore, a high percentage is noted for _mmw= _mma lessthan 1.0, particularly in the region where the convection is taking place from air to water, i.e. theconvection component is negative. These figures clearly show that the percentage of the evapo-ration component is always positive and is highest for low mass flow rate ratios.The process lines of the air on a psychometric chart are presented in Figs. 17–19 for different

values of _mmw= _mma. These curves show that the dry bulb temperature at the outlet of the tower isalways less than that at the inlet for the conditions investigated in this study. However, the relativehumidity and the specific humidity of the air increase as the air moves from the bottom to the topof the tower. This implies that the air is also going to cool in the tower, along with the water,because of evaporation of water in the tower. It should be noted that when water evaporates in thetower, it needs heat that is taken from both water and air. Therefore, one would expect thepossibility of cooling both air and water in the tower.

5. Concluding remarks

A reliable computer model of a counter flow wet cooling tower has been used to study the heattransfer mechanisms from a water droplet as it moves from the top to the bottom of the tower,while the air is forced vertically upward. It is clearly demonstrated that the water temperature, tw,decreases continuously as it approaches the bottom of the tower. However, air, which acts as acoolant, enters from the bottom of the tower, initially at its dry bulb temperature, tdb, decreases intemperature and then increases before leaving from the top of the tower. This cooling phenomenonof the air, i.e. negative convection, in some parts of the tower, along with the water, is explained dueto evaporation of the water in the tower. It is demonstrated that in the negative convection regionof the tower, the evaporation rates are generally high. The effect of water to air mass flow rate ratio,_mmw= _mma, is investigated by varying the mass flow rate of water, _mmw, while keeping the air flow rate,_mma, constant. The results clearly demonstrate that with an increase in water mass flow rate for thesame fill packing, the surface area required both for convection and evaporation is reduced, re-sulting in higher water outlet temperatures and reduced heat transfer rates.

Acknowledgements

The authors acknowledge the support provided by King Fahd University of Petroleum andMinerals through the research project (ME/RISK-FOULING/230).


References

[1] Walker WH, Lewis WK, McAdams WH, Gilliland ER. Principles of chemical engineering. 3rd ed. New York:

McGraw-Hill Inc; 1923.

[2] Merkel F. Verdunstungshuhlung. Zeitschrift des Vereines Deutscher Ingenieure (VDI) 1925;70:123–8.

[3] Webb RL. A unified theoretical treatment for thermal analysis of cooling towers, evaporative condensers, and fluid

coolers. ASHRAE Trans 1984;90(2):398–415.

[4] Webb RL, Villacres A. Algorithms for performance simulation of cooling towers, evaporative condensers, and fluid

coolers. ASHRAE Trans 1984;90(2):416–58.

[5] Jaber H, Webb RL. Design of cooling towers by the effectiveness-NTU method. ASME J Heat Transf

1989;111(4):837–43.

[6] Braun JE, Klein SA, Mitchell JW. Effectiveness models for cooling towers and cooling coils. ASHRAE Trans

1989;95(2):164–74.

[7] El-Dessouky HTA, Al-Haddad A, Al-Juwayhel F. A modified analysis of counter flow cooling towers. ASME J

Heat Transf 1997;119(3):617–26.

[8] Jorge F, Armando CO. Thermal behavior of closed wet cooling towers for use with chilled ceilings. Appl Therm

Eng 2000;20:1225–36.

[9] Bernier MA. Cooling tower performance: theory and experiments. ASHRAE Trans 1994;100(2):114–21.

[10] Bernier MA. Thermal performance of cooling towers. ASHRAE J 1995;37(4):56–61.

[11] Nimr MA. Modeling the dynamic thermal behavior of cooling towers containing packing materials. Heat Transf

Eng 1999;20(1):91–6.

[12] Jose AS. The use of thermo-fluid dynamic efficiency in cooling towers. Heat Transf Eng 2002;23:22–30.

[13] Hyland RW, Wexler A. Formulations for the thermodynamic properties of the saturated phases of H2O from

173.15 to 473.15 K. ASHRAE Trans 1983;89(2):500–20.

[14] Hyland RW, Wexler A. Formulations for the thermodynamic properties of dry air from 173.15 to 473.15 K, and of

saturated moist air from 173.15 to 372.15 K, at pressure to 5 MPa. ASHRAE Trans 1983;89(2):520–35.

[15] Kuehn TH, Ramsey JW, Threlkeld JL. Thermal environmental engineering. 3rd ed. New Jersey: Prentice-Hall Inc;

1998.

[16] Khan JR, Zubair SM. An improved design and rating analyses of counter flow wet cooling towers. ASME J Heat

Transf 2001;123:770–8.

[17] ASHRAE handbook of fundamentals. Atlanta, GA: American Society of Heating, Refrigerating, and Air-

Conditioning Engineers, Inc; 1993, Chapter 6.

[18] ASHRAE equipment guide. Atlanta, GA: American Society of Heating, Refrigerating, and Air-Conditioning

Engineers, Inc; 1983, [chapter 3].

[19] Simpson WM, Sherwood TK. Performance of small mechanical draft cooling towers. Refrig Eng 1946;52(6):525–

43, 574–6.
