A Method for Evaluating the Heat and Mass Transfer

8/8/2019 A Method for Evaluating the Heat and Mass Transfer

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A method for evaluating the heat and mass transfercharacteristics in a reversibly used water cooling tower

(RUWCT) for heat recovery

Kunxiong Tan, Shiming Deng*

Department of Building Services Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China

Received 1 April 2000; received in revised form 27 March 2001; accepted 4 April 2001

Abstract

In sub-tropical regions, a standard water cooling tower may be reversibly used, as part of a desuperheater heat

recovery system for service hot water heating, to extract free heat from ambient air in colder seasons when building

cooling load is reduced. Chilled water is pumped into a reversibly used water cooling tower (RUWCT) where it is

heated by warmer ambient moist air. This paper presents a method by which the heat and mass transfer characteristics

in a counter-flow RUWCT can be evaluated. The method is developed by introducing to the Merkel’s equation for

standard water cooling towers the revisions that account for the differences in heat and mass transfer characteristics

between a water cooling tower and a RUWCT. Field experimental results from a RUWCT installed in a sub-tropical

region in China indicated that the method developed could be used to evaluate the thermal performance of a RUWCT

with an acceptable accuracy. # 2002 Elsevier Science Ltd and IIR. All rights reserved.

Keywords: Cooling tower; Mass transfer; Heat transfe; Calculation; Cooling; Heating; Reversible

Me ´ thode permettant d’e ´ valuer les caracte ´ ristiques de transfert

de chaleur et de masse dans une tour de refroidissement d’eau

utilise ´ e e ´ galement pour le chauffage d’eau

Re ´ sume ´

Dans les re gions subtropicales, on peut utiliser les tours de refroidissement de facon re versible pour fournir de l’eau

chaude sanitaire et pour extraire de la chaleur de l’air ambiant pendant les saisons les plus fraıˆches afin de re´ duire la charge

thermique d’immeubles. On apporte de l’eau refroidie par pompage a ` la tour de refroidissement re versible (RUWCT) ou `

cette eau est alors chauffe e a ` l’aide de l’air humide ambiant plus chaud. Cet article pre sente une me thode permettantd’e valuer les caracte ristiques de transfert de chaleur et de masse dans une RUWCT a ` e coulement a ` contre-courant. Les

auteurs ont de veloppe la me thode a ` l’aide de l’e quation de Merkel, en introduisant, pour les tours de refroidissement

classiques, des modifications tenant compte des diffe rences entre les caracte ristiques de transfert de chaleur et de masse

entre une tour de refroidissement et une RUWCT. Les re sultats obtenus sur le terrain avec une RUWCT installe e dans

une re gion subtropicale chinoise indiquent que la me thode de veloppe e pourrait eˆtre utilise e afin d’e valuer la performance

thermique d’une RUWCT avec une pre cision acceptable.# 2002 Elsevier Science Ltd and IIR. All rights reserved.

Mots cle s : Tour de refroidissement d’eau atmosphe ´ rique ; Transfert de masse ; Transfert de chaleur ; Calcul ; Refroidissement ;

Chauffage ; Re ´ versibilite ´

0140-7007/02/$22.00 # 2002 Elsevier Science Ltd and IIR. All rights reserved.

P I I : S 0 1 4 0 - 7 0 0 7 ( 0 1 ) 0 0 0 4 4 - 5

International Journal of Refrigeration 25 (2002) 552–561

www.elsevier.com/locate/ijrefrig

* Corresponding author. Fax: +852-2774-6146.

E-mail addresses: [email protected] (S. Deng).



1. Introduction

Using desuperheaters to recover heat from central

water chiller plants of building air-conditioning systems

to generate service hot water might be possible in both

the tropics and subtropics. However, in sub-tropical

regions during colder seasons, there may not be suffi-

cient heat to be recovered from buildings due to reduced

building cooling load. In order to provide year-round

service hot water supply, backup water heating pro-

visions, normally by electricity, are required. Given that

in the subtropics in winter, ambient air temperature isnormally at around 15C, a standard water cooling

tower may be operated to extract heat from ambient air

as a heat source for water heating in a desuperheater

heat recovery system. Part of chilled water produced in

the chiller plant for air-conditioning at, say, 7C is

pumped to the tower where the water is heated by

ambient air to, say, 12C. Since in colder seasons, an

air-conditioning system is normally operated in part

load condition, so that an existing water cooling tower

which might be idle can be used as a RUWCT. This is

cost-effective as no additional cost for a water cooling

tower is required.

This paper presents a method by which the heat and

mass transfer characteristics in a counter-flow RUWCT

can be evaluated. Three major differences in the heat

and mass transfer processes between a standard water

cooling tower and a RUWCT have been identified. The

method has been developed by introducing to the Mer-

kel’s equation for water cooling towers the revisions that

account for these identified differences. Field experi-

mental results from a RUWCT installed in a sub-tropical

region in China indicated that the method developed

could be used to evaluate the thermal performance of

RUWCT with an acceptable accuracy.

2. Background

Until recently the performance of counter-flow water

cooling towers was evaluated using the so-called Merkel

model [1]. The heat and mass transfer process taking

place in a RUWCT, where water is heated and air is

cooled, is, however, opposite to that in a standard water

cooling tower. A RUWCT may be considered to operate

in a similar way to a spray room or an air washer where

air is cooled and dehumidified. A number of earlier

Nomenclature

am Surface area per unit tower volume for mass

transfer (m2/m3)

C Constant in Eq. (10)

CMS Humid air flow rate (m3/s)C a Specific heat of humid air (kJ/kgC)

C w Specific heat of water (kJ/kgC)

F Correction factor for the change of chilled

water flow rate

G Dry air flow rate (kg/s)

H Fill height (m)

h Air enthalpy (kJ/kg dry air)

hv Enthalpy of saturated water vapor at water

temperature tw (kJ/kg)

hw Enthalpy of water at water temperature tw (kJ/

kg), hw=C w (twÀtref )ffiC wtw

m Mass flux (kg/m

2

s)L Chilled water flow rate (kg/s)

QT Total heat transfer rate (kW)

Qb Latent heat transfer rate (kW)

QA Measured total heat exchange capacity (kW)

QA0 Calculated total heat exchange capacity (kW)

r0 Latent heat of water at the reference

temperature tref (kJ/kg)

tw Chilled water temperature (C)

ta Humid air temperature at a level where water

temperature is tw (C)

tdb Dry-bulb temperature of humid air (C)

twb Wet-bulb temperature of humid air (C)

tref Reference temperature for 0 enthalpy of air

and water (C), tref ffi 0.01C

tw,n Measured outlet chilled water temperature

(C)tw,n

0 Calculated outlet chilled water temperature

(C)

V Tower volume (m3)

w Air humidity ratio (kg/kg dry air)

XN Constant in Eq. (10)

Heat transfer coefficient for air film (kW/m2

C)

Mass transfer coefficient for air film (waÀ wi)

(kg/m2 s)

Á Difference in Table 1 and Table A1

Ratio of latent heat transfer to the total heat

transfer

Subscripts

0 State of water and air entering a RUWCT

a Humid air

dew Dew-point

i Interface

n States of water and air leaving a tower

s Saturated

w Water

K. Tan, S. Deng / International Journal of Refrigeration 25 (2002) 552–561 553



studies on standard water cooling towers indicated that

the calculation methodologies for cooling towers proved

valid for the analysis of heat and mass transfer in spray

rooms or air washers. For example, it is stated by

Threlkeld that the governing Equation of a counter-flow

spray dehumidifier can be derived in a manner analo-

gous to a cooling tower [2]. Also, as pointed out bySutherland, the analysis and solution of cooling towers

can be extended to describing the thermal behavior of

chilled spray dehumidifiers [3]. However, the heat and

mass transfer process in a RUWCT has been identified

to be different from that in either a standard water

cooling tower or a spray room.

2.1. A RUWCT vs a standard water cooling tower

Three major differences in the heat and mass transfer

processes taking place in a RUWCT and a standard

water cooling tower have been identified, as follows.

2.1.1. Water-side heat transfer resistance

Previous research work on water cooling towers indi-

cated that the water-side heat transfer resistance in a

water cooling process is small and therefore negligible.

Ibrahim et al. provided a model to investigate the effect of

tower parameters on air and water temperature distribu-

tion across air and water film thickness [4]. The results

showed that water-film thermal resistance only caused a

very small reduction in the interface water temperature

and had no significant effect on the water-side Nusselt

number. Gurney et al. concluded that ignoring water-film

resistance would not affect the accuracy of results in gen-

eral refrigeration and air-conditioning calculations [5].

Because water-film resistance is negligible in the ana-

lysis for a standard water cooling tower, a water cooling

process is primarily controlled by air-film resistance.

The temperature at the interface between the air and the

water is considered to be approximately equal to the

bulk water temperature. However, the extensive experi-

ments in Normans work demonstrated that when water

vapor condenses from humid air during direct contact

with refrigerated brine, both the air-film resistance and

water-film resistance would become significant [6]. They

were verified to be approximately equal by Norman’sexperiments. Therefore, the water-film heat transfer

resistance should be accounted for in the analysis of

heat and mass transfer characteristics in a RUWCT.

2.1.2. Reduced latent heat exchange

In a standard water cooling tower, water is cooled by

evaporating a portion of water and by heat exchange

with air at a lower temperature. Heat is removed mostly

by latent heat exchange, through evaporation from the

warm water to the air. It was estimated that more than

80% of the total heat removed, and approximately 100%

during summer operation, is by latent heat transfer [7].

Oachs’ cooling tower study also indicated that 75% of

the total heat is in the form of latent heat [8]. However, it

is expected latent heat exchange is less significant in the

heat gathering process of a RUWCT, as Norman et al.

found in their experiments that the mass transfer coeffi-

cients for air cooling using refrigerated brine were about

50% lower than those obtained in the same tower usedfor water cooling. In most of Norman’s experiments,

latent heat exchange accounted for less than 30% of the

total heat transfer. Therefore, in a RUWCT, the per-

centage for latent heat transfer is expected to differ from

that in a standard water cooling tower.

Norman explained the reasons for the smaller rate of

mass transfer [9]. The wetted area of the fill or packing in

a tower may decrease when absorption of water vapor

occurs. This is associated with the change in surface ten-

sion of water as it flows down along a tower. When heat

is transferred to water or water vapor condenses from

moist air, water surface tension is reduced, and the waterfilm becomes unstable and breaks up, causing dry pat-

ches to appear on tower packing. A possible explanation

can be that there are considerable local variations in the

film thickness and water velocity, and the water tem-

perature increases most rapidly at points where the film

is thin and the velocity is low. This in turn sets up local

surface tension gradients which render the film unstable.

These result in a reduction in mass transfer area, so that

the latent heat transfer is reduced.

2.1.3. Increased chilled water flow

In a RUWCT, water vapor would condense from

moist air when it is in direct contact with the chilled

water. If water loss by carry-over or tower blowdown is

neglected, chilled water flow rate at tower exit is

increased, because of water added from water vapor

condensation. However, in a standard water cooling

tower, water flow rate will drop as a result of evapora-

tion and require make-up supply to replenish the loss.

2.2. A RUWCT vs a spray room

Two differences in the heat and mass transfer environ-

ment between a spray room and a RUWCT exist. Firstly

there is a fill or packing inside a RUWCT, whereas nor-mally there is none in a spray room. The fill retards the

rate of waterfall and increases the water surface that is

exposed to air. This would result in a higher rate of heat

and mass transfer in a RUWCT than that in a spray room.

Secondly, the top water distributor of a RUWCT spreads

water in a high speed in the air stream, compared to a

bundle of tubes with many nozzles in a spray room. This

will allow even better contact between the two fluids in a

RUWCT than in a spray room [10].

It has been shown that differences exist in heat and

mass transfer taking place in a standard water cooling

tower, a spray room and a RUWCT. Although well

554 K. Tan, S. Deng / International Journal of Refrigeration 25 (2002) 552–561



established, the standard method for the thermal per-

formance analysis of water cooling towers may not be

directly used for a RUWCT. With the anticipation that

there may be more and more applications of RUWCT

in both tropical and sub-tropical regions, it is necessary

that a suitable method to evaluate the heat and mass

transfer characteristics of a RUWCT be developed.

3. Heat and mass transfer process in a counter-flow

RUWCT

At the bottom of a counter-flow RUWCT, the

incoming air meets ‘‘warmer’’ chilled water. Depending

its dew point temperature, the incoming air may experi-

ence two different processes in the RUWCT.

If the air dew-point temperature is lower than the

chilled water temperature, evaporation of water vapor

occurs. The air will be consequently cooled but humidi-fied first at the tower bottom. As it flows up, the humi-

dified air will meet cooler chilled water. Within the

region in the tower where the air dew-point temperature

is higher than the chilled water temperature, the air will

be cooled and dehumidified. This air cooling and dehu-

midification process continues until the air exits from

the tower. Changes in the state of the air in this process

can be represented by the curve AB in Fig. 1. When the

dew-point temperature of the entering air is greater than

chilled water temperature, air will experience a cooling

and dehumidifying process throughout the tower, as

represented by the curve A0B0.

In Fig. 1, curve PQ is the saturation line. Point C

represents the temperature and humidity ratio of the

interface between the bulk air and bulk water at the air

inlet plane, and D the state of the interface at the air

outlet plane.

Irrespective of which process takes place near the

bottom of a RUWCT, air cooling and dehumidification

is the dominant heat and mass exchange process, while

the chilled water is heated.

Basically, the heat and mass transfer between theambient air and the chilled water in a RUWCT depends

on the temperature difference of the two fluids and the

vapor partial pressure difference between the water

droplet surface and the bulk air. Fig. 2 illustrates sche-

matically the heat and mass transfer process between the

bulk air and the bulk water in a RUWCT.

It is assumed that the bulk air and the bulk water are

separated by two films: the air film and the water film.

The two films are further separated by the plane aa0

(Fig. 2). Sensible heat transfers from the air film to the

surface aa0, and then to the water film, which is driven

by the temperature difference between the air and thewater, (taÀtw). Water vapour, and hence latent heat,

transfer between the air and the water is by diffusion of

water vapour, driven by the water vapour pressure dif-

ference between the air film and the bulk air (waÀwi).

4. The development of the method

As discussed, there are a number of differences in the

heat and mass transfer characteristics between a stan-

dard water cooling tower and a RUWCT. Although the

methodologies for evaluating the thermal performance

of standard water cooling towers have been well estab-

lished, it is necessary that appropriate revisions to the

methodologies should be introduced when they are to be

Fig. 1. Air cooling process by direct contact with the chilled water in a counter-flow RUWCT shown in a psychrometric chart.

Fig. 1. Proce de de refroidissement d’air par contact direct avec l’eau refroidie dans une RUWCT a ` e coulement a ` contre-courant : dia-

gramme psychrome trique.




applied to a RUWCT. The method developed and

reported in this paper is based on the well-known

Merkel’s equation for standard water cooling towers.

For standard water cooling towers, the Merkel’s

equation is

dha

ha À hs

¼amdV

Gð1Þ

This was derived under the assumption that the water

side heat transfer resistance in a water cooling tower can

be neglected and the interface temperature, ti, is

approximately equal to tw. Therefore hs, the enthalpy of

saturated air at the interface, is evaluated at tw.

However, for RUWCT application, as discussed ear-

lier, the water side heat transfer resistance is significant

and cannot be neglected, so that ti6¼tw; and hs should be

evaluated at the interface temperature, ti. Therefore, the

first revision introduced to Eq. (1) is to replace hs by hi

dha

ha À hi

¼amdV

Gð2Þ

It is assumed that the interface temperature, ti, is an

algebraic average of the bulk air temperature and thebulk water temperature i.e. ti ¼ 1

2ðta þ twÞ:

This was initially based on the earlier discussion of

equal heat transfer resistance in both water- and air-

films in Norman’s experiments. A further detailed

analysis based on heat and mass transfer across the

interface, as shown in the Appendix, indicated such an

assumption is of acceptable accuracy[11].

The second revision introduced is that dha in Eq. (2) is

evaluated by

dha ¼LC w

GF dtw ð3Þ

where

F ¼ 1 ÀC wtwdL

Gdha

ð4Þ

F is a correction factor that accounts for the increase

of chilled water flow rate at the bottom of a counter-

flow RUWCT, and is derived as follows.

A schematic diagram of a counter-flow RUWCT that

has a plastic film packing of H height, and is divided into n

sections is shown in Fig. 3. Under steady, adiabatic flow

conditions, for a differential control volume dV (Fig. 3)

within the RUWCT, energy conservation requires

Fig. 2. An indicative schematic diagram of heat and mass transfer between bulk air and bulk water in a RUWCT.

Fig. 2. Sche ma du transfert de chaleur et de masse entre l’air en vrac et l’eau en vrac dans une RUWCT.

Fig. 3. A schematic diagram of a counter-flow RUWCT.

Fig. 3. Sche ma d’une RUWCT a ` e coulement a ` contre-courant.




Gdha ¼ C wd twLð Þ ð5aÞ

or

Gdha ¼ LC wdtw þ C wtwdL ð5bÞ

The second item on the right-hand side of Eq. (5b) isnormally omitted in the analysis of standard water

cooling towers. However, in a RUWCT, the chilled

water flow rate change, dL, resulting from condensation

of water vapor in moist air, cannot be neglected. Divid-

ing both sides of Eq. (5b) by Gdha, and making the

right-hand side of the new equation to be the correction

factor, F

LC wdtw

Gdha

¼ 1 ÀC wtwdL

Gdha

¼ F ð6Þ

Eq. (4) can be manipulated to

F ¼ 1 ÀC wtwðr0 þ hwÞdL

ðr0 þ hwÞGdha

ð7Þ

Given that the latent and the total heat transfer are

given by dQb=hvdL=(r0+hw)dL and dQT=Gdha, and

let =dQb/dQT, Eq. (4) becomes

F ¼ 1 ÀC wtwdQ

ðr0 þ hwÞdQT

¼ 1 À C wtw

r0 þ C wtw

ð8Þ

By definition, is the ratio of latent heat transfer to

the total heat transfer, which varies from plane to plane

inside the tower. It also varies with different tower con-

figurations and operational conditions of a RUWCT.However, for a particular RUWCT under a specific

operating condition, an averaged can be used in order

to simplify the analysis of a RUWCT.

As discussed in the last section, the latent heat trans-

fer is expected to be significantly lower in a RUWCT

than that in a standard water cooling tower. The intro-

duction of here makes it possible to quantify the

degree of reduction of latent heat transfer in a RUWCT.

Eq. (2) can be solved by using the revised Tchebycheff

quadrature method and using manufacturer’s data of a

specific tower [12].

Integrating both sides of Eq. (2) givesð dha

ha À hi

¼amV

Gð9Þ

The left-hand side of Eq. (9) is the dynamic char-

acteristics of tower (DCT), and the right-hand side of

Eq. (9) is the fill characteristics (FC), amV G

; a unique

Fig. 4. The schematic diagram for a desuperheater heat recovery system with a RUWCT.

Fig. 4. Sche ma d’un syste `me a ` de srchauffeur avec re cupe ration de chaleur avec une RUWCT.




characteristic of a specific tower. FC is the function of

L/G, expressed by

amV

G¼ C ð

L

GÞÀXN ð10Þ

where C and XN are constants [12, 13]. Using themanufacturers rating data, Eqs. (9) and (10) can be

solved using two different normal operating conditions

to determine the values of C and XN for a specific

RUWCT.

If the values of x are available either from tower man-

ufacturers or by experiments, Eqs. (2)–(10) can be used

together in an iterative process to calculate the outlet

water temperature tw,n, with the available inlet air states,

dry air flow rate, inlet chilled water temperature and flow

rate, etc. With an initial guess for tw,n, the calculation of

the FC and the DCT can proceed until convergence. The

convergence criteria applied in the calculation is

FC À DCT

FC

40:001 ð11Þ

If the criteria cannot be met in a calculation cycle, a

new guess of tw,n should be used and a new DCT is cal-

culated. Then the iterative procedure is repeated until

Eq. (11) can be satisfied. After the values of tw,n are

obtained, the extracted heat capacity, QA, and the out-

let air temperature, ta,n, can also be determined.

5. Field experimental work

Field experimental work has been carried out in a

chiller plant for a hotel building in a sub-tropical region

in China. The results of the field experimental work

helped obtain the values of , and demonstrated also

that the method developed is of an acceptable accuracy

for the performance evaluation of a RUWCT.

A water chiller of 116.3 kW (100,000 kcal/h) total

cooling capacity, which was retrofitted with a desuper-

heater, supplied both space cooling chilled water and

service hot water to the hotel building. The desuper-

heater, a shell-and-tube heat exchanger with appropriateinsulation, was installed outside the chiller. A standard

water cooling tower, which worked as a RUWCT, was

connected to chilled water loop in parallel with the fan

coils. This RUWCT was operated when necessary.

The schematic diagram of the experimental site is

shown in Fig. 4. Part of chilled water from the chiller

was pumped into the RUWCT for extracting heat from

the warm humid ambient air. With the extra heat source

from the operation of RUWCT, the desuperheater heat

recovery system can supply service hot water con-

tinuously to guestrooms in colder seasons, without

requiring any other backup heating provisions.

During the period of field measurements, outdoor

weather conditions varied. Measurements at five differ-

ent outdoor air dry-bulb temperatures were taken: 11.8,

15.2, 17.5, 21.7, 25.5C. Under each outdoor air dry-bulb

temperature, the supply chilled water flow rate to the

RUWCT was manually varied in order to obtain per-

formance data at different operating conditions. Fivedifferent chilled water flow rates were manually set:

1.48, 2.22, 2.96, 3.70 and 4.44 l/s.

To determine the actual values of at each chilled

water flow rate under a specific outdoor air temperature,

the measured air humidity ratio (from measured air dry-

and wet-bulb temperature) at the tower exit was com-

pared with the calculated air humidity ratio under an

initially assumed value. The value of could be mod-

ified and the comparison repeated until the measured

and calculated air humidity ratios were equal. The same

procedures were repeated for each chilled water flow

rate at a specific outdoor temperature to obtain the values at all operating conditions.

With the availability of values of , the outlet chilled

water temperature tw,n, and the total heat exchange QA

Table 1

Comparison of the measured and calculated results

Tableau 1

Comparaison des re sultats des mesures et calcule s

tdb twb tw,n tw,n0 Á QA QA0 Á

C C – C C C kW kW kW

L=1.48 l/s 11.8 10.7 0.39 8.7 8.93 0.23 10.5 10.16 0.3415.2 13.5 0.37 10.0 10.58 0.58 21.1 19.20 1.90

17.5 16.6 0.43 12.5 12.93 0.43 36.3 33.31 2.99

21.7 20.7 0.53 17.6 16.02 1.58 51.3 52.93 1.63

25.5 23.5 0.48 18.3 18.37 0.07 74.2 70.25 3.95

L=2.22 l/s 11.8 10.7 0.43 8.6 8.86 0.26 13.8 12.72 1.08

15.2 13.5 0.37 9.8 10.38 0.58 26.3 24.21 2.09

17.5 16.6 0.45 12.4 12.47 0.07 45.3 42.88 2.42

21.7 20.7 0.56 17.0 15.51 1.49 66.3 67.93 1.63

25.5 23.5 0.48 17.9 17.54 0.36 93.8 91.75 2.05

L=2.96 l/s 11.8 10.7 0.46 8.4 8.80 0.40 16.5 15.00 1.50

15.2 13.5 0.38 9.7 10.29 0.59 30.4 28.69 1.71

17.5 16.6 0.48 12.4 12.18 0.22 50.2 51.10 0.90

21.7 20.7 0.58 16.4 15.55 0.85 79.6 77.31 2.29

25.5 23.5 0.50 17.5 17.37 0.13 108.8 106.46 2.34

L=3.70 l/s 11.8 10.7 0.41 8.5 8.84 0.34 17.7 16.30 1.4

15.2 13.5 0.38 9.5 10.45 0.95 31.2 30.38 0.82

17.5 16.6 0.50 12.9 12.26 0.64 60.2 55.78 4.42

21.7 20.7 0.60 16.5 16.16 0.34 84.9 79.68 5.22

25.5 23.5 0.55 17.6 17.63 0.03 125.3 116.93 8.37

L=4.44 l/s 11.8 10.7 0.46 8.8 9.05 0.25 17.7 15.97 1.73

15.2 13.5 0.40 9.6 10.60 1.00 35.0 31.83 3.17

17.5 16.6 0.50 13.0 12.74 0.26 56.2 55.14 1.06

21.7 20.7 0.60 16.8 16.40 0.40 90.1 83.15 6.95

25.5 23.5 0.58 17.8 18.39 0.41 128.1 117.11 10.99






7. Conclusions

This paper reports on a study of the heat and mass

transfer characteristic in a RUWCT for heat recovery

purpose. The differences in heat and mass transfer process

taking place in a RUWCT, a spray room and a standard

water cooling tower have been identified. A method bywhich the heat and mass transfer characteristics in a

counter-flow RUWCT can be evaluated has been devel-

oped. This was done by introducing to the Merkel’s

Equation for standard water cooling towers the revi-

sions that account for the identified differences in heat

and mass transfer between a water cooling tower and a

RUWCT. Field experimental results from a RUWCT

installed in a sub-tropical region in China indicated that

the method developed could be used to evaluate the

thermal performance of RUWCT with an acceptable

accuracy.

The introduction of is important in developing theevaluation method. The values obtained from the field

experimental work confirmed that the latent heat

exchange is reduced in a RUWCT.

The research work reported in this paper provides a

fundamental basis for studying heat and mass transfer

characteristics in a RUWCT. However, considering that

the current work was based on field experiments, further

experimental work in a controlled environmental labora-

tory is highly recommended, in order to have an

improved accuracy of analysis of the heat and mass

transfer characteristics in a RUWCT.

Acknowledgements

The fund from The Hong Kong Polytechnic Uni-

versity to support the project is gratefully acknowledged.

Appendix I The calculation of water-air interface tem-

perature ti based on heat and mass transfer across the

interface.

Based on the principle of energy conservation, heat

transferred from air should be equal to the heat obtained

by water, as in Fig. A1.

dQ ¼ hvdzdmð1Þ ðA1Þ

ordQ

dz¼ hvdm

dQ ¼ kdt

d ydzð1Þ ðA2Þ

or

dQ

dz¼ k

dt

d y

then

hvdm ¼ kdt

d yðA3Þ

The following approximations can be used in solving

Eq. (A3).

dt ffi Át ¼ ti À tw

Dy ffi droplet radius=2

where the droplet diameter is 2.8 mm, so dy=0.7Â10À3

m [14]. dm is determined by the following equation for

the rate of water vapor transfer from the air to the

interface

Gdw ¼ dL ¼ amðwa À wiÞdV ðA4Þ

dm ¼dL

amdV ¼ ðwa À wiÞ ðA5Þ

Therefore; hvðwa À wiÞ À kti À tw

d y¼ 0 ðA6Þ

where wi =f(ti ) and hv ffir0.

The mass transfer coefficient was determined [15]

¼

aC aLe ; where Le ¼ 1; and

a ¼Nul

D; where D is hydraulic diameter; D ¼ 1:0 ðmÞ

Nu ¼ 0:023Re0:8Pr0:3; where Re ¼uD

v

and u ¼CMS

s¼

CMS

D2

4

¼4CMS

D2m=sð Þ

Fig. A1. An indicative diagram of the interface between air

and water.

Fig. A1. Sche ma de l’interface entre l’air et l’eau.




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A Method for Evaluating the Heat and Mass Transfer