Int J Thermophys (2012) 33:1055–1067DOI 10.1007/s10765-012-1210-4

Experimental Investigation of Thermal Performance ina Concentric-Tube Heat Exchanger with Wavy InnerPipe

Gülsah Çakmak · H. Lütfi Yücel ·Zeki Argunhan · Cengiz Yıldız

Received: 20 December 2011 / Accepted: 5 May 2012 / Published online: 24 May 2012© Springer Science+Business Media, LLC 2012

Abstract In this article, the heat transfer, friction factor, and thermal performancefactor characteristics of a concentric-tube heat exchanger are examined experimen-tally. A wavy inner pipe is mounted in the tube with the purpose of generating swirlflow that would help to increase the heat transfer rate of the tube. The examination isperformed for a Reynolds number ranging from 2700 to 8800. An empirical correlationis also formulated to match with experimental data of the Nusselt number using theWilson plot method. In addition, to obtain the real benefits in using the swirl generatorat a constant pumping power, the thermal enhancement factor is also determined. Overthe range considered, the increases in the Nusselt number, friction factor, and thermalperformance factor are found to be, respectively, about 113 %, 81 %, and 196 % higherthan those obtained from a smooth-surface inner pipe.

Keywords Enhanced heat transfer · Heat exchanger · Wavy inner pipe ·Wilson plot method

List of Symbols

A Area (m2)d Diameter of wave (m)f Friction factorh Heat transfer coefficient (W · m2 · K−1)

G.Çakmak (B) · H. L. Yücel · C. YıldızDepartment of Mechanical Engineering, Firat University, 23119, Elazig, Turkeye-mail: gulcak@gmail.com; gulcakmak@firat.edu.tr

Z. ArgunhanDepartment of Mechanical Engineering, Batman University, 72060, Batman, Turkey

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k Thermal conductivity (W · m−1 · K−1)Nu Nusselt numberP Wetted perimeter (m)Pr Prandtl numberR Function of independent variablesRe Reynolds numberU Linear velocity (m · s−1)v Kinematic viscosity (m2 · s−1)Wr Total uncertaintyW Uncertainty in the independent variablesx Independent variables

Subcriptsi Inleto Outletn Number of independent variablesw Wavys Smooth

1 Introduction

Efforts for saving energy through efficient heat transfer have revealed enhancementtechniques of heat transfer including the reduction of the size and cost of heat exchang-ers and the improvement of its performance concurrently. Heat exchangers are widelyused in many engineering fields. A heat exchanger operating with minimal cost isregarded as having optimum dimensions. A vast amount of heat discarded by indus-trial operations might be partially recovered by suitable heat exchangers in terms ofreasonable investment cost. Any increase in the heat transfer rate allows heat exchang-ers with smaller dimensions to be designed. Several theoretical and experimentalstudies have been conducted about heat transfer enhancement. These methods are cat-egorized under two broad groups of heat transfer enhancement, namely, active andpassive methods.

Enhanced surfaces are included in an important group of the enhancement tech-niques. One effective method applied in heat transfer enhancement is the inductionof swirl on the fluids, which increases turbulent intensity and reforms the boundarylayer. Naphon [1] examined the heat transfer characteristics and the pressure drop ofa horizontal double pipe with a coil-wire insert. Non-isothermal correlations for theheat transfer coefficient and friction factor were proposed.

Tijing et al. [2] analyzed the effect of internal aluminum fins with a star-shape crosssection on the heat transfer enhancement and pressure drop in a counter flow heatexchanger. The heat transfer rate was increased by 12 % to 51 % over a plain tubevalue depending on the internal fin configurations used. However, the pressure drop

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also increased substantially by 286 % to 399 %. Aziz and Rahman [3] investigatedthe steady-state thermal performance of a radial fin of rectangular profile made of afunctionally graded material. They found that the heat transfer rate, the fin efficiency,and the fin effectiveness were highest when the thermal conductivity of the fin variesinversely with the square of the radius.

Murugesan et al. [4] analyzed experimentally the heat transfer, friction factor, andthermal enhancement factor characteristics of a double-pipe heat exchanger fitted withsquare-cut twisted tapes (STT) and plain twisted tapes (PTT) using water as a workingfluid and Reynolds numbers ranging from 2000 to 12000. Within the range consid-ered, the Nusselt number, friction factor, and thermal enhancement factor in a tubewith STT were 1.03 to 1.14, 1.05 to 1.25, and 1.02 to 1.06 times those in a tube withPTT, respectively.

Çakmak and Yıldız [5] provided the heat transfer enhancement rates by placinginjectors on the entrance section of the inner pipe of a concentric heat exchanger. Theauthors showed that a rather smaller size heat exchanger with the same capacity couldbe proposed by using elements that impose swirling to the fluid flowing through theinner pipe.

Gee and Webb [6] tested the heat transfer enhancement for single-phase forcedconvection in a circular tube containing a two-dimensional rib roughness. Yua [7]presented the thermal performance of wickless thermosyphon-based heat-pipe heatexchangers (HPHEs) for naturally ventilated buildings using a computer simulationprogram. Eiamsa-Ard et al. [8] studied the heat transfer and friction factor characteris-tics in a double-pipe heat exchanger fitted with regularly spaced twisted tape elements.They considered the flow rate of the tube in a range of Reynolds numbers between2000 and 12000.

The Wilson plot is a technique to obtain general heat transfer correlations. Thismethod is an outstanding tool in practical applications. Fernández-Seara et al. [9]described a simple experimental apparatus that allows for the measured data requiredfor the application of the Wilson plot method. Taylor [10] used the Wilson plot forthe determination of the air-side convection coefficient in finned-tube heat exchang-ers. Although the air-side thermal resistance was considered constant, variations wereallowed in the cooling water mass flow. Dirker and Meyer [11] examined a modifica-tion of the Wilson plot to estimate a suitable correlation equation for turbulent flow insmooth concentric annuli.

In this article, it is aimed to examine the possible effect of the surface shape of aninner pipe on improving heat transfer in a concentric-tube heat exchanger. For thispurpose, the inner pipe of the heat exchanger was constructed so as to have interiorand exterior longitudinal wavy surfaces. This design allows for increasing the heattransfer area to a considerable extent. On the other hand, the friction factor throughoutthe tube can be increased. Therefore, the interpretation of results is carried out consid-ering these two factors and heat transfer in a smooth-surface inner pipe. In addition, thethermal performance factor is determined to estimate the quality of the enhancementratio.

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2 Experimental Study and Method

2.1 Experimental Setup

The constructed experimental system is shown in Fig. 1. The outer pipe is 1100 mmlong with an inner diameter of 82 mm and outer diameter of 88 mm. The length ofthe wavy inner pipe is 1100 mm. Hot air is passed through the inner pipe, while coldwater flows through the annulus. The cross-sectional and longitudinal views of theinner pipe are shown in Fig. 2. The cross-sectional view of a wave has the shape of asemicircle as seen in the figure.

Two types of wavy inner pipes were prepared from 1 mm thick galvanized ironplates. The wavy pipes were manufactured by cold bending of the surface using atube bending machine. Each wavy pipe was shaped from a straight plate by fitting itbetween two shaped dies, which were made according to the required wavy config-uration. The rolling sheets were soldered at the edges. The leakage of soldered pipejoints was tested with soap suds and sufficient air pressure.

The wayv pipes are 2 mm and 3 mm high and 1100 mm long. The number of wavesused for 4 mm and 6 mm wavy diameters are 10 and 6, respectively. The main char-acteristics of the inner pipe plates are given in Fig. 3. This pipe was mounted as theinner pipe of the concentric double-pipe heat exchanger. Separate experiments werecarried out with this tube mounted on the heat exchanger.

The air supplied from a radial fan was heated with an electrical heater equipped witha voltage transformer whose flow rate was measured at the pipe inlet using an air rota-meter. The measurement ranges of the water and air rotameter were 2×10−3 m3 ·h−1

Fig. 1 Experimental setup

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Fig. 2 Wavy inner pipe used in the experiments

to 40 × 10−3 m3 · h−1 and 0.2 m3 · h−1 to 5 m3 · h−1, respectively. The temperatureswere measured with Fe-Constantan thermocouples (J type) and a multichannel digitalthermometer. For this study, the inlet temperatures of air and water were fixed at 45 ◦Cand 20 ◦C, respectively.

The outer pipe of the heat exchanger was insulated to prevent heat losses. Pressurelosses over the inner pipe were determined by using 30◦ inclined manometers filledwith colored water. The temperature and pressure readings were taken after the appa-ratus reached steady-state conditions. The runs were repeated for various flow ratesof the fluids. The results were evaluated and depicted in graphs.

Fig. 3 Main characteristics of the inner pipe plates

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Table 1 Uncertainties of theexperiments

Parameter Uncertainty

Hot-fluid inlet temperature 0.173 ◦C

Hot-fluid outlet temperature 0.173 ◦C

Cold-fluid outlet temperature 0.173 ◦C

Cold-fluid outlet temperature 0.173 ◦C

Inner pipe wall temperature 0.173 ◦C

Pressure drop for water 0.25 mmHg

Pressure drop for air 0.25 mm water

Mass flow rate 0.2 kg · h−1

Reading values 0.1

All measurements have errors and uncertainties. In this study, the uncertainties ofexperimental quantities were computed by using the method presented by Moffat [12].When several independent variables are used in the function R, the individual termsare combined by the root-sum-square method:

Wr =[(

∂R

∂x1w1

)2

+(

∂R

∂x2w2

)2

+ . . . . . .

(∂R

∂xn

wn

)2]1/2

. (1)

The maximum uncertainties of the investigated non-dimensional parameters arefound to be as follows: Re, Nu, and �P are 3 %, 5 %, and 5.4 %, respectively. Inaddition, the uncertainties of the measured physical properties are listed in Table 1.

2.2 Theoretical Analysis

Measurement of the wall temperature in the flow by thermocouples involves some dif-ficulties. The thermocouples generate significant perturbation to the flow; therefore,the Wilson plot method is used for heat transfer analysis.

The heat transfer coefficients can be calculated using Wilson plots based on theoverall temperature difference and the rate of heat transfer. Wilson plots are producedby calculating the overall heat transfer coefficients for a number of trials where onefluid flow is kept constant and the other is varied [13]. In this study, the flow in theannular tube was kept constant, and the flow in the inner tube was varied for ninedifferent flow rates.

The overall thermal resistance of the concentric heat exchanger (Rov) can beexpressed as the sum of the thermal resistances corresponding to external convec-tion (Ro), the tube wall (Rt), and the internal convection (Ri), as shown in

Rov = Ro + Rt + Ri. (2)

The thermal resistances in each one of the heat transfer processes are obtained fromthe following equations:

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Ro = 1

hoAo(3)

Rt = ln(do/di)

2πktLt(4)

Ri = 1

hiAi, (5)

where hi and ho are the internal and external convection coefficients, do and di are theexterior and interior tube diameters, kt is the tube thermal conductivity, Ai and Ao arethe interior and exterior tube surface areas, and Lt is the tube length.

The thermal resistance due to the flow in the annular tube and the tube wall can beconsidered constant.

Ro + Rt = C1, (6)

where C1 is a constant.The heat transfer coefficient for a turbulent flow in circular tubes can be obtained

from the following equation, according to the correlation proposed by Dittus–Boelter[14] with the exponent of the Prandtl number assumed to be known and equal to 0.4:

hi = CRemP r0.4(k/di). (7)

According to Eq. 7, the internal convection coefficient will be proportional to Rem,and the inner convection thermal resistance will be proportional to 1/Rem, as shownby the following equation, where C2 is a constant:

Ri = C2/Rem. (8)

The overall thermal resistance is obtained as follows:

Rov = C1 + C2/Rem. (9)

The external and internal convection coefficients for a given flow rate and theunknown parameter C can be calculated from Eqs. 10, 11, and 12, respectively:

ho = 1

[C1 − Rt]Ao(10)

hi = Rem

C2Ai(11)

C = 1

C2

(kdi

)Pr0.4Ai

. (12)

Re and Nu numbers based on the hydraulic diameter (Dh) are expressed as follows:

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Nu = hDh

k(13)

Re = UDh

ν, (14)

where the hydraulic diameter is defined as follows:

Dh = 4A/P. (15)

The results of the smooth and wavy tubes were compared with the correlationsof Dittus and Boelter [14], Gnielinski [15], and Petukhov [16] for a fully developedturbulent flow in circular tubes. This may be taken as an indication of the consistencyof the constructed experimental system.

Correlation from Dittus and Boelter is as follows:

Nu = 0.023 Re0.8 Pr0.4. (16)

Correlation from Gnielinski is as follows:

Nu = (f/8)(Re − 1000)P r

1 + 12.7(f/8)0.5(P r2/3 − 1). (17)

Correlation from Petukhov is as follows:

f = (0.79 ln(Re) − 1.64)−2. (18)

To assess the practical use of the wavy tube, the performance of the wavy tube isevaluated relative to the smooth tube at an identical pumping power in terms of thethermal performance factor which can be expressed as follows [17]:

η = (Nuw/Nus)/(fw/fs)1/3. (19)

3 Results and Discussion

The inlet flow should be fully developed before the test region. To ensure full devel-opment, the hydrodynamic entry length should be examined. In many pipe flowsof practical engineering interest, the entrance effects become insignificant when thelength of the pipe is more than ten times its diameter, and the hydrodynamic entrylength is approximated as Lh,turbulent = 10D. Therefore, the average entrance lengthwas taken as 400 mm (∼10D).

The results obtained from the measurements involving wavy inner pipes are shownin Figs. 4 and 5 for the counter current and parallel flow modes of the fluids, respec-tively. As expected, Nu numbers increase steadily with Re numbers. An interestingfinding may be that the differences in Nu numbers formed by the wavy surface shapeof the inner pipe also increase with Re number. This may be explained by the factthat the extent of mixing between the main turbulent core and the complex flow in the

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Fig. 4 Relation between Nu and Re numbers for the countercurrent flow mode

Fig. 5 Relation between Nu and Re numbers for the parallel flow mode

longitudinal hollow regions becomes more violent as the turbulent intensities increasewith flow rate. This effect increases with the decreasing diameter or with the increaseof the number of the waves. Thus, the main reason is accompanied by the generationof secondary swirl flow’s small wavy diameter. The waves with a small diameter hadan impact on the main flow direction both inside and outside of the exchanger and pro-vided an additional disturbance to the fluid in the vicinity of the pipe wall and vorticesbehind the cuts, which in turn led to a higher heat transfer enhancement compared tothose with a bigger diameter.

The highest heat transfer enhancement occurred in the heat exchanger with 4 mmdiameter waves at the highest Re number (8800) in the counter-current flow mode.Figure 4 shows that the highest increase in Nusselt number is about 113 % above theplain tube and 5 % below the reference study. Although similar enhancements wereobserved in the parallel flow mode, their level was 10 % to 15 % lower with respect

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Fig. 6 Uncertainties of the investigated non-dimensional Nu number

Fig. 7 Wilson plot

to the counter-current flow mode of the fluids. Figures 4 and 5 compare the presentexperimental work and its relations with the literature. In the figures, results of thisstudy agree reasonably well with the available correlations within ±10 % in compar-ison with Nusselt number correlations of Dittus and Boelter [14] and Gnielinski [15].Figure 6 presents the Nusselt number for a swirl of different diameters along withthe corresponding percentage uncertainty. The percentage uncertainty in heat transferresults is estimated to be <5 %.

Figure 7 shows the straight line that fits the experimental data as well as the equationobtained by linear regression for the counter-current flow mode,

Rov = 246.21Re−0.7 + 0.4811. (20)

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Fig. 8 Change in friction factors with Re numbers in the exchanger

From this equation, the values of the constants C1 and C2 were obtained as 0.4811and 246.21, respectively. The coefficient C of the general correlation was obtained as0.048328 from Eq. 12. Thus, the general correlation for the smooth tube is given asfollows:

Nu = 0.048328Re0.7Pr0.4. (21)

The relation between the friction factor and the Reynolds number is obtained forall pipes (Fig. 8). In addition, Fig. 8 gives the results of the friction factor obtainedfrom the Petukhov equation (Eq. 18) for the smooth pipes. The experimental resultsfrom the smooth tube were found to be consistent with the Petukhov equations.

It is observed that the friction factor tends to decrease with the Reynolds number.The friction factor values for the wavy pipes used are higher than those for the smoothpipe. The maximum value of the friction factor is found in the case of 4 mm diameterwaves. The highest increase in the friction factor is about 81 % above the plain tubeand 15 % below the reference study.

The quality of the enhancement concept is derived from the performance factor. Thevariation of the performance factor with the Reynolds number is given in Fig. 9. Theperformance factor was obtained for 4 mm and 6 mm wavy diameters. It shows that theperformance factor in all cases is larger than unity which means that the applicationof enhancement is reasonable from the point of total energy savings. The maximumvalue of the thermal performance ratio is found as 196 % for a 4 mm wavy diameter.

The following relations for this experimental study may be derived by curves whichconsists of experimental data in the figures [depend on the ratio of (d/Dh)]:

Nu = 0.052607 Re0.698Pr0.543(

d

Dh

)−0.416

(22)

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Fig. 9 Change in the thermal performance factor with Re numbers in the exchanger

f = 3.254367 Re−0.646(

d

Dh

)−1.214

(23)

η = 2.2962502 Re−0.170(

d

Dh

)−0.465

. (24)

Equations 22–24 are applicable in the following ranges: 2700 < Re < 8800,0.10 < d/Dh, and Pr = 0.710. These equations were found as representing theexperimental data within ±10 % error limits.

4 Conclusions

The thermal performance, heat transfer enhancement, and friction factor characteris-tics of a concentric-tube heat exchanger with a wavy tube have been tested in this study.The values of these characteristics are significantly higher than those of a smooth tube.At the same time, thermal performance factors are greater than unity meaning that theeffect of heat transfer enhancement due to the wavy tube is more than the effect ofthe rising friction factor. Empirical correlations of the Nusselt number, friction factor,and thermal performance factor have also been determined.

References

1. P. Naphon, Int. Commun. Heat Mass Transf. 33, 753 (2006)2. L.D. Tijing, C.B. Pak, B.J. Baek, D.H. Lee, Int. Commun. Heat Mass Transf. 33, 719 (2006)3. A. Aziz, M.M. Rahman, Int. J. Thermophys. 30, 1637 (2009)4. P. Murugesan, K. Mayilsamy, S. Suresh, Chin. J. Chem. Eng. 18, 609 (2010)5. G. Çakmak, C. Yıldız, Int. Commun. Heat Mass Transf. 34, 728 (2007)6. D.L. Gee, R.L. Webb, Int. J. Heat Mass Transf. 23, 1127 (1980)7. Y.H. Yua, Proc. IMechE Part A 215, 389 (2001)8. S. Eiamsa-Ard, C. Thianpong, P. Promvonge, Int. Commun. Heat Mass Transf. 33, 1225 (2006)9. J. Fernández-Seara, F. José Uhía, J. Sieres, A. Campo, Eur. J. Phys. 26, 1 (2005)

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10. C. Taylor, Measurement of Finned-Tube Heat Exchanger Performance, Master of Science Thesis inMechanical Engineering, Georgia Institute of Technology, Atlanta, 2004

11. J. Dirker, J.P. Meyer, Heat Transf. Eng. 26, 38 (2005)12. R.J. Moffat, Exp. Therm. Fluid Sci. 1, 3 (1988)13. J. Fernández-Seara, F. José Uhía, J. Sieres, A. Campo, Appl. Therm. Eng. 27, 17 (2007)14. F.W. Dittus, L.M.K. Boelter, Int. Commun. Heat Mass Transf. 12, 3 (1985)15. V. Gnielinski, Heat Transf. Eng. 30, 431 (2009)16. B.S. Petukhov, Advances in Heat Transfer, ed. by T.F. Irvine, J.P. Hartnett (Academic Press, New York,

1970)17. S.D. Hwang, H.G. Kwon, H.H. Cho, Energy 35, 5357 (2010)

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