an evaluation of heat and mass transfer in open counter

117

An Evaluation of Heat and Mass Transfer in Open

Counter Flow Cooling Towers

Amin Jodat Department of Mechanical Engineering,

University of Bojnord, Iran

Abstract: Cooling towers are regarded as the most important equipments in oil industry. Most of

equipments and processes need cooling to work and the main fluid required for this industrial

work is water. Cooling tower makes water cool. The results obtained from testing evaporative

cooling can be evaluated through confirmed theories that have been created using dimensionless

analyses. These basic methods and theories can be used to design and predict working conditions

in points other than working points of device. The solution of many heat and mass transfer

devices is determined through dimensionless analyses and theory methods. The present study is

an attempt to analyze heat and mass transfer process in open counter flow cooling water. After

reviewing the related literature and rewriting the governing equations, a method has been

proposed. Also, the proposed method has been presented at two states of designing and rating.

Compared to previously conducted study, this method is more comprehensive. Finally, using

functional information of an industrial cooling tower, the obtained results of the proposed method

have been analyzed in terms of thermal exchanges, efficiency and NTU changes evaluation.

Keywords: counter flow cooling tower, Merker method, Sutherland method, thermal design,

efficiency, thermal exchanges

1- Introduction

Using cooling towers to remove heat and avoid its excessive emission in the environment

dates back to the 1940s and after that. Although simple water cooling systems were

used during the previous years, these systems were gradually evolved. In the 1940s,

these systems were changed into cooling towers. In general, cooling processes used in

chemical industries are divided into three classes of cooling with fresh water, cooling

with recirculation, and combination cooling. In cooling with fresh water, water passes

through condenser only one time while in cooling with recirculation, the same water is

circulating in cooling system constantly and convection is slightly performed. In

combination cooling, there is a combination of various systems.

Cooling with recirculation, in its own right is divided into two systems of open (i.e. wet

cooling processes) and close (i.e. dry cooling processes). The name of these systems can

describe their nature. In other words, a system pertains to open atmosphere and

another is a close system. That is, in wet heat exchange, water and air are in direct

contact with each other. However, in dry heat exchange, water or stem are not in direct

contact with air. Cooling towers also need a certain amount of makeup to compensate

the consumed water.

Cooling towers are fallen into the following types:

1. Induced draft cooling tower

2. Forced draft cooling tower

An Evaluation of Heat and Mass Transfer in Open …

Jodat / Argos Special Issue, 2016/pp. 117-132

118

3. Atmosphere cooling tower

In general, the structure of cooling towers consists of wooden water distributing plates,

air trap, water distributing pipes, cooled water tank, and fan. Basically, cooling towers

works in the following way: warm water returning from thermal convertors enters into

the top of the tower, is pour on distributing plates; air moves upward from the bottom of

the tower; heat is exchanged between air and warm water; cooled water enters the tank,

and is transferred into thermal convertors through air pump. The amount of water

evaporation depends on the level of air and water contact. In induced draft cooling

towers, fans are installed and send the air saturated by stem from the inside of the

tower to the outside and the fresh air is placed around the tower instead of the exited

air.

In forced draft cooling towers, fans are installed at the bottom of the tower on the

ground and the air is derived upward from the bottom of the tower. In this type of

cooling water, fans are easier to be repaired due to their low height. Around forced draft

cooling tower is closed while around the induced draft cooling tower is open. Therefore,

in induced draft towers, the air is in contact with water from all directions and evenly.

However, in forced draft cooling towers, the air is not in contact with water everywhere.

Atmosphere cooling towers works with atmosphere pressure through natural air flow

and fan is not used in these towers to set up air. The efficiency of these towers depends

on wind speed and air moisture. If wind speed is high, more water is lost and if wind

speed is slight, water is not adequately warmed. A mild wind flow has a good effect.

Further, if air moisture is high, water evaporation is not well occurred and water is not

cooled.

In the present study, two independent methods have been introduced to solve a

cooling tower. In the following, it has tried to evaluate the obtained results with

the aim of mass and thermal analysis of these two methods in an accumulated

tower. Also, a model has been proposed in counter flow cooling tower.

2- Related Litrature

For the first time, Walker at l. (1923) proposed the primary theory of cooling tower.

However, Merkel (1925) was the first person who practically attempted to solve the

problem of towers with direct flow. Merkel‟s method was based on a combination of

differential equations of water heat and mass transfer within a tower. In his method,

Merkel assumed that each drop within the tower is surrounded with air flowed from the

bottom of the tower. He also assumed that heat transfer is performed in the form of

tangible and covert heat transfer due to the evaporation of a part of water drop (Robert,

2001). Later on, cooling towers were designed based on rewriting Merkel‟s relations and

justifying the differences between theoretical and experimental forecasts. For instance,

it can be referred to the works of Nottage (1941) and changing his method to a graphical

solving method by Liehtenstein as well as presenting another graphical method to

determine air performance in a cooling tower by Michely (19490.



119

Caytan (1982) presented a method to solve counter and cross flow cooling towers by

writing STAR computer code. In this method, he solved 2D differential equations

resulted by fluids dynamic and thermodynamic analyses through a finite differential

method on a network with rectangular meshes (Caytan, 1982).

Sutherland (1983) proposed a method in which an accurate solution was used to solve

equations governing cooling tower. In his model, Sutherland considered a control volume

and regulated differential equations based on quantities‟ changes from the bottom of the

tower to the up the tower (Sutherland, 1983). In this model, he considered the effects of

input water evaporation and assumed Lewis number single in opposite tower. He solved

differential equations related to his accurate solving and approximate solving through

TOWER A program and TOWER B program using the 4th order Runge Kutta method,

respectively. Additionally, he showed that ignoring water evaporation for sample

functional conditions in a tower can lead to higher errors in higher ratios of water to air

flow rate (e.g. for the ratio of water to air flow rate equals 2 in about 14%).

Fujita and Tezuka (1986) solved thermal function of counter and cross cooling towers

with compulsory air flow using Enthalpy potential theory (Fujita and Tezuka, 1986).

Webb (1988) proposed an accurate design instruction for cooling towers. This method

was a 1D mode that considered water losses due to evaporation. Louis‟ number was

assumed 87% in this method (Webb, 1988). The model proposed by Jaber and Webb

(1989) presented an efficient design method based on NTU computation for counter and

cross flow cooling towers (Jaber, 1989).

Mohiuddin and Kant (1995) presented two articles. The first article explains details of a

method to design cross and counter flew cooling towers. In this article, a method has

been proposed for step by step design of cooling tower. Also, in this article, computer

codes existed have been reviewed. The second article explains and presents transfer

coefficients for various networks (Mohiuddin and Kant, 1995).

El-Dessouky et al. (1997) theoretically investigated a counter flow cooling tower with

modified concepts of NTU and thermal efficiency of the tower. In the model, some

assumptions such as water film resistance, counter unit Lewis factor, and curvature in

saturated air‟s enthalpy curve were considered. According to the research findings,

ignoring water film resistance and Lewis hypothesis causes an error that depends on

mass and heat transfer coefficients values (El-Dessouky et al., 1997). Through empirical

studies on PVC made packing, Goshayshi et al. (1999) obtained the effects of distance

and coarseness of packings on mass and heat transfer coefficients as well as the level of

their pressure loss (Goshayshi et al., 1999).

Halasaz (1999) proposed a dimensionless mathematical model for governing equations

and obtained the tower efficiency based on only two variables. Using this method, he

presented acceptable results for both counter flow and cross flow cooling towers

(Halasaz, 1999).



120

Stefanović et al. (2000) constructed a laboratory cooling tower with plexi glass-

made parallel plates and obtained temperature distribution along the tower

(Stefanović et al., 2000).

Using PHOENICS, Stefanović et al. (2001) solved heat and mass transfer in cooling

tower through 3D way and compared the obtained results with their previous obtained

results (Stefanović et al., 2001).

Jameel-ur-Khan and Zubair (2001) proposed a model similar to Sutherland‟s model in

which water film resistance was considered. The results obtained from their research

indicated that ignoring water film resistance and Lewis hypothesis causes considerable

error in computing NTU values and efficiency in tower compared to previous methods

such as Sutherland‟s method (Jameel-ur-Khan and Zubair, 2001).

In another article, Jameel-ur-Khan and Zubair (2003) investigated functional properties

of counter flow wet cooling towers. In their article, thermal performance of cooling

towers as well as convective and evaporative heat transfer in line with tower‟s height

have been intangibly shown (Jameel-ur-Khan and Zubair, 2003).

Soylemez (2004) analyzed hydraulic-thermal performance of counter flow cooling towers

optimization through a simple algebraic formula. In this work, NTU efficiency method

with extracting psychometric properties of humid air were used to analyze thermal

performance of counter flow cooling towers (Soylemez, 2004).

Kloppers and Kroger (2005) proposed equations governing cooling towers using Rigorous

Pope method, Merkel method and NTU method. They solved Rigorous Pope by the 4th-

order Runge Kutta method and compared the results of the three methods (Kloppers

and Kroger, 2005).

3- Mathematical Model

3-1- Merkel‟s Model

After 1925 when the first mathematical model to solve cooling tower was proposed by

Merkel, many researchers tried to present a more comprehensive model to more

accurately solve cooling tower problem without restricting hypotheses. The basic point

in all new works has been their comparison with previous models and empirical results.

Merkel‟s model is based on a combination of differential equations of mass and heat

transfer of water and air within a tower. Figure 1 shows the schematic of a water drop

within a tower. In this method, Merkel assumed that each drop within the tower is

surrounded with air flowed from the bottom of the tower. He also assumed that heat

transfer is performed in the form of tangible and covert heat transfer due to the

evaporation of a part of water drop. Merkel‟s model includes the following hypotheses:

1. A resistance in mass transfer from water mass (it is referred to a falling drop or

drop collection that are in identical temperature of Tw). There is no common



121

border (thin layer surrounding water drops in which air saturation exist with

Tw).

2. There is no temperature difference between water mass and air-water common

border.

3. Input water flow rate is not decreased due to its evaporation within tower.

4. Lewis number equals unit.

Writing survival equations and applying referred hypotheses, Merkel obtained

governing equations as following:

∫

(1)

∫

(2)

Since Merkel did not consider the effect of evaporation in his computations, the amount

of mw in the tower assumed a constant number; therefore, he defined NUT as

in his

equations.

Given to energy conservation law in the tower, air enthalpy in the tower relative to

water temperature within the tower will be as following:

(3)

With respect to enthalpy diagram, the temperature of air and water within the tower

and the assumption of air enthalpy linearity relative to water temperature and the

equality of water mass temperature with air-water common border, thus:

(4)

Finally, Eq. 3 and Eq. 4 lead to E. 5 to solve tower problem using Merkel‟s method.

و

(5)

Moreover, sorting Eq. 1, the magnitude of the tower volume is obtained as following:

∫

(6)



122

3-2- Sutherland‟s Model

Sutherland differentially wrote equations governing water cooling process based on

quantities‟ changes from bottom to up the tower. In Sutherland‟s model, input water

evaporation effects as well as Lewis number in the tower have been considered opposite

the unit (0.9). Finally, using this model, tower solving equations led to Eq. 7 device.

This device includes two the 1st order differential equations that entails air enthalpy

changes and water temperature based on absolute humidity of the air within the tower:

(

) ( ) ( )

(

) ( )

(

( ))

(7)

The right side of the above equations can be shown according to what shown as

functions of enthalpy, air absolute humidity and water temperature. These equations

have solved by Sutherland, assuming Lewis number constant and only in design state

(Sutherland, 1983). In this paper, assuming Lewis factor variable, at both states of

designing and rating, the above equations have been solved.

3-3- The Proposed Model

Principally, the problem of cooling tower is propounded int two general forms:

a. Designing:

( )

a. Rating

( )

In designing, having functional information of a cooling tower, the capacity or volume of

the tower is obtained. In rating, having the volume of the tower and information related

to input conditions and air exiting as well as input warm water conditions, output cold

water is obtained.

To solve the problem of cooling tower through the proposed method, Eq. 7 is used.

In his method, Sutherland assumed Lewis number as a value opposite unit that is

considered constant in line with the tower; however, given to the relation:

[

(

)

(

)]

(8)



123

Lewis number is a function of absolute moisture and molecular ratio of gas and liquid

mixture (Poppe & Ronger, 1991). Using the Eq. 8, the proposed method computes Lewis

factor independently from each section of the tower and solve it.

To determine quantities required to solve equations, the phrase of ,

from reference equations (17) given based on and constant numerical

coefficients are used. Computing thermodynamic constants such as , in

each section of tower has been performed by interpolating the information of

temperature limit related to water and air. To solve Eq. 5 and Eq. 7, and to compute

numerical integrals, the 4th order Runge Kutta and Romberg integration are employed,

respectively. Figure 3 presents the process of solving tower using the proposed method.

To evaluate the accuracy of the responses obtained from the proposed model, functional

information and empirical NTU presented in Sutherland‟s articles (1983) and Jameel-

ur-Khan and Zubair (2001) are used. The formula used for experimental NTU in the

reference (28) is as following:

(

)

(9)

Where c and n are empirical constants that are certain for each cooling tower. C and n

coefficients in Eq. 9 have been determined for four types of cooling towers using Simpson

and Sherwood‟s experimental information (7).

Computing the errors of Merkel, Sutherland and the proposed methods relative to

experimental values, the following formula has been used:

( )

(10)

As observed in Table 1, the accuracy of the results obtained from MATMER model are

consistent with the results of NTU parameter obtained from Merkel‟s model presented

in Sutherland‟s article; however, NTU of Sutherland‟s model has an error equal to 18%

compared to the proposed method.

Further, Table 2 shows that the error of Merkel‟s method, compared to the experimental

results obtained by Zaiber (28), is higher than the proposed method. In other words, the

proposed method more accurately predicts the tower volume. Both methods also predict

the tower volume less than the actual amount; however, only in low ranges values of the

present method, the tower volume is predicted more than its actual value.

In Table 1, NTU and the volume related to Merkel and Sutherland methods have been

completed and compared with experimental values. A) NTU values given in

Sutherland‟s article (17) with

and comparing it with MATMER and

MATPERS models.



124

Table 1. The values comparison in Sutherland‟s article

( ) ( ) ( ) ⁄

| | %

26.67 26.67 22.11 1.2 1.054 1.0461 0.74

26.67 26.67 22.11 1.2 2.866 2.856 0.02

29.44 35.00 23.89 1.0 1.188 1.165 1.8

b. NTU values and the volume obtained from Zubair

and

comparing it with MATMER and MATPERS models.

Table 2. The values comparison in Zubair‟s article

( )

( )

( )

( )

(kg/s)

(kg/s)

(m3)

(m3)

(m3)

1 31.22 23.88 37.05 21.11 1.158 0.754 1.297 0.4965 1.8357 0.457 7.9 1.2312 0.471 5.13

2 28.72 24.22 29.00 21.11 1.187 1.259 1.745 0.6847 1.5748 0.655 4.23 1.8291 0.712 -3.98

3 24.50 26.22 30.50 21.11 1.187 1.259 1.745 0.6847 1.5107 0.619 9.59 1.7143 0.672 1.85

4 38.78 29.23 35.00 26.67 1.265 1.008 1.467 0.6134 1.7532 0.582 5.11 1.4301 0.598 2.51

5 38.78 29.23 35.00 26.67 1.250 1.008 1.467 0.6099 1.7575 0.585 4.08 1.4581 0.602 1.29

4- Thermal Design of Cooling Tower

4-1- Tower Demand and the Curve Characteristic the Tower

Liechtenstein (1943) introduced cooling tower using Merkel‟s theory and based on the

base equations to determine border conditions in cooling tower. The result of this

equation causes to obtain the relation of dimensionless numbers group and heat and

mass transfer variables in a counter flow cooling tower. Liechtenstein performed some

experiments and specified that his equation does not cover mass rate of air and water.

His experiments performed in California University revealed the changes in demand

curve with input water temperature.

Merkel‟s equation is used to compute cooling demand based on designing temperature

and water-air rate. In other words, the value of KaV/L indicates a criterion for liquid

cooling rigidity. This equation associates designing temperature and air-water rate and

cooling demand to MTD (mean of temperature difference) that is used in all heat

transfer issues. Cooling demand curves and KaV/L value have been depicted as a

function of air-water rate. Approach temperature lines (tw1-WBT) have been shown as

the main parameters in these diagrams. These diagrams include 821 curves showing

KaV/L values for 40 wet bubble temperature and 21 cooling areas as well as 35 different

approaches temperature.

4-2- The Tower Characteristic

To analyze cooling performance and capability of a certain cooling tower, a certain

equation is needed. The following equation is commonly used to design tower and covers



125

most of demand curves. In this equation, the relation of KaV/L indicates air-water rate

in linear and logarithmic form.

KaV/L = C (L/G)-m (11)

Where the value of KaV/L is determined by Merkel‟s equation. The constant value of C

depends on the tower design or the place of characteristic curve in L/G=1. The value of

m also depends on the tower design and is called slope. This value is obtained through

experiment. The characteristic curve is determined through the following ways:

The performance is obtained by the curve‟s constructor (if any) using the

constructor‟ information. At all states, the slope of these curves indicates function

slope.

Through experiment at installation place and finding a characteristic point and

depicting characteristic curve passing through this point parallel to the main

characteristic curve or the line passing through this point with the appropriate

slope of -0.5 to -0.8.

Through experimental at the place for at least two points for various rates of air-

water, lines passing through these two points are characteristic curve. The slope

of this line should be in an acceptable area and can be a criterion for efficient

accuracy. The characteristic point is experimentally obtained by measuring wet

temperature and discharge air temperature as well as input and output water

temperature.

Figure 1. Demand Curve

Air-water rate is also obtained through the following ways:

Confidently, it can be assumed that discharge air of the tower is saturated. Therefore,

output air of the tower equals wet temperature. Knowing output wet temperature of the

tower, the increase of air flow enthalpy can be obtained from psychometric equations.

For even distribution, air-water discharge rate should have an appropriate proportion.

When air discharge in the tower is re-circulated, input air of the tower should be

considered 1-2 ℉ higher than wet temperature of the environment.



126

Using thermal and mass balance equation, dry air-water rate can be determined. Now,

through obtaining air-water rate and characteristic curve, KaV/L value can be obtained

by depicting in diagram.

4-3- Cooling Tower‟s Performance Variables

Many parameters influence the design and performance of cooling towers. Some of these

parameters are as following: tower‟s working water is one of the most effective and key

factors. One of the practical problems is the changes in water working rate and its effect

on input and output water temperature. Assume a tower that works under the following

conditions: water discharge rate is increased up to 20000 gpm. Assume that there is no

change in input air mass, wet temperature and cooling load (practically, due to the

increase of water discharge and pressure loss, air mass discharge is decreased).

Data:

(L1): 16000 gpm = the primary water discharge rate

(G1): 808048 lb/min = input air discharge rate

80.0℉ = wet bubble temperature of the environment

Sea level = the site‟s height

(HWT, tw2): 104.0 ℉ = warm water temperature

(CWT, tw1): 89.0 ℉ = cold water temperature

(m): -0.800 = characteristic curve slope

(L2): 20000 gpm= the secondary water discharge rate

Solution:

R1 = HWT - CWT = tw2 - tw1 = 104 - 89 = 15°F

L1= water discharge rate × (500 / 60) = 16,000 × (500 / 60) = 133,333.3 lb/min

Cooling load/time rate D1 = L1 × R1 = 133,333.3 × 15 = 2,000,000 BTU/min

Air mass discharge rate G1 = 80,848 lb/min

Liquid/gas ratio = L1 / G1 = 133,333.3 / 80,848 = 1.6492

L2= water discharge × (500 / 60) = 20,000 × (500 / 60) =166,666.7lb/min

Cooling load/time rate D2 = D1 = 2,000,000 BTU/min

Air mass discharge rate G2 = G1 = 80,848 lb/min

Liquid/gas ratio = L2 / G2 = 166,666.7 / 80,848 = 2.0615



127

R2 = D2 / L2 = 2,000,000 / 166,666.7 or = R1 × (L1 / L2) = 12°F

Figure 2. Kv/l characteristic curve

4-4- Pressure Loss in Cooling Tower

Sudden change in movement path or air speed leads to a high pressure loss. The areas

which cause pressure loss in cooling tower are as following:

1. Input air

2. Packings

3. Water distribution pipes

4. Eliminator

5. Fan input (it is sometimes called plenum loss).

Computing air pressure loss, except than air pressure loss in packings, can be easily

computed. The following relation is used to compute pressure loss in different areas. In

the following relation, the coefficient of k depends on its area. Also, air density is in 7°F

and equals 0.075 lb/ft3. This pressure loss is called static pressure.

(12)

The performance of fan depends on this static pressure loss. K coefficient for input air is

as following:

When shutter is used in air entrance, a number between 2-3 is considered for a large

shutter with high distance between its blades. For small shutters with low distance

between its blades, a number between 2.5-3.5 is considered.

When instead of shutter, square-section columns are used, k coefficient equals 1.5 and

when circular-section is used, k coefficient equals 1.3. For columns with conic section, k

coefficient is considered 1.2.

Computing pressure loss of water distribution is considered with eliminator and k

coefficient is usually considered 3-1.6. K coefficient of pressure loss in fan entrance is

also considered 0.1-0.3.



128

Open from one side: such arrangement is an entrance for cases in which the tower is

located in a place that causes the increase of input wet bubble temperature and enters

into the tower only from one side without any disturbance. In such arrangement, it

should be considered that air distribution on packings is performed evenly and

accurately. Open from two sides: this arrangement is usually used in industrial towers.

Open from all sides: back-to-back and open from all sides: this arrangement is

appropriate for places with limit area for installation.

5- Discussion and Results

To investigate and compare the results obtained from the proposed method, functional

information of an industrial cooling tower in maximum load conditions is considered:

( ) (

)

(

)

The efficiency (ε ) and temperature ratio (κ) for a cooling tower is defined as following:

ε

(13)

κ

(14)

The efficiency of a cooling tower indicates that to what extent a tower can enhances

input air enthalpy relative to the ideal state.

6- Design

Figure 3 shows NTU values of the tower based on temperature ratio changes for various

ratios of air-water mass flow rate. The changes of temperature ratio for change in input

air humid temperature ( ) from the temperature of to the temperature of

has been obtained. With respect to the fact that this curve for mass ratio of

ma/mw equals 0.5 from the ratio of temperature 0.7 and higher, the value of NTU

approaches a very large number. It indicates that in this area, to achieve lower output

water temperature, a very larger tower should be considered. In other words, in low

ratios of air-water mass flow rate, it is not possible to increase the temperature of humid

air from a certain limit without considering the tower with very larger volume.



129

Figure 3. The changes of NTU values of the tower based on temperature ratio changes

Take a careful look at Figure 4, it can seen that a main part of heat exchanged in the

tower derives from the covert temperature of water evaporation. On the other hand,

heat transfer due to displacing from bottom to up the tower with 1400 m3 has been from

air to water and after this point, its direction has been reversed and increased to up the

tower.

Figure 4. The changes of heat exchanged in the maximum load conditions

Figure 5 shows curves related to the tower efficiency with respect to the changes of

output wet bubble temperature. Taking a careful look at the curve, it can be found that

the increase of ma/mw leads to the decrease of input air bubble temperature. On the

other hand, the decrease of input air bubble temperature in a certain ration of ma/mw

leads to the decrease of the tower‟s efficiency with a mild slope.

Figure 5. The changes in the tower‟s efficiency level based on changes in input air bubble

temperature



130

7- Conclusion

According to the aforementioned, it can be concluded that using computer methods in

thermal computations of cooling tower provide acceptable results compared to the

presented diagrams. Combining computer and empirical methods, through measuring

wet bubble, input and output water temperatures and the discharge of water passing

through the tower as well as various arrangements, the performance of towers can be

predicted in conditions out of the design.

Given to the information provided in Tables 1 and 2, it can be stated that MATPRES

model is more accurate than Merkel and Sutherland‟s models. With respect to the fact

that input warm water flow rate and its temperature is constant, the performed

analyses have focused on the changes in parameters such as wet and dry air

temperature, water and air flow rate, evaporation losses and efficiency in the tower.

Moreover, it was revealed that to achieve lower output water temperature in lower

ma/mw ratios, very larger towers are required. On the other hand, it was found that a

main part of heat exchanged in the tower is due to the covert heat of water evaporation

and the proportion of heat transfer due to displacement in cooling water is slight. The

decrease of input air humid temperature also leads to the decrease of efficiency

coefficient in the tower. This fact confirmed the previously reported results.

Based on the performed analyses, at rating state, it was revealed that in a certain

ma/mw, the decrease of approaches in the tower leads to the decrease of range values.

The independency of a tower‟s efficiency in a certain ma/mw ratio to input dry air

temperature changes was confirmed in the present paper.

References

1. Author, A., Author, B., and Author, C., 1994. “Article Title”. Journal Name, 1(5),

May, pp. 1–3.

2. Author, A., 1986. Book Name. Publisher Name, Address.

3. Booklet, A., 1994. Booklet title. On the WWW, at http://www.abc.edu,May. PDF

file.

4. Walker, W. H., Lewis, W. K., MeAdams, W. H., and Gilliland, E. R., "Principles of

Chemical Engineering" , 3rd ed,McGraw-Hill, NewYork (1923).

5. Merkel, F.," VerdunstungskfJhlung", VDI Forschungsarbeiten, No. 275, Berlin

(1925).

6. Robert, E., Treybal, Mass-Transfer Operation", Third Edition, Mc Graw-Hill

Book Company, Reprinted in Tokyo, pp.259 (2001).

7. Nottage, H. B., "Merkel‟s Cooling Diagram as a Performance Correlation for Air –

Water Evaporative cooling systems", ASHVE Transactions, Vol. 47 ,

pp.429(1941).

8. Liehtenstein, J., "Performance and selection of mechanical-draft cooling towers",

ASME Transactions Vol.65, pp. 779-787 (1943).

9. Michley, H. S., "Design of force Draft Air Conditioning Equipment”, Chemical

Engineering Progress, Vol.45, pp.739 (1949).



131

10. Simpson, W. M., Sherwood, T. K., "Performance of small mech. Draft cooling

towers", Refrigrating Eng, Vol.52, No.6, pp.535-543, 574-576 (1944).

11. Carey, W.F., and Williamson, G. J., "Gas Cooling and Humidification: Design of a

Packed Tower from Small-Scale Tests", proceeding of the Institution of

Mechanical Engineers, Vol. 163, pp.41-53, (1950).

12. Baker, D. R., Shryock, H. A., "A comprehensive approach to the analysis of

cooling tower performance", Trans ASME, J Heat Transfer, Vol.83, No.3, pp.339-

350, 339-35 (1961).

13. Berman, L. D., "Evaporative cooling of circulating water”, ch. 2, Pergamon,

Oxford, (1965).

14. Hsu, H. L., Davis, G., de Vahl., and Sapsford, C. M., "An Investigation of the tie

line Method of Cooling Tower Analysis", ASHRAE Transactions, Vol.72,pt.II ,

pp.3.1-3.10 (1966).

15. Threlkeld, J. L., "Thermal Envirnomental engineering”, Prentice-Hall, Inc.,

ch.11, New Jersey (1970).

16. Yadigaroglu, G., and Pastor, E. J., “An Investigation of the Accuracy of the

Merkel Equation for Evaporative Cooling Tower Calculations, "ASME

Thermophysics and Heat Transfer Conference, Boston (1974).

17. Whillier, A., "A Fresh Look at the Calculation of Performance of Cooling Towers",

ASHRAE Transactions, Vol.82, pt. I, pp.269-282(1976).

18. American Society of Heating, Refrigerating and Air Conditioning Engineers",

ASHRAE Handbook and product Directory –Equipment, ch.21 (1975).

19. Caytan, Y., "Validation of the two-dimensional numerical model „STAR‟

developed for cooling tower design", Proc 3rd Cooling (1982).

20. Suthedand, J. W., "Analysis of mechanical draught counterflow air/water cooling

towers", Trans ASME, J Heat Transfer (1983).

21. Fujita, T., Tezuka, S., "Calculations on thermal performance of mechanical draft

cooling towers", ASHRAE Trans 92 (1986).

22. Webb, R. L., "A critical evaluation of cooling tower design methodology, in Heat

Transfer Equipment Design" , (Ed. R. K. Shah et al) Hemisphere Publishing

Washington, DC, pp. 547 -558 (1988).

23. Jaber, H., Webb, R. L., "Design of cooling towers by the effectiveness-NTU

method", Trans ASME, J Heat Transfer, 111 837-843, (1989).

24. A, K. M., Mohiuddin, K., Kant, "Knowledge base for the systematic design of wet

cooling towers", Part I: "Selection and tower characteristics", Int J. Refrig. Vol.

19, No. 1, pp. 43-51, (1996).

25. A, K. M., Mohiuddin, K., Kant, "Knowledge base for the systematic design of wet

cooling towers", Part II: "Fill and other design parameters", lntJ. Re/kig. Vol. 19,

No. 1, pp. 52 60, (1996).

26. H. T. A., El-Dessouky, A. Al-Haddad F. Al-Juwayhel, "A modified analysis of

counter flow cooling tower", J. Heat Transfer, Vol. 119, pp.617- 625, August,

(1997).

27. Goshayshi, H.R., J.F. Missenden and R. Tozer, "Cooling Tower-An energy

conservation resource", Applied Thermal Engineering, Vol. 19, pp.1223-1235,

(1999).



132

28. Halasaz, B., "Application of general non-dimensional mathematical model to

cooling towers", International Journal of Thermal Science, Vol. 38, pp. 75-88,

(1999).

29. Stefanović, V., Laković, S., Nenad Radojković, Gradimir Ilić, "Experimental study

on heat and mass transfer in cooling towers", Facta Universitatis, Series:

Mechanical Engineering, Vol. 1, No. 7, pp.849-861., ( 2000).

30. Stefanović, V., Gradimir Ilić, Mića Vukić,Nenad Radojković, Goran Vučković,

Predrag Živković, "3D model in simulation of heat and mass transfer processing

in wet cooling towers, Facta Universitatis", Series: Mechanical Engineering, Vol.

1, No. 8, pp.1065-1081., (2001).

31. Jameel-ur-Khan, Syed. M Zubair, “An improved design and rating analyses of

counter flow wet cooling towers", ASME J Heat Trans; 123:770–8, (2001).

32. Jameel-Ur-Rehman Khan, M. Yaqub, SyedM. Zubair, "Performance

characteristics of counter flow wet cooling towers", Energy Conversion

andManagement 44, pp. 2073–2091, (2003).

33. Soylemez, M. S., "On the optimum performance of forced draft counter flow

cooling towers", Energy conversion and Management 45, pp. 2335–2341, (2004).

34. Johannes, C., Kloppers and Detlev, G., Kroger, "A critical investigation into the

heat and mass transfer analysis of counterflow wet-cooling towers", International

Journal of Heat and Mass Transfer pp. 48765–777, (2005).

35. Johannes, C., Kloppers and Detlev, G., Kroger, "The Lewis number and its

influence on the performance prediction of wet-cooling tower", International

Journal of Thermal Sciences 44, pp. 879- 884, (2005).

36. Poppe, M., Rogner, H., "Berechung von Ruckkuhlwerken", VDI-armeatlas, Mi 1-

Mi 15. , (1991).

37. Paisarn, Naphon, "Study on the heat transfer characteristics of an evaporative

cooling tower", International Communications in Heat and Mass Transfer 32, pp.

1066–1074, (2005).

38. Bilal A. Qureshi, and Syed M. Zubair, “Second-law-based performance evaluation

of cooling towers and evaporative heat exchangers", International Journal of

Thermal Sciences 46 (2): pp.188-198, accepted 13 April, (2006).

an evaluation of heat and mass transfer in open counter

Documents