air-side performance of a wavy-ﬁnned-tube direct expansion ... benha... · air-side performance...

International Journal of Refrigeration 30 (2007) 230e244www.elsevier.com/locate/ijrefrig

Air-side performance of a wavy-finned-tube directexpansion cooling and dehumidifying air coil

A.S. Huzayyin, S.A. Nada*, H.F. Elattar

Mechanical Engineering Department, Benha High Institute of Technology, Benha 13512, Egypt

Received 26 February 2006; received in revised form 16 July 2006; accepted 30 July 2006

Available online 27 October 2006

Abstract

Airside heat and mass transfer and fluid flow characteristics of a wavy-finned-tube direct expansion air coil under cooling anddehumidifying condition have been experimentally investigated. Experiments were carried out to study the effects of operatingconditions such as: air temperature, air relative humidity, air face velocity, and evaporator pressure on the airside performance(cooling capacity, dehumidification capacity, pressure drop, and heat transfer coefficient) of the coil. Charts for coil wet con-ditions, partially wet or totally wet, were conducted to identify the coil wet conditions in terms of the operating conditions. Twotechniques, enthalpy potential method and equivalent dry-bulb temperature method, were used to analyze the data and to deducecorrelations for Colburn factors for the different coil wet conditions. Comparison between the correlations predictions of the twotechniques was presented.� 2006 Elsevier Ltd and IIR. All rights reserved.

Keywords: Air conditioning; Evaporator; Finned tube; Experiment; Heat transfer; Mass transfer; Humid air; Pressure drop

Performance cote air d’un tube ondule a ailettes dans le serpentind’un systeme a detente directe en application refroidissement

Mots cles : Conditionnement d’air ; Evaporateur ; Tube ailete ; Experimentation ; Transfert de chaleur ; Transfert de masse ; Air humide ;

Chute de pression

1. Introduction

Finned tube heat exchangers are widely used in a varietyof applications of air-conditioning, refrigeration and processindustry. Air coil is an example of finned tube heat

* Corresponding author. Tel.: þ2012 1723182; fax: þ2013

3230297.

E-mail address: [email protected] (S.A. Nada).

0140-7007/$35.00 � 2006 Elsevier Ltd and IIR. All rights reserved.

doi:10.1016/j.ijrefrig.2006.07.023

exchangers. Generally, air coils consist of tubes throughwhich water, oils, or refrigerants are forced to flow insidethe tubes while air is directed across the tubes. Since the dom-inate heat transfer resistance is usually on the air-side, usingenhanced finned surface on this side is very common to effec-tively improve overall heat transfer performance. Air coils,heating or cooling, are usually employing different finned-tube configurations. Extensive investigations have been per-formed for wavy-finned-tube air coils under air-side dry con-dition to study the effects of the fins geometrical parameters

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231A.S. Huzayyin et al. / International Journal of Refrigeration 30 (2007) 230e244

Nomenclature

A Area (m2)Af fins heat transfer surface area (m2)Afr coil air frontal flow area (m2)Amin minimum air flow area (m2)Ao total coil surface area (m2)At tubes heat transfer outer surface area (m2)Cpa specific heat of moist air (Cpa¼ Cpdaþu Cpv)

(J kg�1 K�1)Cpa,i specific heat of moist air at coil inlet

(J kg�1 K�1)Cpa,o specific heat of moist air at coil outlet

(J kg�1 K�1)Cpda specific heat of dry air (J kg�1 K�1)Cpv specific heat of water vapour (J kg�1 K�1)CPW parameter defined for partially wet condition by

Eq. (11) (dimensionless)CW parameter defined for totally wet condition by

Eq. (5) (dimensionless)Dh coil hydraulic diameter (Dh¼ 4Ld Amin/Ao) (m)Gmin maximum air mass velocity based on minimum

flow area (kg m�2 s�1)h heat transfer coefficient (W m�2 K�1)how total heat transfer coefficient (airewater film

heat transfer), calculated based on enthalpypotential difference method (W m�2 K�1)

hpw heat transfer coefficient under partially wetcondition (calculated based on EDT method)(W m�2 K�1)

htw heat transfer coefficient under totally wet con-dition (calculated based on EDT method)(W m�2 K�1)

hw heat transfer coefficient under wet condition(calculated based on enthalpy potentialmethod) (W m�2 K�1)

i enthalpy (J kg�1)ia,i enthalpy of moist air at coil inlet (J kg�1)ia,o enthalpy of moist air at coil outlet (J kg�1)is enthalpy of saturated air at tube surface temper-

ature (J kg�1)J Colburn factor (dimensionless)Jpw Colburn factor under partially wet conditions (cal-

culated based on EDT method) (dimensionless)Jtw Colburn factor under totally wet condition (cal-

culated based on EDT method) (dimensionless)Jw Colburn factor under wet conditions (cal-

culated based on enthalpy potential method)(dimensionless)

kf thermal conductivity of fin material(W m�1 K�1)

kw thermal conductivity of condensate water film(W m�1 K�1)

Ld coil depth (m)M parameter defined by Eq. (7) (m�1)_ma air mass flow rate (dry air) (kg s�1)_mcond rate of water condensate (kg s�1)Pevap evaporator gauge pressure (Pa)Pr Prandtl number (dimensionless)DPcoil air pressure drop across the coil (Pa)_Q rate of heat transfer (W)RHa,i air relative humidity at coil inlet

(dimensionless)Re Reynolds number based on hydraulic diameter

(Re¼GmaxDh/m) (dimensionless)ri radius from tube center to fin base (m)ro radius from tube center to fin tip (m)St stanton number (St¼ h/(GmaxCpa

))(dimensionless)

Ta,dew air dew point temperature (�C)Ta,i air dry-bulb temperature at coil inlet (�C)Ta,o air dry-bulb temperature at coil outlet (�C)Ta,ie equivalent air inlet dry-bulb temperature (�C)Tavf average fin temperature (�C)Tftip fin tip temperature (�C)Tftipc critical temperature to differentiate partially

wet and totally wet modes (�C)Ts tube surface temperature (�C)DT air temperature drop across coil

(DT¼ Ta,o� Ta,i) (�C)Va,i air coil face velocity (m s�1)wa,i humidity ratio of moist air at coil inlet

(kgv kga�1)

wa,i humidity ratio of moist air at coil outlet(kgv kga

�1)

Greek symbolshf,pw partly wet fin efficiency (dimensionless)hf,tw totally wet fin efficiency (dimensionless)hfw wet fin efficiency (dimensionless)d fin thickness (m)f parameter defined by Eq. (8) (dimensionless)m dynamic viscosity (N s m�2)

and number of tubes rows on the coil performance [1e8].Relatively, researches on cooling and dehumidifying air coilsare quite limited due to the complication of simultaneous heatand mass transport of the moist air over the coil surface. Most

of these studies [9e16] have been conducted onplate-finned tube chilled water coils. Similar study has beencarried out by Theerakulpisut and Priperm [17] for plate-finned tube direct expansion air coil. Effects of fins

232 A.S. Huzayyin et al. / International Journal of Refrigeration 30 (2007) 230e244

geometrical parameters and number of tube rows on fluidflow and heat transfer characteristics were the aim of thesestudies. Very limited researches on the performance ofwavy-finned-tube cooling and dehumidifying chilled waterair coils are available. Mirth and Ramadhyani [18,19] havecarried out experimental and numerical works, respectively,to predict the performance of five samples of wavy-finned-tube chilled water cooling coils under dry and wet conditions.Later Lin et al. [20] carried out an experimental study on theairside performance of herringbone wavy-finned-tube aircoils in wet conditions. Correlations of Nusselt numberwere developed.

Traditionally, air coils under dehumidification conditionare analyzed by the enthalpy potential difference approachassuming that the entire coil surface is covered by a vapourcondensate layer of uniform thickness [21]. However, underdifferent operating conditions, the coil surface may have threedifferent modes of wet conditions. These modes are totallywet, partially wet and totally dry coil surface conditions.When the air dew point temperature is equal to or greaterthan the fins tip temperature, all fins and tube surfaces are wet-ted and the coil becomes under a totally wet condition. Whenthe air dew point temperature lies between the fins tip temper-ature and the tube surface temperature (fins base temperature),only part of fins surfaces are wetted and the coil becomes undera partially wet condition. When the air dew point temperatureis smaller than the tube surface temperature (fins base temper-ature) no condensation occurs and the coil is under a totally drycondition. Fig. 1 shows these different modes on the Psychro-metric chart. Basically, fins performance depend on the fin wetconditions; dry, totally wet or partially wet fins [22e25]. Thusa large error is expected if the coil is analyzed by the enthalpypotential difference approach without distinguish between thedifferent coil wet conditions modes. More recently, Wang andHihara [26] have described a new method, equivalent dry-bulbtemperature (EDT) method, to predict the airside coil perfor-mance under dry, partially wet and totally wet cooling

Totally dry

Partially wet

Totally wet

1

2

2

1

1

1e2e3

Critical fin

state Totally

wet

Totally dry

Partially wet

Tftipc

Ta,ie

Dry bulb temperature, oC

Hu

mid

ity

ra

tio

, g

v/k

ga

Ts

2

Fig. 1. Different cooling modes.

conditions. In this method, an equivalent dry process, process1ee2ee3 (for the partially wet condition as an example) withidentical cooling capacity of the actual process, process1e2e3, is assumed (see Fig. 1). Doing this, the heat transfercharacteristics of the coil were analyzed based on the temper-ature difference (T1e� Ts). Different equations for predictingfin surface efficiency were used in the analysis of the differentcoil wet conditions. Wang and Hihara [26] have used thismethod (EDT) to predict the heat and mass transfer rates andthe coil wet conditions of previous experimental data ofplain-finned tube coils which have been analyzed by theenthalpy potential method.

The present literature review reveals that most of the pre-vious investigations have not studied the effects of the oper-ating conditions (air temperature, air relative humidity, andevaporator pressures) on the airside performance of the cool-ing and dehumidifying coils. Moreover, most of the previousinvestigations analyzed the heat transfer characteristics ofthe cooling and dehumidifying coils using the enthalpypotential method without distinguish between the differentcoil wet conditions. In addition to that, most of these studieswere carried out on plain-finned-tubes chilled water coils.Investigations on direct expansion wavy-finned tube air coilsare very limited. Therefore, the present study aims to studythe effects of the operating conditions (air temperature, airrelative humidity, air velocity, and evaporator pressure) onthe airside performance of a direct expansion wavy-finnedtube air cooling and dehumidifying coil using R134a as arefrigerant. The operating conditions were chosen to obtaindifferent coil wet conditions (partially wet or totally wet).The equivalent dry-bulb temperature method was used tocharacterize the heat transfer for each coil wet condition.Moreover, the traditional enthalpy potential differencemethod was used to characterize heat transfer for all dataas an aim to evaluate and compare the two methods.

2. Experimental setup and procedure

2.1. Experimental setup

The experimental setup is shown schematically inFig. 2a. It consisted of three sections: wind tunnel, refriger-ation circuit, and tested air coil. The tunnel was an opencircuit, delivery type rectangular duct of 390 mm(width)� 335 mm (height) and had an overall length of5130 mm. Air was forced through the tunnel using upstreamvariable speed centrifugal fan. The fan was connected to thediverging section of the tunnel through a flexible section toavoid noise and vibration of wind tunnel. The tunnel wallswere thermally insulated by 1-inch thick glass wool insula-tion. The air, delivered from the fan, flow through the follow-ing tunnel sections: heating section, humidification section,mixing and turbulence eliminating sections and test coil sec-tion. The heating and humidification sections were used toadjust the air temperature and humidity at the coil entrance


Test coil

Digital thermo hygrometres

R134aREFRIGERATION

UNIT

wet bulb sensor Drain

Stopwatch

Outlet air

Thermocouple grid

220 V, 50 HZ

Variac

220 V, 50 HZWater heater supply

(9 Nos. of 3 kW, each)

Steam boilerDigital pressure

manomiters

Thermocouple grid

A

220 V, 50 HZAir heater supply

(3 Nos. of 3 kW, each)

Dims. in mm

Globe valve

Flexible connection

Centrifugal fan

Inlet air

390

Section A-A

DAQsystem

Extension wirs

Straightener A

Mixer

Personalcomputer

335

Steam distributorOrifice Galvanized

steel

Glass wool, 1 in thickness

Variac

Coil outlet thermocouple

Expansion inlet thermocouple

Upstream wet thermocouple

Down stream wet thermocouple

Fin tip thermocouples

Down stream thermocouple grid

Ambient dry thermocouple

Upstream thermocouple grid

Coil inlet thermocouple

Ambientwet thermocouple

108 fin,fin coller point

in this way

304.8

Refrigerant in

1

65.988Refrigerantout

9.525

20.64

Wavy fins

11.112

Dims. in mm

2

Supportwall

Top view

Front view Right side view

22.475

6.5

1

17°

2.82

22.

683

9.525 0.13

97

Thermocouples distribution

(a)

(b) (c)

Fig. 2. (a) Schematic diagram of experimental setup and thermocouples distribution, (b) test coil views, and (c) geometry of wavy fins.

to the required value. The heating section consisted of threeelectric heaters; each had a power of 3 kW. Each heater wasmade from 3 m steel bare of 8.5 mm diameter and formed inserpentine shape. The heaters were in staggered arrangementto cover the entire duct cross section area. The intermediateheater was connected to a variac to smoothly control the airtemperature. The humidification section consisted of fiveparallel vertical aluminum tubes (diameter¼ 16 mm), eachtube had 38 holes of 2 mm diameter uniformly distributedalong and around the axis and circumference of the tube.The tubes were connected to an aluminum header (diameter¼ 25 mm) from each side. Humidifier dimensions were cho-sen to cover the entire cross section of the tunnel to obtainuniform humidity distribution. Steam was supplied to the

humidifier from an electrical boiler that had nine electricalheaters, 3 kW each. The rate of steam flowing through thehumidifier was controlled by mean of a globe valve andalso by controlling the power input to the electric boiler.The mixing and turbulence eliminating section was used toassure uniform air velocity and properties through thewind tunnel cross section at coil entrance. A flow straight-ener consisting of three layers of mesh screen was placeddown stream the mixing section to eliminate the flowturbulences.

The test coil was a wavy-finned tube air coil of304.8 mm� 228.6 mm face area and had three tubesrows in staggered arrangement (see Fig. 2b). The geome-try and configurations of the wavy fins with respect to the


coil tubes are shown in Fig. 2c. The physical data of thetest coil are given in Table 1. Refrigerant 134a, originallycoming from the refrigeration circuit, passes inside thetubes of the coil, while air coming from the tunnel passesthrough the fins of the air coil in cross flow arrangementwith the coil tubes. A basin with a collecting and measur-ing tank was placed under the air coil to collect and mea-sure the condensate drain.

A refrigeration circuit was used to supply refrigerantR134a to the air coil. The main components of the refrigera-tion circuit were reciprocating compressor, oil separator, aircooled condenser, liquid receiver, filter and liquid indicators,heat exchanger, automatic expansion valve, back pressureregulator, suction line accumulator and evaporator (testedair coil). Further details of the experimental set up are givenin Elattar [27].

2.2. Measuring instruments and calibration method

Measuring instruments were used to measure the physi-cal quantities which are necessary to study the coil perfor-mance. As shown in Fig. 2a, two groups of thermocouples,each contains nine thermocouples, were used to measurethe air temperatures (dry-bulb) distributions through thewind tunnel cross sections just upstream and downstream

Table 1

Coil geometric parameters

Coil dimensions

Coil face width 304.8 mm

Coil face height 228.6 mm

Coil deep 65.989 mm

Coil face area 0.06968 m2

Coil actual flow area 0.041395 m2

Coil total external surface area 3.2621 m2

Tubes specifications

Number of tube rows 3

Number of tubes in each row 9

Tube material Copper

Tube arrangement Staggered

Length of straight tube 304.8 mm

Transverse tube spacing 22.475 mm

Longitudinal tube spacing 25.715 mm

Outside tube diameter 9.525 mm

Inside tube diameter 8.712 mm

Fins specifications

Type Wavy

Material Aluminum

Thickness 0.1397 mm

Collar diameter 9.8044 mm

Number 108

Pitch 9 fins/inch

Wavelength 6.5 mm

Wave height 1 mm

Corrugation angle 17�

the coil. Two other thermocouples (placed in continuouslywetted cotton bulb) were used to measure the air wet bulbtemperatures just upstream and downstream the coil.Another eleven thermocouples were used to measure thecoil surface temperatures at different locations: the refriger-ant inlet and exit pipes of the coil, fins tips, the refrigerantpipe surface at the entrance of the expansion device andthe surface of the coil tube (five thermocouples were at-tached on coil tubes surfaces). Two other thermocoupleswere used to measure the ambient dry and wet bulb temper-atures. All thermocouples were 0.5 mm K-type (ChromeleAlumel). All thermocouples were connected to a dataacquisition system and a PC through extension wire to recordthermocouples readings. The thermocouples were calibratedusing standard thermometer of accuracy�0.2 �C. An orificemeter with a digital differential pressure manometer withaccuracy �0.1 Pa was used to measure the air flow rate bymeasuring the pressure drop across the orifice. The orificemeter was calibrated by measuring the air velocity distribu-tion through the tunnel cross section using a hotwire ane-mometer and at the same time recording the pressure dropacross the orifice. Equal area traverses method was used tocalculate the average air velocity over the duct cross sectionarea and consequently the air flow rate. The air pressuredrop across the coil was measured by another digital dif-ferential pressure manometer with accuracy �0.1 Pa. Twodigital Thermo Hygrometers of measuring ranges (5e98%RH) with resolution (�0.1% RH) were used to measurethe air relative humidity just upstream and downstreamthe coil. Six pressure gauges of different ranges wereused to indicate the refrigerant pressure at inlets and out-lets of the compressor, the condenser, and the evaporator.Another pressure gauge was used to indicate the boilerpressure.

2.3. Experimental conditions

The ranges of the test variables used in this study were:

Air inlet temperature 20e30 �C

Air inlet relative humidity 40e95%

Frontal air velocity 0.5e1.5 m s�1

Evaporator gauge pressure 308e377 kPa.

3. Data reduction

The airside performance of the test coil was measured bythe dimensionless Colburn factor (J) that characterizes theairside heat transfer coefficient. The heat transfer ratethrough the coil surface and the dehumidification capacitywere calculated from the measurements of the air propertiesjust upstream and downstream the coil as follows

_Q¼ _maðia;i � ia;oÞ ð1Þ

_mcond ¼ _maðua;i �ua;oÞ ð2Þ


In the analysis of the present data, two techniques wereused to calculate the airside heat transfer coefficient. Thefirst one is the conventional enthalpy potential method tech-nique (Threlkeld [21]). The second technique, recently pre-sented by Wang and Hihara [26], is the equivalent dry-bulbtemperature technique (EDT).

3.1. Enthalpy potential method

In analyzing the data using the enthalpy potentialmethod, the total heat transfer coefficient was calculatedfrom Eqs. (3)e(5) [21]

_Q¼ how

CwCpa

�Asþ hf;w Af

�ðia;i � isÞ; ð3Þ

how ¼1�

1

hwCw

þ yw

kw

� ð4Þ

Cw ¼di=dT

Cpa

at T ¼ Tavf ð5Þ

In Eq. (4), the condensate film thickness, yw, was assumed0.127 mm as recommended by many previous investigators[12,21,23,26]. The wet fin efficiency was calculated by Eqs.(6)e(8) that recommended by many previous investigations(see Hong and Webb [23] and Wang and Hihara [26]).

hf;w ¼tanhðMrifÞcosð0:1MrifÞ

Mrifð6Þ

M ¼�

2hwCw

kfd

�0:5

ð7Þ

f¼�

ro

ri

� 1

��1þ 0:35 ln

�ro

ri

��ð8Þ

In Eq. (8), the fin area served by each tube was assumed to beequivalent in performance to a flat circular-plate fin of equalarea [23].

3.2. Equivalent dry-bulb temperature (EDT) method

According to the air dew point temperature relative to thecoil surface temperature distribution, two different coil wetconditions were obtained in the present experiments; namelytotally wet and partially wet coil conditions. Totally wetoccurred when the air dew point temperature was equal toor greater than the fins tip temperature, i.e. Tadew� Tftip. Par-tially wet conditions occurred when the air dew point temper-ature lies between the fins tip temperature and the fins basetemperature, i.e. Ts< Tadew< Tftip. Since Tadew, Ts and Tftip

depend on the operating conditions (air temperature, airrelative humidity, air Reynolds number and evaporatorpressure), the existence of a partially wet or totally wet condi-tion depends on these operating conditions. Therefore, mea-surements of Tadew, Ts and Tftip in each experiment were

used to determine if the operating conditions of this experi-ment give partially wet or totally wet condition. After the de-termination of the coil wet conditions to all experiments,cooling mode charts were conducted. Fig. 3 shows the coolingand dehumidification mode charts obtained from the presentexperimental data. As shown in Fig. 3, totally wet conditionsprobably occur at high relative humidity and air temperaturesand low evaporator pressures and air velocities.

EDT method was proposed by Wang and Hihara [26] tocalculate the heat transfer coefficients under totally wet andpartially wet coil conditions. To simplify the analysis anddeduce correlations which can be used directly to predictthe coil performance of a direct expansion coils in termsof the evaporator pressure, the tube surface temperaturewas considered to be uniform and equal to the saturationtemperature of the refrigerant. The heat transfer coefficientsfor totally wet and partially wet coil conditions were calcu-lated from Eqs. (9) and (10), respectively [26].

_Q¼ htw

�At þ hf;twAf

�ðTa;ie � TsÞ ð9Þ

_Q¼ hpw

�At þ hf;pwAf

�ðTa;ie � TsÞ ð10Þ

where, Ta,ie is the equivalent dry-bulb temperature of inletstate (see Fig. 1). The fin efficiency at totally wet conditionis calculated from Eqs. (6)e(8) and hw in Eq. (7) is replacedby htw. Also the fin efficiency under partially wet conditionsis calculated from Eqs. (6)e(8) and hw in Eq. (7) is replacedby hpw and Cw in Eq. (7) is replaced by Cpw that defined asfollow [26].

Cpw ¼ 1:0þ�

Cw� 1

Ta;ie � Tftipc

�ðTa;ie� Ta;iÞ ð11Þ

where Tftipc is the temperature of the projection of the criticalfin state on the constant enthalpy line that pass by state 1(see Fig. 1).

The Colburn factor (J) is the main parameter that charac-terizes the airside heat transfer coefficient in a dimensionalform. It was calculated by Eqs. (12) and (13)

J ¼ StPr2=3 ð12Þ

St ¼ h

GmaxCpa

ð13Þ

where, (h and J) is (hw and Jw) in the analysis of the enthalpypotential method and are (htw and Jtw) and (hpw and Jpw) inthe analysis of the EDT method for totally wet and partiallywet conditions, respectively.

A computer program was developed to solve Eqs.(1)e(13) to find the J factor (using both of enthalpy potentialmethod and EDT method). Eqs. (1)e(13) can be put on theform J¼ f(x1, x2, x3,.,xn) where (x1, x2, x3,.,xn) are themeasured parameters. The errors in the measurements ofthese parameters were �0.2 �C for any temperature mea-surements, �0.1 Pa for pressure measurements, �0.1% for


0.4 0.6 0.8 1RHa,i

0.4

0.8

1.2

1.6

2

v a,i (

m/s

)

0.4 0.6 0.8 1RHa,i

0.4

0.8

1.2

1.6

2

v a,i (

m/s

)

0.4 0.6 0.8 1RH

0.4

0.8

1.2

1.6

2

v (m

/s)

0.4 0.6 0.8 1RHa,i

0.4

0.8

1.2

1.6

2

v a,i (

m/s

)

0.4 0.6 0.8 1RHa,i

0.4

0.8

1.2

1.6

2v a

,i (m

/s)

0.4 0.6 0.8 1RHa,i

0.4

0.8

1.2

1.6

2

v a,i (

m/s

)

Totally wet zone

Partially wet zone

Totally wetPartially wet

Pevap

= 308 kPa (Ts=1.388

o

C)

Totally wet zone

Totally wet zone

Partially wet zone

Pevap

= 308 kPa (Ts=1.388

o

C)

Partially wet zone

Pevap

= 308 kPa (Ts=1.388

o

C)

Pevap

= 377 kPa (Ts=7.167

o

C)

Partially wet zone

Pevap

= 377 kPa (Ts=7.167

o

C)

Partially wet zone

Pevap

= 377 kPa (Ts=7.167

o

C)

Partially wet zone

Totally wet zone

Totally wet zone

Totally wet zone

(a)

(b)

(c)






Fig. 3. Cooling modes charts. (a) Ta,i¼ 20 �C, (b) Ta,i¼ 25 �C, and (c) Ta,i¼ 30 �C.


relative humidity measurements and �0.008 m s�1 for airvelocity measurements. The uncertainty in J due to theuncertainties of these parameters can be calculated fromEq. (14) that was given by Holman and Gajda [28].

DJ

J¼��

vJ

vx1

Dx1

J

�2

þ�

vJ

vx2

Dx2

J

�2

þ/þ�

vJ

vxN

DxN

J

�2�1=2

ð14Þ

where vJ=vxi was calculated by numerical differentiationusing the developed computer program. The minimum andmaximum uncertainty in Jw, Jtw, and Jpw for all the datawere found to be (5.5 and 9.5%), (2 and 4%), and (2.5 and9%), respectively.

4. Results and discussions

The results of the present work were presented to inves-tigate the effects of the operating conditions: air coil facevelocity, air relative humidity, air temperature and evapora-tor pressure on coil performance and characteristics. In thefirst part of this section, the effects of the operating condi-tions on the temperature drop across the coil, the coil dehu-midification capacity and the pressure drop across the coilwere presented and investigated. In the second part, the ef-fects of the operating conditions on the heat and mass trans-fer characteristics were analyzed and discussed.

4.1. Effect of operating conditions on cooling anddehumidification capacities and pressure drop

4.1.1. Effects of air inlet relative humidityFig. 4aec shows the variation of the cooling capacity

(DT), dehumidification capacity ð _mcondÞ and the air pressuredrop across the coil (DPcoil), respectively, against the air inletrelative humidity with the air coil face velocity as a parameterfor Ta,i¼ 20 �C and Pevap¼ 308 kPa (curves for other Ta,i andPevap are given in Elattar [27]). Fig. 4a shows that, for any airface velocity, DT significantly decreases with increasing theair inlet relative humidity. The trend is same for all evaporatorpressures and air temperatures (see Elattar [27]). This trendcan be attributed to the increase in the motive force of watervapour diffusion with the increase of the air relative humidityand this increases the number of water vapour molecules con-densing on the tubes and fins surfaces. This increases the ther-mal resistance of the condensate layer. The increase of thethermal resistance of the condensate layer reduces the fins ef-ficiency and this leads to a high fin and tube surface temper-ature and in consequently a high air exit temperature. This issupported by the results of Wang et al. [12] and Hong andWeb [23] that showed the decrease of fin efficiency with in-creasing inlet air relative humidity.

Fig. 4b shows the increase of the dehumidification capac-ity ð _mcondÞ with increasing the air relative humidity for anyair face velocity. This can be attributed to the increase ofthe vapour pressure of the air. Increasing the vapour pressure

0.4 0.6 0.8 1RHa,i

0.4 0.6 0.8 1RHa,i

0.4 0.6 0.8 1RHa,i

0

4

8

12

16

ΔT (o C

)

Va,i= 1.5 m/sVa,i= 1.25 m/sVa,i= 1 m/sVa,i= 0.75 m/sVa,i= 0.5 m/s

0

0.0005

0.001

0.0015

0.002

0.0025

mco

nd (k

g/s)

0

40

80

120

160

ΔPco

il (Pa

)

(a)

(b)

(c)



•

Fig. 4. Effect of RHa,i and Va,i on DT, _mcond and DPcoil (Ta,i¼ 20 �Cand Pevap¼ 308 kPa). (a) Effect on temperature drop across the

coil, (b) effect on coil dehumidification capacity, and (c) effect

on air pressure drop across the coil.


increases the potential of water vapour transfer to the cool-ing surface and this increases the dehumidifying capacity.The trend is the same for different evaporator pressuresand air temperatures (see Elattar [27]).

Fig. 4c shows the increase of the air pressure drop acrossthe coil with increasing the air relative humidity. The trend isthe same for all air temperatures, air face velocities and evap-orator pressures (see Elattar [27]). Increasing the air relativehumidity increases the rate of water vapour condensationand this increases the area of the wet portions of coil surfaceand also increases the thickness of the condensate film formedon fins and tubes surfaces. These lead to higher surface rough-ness at the air coil interface and thinner free flow area of the air.Both cause the increase of the air pressure drop across the coil.

4.1.2. Effects of air coil face velocityFig. 4aec shows also the effect of the air coil face velocity

on the cooling capacity, dehumidification capacity and thepressure drop across the coil, respectively, for Ta,i¼ 20 �Cand Pevap¼ 308 kPa (curves for other Ta,i and Pevap are givenin Elattar [27]). As shown in Fig. 4a, DT decreases with in-creasing the air face velocity. The trend is the same for allair temperatures and evaporator pressures. This trend canbe attributed to the increase of air bypass across the coil sur-faces with increasing air flow rate. Increasing the coil bypassfactor increases the air outlet temperature. In contradictory,increasing the air face velocity increases the rate of heattransfer between the air contact to the coil and the coil sur-face. This leads to the decrease of the outlet air temperaturebut this reduction in the temperature cannot overcome onthe increase of the air exit temperature due to the increaseof the air bypass factor.

Fig. 4b shows the increase of the dehumidification capac-ity with increasing the coil face velocity. This can be attrib-uted to the following: (1) increasing the air velocity increasethe rate of mass transfer between the air and the coil surfaceand this increases the dehumidification capacity, and (2) in-creasing the air face velocity increases the process of renew-ing the air that in contact to the coil surface and this causesan increase in the dehumidification capacity. The trend isthe same for all air temperatures and evaporator pressures(see Elattar [27]).

Fig. 4c shows the increase of the air pressure drop acrossthe coil with increasing the air face velocity. This can be at-tributed to the following: (1) increasing the air face velocityincreases the shear stress between the air and the coil surfaceand this significantly increases the pressure drop across thecoil, and (2) as shown in Fig. 4b, increasing the air coilface velocity increases the dehumidification rate and thisincreases the pressure drop across the coil.

4.1.3. Effects of air inlet temperatureThe effects of the air inlet temperature on the dehumidifi-

cation capacity, cooling capacity, and the air pressure dropacross the coil are shown in Fig. 5aec, respectively, for air

face velocity, and evaporator pressures of 1 m s�1, and308 kPa, respectively. As shown in Fig. 5a and b, the dehumid-ification capacity increases and the cooling capacity decreasesas the air inlet temperature increases. This can be attributed to

0.4 0.6 0.8 1RHa,i

0.4 0.6 0.8 1RHa,i

0.4 0.6 0.8 1RHa,i

0

0.0005

0.001

0.0015

0.002

0.0025

mco

nd (k

g/s)

Ta,i= 30 oC

Ta,i= 25 oC

Ta,i= 20 oC

0

4

8

12

16

ΔT (º

C)

0

40

80

120

160

ΔPco

il (P

a)

(a)

(b)

(c)

Ta,i= 30 oC

Ta,i= 25 oC

Ta,i= 20 oC

Ta,i= 30 oC

Ta,i= 25 oC

Ta,i= 20 oC

•

Fig. 5. Effect of air temperature on (a) dehumidification capacity,

(b) temperature drop across the coil, and (c) air pressure drop

across coil, at Va,i¼ 1 m s�1 and Pevap¼ 308 kPa.


the increase of water vapour pressure with the increase of theair temperature for the same inlet relative humidity. Increasingthe vapour pressure increases the potential difference thatcause vapour transfer between air and coil surface and this in-creases the dehumidification capacity. Increasing the dehu-midification capacity increases the latent heat transfer on theaccount of the sensible heat transfer and this causes a reductionin the air temperature drop across the coil. These results areconsistent with the result of the theoretical analysis of Lianget al. [25] that showed the increase of the water condensationrate and the decrease of the air temperature drop across thecoil with the increase of the air inlet temperature. Fig. 5c showsthat the air temperature has approximately no effect on the airpressure drop across the coil.

4.1.4. Effects of evaporator pressureFig. 6aec shows the effect of the evaporator pressure on

the dehumidification capacity, cooling capacity and the airpressure drop across the coil for air velocity and air temper-ature of 1 m s�1 and 20 �C, respectively. As shown in Fig. 6aand b, the dehumidification and the cooling capacitiesincrease as the evaporator pressure decreases. This can beattributed to the decrease of the coil apparatus dew pointwith the decrease of evaporator pressure. This is consistentwith the results of the theoretical analysis of Liang et al.[25] that showed the increase of the coil air outlet tempera-ture and the decrease of the water condensate rate with theincrease of the coil saturation temperature. Fig. 6c showsthat the evaporator pressure has approximately no effecton the air pressure drop across the coil.

4.2. Heat transfer characteristics

Fig. 7 shows the variations of hw, Jw, Jtw and Jpw againstRe with RHa,i as a parameter for Ta,i¼ 20 �C and Pevap¼308 kPa (curves for other Ta,i and Pevap are given in Elattar[27]). As shown in the figure, for the entire range of Re, hw,Jw, Jtw and Jpw decrease with increasing the air relative hu-midity. The trend is the same for all evaporator pressures andair temperatures (see Elattar [27]). This trend can be attrib-uted to the increase of the condensation rate with increasingthe air relative humidity and this leads to higher fin and tubesurface temperatures as a result of the increase of thermal re-sistance of the condensate layer and in consequently the de-crease of the fins efficiency. Higher fin and tube surfacetemperatures lead to a lower heat transfer rate and in conse-quently a lower heat transfer coefficient and Colburn factor.

Fig. 7 also shows the increase of the heat transfer coeffi-cient and the decrease of the Colburn factor with increasingRe. The trend is the same for all evaporator pressures, airtemperatures and relative humidity. The increase of theheat transfer coefficient with Re can be attributed to the in-crease of the heat transfer rate as a result of the increase ofthe air flow momentum. The decrease of the Colburn factorcan be investigated based on the definition of the Colburnfactor (Eqs. (12) and (13)). Increasing Re increases both of

the heat transfer coefficient and the mass flux. The increaseof the Colburn factor due to the increase of the heat transfercoefficient cannot overcome on the decrease of the Colburnfactor due to the increase of the mass flux. This is supported

0.4 0.6 0.8 1

0.4 0.6 0.8 1

0.4 0.6 0.8 1

0

0.0004

0.0008

0.0012

0.0016

mco

nd (k

g/s)

0

4

8

12

ΔT (o C

)

RHa,i

RHa,i

RHa,i

0

40

80

120

160

ΔPco

il (P

a)

Pevap= 308 kPa (Ts=1.388 ºC)Pevap= 377 kPa (Ts=7.167 ºC)



(a)

(b)

(c)

•

Fig. 6. Effect of evaporator pressure on (a) dehumidification capac-

ity, (b) temperature drop across coil, and (c) air pressure drop

across coil, at Va,i¼ 1 m s�1 and Ta,i¼ 20 �C.


RHa,i= 50%

RHa,i= 70% RHa,i= 90%

Totally wet

ReDh

0

0.002

0.004

0.006

0.008

0.01

J pw

Partially wet

200 400 600 800 1,000 1,200ReDh

0

0.01

0.02

0.03

0.04

0.05

h w (k

W/m

2 .K)

200 400 600 800 1,000 1,200ReDh

0

0.002

0.004

0.006

0.008

J w

200 400 600 800 1,000 1,200 200 400 600 800 1,000 1,200ReDh

0

0.002

0.004

0.006

0.008

J tw

(a)

(b)

RHa,i= 50%

RHa,i= 70%

RHa,i= 50% RHa,i= 60% RHa,i= 70%

RHa,i= 90%

RHa,i= 85%

RHa,i= 90% RHa,i= 95%

Fig. 7. Effect of RHa,i and Re on (a) hw and Jw, and (b) Jtw and Jpw (Ta,i¼ 20 �C at Pevap¼ 308 kPa).

by the results of Wang et al. [13] and Wang and Hihara [26]which showed the decrease of Colburn factor under dehu-midification conditions with increasing Re.

The effects of the air inlet temperature on hw, Jw, Jtw andJpw are shown in Fig. 8 for specific values of RHa,i and Pevap

(curves for other RHa,i and Pevap are given in Elattar [27]). Asshown in Fig. 8, the Colburn factor slightly decreased as theair inlet temperature increased from 20 to 25 �C and it signif-icantly decreased as the air inlet temperature increased from25 to 30 �C. The trend was the same for all Reynolds num-bers, air relative humidity and evaporator pressures. Thistrend can be attributed to the increase of the air inlet enthalpywith increasing the air inlet temperature for the same air inletrelative humidity. This causes an increase in (ia,i� is) and(Ta,ie� Ts) which leads to a lower heat transfer coefficientsand Colburn factors (see Eqs. (3), (9) and (10)).

Fig. 9 shows the effect of the evaporator pressure on hw,Jw, Jtw and Jpw for different Reynolds numbers and at certainrelative humidity and air temperature (curves for other RHa,i

and Ta,i are given in Elattar [27]). As shown in Fig. 9, theColburn factor decreases with decreasing the evaporatorpressure. The result is the same for all Reynolds numbers,relative humidity and air temperatures. This trend can beattributed to the decrease of the apparatus dew point withthe decrease of the evaporator pressure. Decreasing thecoil apparatus dew point causes an increase in (ia,i� is)and (Ta,ie� Ts) and also an increase in the dehumidificationcapacity and these lead to a lower heat transfer coefficientand consequently lower Colburn factor.

The variation of the Colburn J factors, calculated fromenthalpy potential method and EDT method, with Re,RHa,i, Ta,i and Ts are correlated as follows:

1. Enthalpy potential method

J ¼ 0:029Re�0:232RH�0:35a;i

�Ta;i � Ts

Ts

��0:18

ð15Þ


200 400 600 800 1,000 1,200

ReDh

200 400 600 800 1,000 1,200

ReDh

0

0.01

0.02

0.03

0.04

0.05

h w (k

W/m

2 .K)

Ta,i= 20 oCTa,i= 25 oC

Ta,i= 30 oC

0

0.002

0.004

0.006

0.008

J w

200 400 600 800 1,000 1,200

ReDh

0

0.002

0.004

0.006

0.008

J tw

200 400 600 800 1,000 1,200

ReDh

0

0.002

0.004

0.006

0.008

J pw

Partially wetTotally wet

(a)

(b) (c)


Ta,i= 30 oC


Ta,i= 30 oC


Ta,i= 30 oC

Fig. 8. Effect of air inlet temperature on hw, Jtw and Jpw at Pevap¼ 308 kPa. (a) RH¼ 70%, (b) RH¼ 90%, and (c) RH¼ 50%.

Eq. (15) is correlated for data in the ranges:300� Re� 1050, 50%�RH� 95%, 20 �C� Ta,i� 30 �Cand 1.388 �C� Ts� 7.167 �C.

2. EDT method; totally wet mode

Jaw ¼ 0:044Re�0:29RH�0:45a;i

�Ta;i � Ts

Ts

��0:17

ð16Þ

3. EDT method; partially wet mode

Jpw ¼ 0:029Re�0:24RH�0:57a;i

�Ta;i � Ts

Ts

��0:21

ð17Þ

Eqs. (16) and (17) are correlated for the data that lie in thetotally wet and partly wet regions that were shown in Fig. 3,respectively. Comparison between the predictions of Eqs.(15), (16) and (17) and the present experimental data areshown in Fig. 10aec, respectively. Regression analysisshowed that Eqs. (15)e(17) predict all the experimental

data within errors of �21.6, �17.48, and �15.5% and pre-dict 80% of the experimental data within �14.23, �10.37and �9.13%, respectively.

4.3. Evaluation and comparison of enthalpy potentialand ETD method

From the discussion of Sections 4.1 and 4.2, we can con-clude that: (1) in the enthalpy potential method, an unique cor-relation for the Colburn factor was proposed for all operatingconditions, while for EDT method, two correlations are pro-posed, differentiated with respect to the wetting conditions;this gives an advantages of the enthalpy potential methodover the EDT method, (2) it is obvious that the correlations pre-dicted from the EDT method get closer to the experimentaldata; this gives an advantage of the EDT method over the en-thalpy potential method, and (3) the EDT method requires thedetermination of the wetting conditions corresponding to thecoil operating conditions from the cooling mode chart; this


200 400 600 800 1,000 1,200 200 400 600 800 1,000 1,200ReDh ReDh

0

0.02

0.04

0.06

0.08

h w (k

W/m

2 .K)

Pevap= 308 kPa (Ts=1.388 oC)


0

0.002

0.004

0.006

0.008

0.01

J w

200 400 600 800 1,000 1,200ReDh

0

0.002

0.004

0.006

0.008

0.01

J tw

200 400 600 800 1,000 1,200ReDh

0

0.002

0.004

0.006

0.008

0.01

J pw

Totally wet Partially wet

(a)

(b) (c)







Fig. 9. Effect of evaporator pressure on hw, Jtw and Jpw at Ta,i¼ 20 �C. (a) RH¼ 70%, (b) RH¼ 90%, and (c) RH¼ 60%.

gives disadvantages of the EDT method. Therefore, using thecooling modes chart (Fig. 3) to determine the cooling modesfor a specified operating conditions and then using the correla-tion deduced from EDT method gives accurate value of J thanusing a correlation deduced from the enthalpy potentialmethod. On the other hand if the cooling mode chart is notavailable, a correlation deduced from the enthalpy potentialmethod can be used to predict the heat transfer coefficientwith larger but acceptable error.

5. Comparison with previous work

As shown in Section 4.2, the Colburn J factor dependson the operating conditions. Also it is known from theliterature review that the Colburn J factor depends on thecoil geometrical parameters. To the author’s knowledgeno experimental works about the performance of wavy-finned-tube D-X cooling and dehumidifying coil underthe geometric and operating conditions of the present study

are available on the open literature. Moreover, using theEDT method to measure the performance of the coolingcoils under different coil wetting conditions have notbeen used until now. Therefore, quantitative comparisonof the present work with previous works is difficult. How-ever, the trend of Jw of the present data can be compared inFig. 11 with the trends of the data of Halici et al. [15],Wang et al. [13] and Wang et al. [29]. In these studieschilled water cooling and dehumidifying coils were used.As shown in the figure, all trends show the decrease ofJw with increasing Reynolds number. Also the figure showsthat the data of Halici et al. [15] and Wang et al. [13] aresignificantly higher than the present data while the data ofWang et al. [29] is closer to the present data. This may beattributed to that the work of Halici et al. [15] and Wanget al. [13] were carried out on a flat-plate-finned tubecoil, while the work of Wang et al. [29] was carried outon a wavy-finned tube air coil, as the present study butfor different coil geometrical parameters.


200 400 600 800 1,000 1,200ReDh

ReDh

0

0.004

0.008

0.012

0.016

200 400 600 800 1,000 1,2000

0.004

0.008

0.012

0.016

J w*R

Ha,

i0.35

* ((T

a,i-T

ref)/

T ref

)0.18

J w*R

Ha,

i0.45

* ((T

a,i-T

ref)/

T ref

)0.17

J pw*R

Ha,

i0.57

* ((T

a,i-T

ref)/

T ref

)0.21

ReDh200 400 600 800 1,000 1,200

0

0.004

0.008

0.012

0.016

Exp dataCorrelation

(a)

(b)

(c)

Exp dataCorrelation

Exp dataCorrelation

Fig. 10. Predictions of Eqs. (15)e(17). (a) Eq. (15), (b) Eq. (16),

and (c) Eq. (17).

6. Summary and conclusions

An experimental investigation of the airside perfor-mance of a wavy-finned-tube direct expansion air coil un-der dehumidification condition using R134a asa refrigerant was presented. The effects of the air inletPsychrometric properties (air inlet temperature and air in-let relative humidity), Reynolds number and the coilpressure on the heat/mass transfer and the pressuredrop characteristics were investigated. The results showedthat: (1) the air temperature drop across the coil de-creases with increasing the air inlet relative humidity,the air coil face velocity, and the air inlet temperature,(2) the dehumidification capacity increases with increas-ing the air inlet relative humidity, the coil face velocity,and the air inlet temperature and decreases with increas-ing the evaporator pressure, and (3) the pressure dropacross the coil increases with increasing both of the airinlet relative humidity and the coil face velocity andwas insensitive to the air inlet temperature and the coilpressure. The airside thermal performance of the coilwas analyzed using two different techniques; the enthalpypotential method and the equivalent dry-bulb temperature(EDT) method. In the first technique, the Colburn J fac-tor under wet condition was calculated regardless the coilwet conditions (partially wet or totally wet), while in thesecond technique, cooling and dehumidification modescharts were firstly proposed to classify the data to twogroups; group for totally wet coil condition data andgroup for partially wet coil condition data. The ColburnJ factor for each group was calculated using differentmethod of analysis. The two techniques showed thatthe Colburn J factor decreases with increasing Re, rela-tive humidity and air inlet temperature. Correlations forthe Colburn J factor using enthalpy potential and EDTanalysis methods were developed in terms of Reynoldsnumber, air inlet relative humidity, air inlet temperature

200 400 600 800 1,000 1,200

ReDh

0

0.004

0.008

0.012

0.016

0.02

J w

Halici et al. [15] Wang et al. [13]Wang et al. [29]Present correlation

Fig. 11. Comparison of present results with previous works.


and refrigerant saturation temperature. The analysisshowed that the prediction of the EDT method is closerto the experimental data than the prediction of the en-thalpy potential method.

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