Simultaneous Heat and Mass Transfer Characteristics for Wavy Fin-And-tube Heat Exchangers Under Dehumidifying Conditions

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Simultaneous heat and mass transfer characteristicsfor wavy fin-and-tube heat exchangers under

dehumidifying conditions

Worachest Pirompugd a, Somchai Wongwises a,*, Chi-Chuan Wang b

a Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Laboratory (FUTURE),

Department of Mechanical Engineering, King Mongkuts University of Technology Thonburi,

Bangmod, Bangkok 10140, Thailandb Energy and Resources Laboratory, Industrial Technology Research Institute, Hsinchu 310, Taiwan, ROC

Received 3 February 2005; received in revised form 8 May 2005Available online 3 October 2005

Abstract

The present study proposes a new reduction method to calculate the heat and mass transfer characteristics of thewavy fin-and-tube heat exchangers under dehumidifying conditions. For fully wet conditions, the sensible heat transferand mass transfer characteristics are relatively insensitive to the inlet relative humidity. The heat and mass transfer per-formances show appreciable influence of fin spacing at 1-row configuration. Both the heat and mass transfer perfor-mances increase when the fin spacing is reduced. However, the difference becomes less noticeable when ReDc > 3000.

For 1-row configuration, larger wave height shows much larger difference with the fin spacing. However, the effectof inlet conditions and geometrical parameters on the heat and mass performance becomes less significant with the riseof number of tube rows. Test results show that the heat and mass transfer analogy is roughly applicable (the ratios ofhc,o/hd,oCp,a are in the range 0.61.1, and is insensitive to change of fin spacing). The correlations are proposed todescribe the heat and mass transfer characteristics. These correlations can describe 94.19% of the jh factors within15% and 83.72% of the jm factors within 15%. Correspondingly, 93.02% of the ratios of hc,o/hd,oCp,a are predictedby the proposed correlation within 15%. 2005 Elsevier Ltd. All rights reserved.

Keywords: Wavy fin-and-tube heat exchangers; Dehumidifying; Heat transfer; Mass transfer

1. Introduction

The plate fin-and-tube heat exchangers are the mostwidely used heat exchangers in association with the

application of air-conditioning and refrigeration sys-tems. The heat exchangers can be used for condenserswhere surface is dry and evaporators in which surfacemay be wet provided the fin temperature is below thedew point temperature. In regard to the wet surface,simultaneous heat and mass transfer occurs along thefin surfaces. In general, the complexity of the moist airflow pattern across the fin-and-tube heat exchangersunder dehumidifying conditions makes the theoretical

0017-9310/$ - see front matter 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijheatmasstransfer.2005.05.043

* Corresponding author. Tel.: +66 2 470 9115; fax: +66 2 4709111.

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

International Journal of Heat and Mass Transfer 49 (2006) 132143

www.elsevier.com/locate/ijhmt
mailto:[email protected]:[email protected]


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Nomenclature

Af surface area of fin, m2

A0 total surface area, m2Ap,i inside surface area of tubes, m

2

Ap,o outside surface area of tubes, m2

b0p slope of the air saturation curved betweenthe outside and inside tube wall tempera-ture, J kg1 K1

b0r slope of the air saturation curved betweenthe mean water temperature and the insidewall temperature, J kg1 K1

b0w;m slope of the air saturation curved at themean water film temperature of the finsurface, J kg1 K1

b0w;p slope of the air saturation curved at themean water film temperature of the tubesurface, J kg1 K1

Cp,a moist air specific heat at constant pressure,J kg1 K1

Cp,w water specific heat at constant pressure,J kg1 K1

Dc tube outside diameter (include collar), mDi tube inside diameter, m

fi in-tube friction factors of waterF correction factorGmax maximum mass velocity based on minimum

flow area, kg m2 s1

hc,o sensible heat transfer coefficient, W m2 K1

hd,o mass transfer coefficient, kg m2 K1

hi inside heat transfer coefficient, W m2

K1

ho,w total heat transfer coefficient for wet exter-nal fin, W m2 K1

I0 modified Bessel function solution of the firstkind, order 0

I1 modified Bessel function solution of the firstkind, order 1

i enthalpy, kJ kg1

ia air enthalpy , kJ kg1

ia,in inlet air enthalpy, kJ kg1

ia,m mean air enthalpy, kJ kg1

ia,out outlet air enthalpy, kJ kg1

ig saturated water vapor enthalpy, kJ kg1

im mean enthalpy, kJ kg1

ir,in saturated air enthalpy at the inlet water tem-perature, kJ kg1

ir,m mean saturated air enthalpy at the meanwater temperature, kJ kg1

ir,out saturated air enthalpy at the outlet watertemperature, kJ kg1

is,fm saturated air enthalpy at the fin mean tem-perature, kJ kg1

is,fb saturated air enthalpy at the fin base tem-perature, kJ kg1

is,p,i,m mean saturated air enthalpy at the mean

inside tube wall temperature, kJ kg

1

is,p,o,m mean saturated air enthalpy at the meanoutside tube wall temperature, kJ kg1

is,w saturated air enthalpy at the water filmtemperature, kJ kg1

is,w,m mean saturated air enthalpy at the meanwater film temperature of the fin surface,kJ kg1

jh ChiltonColburn j-factor of the heat trans-fer

jm ChiltonColburn j-factor of the mass trans-fer

K0 modified Bessel function solution of thesecond kind, order 0

K1 modified Bessel function solution of thesecond kind, order 1

kf thermal conductivity of fin, W m1K1

ki thermal conductivity of water, W m1K1

kp thermal conductivity of tube, W m1K1

kw thermal conductivity of water film,W m1K1

Lp tube length, m_ma air mass flow rate, kg s

1

_mw water mass flow rate, kg s1

N number of tube rowsP pressure, PaPd wave height, m

Pl longitudinal tube pitch, mPr Prandtl numberPt transverse tube pitch, m_Q heat transfer rate, W_Qa air side heat transfer rate, W_Qavg average heat transfer rate, W_Qtotal total heat transfer rate, W_Qw water side heat transfer rate, W

R ratio of heat transfer characteristic to masstransfer characteristic

RH relative humidityri distance from the center of the tube to the

fin base, mro distance from the center of the tube to the

fin tip, mReDi Reynolds number based on inside diameterReDc Reynolds number based on outside diameter

(include collar)Sc Schmidt numberSp fin spacing, mTa air temperature, KTw water temperature, KTw,m mean temperature of the water film, KTp,i,m mean temperature of the inner tube wall, K

W. Pirompugd et al. / International Journal of Heat and Mass Transfer 49 (2006) 132143 133


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simulations very difficult. Hence, most of the publishedwork is resorted to experimentation.

For better improvement of the overall performanceof fin-and-tube heat exchangers, the fin surface can bein the form of enhanced surfaces such as wavy, louver,and slit. The wavy fin surface is one of the most popularsurfaces for it can lengthen the flow path and disturb theair flow without considerable increase of pressure drop.The air-side performance of wavy fin-and-tube heat ex-changer had been studied by many researchers [17].Even though many efforts have been devoted to thestudy of the wet-coils, the available literature on thedehumidifying heat exchangers still offers limited infor-mation to assist the designer in sizing and rating a fin-and-tube heat exchanger. This can be made clear fromthe reported data were mainly focused on the study ofthe sensible heat transfer characteristics, little attention

was paid to the mass transfer characteristics. Therefore,the objective of the present study is to provide furthersystematic experimental information relevant to themass transfer performance and propose a new reduction

method to determine the air-side performance of fin-and-tube heat exchangers under dehumidifying condi-tions. The effects of inlet relative humidity, fin spacing,and the number of tube rows on the mass transfer char-acteristics are examined in this study.

2. Experimental apparatus

The schematic diagram of the experimental air circuitassembly is shown in Fig. 1. It consists of a closed-loopwind tunnel in which air is circulated by a variable speedcentrifugal fan (7.46 kW, 10 HP). The air duct is madeof galvanized sheet steel and has an 850 mm 550 mmcross-section. The dry-bulb and wet-bulb temperaturesof the inlet air are controlled by an air-ventilator thatcan provide a cooling capacity up to 21.12 kW (6RT).

The air flow-rate measurement station is an outlet cham-ber setup with multiple nozzles. This setup is based onthe ASHRAE 41.2 standard [8]. A differential pressuretransducer is used to measure the pressure difference

Tp,o,m mean temperature of the outer tube wall, KTr,m mean temperature of water, Kt fin thickness, m

Uo,w wet surface overall heat transfer coefficient,based on enthalpy difference, kg m2s1

V average velocity, m s1

Wa humidity ratio of moist air, kg kg1

Wa,m mean air humidity ratio, kg kg1

Ws,p,o,m mean saturated air humidity ratio at themean outside tube wall temperature,kg kg1

Ws,w saturated air humidity ratio at the water filmtemperature, kg kg1

Ws,w,m mean saturated air humidity ratio at the

mean water film temperature of the fin sur-face, kg kg1

Xf projected fin length, myw thickness of condensate water film, me fin factorgf,wet wet fin efficiencyl dynamic viscosity, N s m2

q mass density, kg m3

Fig. 1. Schematic of experimental set-up.

134 W. Pirompugd et al. / International Journal of Heat and Mass Transfer 49 (2006) 132143


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across the nozzles. The air temperatures at the inlet andexit zones across the sample heat exchangers are mea-sured by two psychrometric boxes based on the ASH-RAE 41.1 standard [9].

The working medium or the tube side is cold water. Athermostatically controlled reservoir provides the coldwater at selected temperatures. The temperature differ-ences on the water side are measured by two precali-brated RTDs. The water volumetric flow rate ismeasured by a magnetic flow meter with a 0.001 L/sprecision. All the temperature measuring probes areresistance temperature devices (Pt100), with a calibratedaccuracy of 0.05 C. In the experiments, only the datathat satisfy the ASHRAE 33-78 [10] requirements,(namely, the energy balance condition, j _Qw _Qavgj=_Qavg, is less than 0.05, where _Qw is the water-side heat

transfer rate for _Qw and air-side heat transfer rate _Qa,are considered in the final analysis. Detailed geometryused for the present plain fin-and-tube heat exchangersis tabulated in Table 1. The test fin-and-tube heatexchangers are tension wrapped having a L type fincollar. The test conditions of the inlet air are as follows:

Dry-bulb temperatures of the air: 27 0.5 CInlet relative humidity for the incoming air: 50% and90%Inlet air velocity: from 0.3 to 3.8 m/s

Inlet water temperature: 7 0.5 CWater velocity inside the tube: 1.51.7 m/s

The test conditions approximate those encountered withtypical fan-coils and evaporators of air-conditioningapplications. Uncertainties reported in the present inves-tigation, following the single-sample analysis proposedby Moffat [11], are tabulated in Table 2.

3. Data reduction

3.1. Heat transfer coefficient (hc,o)

Basically, the present reduction method is based onthe Threlkeld [12] method. Some important reductionprocedures of the original Threlkeld method is describedas follows:

Table 1Geometric dimensions of the sample wavy fin-and-tube heat exchangers

No. Fin thickness (mm) Sp (mm) Xf (mm) Dc (mm) Pd (mm) Pt (mm) Pl (mm) Row no.

1 0.00012 0.00148 4.7625 0.01038 1.18 0.0254 0.01963 12 0.00012 0.00152 4.7625 0.00862 1.58 0.0254 0.02007 13 0.00012 0.00270 4.7625 0.01038 1.18 0.0254 0.01963 14 0.00012 0.00280 4.7625 0.00862 1.58 0.0254 0.02007 1

5 0.00012 0.00342 4.7625 0.00862 1.58 0.0254 0.02007 16 0.00012 0.00351 6.3500 0.00862 1.68 0.0254 0.02627 17 0.00012 0.00157 4.7625 0.00862 1.18 0.0254 0.01963 28 0.00012 0.00305 4.7625 0.00862 1.18 0.0254 0.01963 29 0.00012 0.00159 4.7625 0.00862 1.58 0.0254 0.02007 210 0.00012 0.00300 4.7625 0.00862 1.58 0.0254 0.02007 211 0.00012 0.00152 4.7625 0.00862 1.58 0.0254 0.02007 412 0.00012 0.00158 4.7625 0.00862 1.18 0.0254 0.01963 413 0.00012 0.00302 4.7625 0.00862 1.18 0.0254 0.01963 414 0.00012 0.00295 4.7625 0.00862 1.58 0.0254 0.02007 415 0.00012 0.00145 4.7625 0.01038 1.18 0.0254 0.01963 616 0.00012 0.00153 4.7625 0.00862 1.58 0.0254 0.02007 617 0.00012 0.00270 4.7625 0.01038 1.18 0.0254 0.01963 618 0.00012 0.00294 4.7625 0.00862 1.58 0.0254 0.02007 6

Table 2Summary of estimated uncertainties

Primary measurements Derived quantities

Parameter Uncertainty Parameter Uncertainty ReDc = 400 Uncertainty ReDc = 5000

_ma 0.31% ReDc 1.0% 0.57%_mw 0.5% ReDi 0.73% 0.73%

DP 0.5% _Qw 3.95% 1.22%Tw 0.05 C _Qa 5.5% 2.4%

Ta 0.1 C j 11.4% 5.9%



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The total heat transfer rate used in the calculation isthe mathematical average of _Qa and _Qw, namely,

_Qa _maia;in ia;out 1

_Qw _mwC

p;wTw;out Tw;in 2

_Qavg _Qa _Qw

23

The overall heat transfer coefficient (Uo,w) based on theenthalpy potential is given as follows:

_Qavg Uo;wA0DimF 4

where F is the correction factor accounting for a single-pass, cross-flow heat exchanger and Dim is the meanenthalpy difference for counter flow coil,

Dim ia;m ir;m 5

According to Bump [13] and Myers [14], for the

counter flow configuration, the mean enthalpy differenceis

ia;m ia;in ia;in ia;out

lnia;inir;outia;outir;in

ia;in ia;outia;in ir;outia;in ir;out ia;out ir;in

6

ir;m ir;out ir;out ir;in

lnia;inir;outia;outir;in

ir;out ir;inia;in ir;outia;in ir;out ia;out ir;in

7

The overall heat transfer coefficient is related to theindividual heat transfer resistance [14] as follows:

1

Uo;w

b0rA0

hiAp;i

b0pA0 ln Dc

Di

2pkpLp

1

ho;wAp;o

b0w;pA0

Afgf;wetb0w;mA0

8where

ho;w 1

Cp;ab0w;mhc;o

ywkw

9

yw in Eq. (9) is the thickness of the water film. A con-stant of 0.005 inch was proposed by Myers [14]. In prac-tice, (yw/kw) accounts for only 0.55% compared to(Cp;a=b

0w;mhc;o, and has often been neglected by previous

investigators. As a result, this term is not included in the

final analysis.In this study, we had proposed a more detailed reduc-tion method relative to the conventional lump approach.The proposed method can divide the fin-and-tube heatexchangers into many tiny segments (number of tuberows number of tube passes per row number of fins)as shown in Fig. 2. The tube-side heat transfer coeffi-cient, hi is evaluated from the Gnielinski correlation(Gnielinski, [15]),

hi fi=2ReDi 1000Pr

1:07 12:7ffiffiffiffiffiffiffiffi

fi=2p

Pr2=3 1

ki

Di10

and the friction factor, fi is

fi 11:58lnReDi 3:28

211

The Reynolds number used in Eqs. (10) and (11) is basedon the inside diameter of the tube and ReDi = qVDi/l.In all case, the water side resistance is less than 10% ofthe overall resistance.

In Eq. (8) there are four quantities (b0w;m; b0w;p; b

0p, and

b0r involving enthalpy-temperature ratios that must beevaluated. The quantities of b0p and b

0r can be calculated

as

b0r is;p;i;m ir;mTp;i;m Tr;m

12

b0p is;p;o;m is;p;i;mTp;o;m Tp;i;m13

The values ofb0w;p and b0w;m are the slope of saturated en-

thalpy curve evaluated at the outer mean water film tem-perature at the base surface and the fin surface. Withoutloss of generality, b0w;p can be approximated by the slopeof saturated enthalpy curve evaluated at the base surfacetemperature [16]. The wet fin efficiency (gf,wet) based onthe enthalpy difference is proposed by Threlkeld [12].i.e.,

gf;wet i is;fmi is;fb

14

where is,fm is the saturated air enthalpy at the mean tem-perature of fin and is,fb is the saturated air enthalpy atthe fin base temperature. The use of the enthalpy poten-tial equation, greatly simplifies the fin efficiency calcula-tion as illustrated by Kandlikar [17]. However, theoriginal formulation of the wet fin efficiency by Threl-keld [12] was for straight fin configuration (Fig. 3(a)).For a circular fin (Fig. 3(b)), the wet fin efficiency is [16]

gf;wet 2ri

MTr2o r2i

K1MTriI1MTro K1MTroI1MTri

K1MTroI0MTri K0MTriI1MTro

15

4 3 2 1

number of fins

number of

tube passes per row

1

2

3

4

Cold waterinlet

32

1number of tube rows

Moist air inlet

Fig. 2. Dividing of the fin-and-tube heat exchanger into thesmall pieces.



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where

MT

ffiffiffiffiffiffiffiffiffiffi2ho;w

kft

s16

The test heat exchangers are of Fig. 3(c) configura-

tion. Hence, the corresponding fin efficiency is calculatedby the equivalent circular area as depicted by Wanget al. [16]. Evaluation of b0w;m requires a trial and errorprocedure. For the trial and error procedure, is,w,m mustbe calculated using the following equation:

is;w;m ia;m Cp;aho;wgf;wet

b0w;mhc;o

1 Uo;wA0b0r

hiAp;i

b0p lnDcDi

2pkpLp

24

35

0@

1Aia;m ir;m

17

An algorithm for solving the sensible heat transfercoefficient hc,o for the present row-by-row and tube-by-tube and fin-by-fin reduction method approach is givenas follows:

1. Based on the measurement data, calculate the totalheat transfer rate _Qtotal using Eq. (3).

2. Assume a hc,o for all elements.3. Calculate the heat transfer performance for each seg-

ment with the following procedures.3.1. Calculate the tube side heat transfer coefficient

of hi using Eq. (10).3.2. Assume an outlet air enthalpy of the calculated

segment.3.3. Calculate ia,m by Eq. (6) and ir,m by Eq. (7).3.4. Assume Tp,i,m and Tp,o,m.

3.5. Calculate b0rA0

hiAp;iand

b0pA0 lnDcDi

2pkpLp.

3.6. Assume a Tw,m.3.7. Calculate the gf,wet using Eq. (15).3.8. Calculate Uo,w from Eq. (8).3.9. Calculate is,w,m by Eq. (17).3.10. Calculate Tw,m from is,w,m.3.11. IfTw,m derived in step 3.10 is not equal that is

assumed in step 3.6, the calculation steps 3.7

3.10 will be repeated with Tw,m derived in step3.10 until Tw,m is constant.

3.12. Calculate _Q of this segment.3.13. Calculate Tp,i,m and Tp,o,m from the inside con-

vection heat transfer and the conduction heattransfer of tube and collar.

3.14. IfTp,i,m and Tp,o,m derived in step 3.13 are notequal that is assumed in step 3.4, the calcula-tion steps 3.53.13 will be repeated with Tp,i,mand Tp,o,m derived in step 3.13 until Tp,i,m andTp,o,m are constant.

3.15. Calculate the outlet air enthalpy by Eq. (1) andthe outlet water temperature by Eq. (2).

3.16. If the outlet air enthalpy derived in step 3.15 isnot equal that is assumed in step 3.2, the calcu-lation steps 3.33.15 will be repeated with theoutlet air enthalpy derived in step 3.15 untilthe outlet air enthalpy is constant.

4. If the summation of _Q for all elements is not equal_

Qtotal, hc,o will be assumed a new value and the calcu-lation step 3 will be repeated until the summation of_Q for all elements is equal _Qtotal.

3.2. Mass transfer coefficient (hd,o)

For the cooling and dehumidifying of moist air by acold surface involves simultaneously heat and masstransfer, and can be described by the process line equa-tion from Threlkeld [12]:

diadWa

Ria is;w

Wa Ws;w ig 2501R 18

where R represent the ratio of sensible heat transfercharacteristics to the mass transfer performance,

R hc;o

hd;oCp;a19

However, for the present fin-and-tube heat exchan-ger, Eq. (18) did not correctly describe the dehumidifica-tion process on the psychrometric chart. This is becausethe saturated air enthalpy (is,w) at the mean temperatureat the fin surface is different from that at the fin base. In

(a) (b) (c)

Fig. 3. Type of fin configuration. (a) Straight fin, (b) circular fin, (c) continuous plat fin.

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this regard, a modification of the process line on thepsychrometric chart corresponding to the fin-and-tubeheat exchanger is made. The derivation is as follows:

From the energy balance of the dehumidification one

can arrive at the following expression:

_madia hc;o

Cp;adAp;oia;m is;p;o;m

hc;o

Cp;adAfia;m is;w;m

20

Note that the first term on the right-hand side de-notes the heat transfer for the outside tube part whereasthe second term is the heat transfer for the fin part. Con-servation of water condensate gives

_madWa hd;odAp;oWa;m Ws;p;o;m

hd;odAfWa;m Ws;w;m 21

Dividing Eq. (20) by Eq. (21) yields

diadWa

R ia;m is;p;o;m R e 1 ia;m is;w;mWa;m Ws;p;o;m e 1 Wa;m Ws;w;m

22

where

e A0

Ap;o23

By assuming a value of the ratio of heat transfer tomass transfer, R, and by integrating Eq. (22) with aniterative algorithm, the mass transfer coefficient can beobtained. Analogous procedures for obtaining the masstransfer coefficients are given as

1. Obtain Ws,p,o,m and Ws,w,m from is,p,o,m and is,w,mfrom those calculation of heat transfer.

2. Assume a value of R.3. Calculations is performed from the first element to

the last element, employing the following procedures:3.1. Assume an outlet air humidity ratio.3.2. Calculate the outlet air humidity ratio of each

element by Eq. (22).3.3. If the outlet air humidity ratio obtained from

step 3.2 is not equal to the assumed value ofstep 3.1, the calculation steps 3.13.2 will berepeated.

4. If the summation of the outlet air humidity ratio foreach element of the last row is not equal to the mea-suredoutlet airhumidityratio, assuming a new R valueand the calculation step 3 will be repeated until thesummation of the outlet air humidity ratio of the lastrow is equal to the measured outlet air humidity ratio.

3.3. ChiltonColburn j-factor for heat and mass

transfer (jh and jm)

The heat and mass transfer characteristics of the heatexchanger is presented by the following non dimensionalgroup:

jh hc;o

GmaxCp;aPr2=3 24

jm hd;o

GmaxSc2=3 25

4. Results and discussion

The heat and mass transfer characteristics of the testsamples are in terms of dimensionless parameter jh and

jm, respectively. Test results were first compared withthe original Threlkeld method. The comparison is shownin Fig. 4(a) and (b). For the heat transfer performance,one can see the difference between the original lumpedapproach is in fair agreement with the present discret-ized approach. The mean deviation is 10.7%, the dev-

0

0.01

0.02

0.03

0.04

0.05

0 0.01 0.02 0.03 0.04 0.05

jh (Threlkeld's model)

jh(Presentedmodel)

15%

-15%

(a)

0

0.01

0.02

0.03

0.04

0.05

0 0.01 0.02 0.03 0.04 0.05

jm (Threlkeld's model)

jm(Presentedmodel)

30%

-30%

(b)

Fig. 4. Comparison of jh and jm between those derived by thepresent method and Threlkeld method. (a) Comparison of jhand (b) comparison of jm.



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iations lies in larger tube row at RH = 50% where par-tially dry out occurred on the fin surface. By contrast,for the reduced results of mass transfer performanceby the original Threlkeld method, one can see a much

larger departure relative to the present reduction method(the mean deviation is 22.9%). This is attributed to theoriginal Threlkeld method is more suitable for coun-ter-cross-flow arrangement and the original methodreveals irrational dependence of inlet humidity. Aprevious study by the present authors [18] had shownan analogous trend for the plain fin geometry underdehumidifying conditions.

The heat and mass transfer performance for 1-rowconfiguration subject to the influence of inlet relativehumidity is schematically shown in Fig. 5(a) and (b).As seen in Fig. 5(a), for the same wave height and tube

diameter (samples #1 and #3), one can see the heattransfer performance for small fin spacing is higher thanthat having larger fin spacing. The difference becomesespecially pronounced at low Reynolds number but is

negligible when ReDc is above 3000. Theresults are analo-gous to those tested in fully dry conditions [19]. Thephenomenon can be further explained from the numeri-cal results about the effect of fin pitch on the heat trans-fer performance which was carried out by Torikoshiet al. [20]. They conducted a 3-D numerical investigationof a 1-row plain fin-and-tube heat exchanger. Theirinvestigation shows that the vortex forms behind thetube can be suppressed and the entire flow region canbe kept steady and laminar when the fin pitch is smallenough. Further increase of fin pitch would result in anoticeable increase of cross-stream width of vortex re-gion behind the tube. As a result, lower heat transferperformance is seen for larger spacing. In the meantime,the difference vanishes when ReDc is above 3000, this isattributed to the change of flow pattern into vortexdominated region. Note that their simulations alsoshowed that higher velocity may result in the occurrenceof vortex along the fins, therefore the effect of fin pitchon heat transfer coefficient would be negligible.

In Fig. 5(a), one can also examine the influence ofwave height on the heat transfer performance. At a lar-ger fin spacing (samples #3 and #4), the effect of waveheight on heat transfer performance is relatively small.In fact, for a wide spacing of 2.72.8 mm, the effect ofwave height is negligible whether Pd is 1.18 mm or1.58 mm. Nevertheless, one can see the effect of wave

height on heat transfer performance is rather notewor-thy at a smaller fin spacing (sample #2). The resultsare analogous to those tested in dry conditions [35].Based on the simulation results by Ramadhyani [21]and Jang and Chen [22], Wang et al. [23] pointed outappreciable increase of heat transfer coefficients can beobtained only when the corrugation angle is larger than20. Hence, compared to the present results in wet con-dition, it seems that this finding is still applicable to thetest results under dehumidifying conditions. In Fig. 5(a),the influence of relative humidity on heat transfer per-formance is rather small, the results are in line with pre-vious studies [16,7].

The effect of inlet relative humidity on the masstransfer characteristics is shown in Fig. 5(b). Similarly,the influence of inlet relative humidity is rather smallwhen the fin spacing is sufficiently large (>2.0 mm, sam-ples #3, #5, and #6). However, at a smaller fin spacing(samples #1, #2) one observe a slight decrease of jmwhen the inlet relative humidity is increased from 50%to 90%. The slight decrease of mass transfer perfor-mance with inlet relative humidity at dense fin spacingmay be associated with the condensate retention phe-nomenon. Yoshii et al. [24] conducted a flow patternobservation about the air flow across tube bank, their

ReDc

250 500 750 2500 5000 75001000

jh

.006

.008

.02

.04

.06

.01

#1

#2

#3

#4

#5

#6

#1

#2

#3

#4

#5

#6

RH=0.5RH=0.9

(a)

(b) ReDc

250 500 750 2500 5000 75001000

jm

.006

.008

.02

.04

.06

.01

#1

#2

#3#4

#5

#6

#1

#2

#3

#4

#5

#6

RH=0.5RH=0.9

Fig. 5. Influence of relative humidity on the heat and masstransfer performances vs. ReDc for 1-row configuration. (a)Influence of relative humidity on the heat transfer performanceand (b) influence of relative humidity on the mass transferperformance.



9/12

results indicate the blockage of the tube row by the con-densate retention may hinder the performance of theheat exchangers. Thus one can see a slight drop of masstransfer performance. However, a considerable increase

of mass transfer performance when RH = 0.5 andReDc > 1000 is encountered. This is attributed to theblow-off condensate by flow inertia which makes morezoom for water vapor to condense along the surface.

The aforementioned results are applicable for the 1-row configurations, test results for the 2-rows configura-tion is shown in Fig. 6(a) and (b). For the heat transferperformance shown in Fig. 6(a), one can see the perfor-mance difference is reduced regardless the influences arefrom inlet relative humidity, Pd, or from fin spacing.With the increase of the number of tube rows, the con-densate blow-off phenomenon in the row is blocked by

the subsequent row. In that regard, the influence ofrelative humidity on the mass transfer performancebecomes less profound and is deferred to a even higherReynolds number (ReDc > 2000). Analogous results

(the influence of relative humidity, Pd, and fin spacingon the heat and mass transfer performance) are obtainedwhen the number of tube rows is further increased to 4or 6. The results agree with those reported by Wanget al. [16]. They reported negligible influence of fin pitchand inlet conditions on the heat transfer performance ofa plain fin geometry when N= 4. The decrease of geo-metrical influences on the heat and mass transfer withthe rise number of tube rows can be made more clearfrom a previous flow visualization study using scale-upfin-and-tube heat exchangers [25]. Their flow visualiza-tion experiment shows the injected dye in front of thefirst tube row hits the round tube and twists and swirlsto the subsequent row. A clear horseshoe vortex isshown in front of the tube. The strength of the verticalmotion is apparently stronger near the first row whencomparing to the second and third row. The strengthof swirled motion decays markedly with increasingrow. As a consequence, the associated influences ofgeometries becomes less profound.

The dehumidifying process involves heat and masstransfer simultaneously, if mass transfer data areunavailable, it is convenient to employ the analogy be-tween heat and mass transfer. The existence of the heatand mass analogy is because the fact that conductionand diffusion in a liquid are governed by physical lawsof identical mathematical form. Therefore, for air-water

vapor mixture, the ratio of hc,o/hd,oCp,a is generallyaround unity, i.e.

hc;o

hd;oCp;a% 1 26

The term in Eq. (26) approximately equals to unityfor dilute mixtures like water vapor in air near the atmo-spheric pressure (temperature well-below correspondingboiling point). The validity of Eq. (26) relies heavily onthe mass transfer rate. The experimental data of Hongand Webb [26] indicated that this value is between0.7 and 1.1, Seshimo et al. [27] gave a value of 1.1. Eck-els and Rabas [28] also reported a similar value of 1.11.2 for their test results of plain fin-and-tube heatexchangers. The aforementioned studies all showed theapplicability of Eq. (26). In the present study, we noticethat the values of hc,o/hd,oCp,a were generally between0.6 and 1.1 (shown in Fig. 7) which indicates the analogyis roughly applicable. However, the present authorsfound that the analogy is not applicable using the origi-nal Threlkeled method (the ratio is from 0.52.2). Thereare two differences between the original Threlkeld meth-od and the present row-by-row and tube-by-tube ap-proach. Firstly, larger deviation occurs via using theoriginal Threlkeleds methods. This is associated with

ReDc

250 500 750 2500 5000 75001000

jh

.006

.008

.02

.04

.06

.01

#7

#8

#9

#10

RH=0.5RH=0.9

#7

#8

#9

#10

(a)

(b) ReDc

250 500 750 2500 5000 75001000

jm

.006

.008

.02

.04

.06

.01

#7

#8

#9

#10

RH=0.5RH=0.9

#7

#8

#9

#10

Fig. 6. Influence of relative humidity on the heat and masstransfer performances vs. ReDc for 2-row configuration. (a)Influence of relative humidity on the heat transfer performanceand (b) influence of relative humidity on the mass transferperformance.



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the considerable influence of inlet humidity of the origi-nal Threlkelds method whereas for the present reduc-tion method, the ratio is relatively insensitive tochange of inlet humidity provided that the surface isfully wet. Secondly, reduction by the present methodindicates that the ratio of hc,o/hd,oCp,a is slightly de-creased with the rise of Reynolds number whereas theoriginal Threlkeld method shows the opposite trend(slightly increases with the Reynolds number). As afore-mentioned in previous section, with the rise of inlet flow

inertia, the condensate can be easily removed for makingmore room for further condensation. The condensate re-moval becomes even pronounced with smaller fin spac-ing. In that regard, the removal of condensate subjectto larger flow inertia help to improve the mass transferperformance. Therefore, one can see the ratio of hc,o/hd,oCp,a is slightly decreased with the fin spacing. Noticethat the effect of fin spacing on the ratio of hc,o/hd,oCp,ais also insignificant. This is associated with the high airflow rate would increase the vapor shear, and wipe awaythe condensate that leads to increase heat and masstransfer simultaneously. Therefore, the effect of fin spac-ing on the ratio of hc,o/hd,oCp,a is comparatively small.

Based on previous discussions, there is not single

curve that can describe the phenomena for both jh andjm. In that regard, we had performed a multiple regres-sion technique in a practical range of experimental data(300 < ReDc < 4500) to generate design correlations, theappropriate correlation form ofjh and jm for the presentdata are as follows:

jh 0:171e0:377NRe

0:0142N0:478 Dc

Sp

Dc

0:00412N0:0217

A0

Ap;o

0:114N0:440 27

jm 0:315e0:441NRe

0:0580N0:475 Dc

Sp

Dc

0:00471N0:0216

A0

Ap;o

0:00223N0:223 28

hc;o

hd;oCp;a 0:490e0:792NRe

0:0714N0:00361 Dc

Sp

Dc

0:00867N0:0425

A0

Ap;o

0:107N0:203 29

ReDc

250 500 750 2500 5000 75001000

hc,o

/hd,o

Cp,a

.2

.4

.6

.8

2

.1

1

#1

#2

#3

#4

#5

#6

#11

#12

#13

#14

#7

#8

#9

#10

1 Row 2 Rows 4 Rows

Fig. 7. hc,o/hd,oCp,a plotted against ReDc.

0.00

0.01

0.02

0.03

0.04

0.05

0 0.01 0.02 0.03 0.04 0.05

Experimental jh

Correlatedjh

15%

-15%

Fig. 8. Comparison of jh between those derived by correlationand experiment.

0

0.01

0.02

0.03

0.04

0 0.01 0.02 0.03 0.04

Experimental jm

Corr

elatedjm

15%

-15%

Fig. 9. Comparison ofjm between those derived by correlationand experiment.



11/12

As shown in Figs. 810, Eq. (27) can describe 94.19%of jh within 15%, Eq. (28) can describe 83.72% of

jm within 15%, and Eq. (29) can describe 93.02% ofhc,o/hd,oCp,a within 15%.

5. Conclusions

The present study examines the heat and mass trans-

fer characteristics of 18 wavy fin-and-tube heat exchang-ers under dehumidifying conditions. On the basis of theresults and discussions, the following results areconcluded:

1. A new reduction method based on the Threlkeldmethod is proposed in this study for reducing the testresults. For fully wet conditions, the sensible heattransfer characteristic and mass transfer characteris-tic by the present method are relatively insensitiveto the inlet relative humidity.

2. For fully wet conditions having 1-row configuration,the heat transfer performance and mass transfer per-formance shows appreciable influence of fin spacing.

Both the heat transfer performance is increased whenthe fin spacing is reduced. However, the differencebecomes less noticeable when ReDc > 3000. The influ-ence is also related to the wave height, larger waveheight shows much larger difference with the fin spac-ing. Moreover, both jh and jm are comparatively inde-pendent of the fin spacing when the number of tuberows is increased (e.g. N> 2).

3. The effect of inlet conditions and geometrical param-eters on the heat and mass performance becomes lesssignificant with the number of tube rows.

4. The ratio ofhc,o/hd,oCp,a is in the range 0.61.1 and isinsensitive to change of fin spacing.

5. The correlations are proposed for the wavy fin-and-tube heat exchangers. These correlations can describe

94.19% of the jh factors within 15%, can describe83.72% of the jm factors within 15%, and can des-cribe 93.02% of the ratio hc,o/hd,oCp,a of within 15%.

Acknowledgement

The authors are indebted to the Thailand ResearchFund (TRF) and the Energy R&D foundation fundingfrom the Bureau of Energy of the Ministry of EconomicAffairs, Taiwan for supporting this study.

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0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Experimental hc,o/hd,oCp,a

Correlatedh

c,o

/hd,o

Cp,a

15%

-15%

Fig. 10. Comparison of hc,o/hd,oCp,a between those derived bycorrelation and experiment.



12/12

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Simultaneous Heat and Mass Transfer Characteristics for Wavy Fin-And-tube Heat Exchangers Under Dehumidifying Conditions