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Experimental Determination of the Heat TransferCoefficient of a Plate-Fin Heat ExchangerMichel De Paepe a , An Willems a & Alexis Zenner aa Department of Flow, Heat and Combustion Mechanics, Ghent University, UGent, Ghent,BelgiumPublished online: 21 Aug 2006.

To cite this article: Michel De Paepe , An Willems & Alexis Zenner (2005) Experimental Determination of the Heat TransferCoefficient of a Plate-Fin Heat Exchanger, Heat Transfer Engineering, 26:7, 29-35, DOI: 10.1080/01457630590959403

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Heat Transfer Engineering, 26(7):2935, 2005Copyright C Taylor and Francis Inc.ISSN: 0145-7632 print / 1521-0537 onlineDOI: 10.1080/01457630590959403

Experimental Determinationof the Heat Transfer Coefficientof a Plate-Fin Heat Exchanger

MICHEL DE PAEPE, AN WILLEMS, and ALEXIS ZENNERDepartment of Flow, Heat and Combustion Mechanics, Ghent University, UGent, Ghent, Belgium

Heat transfer in compact plate-fin heat exchangers is augmented by the introduction of complex fin patterns in the channels.Kays and London presented a lot of experimental data for several types of fin configurations, and many authors followedtheir example with other types of fins. For some fin types, the heat transfer correlation for the Nusselt number cannot befound in literature. Most of the data are given for large scale model fins in good controlled laboratory environmentslittledata is available for real heat exchangers.

A test rig was constructed at Ghent University to verify the performance of several fin types. Measurements were done on areal heat exchanger and not on a large scale model in order to determine the performance under real operational conditions.

The measurement setup consists of a hot water circuit and an air circuit with a fan. In the heat exchanger, 40 thermocouplesare introduced on the air side and the wall. This way, the convection coefficient of the fins can be determined for a broadrange of Reynolds numbers.

In the paper the measurement set-up is discussed and the measurements are presented. An in depth error analysis isperformed on the measurements. This way a heat transfer correlation is provided with a tight error margin for compactplate-fin air coolers.

INTRODUCTION

Plate-fin heat exchangers are important heat exchangers inindustry. They are often used because of their compactness andtheir high effectiveness. As shown in Figure 1, plate-fin heatexchangers are constructed out of parallel plates (a). In eachchannel created by the plates, thin corrugated plates are inserted(c). These plates are used as fins to enhance the heat transfer.Very different fins can be found, such as straight, wavy, louvered,and corrugated.

Due to the complex geometry and the wide range of fin types,no general correlation to determine the heat transfer in plate-finheat exchangers can be found with good accuracy. For severalfin types, different authors have experimentally determined theheat transfer characteristics. A relation is established betweenthe characteristics of the flow (Re number), geometry, and theheat transfer (Nusselt number or Colburn j factor).

One of the first and generally referenced works is that by Kaysand London [1], who have proposed different correlations in

Address correspondence to Michel De Paepe, Department of Flow, Heat andCombustion Mechanics, Ghent University, Sint-Pietersnieuwstraat 41, B9000UGent, Ghent, Belgium. E-mail: michel.depaepe@UGent.be

graphical form. For louvered fins, an important correlation wasproposed by Davenport [2], and several other authors also referto them [35]. New correlations have been proposed, resultingin a unified form by Chang and Wang [5].

Different experimental techniques are used. Most of them usea large-scale mock-up of a fin channel. The difference in methodis mostly situated in the determining of the surface temperature:it is either measured or kept constant. Earlier experiments usestationary techniques [68]; more recent experiments use tran-sient measurements [4, 9].

In this paper, a real heat exchanger was inserted in a setup.The heat exchanger served as an air cooler for compressors. Theheat transfer correlation was determined with great precision forair flowing over one side of the finned plates and compared withdata found in literature.

The derived correlation can be used to design air coolers withless of a need for oversizing, thus resulting in more cost effectiveheat exchangers. As the measurements were done on a real heatexchanger, the validity of other correlations determined by mockups can be tested.

The presented technique for determining the heat transfercoefficient is relatively simple as it only uses thermocouple

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30 M. DE PAEPE ET AL.

Figure 1 Compact heat exchanger assembly.

measurements, which results in a high degree of precision. Thedeveloped method can be used to test other types of heatexchangers.

EXPERIMENTAL METHOD

Facility

The tested heat exchanger is placed in a test rig consisting ofan open air channel and a closed water cycle. The experimentswere performed on the air side of the heat exchanger.

The air channel (Figure 2) is made of a radial fan (3), a settlingchamber with a honeycomb (4), the actual test section (6) withthe heat exchanger (7), and an orifice plate to measure the airflow rate (9). The fan is driven by a frequency-controlled engine;with this, a flow rate of 0.0560.518 kg/s can be set. To obtaina uniform flow over the heat exchanger, a settling chamber isintroduced, after which the section of the tube is reduced to39.7 cm 19.6 cm to allow the measurement of a central part ofthe heat exchanger. After the heat exchanger, a second straightsection is inserted. In this part, the flow coming from the heatexchanger has time to mix, so a uniform exit temperature canbe measured at the end. Finally, the air flows through a long

Figure 2 Experimental facility.

Figure 3 Water circuit.

tube (8) before entering the orifice plate (9), as described by theinternational standard [10].

The heat exchanger itself is placed in a wooden frame. Itis completely insulated, with 7 cm of PUR foam plates. At thehighest operational temperature, the heat losses were determinedas being only 0.25% of the heat transferred in the heat exchanger.

The water circuit (Figure 3) is made of a water tank (1)with five resistor heaters (7), a circulation pump (2), and severalvalves (3). The pump circulates the water through the heatingvessel in closed circuit. The valve (3b) is a bypass valve. Bycontrolling the valves (3a), (3b), the flow going through the heatexchanger can be set. The water flow rate is measured by anelectronic flow meter (4).

All temperature measurements were done with thermocou-ples, which are read by a scanner and a high precision voltmeter.

Placement of the Thermocouples

K-type thermocouples were inserted in the heat transfer sur-face and into the air channels of the heat exchanger.

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M. DE PAEPE ET AL. 31

The thermocouples placed in the air channels have to beinserted without obstructing the main flow passage. They areplaced along the water channels and are bent with the heads intothe channels. They are kept in place by two component glue. Thethermocouples have a diameter of 1 mm. At the top of the ther-mocouple, a plastic cover was placed (leaving the thermocouplehead-free) to prevent contact with the fins and thus assure thatthe air temperature was measured.

The wall temperature was measured by inserting thermocou-ples of 0.5 mm into the wall. A cut was made into the wall; thehead of the thermocouple was smeared with a heat-conductingpaste and then glued into the wall.

The test section was 400 mm (Z) by 214 mm (Y) by 113 mm(X), as shown in Figure 4. This resulted in fourteen parallelair channels to be measured. On four different levels in the Z-direction, thermocouples were placed at 35 mm (A), 145 mm(B), 255 mm (C), and 365 mm (D). On four places in theX-direction at these levels, four thermocouples were insertedafter 1 and 4 cm, respectively, measured from the front and therear surface. At each point, the air and wall temperature weremeasured, resulting in 32 thermocouples. Figure 5 depicts thesetup.

Figure 4 Placement of the thermocouples.

Figure 5 Placement of the thermocouples on the heat exchanger.

Next to these measurement points, the inlet and outlet air andwater temperature were measured to be able to make the heatbalance.

Experimental Procedure and Data Reduction

Local Heat Transfer CoefficientFigure 6 shows the position of the thermocouples along an

air channel. To determine the local convection coefficient, fourtemperature measurements are taken. The heat absorbed by theair between the thermocouples placed at 10 mm (A1) and 40 mm(A2) for example, is given by:

Q = maircp,air(TA,Air,m12)(TA2,Air TA1,Air) (1)The local convection coefficient at position (A1A2) is thengiven by:

h A12 =Q

A1040(TAWm12 TA,Air,m12) (2)

Figure 6 Placement of the thermocouples along an air channel.

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32 M. DE PAEPE ET AL.

with the average temperature between two measurement pointsbeing:

Tm12 = (T2 + T1)2 (3)The air mass flow rate in Eq. (2) is then calculated, assuming aneven distribution of the air flow rate over the channels.

The local Reynolds and Nusselt numbers are determined by:

NuA12 = h A12 Dh12(TA,m12)

(4)

ReA12 = m Dh12Ac(TA Airm12) (5)

The hydraulic diameter is defined as:

Dh = 4Ac LA (6)

Heat Transfer CorrelationFor the other measuring points, the same method was used.

For each channel, the average convection coefficient can be de-termined by averaging over the length:

h = 1L

h(x)dx (7)

According to Figure 7, this integral can be approximatedby:

h A = 193 mm

(h A1215 mm + h A12+h A232 31.5 mm + h A23+h A342 31.5 mm + h A3415 mm

)(8)

The Colburn factor can be defined as:

j = NuRe

Pr1/3 (9)

In general, the Colburn factor is given by a general function:

j = C Rex (10)The coefficient C and the exponent x have to be determined bymeasurements.

Figure 7 Integration of the convection coefficient.

Procedure

The heat exchanger is supplied with two different fluidstreams. The interior channels are heated with water and theexterior is cooled by air. The water flow rate was kept con-stant with a constant entrance temperature. Four different waterflow rates were used: 0.058 kg/s, 0.116 kg/s, 0.180 kg/s, and0.239 kg/s.

For each water flow rate, the air flow rate was varied overthirty different flow rates, going from 0.145 kg/s to 0.519 kg/sin equal steps. This way, thirty different Reynolds numbers canbe set. Every time the air flow rate changed, temperature mea-surements in the heat exchanger were taken every second. Theheat transfer coefficient was determined when, after a certaintime, a stationary situation was reached, as detected by a con-stant temperature distribution.

The heat balance is given by:Qair

Qwater= maircp,air(Tair,out Tair,in)

mwatercp,water(Twater,in Twater,out) (11)

RESULTS

In Figure 8, the heat transfer coefficients for the four differenttest series, are presented.

For all the measurement series a correlation can be derived:

Water flow rate 0.058 kg/s: j = 0.407 Re0.444 Water flow rate 0.116 kg/s: j = 0.275 Re0.395 Water flow rate 0.180 kg/s: j = 0.217 Re0.367 Water flow rate 0.239 kg/s: j = 0.223 Re0.369

This correlation can be averaged over the different water flowrates, resulting in:

j = 0.267 Re0.391 (12)In Figure 9, the deviation of the measured data compared to thej calculated with Eq. (12) is shown: it can be seen that 93% of themeasurements lie within 100% 7%. The averaged correlationis thus useful for actual design calculations.

Figure 8 Measurement results.

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M. DE PAEPE ET AL. 33

Figure 9 Measurement versus general correlation.

ERROR ANALYSIS

All measurement instruments are liable to errors. In orderto indicate the quality of the measurements, a thorough erroranalysis was made.

Instrumentation Errors

To measure the air flow rate, an orifice plate was used. Theerror on the manometer was 0.5 Pa, with a 0.6% relative erroron the measurement. This resulted in a relative error of 1.4% onthe air mass flow rate. The relative error for the electronic waterflow meter was 1%.

The error on the thermocouples was evaluated by a calibrationmeasurement. Ten arbitrary temperatures were measured withall the thermocouples, and the average error was determined.This resulted in an error of 0.02 K.

The relative error on the determination of the surface area is2%.

Error on the Measurements

The local value of the convection coefficient is a functionof mass flow rate, temperatures, heat transfer area, and heatcapacity.The relative error is given by:(

h A12h A12

)2=

(m

m

)2+

( 2T

TA2air TA1air

)2

+(

2 TTAW m12 TAairm12

)2+

(A1040A1040

)2

The error on the Nusselt number, Reynolds number, and jfactors given by:(

NuNu

)2=

(hh

)2+

(DhDh

)2

(ReRe

)2=

(m

m

)2+

(DhDh

)2+

(AcAc

)2

( jj

)2=

(NuNu

)2+

(ReRe

)2For each flow rate, the relative error is different. In Table 1,the relative errors are given for the different calculated values.

Curve-Fitting Error

For linear regression Y = Ax + B, of n pairs of experimen-tally determined couples (xexp, yexp), the error on A and B isgiven by:

(A)2 = 1n 2

ni=1

(yexp Axexp B)2

nn

ni=1 x2exp

(ni=1 xexp

)2Table 1 Error on measurement

hh

(%) NuNu

(%) ReRe

(%) jj (%)Water flow rate (l/s)

0.058 1.17 2.02 2.28 3.040.116 1.16 2.00 2.28 3.030.180 1.17 2.01 2.28 3.040.239 1.19 2.10 2.28 3.10

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34 M. DE PAEPE ET AL.

(B)2 = 1n 2

ni=1

(yexp Axexp B)2

n

i=1 x2exp

nn

i=1 x2exp (n

i=1 xexp)2

The curve fitting of j can be linearized by:ln ( j) = ln (C) + x ln (Re)

This way, the relative errors on x and C can be calculated, takinginto account that

C = (ln(C))Cand(

jj

)2=

(Cc

)2+ x2

(ReRe

)2+ (x ln(Re))2

(x

x

)2The calculated errors are given in Table 2 for the four flow

rates and the averaged correlation (12). This means that the erroron the average correlation is less then 13%.Using a simpler approach, as in [5], the mean deviation can bedefined as:

mean deviation = 1n

ni=1

jcorrelation jexpjexp

This results for all measurements taken together in 3.72%.The error analysis shows that the derived correlation has a goodaccuracy.

COMPARISON WITH EXISTING DATA

Davenport [2] published a correlation for louvered fins:

j = 0.249Re0.42lp l0.33h H 0.26l(

llHl

)1.1(13)

for 300 < Re < 4000.This correlation can be transformed to the louvered fin char-

acteristics of the studied heat exchanger, taking into account thatDavenport calculates the Reynolds number with fin pitch, andin this paper hydraulic diameter is used. This gives:

j = 0.339Re0.42 (14)

Table 2 Error on curve fitting

x

x(%) C

C(%) jj (%)Water flow rate (l/s)

0.058 1.94 7.41 10.90.116 2.17 8.98 13.20.180 1.74 7.54 11.20.239 0.87 3.76 5.7Averaged correlation 2.1 8.74 12.9

Figure 10 Comparison of Davenport and measured correlation.

In Figure 10, these two correlations are compared. The twocurves have a similar shape. At the maximum distance, the dif-ference is about 10%.

CONCLUSIONS

In this paper, a detailed description of an experimental setup isgiven with which the heat transfer correlation of plate-fin heat ex-changers can be determined under real operational conditionsnot using a large-scale mock-up of the heat transfer channel.This results in heat transfer data of real heat exchangers underreal operational conditions.

The presented method is relatively simple to implement asonly thermocouples are used.

With this setup, an air cooler was tested. A j-Re correlation isderived with an error rate less than 13% using local temperaturemeasurements. This correlation is compared with correlationsfound in the literature, and a good comparison is found.

The presented setup is thus suitable for measuring other typesof fins for plate-fin heat exchangers. In the near future, these testswill be performed on new types of fins, under real conditions asassembled in the heat exchanger.

NOMENCLATURE

A area, m2cp specific heat, J/kgKDh hydraulic diameter, mh convection coefficient, W/m2KHl fin height, mj Colburn j factorL channel length, W/m2Klh louvre height, mll louvre length, ml p louvre pitch, mm mass flow rate, kg/sNu Nusselt numberPr Prandtl numberQ transferred heat, W

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M. DE PAEPE ET AL. 35

Re Reynolds numberT temperature, K

Greek Symbols

density, kg/m3 thermal conductivity, W/mK viscosity, Ns/m2

Subscripts

c cross-sectionm averageW wall

REFERENCES

[1] Kays, W. M., and London, A. L., Compact Heat Exchangers, 3rded., McGraw-Hill, New York, 1984.

[2] Kuppan, T., Heat Exchanger Design Handbook, Marcel DekkerInc., New York, 2000.

[3] Sahnoun, A., and Webb, R. L., Prediction of Heat Transfer andFriction for the Louver Fin Geometry, ASME Journal of HeatTransfer, vol. 114, pp. 893900, 1992.

[4] Leong, K. C., and Toh, K. C., An Experimental Investigation ofHeat Transfer and Flow Friction Characteristics of Louvered FinSurfaces by Modified Single Blow Technique, Int. J. Heat andMass Transfer, vol. 35, pp. 5363, 1999.

[5] Chang, Y. J., and Wang, C. C., A Generalised Heat Transfer Cor-relation for Louver Fin Geometry, Int. J. Heat and Mass Transfer,vol. 40, pp. 533544, 1997.

[6] Beziel, M., and Stephan, K., Temperature Distribution in the Outletof Cross-Flow Heat Exchangers, Int. J. Heat and Mass Transfer,vol. 38, pp. 371380, 1995.

[7] Kim, S. Y., Peak, J. W., and Kang, B. H., Flow and Heat TransferCorrelations for Porous Fin in a Plate-Fin Heat Exchanger, ASMEJournal of Heat Transfer, vol. 122, pp. 572578, 2000.

[8] Dubrovsky, E. V., Experimental Investigation of Highly EffectivePlate-Fin Heat Exchanger Surfaces, Experimental Thermal andFluid Science, vol. 10, pp. 200220, 1995.

[9] Stasiek, J. A., Experimental Studies of Heat Transfer and FluidFlow across Corrugated-Undulated Heat Exchanger Surfaces, Int.J. Heat and Mass Transfer, vol. 41, pp. 899914, 1998.

[10] N. N., Measurement of Fluid Flow by Means of Pressure Differ-ential Devices, Part 1: Orifice Plates, Nozzles and Venturi TubesInserted in Circular Cross-Section Conduit Running Full, CENEN ISO, 51671, 1995.

Michel De Paepe is professor of AppliedThermodynamics at Ghent University, Ghent,Belgium. He received his Ph.D. from the sameuniversity in 1999 on the topic of steam-injectedgas turbines. His main topics of research are heatexchangers, numerical heat transfer, gas turbines,cogeneration, and HVAC. He has published aboutthirty papers in international journals and confer-ence proceedings.

An Willems is a mechanical engineer who re-ceived her masters degree at Ghent Universityin Ghent, Belgium, in 2002. She is now com-pleting her masters degree in Nuclear Engineer-ing from the joint Nuclear Education program inFlanders. She is currently employed by Electrabeland is working in a nuclear power plant in Doel,Belgium.

Alexis Zenner is a mechanical engineer who re-ceived his masters degree at Ghent University inGhent, Belgium, in 2002. In 2003, he obtainedhis masters degree in General Management atVlerick Leuven Gent Management School inGhent, Belgium. He is currently employed byExxon Mobil at the Virton plant in Belgium.

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