chapter 7 air-side heat transfer and friction ......air-side heat transfer and friction...

CHAPTER 7

Air-Side Heat Transfer and Friction Characteristics of Fin-and-Tube Heat Exchangers with Various Fin Types

L.B. Wang1, M. Zeng2, L.H. Tang2 & Q.W. Wang2

1Department of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou, Gansu, China.2Key Laboratory of Thermo-Fluid Science and Engineering, MOE, Xi’an Jiaotong University, Xi’an, Shaanxi, China.

Abstract

Tube bank fi n heat exchangers have widespread applications, they are transferring enormous amounts of energy, and also consuming very large amount of mechani-cal energy. Because the dominant thermal resistance in such heat exchangers is usually on the air side in practical applications, and therefore the use of the fi n sur-faces on the air side is very common to effectively improve their overall thermal performance. Energy costs and environmental considerations continue to motivate attempts to derive better performance over the existing designs. As a result, during the past few years, there are also many investigations to the slit fi n pattern and to the longitudinal vortex generator fi ns. Because it involves a huge cost and a strenu-ous work to compare the heat transfer performances of these fi n patterns, up to now there are no enough data to summarize the comparisons thoroughly. However, there are a few reported results now available to make a brief summary on the air-side performances of the various fi n patterns with aims to provide information for some readers to utilize the available data, to fi nd the work need to be done further, and fi nd out new fi n pattern having good heat transfer performance. Therefore, in this chapter the heat transfer performances of fi ve fi n patterns of circular tube bank fi n heat exchangers are compared. In addition, the heat transfer performances of three fi n patterns of fl at tube bank fi n heat exchangers are also compared. Three sets of criteria, namely, the identical mass fl ow rate, pressure drop, and the identi-cal pumping power, are used in judging. The results show that for the circular tube bank fi n heat exchangers, with the Reynolds number ranging from 4,000 to 10,000,

doi:10.2495/978-1-84564-818-3/007

www.witpress.com, ISSN 1755-8336 (on-line) WIT Transactions on State of the Art in Science and Engineering, Vol 63, © 2013 WIT Press

212 EMERGING TOPICS IN HEAT TRANSFER

at high Reynolds numbers, the slit fi n offers best heat transfer performance; for the fl at tube bank fi n heat exchangers, the fi n with vortex generators has a better heat transfer performance than the fi n punched rhombic formation and the louver fi n; naphthalene heat mass transfer analogy method can be used to screen the fi n pattern with a required accuracy; for the circular tube bank fi n heat exchangers, further optimization and experimental comparisons of the fi n pattern with vortex generators to the slit fi n pattern should be carried out to identify the one with better heat transfer performance.

Keywords: Evaluation criteria; fi n-and-tube heat exchanger; fi n patterns; performance.

1 Introduction

Tube bank fi n heat exchangers are used in a broad range of applications includ-ing industrial and chemical processes, air conditioners for domestic or industrial applications, and automotive radiators. These heat exchangers mostly use three types of the tubes, namely, circular tube, fl at tube, and oval tube as shown in Fig. 1. The basic design consists of a stack of closely spaced fi ns through which tubes have been inserted, and this confi guration has changed little since their introduc-tion over 40 years ago [1].

Because of their widespread applications, they are transferring enormous amounts of energy, and also consuming very large amount of mechanical energy. As global energy consumption is has a negative impact on the environment and causes depletion of our existing fuel stocks, energy utilizations have come under close scrutiny. Heat exchangers are an integral component of the dissemination of energy and their effectiveness is becoming crucial to our lifestyle sustainability. Energy costs and environmental considerations continue to motivate attempts to derive better performance over the existing designs. The dominant thermal resis-tance in such heat exchangers is usually on the air side in practical applications, and therefore the use of the fi n surfaces on the air side is very common to effec-tively improve their overall thermal performance.

Figure 1: Tube bank fi n heat exchangers with different types of the tube.


AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 213

The most simple fi n pattern of these heat exchangers is plain fi n. For circular tube bank plain fi n geometry, McQuiston [2], Gray and Webb [3], and Wang et al. [4–6] established extensive data and correlations of the heat transfer performance. For fl at tube bank plain fi n heat exchangers, Kays and London [1], Wang et al. [7, 8] and Kylikof [9] contributed much to the data and the correlations. For oval tube bank plain fi n heat exchangers, Kays and London [1], Matos et al. [10] and Saboya and Sparrow [11] contributed much to the data and the correlations.

It was found that in most cases, the plain fi n is not enough to decrease the air-side thermal resistance. Therefore, many fi n patterns have been invented in the past years. These have evolved from wavy fi ns to slit fi ns and presently louver fi ns are widely used. However, in general, modifi cations to the fi n surface have resulted in an increase in pressure drop with little improvement in heat transfer perfor-mance [12].

During the past few years, the crimped spiral fi n was addressed by Nuntaphan et al. [13, 14]. There are also many investigations to the slit fi n pattern [15–18] and to the longitudinal vortex generator fi ns [7, 8, 19–28]. Because it involves a huge cost and strenuous work to compare the heat transfer performances of these fi n patterns, up to now there are no enough data to summarize the comparisons thoroughly. However, there are a few reported results now available to make a brief summary on the air-side performances of the various fi n patterns. This may provide information for some readers to utilize the available data, to fi nd the work need to be done further, and fi nd out new fi n pattern having good heat transfer performance.

The following pages are divided into two parts. In fi rst part, the heat transfer performance of the fi n patterns of circular tube bank fi n heat exchangers is com-pared; in the second part, the heat transfer performance of fi n patterns of fl at tube bank fi n heat exchangers is compared. In the comparing processes, three sets of criteria (i.e. the identical mass fl ow rate, pressure drop and the identical pumping power) are used.

2 Heat Transfer Performances of the Fin Patterns for Circular Tube

In this section, the fi n-side heat transfer performances of fi ve fi n patterns as shown in Fig. 2 for circular tube are summarized. The geometrical details of these fi n pat-terns are presented in Table 1.

The experimental details to obtain the heat transfer performances of the aforementioned fi n patterns [27] will not be repeated here, but in order to use these data conveniently and correctly, it is necessary to declare the process of data reduction again. The average value of the inlet and outlet temperatures of air side is used to evaluate the thermal properties of air. The total heat transfer coeffi cient, UA product, is calculated from the following relationship:

UA Q t= ave m/Δ (1)



where Δtm is the logarithmic-mean temperature difference, defi ned by

Δt

t t t tt t

t t

ms in s out

s in

s out

=− − −

−−

( ) ( )

ln (2)

where tin is the inlet temperature of air, tout is the outlet temperature, and ts is the saturated temperature of steam at the corresponding pressure.

The overall heat transfer resistance can be defi ned as

1 1 1

2

1

UA h A

D

A

D

D h A= + +

h lo o o

o

w w

o

i i i

ln (3)

Table 1: Geometric dimensions of fi n-and-tube heat exchangers.

Name Type Di Do Dc Fp Pt Pl sw sl sh Vl Vh α N

P12 Plain 16 18 18.6 3.1 42 34 – – – – – – 12S12 Slit 16 18 18.6 3.1 42 34 2.2 16 1.0 – – – 12V12 Vortex 16 18 18.6 3.1 42 34 – – – 5 2.55 45 12VSM12 Mixed 16 18 18.6 3.1 42 34 2.2 16 1.0 5 2.55 45 12SP12 Spiral 16 18 18 3.1 42 34 – – 10 – – – 12

Note: 1. Fin thicknesses of all test samples are 0.3 mm; 2. VSM12 is mixed by front 6-row vortex-generator fi n and rear 6-row slit fi n.

(a) Crimped spiral fin (b) Plain fin

(c) Slit fin (d) Vortex-generator fin (e) Mixed fin

Figure 2: Fin confi gurations.



In eqn (3), ho is the fi nned surface effi ciency, which may be written in terms of the fi n effi ciency h, fi n surface area Af and total surface area Ao, as follows:

h hof

o

= − −1 1A

A( ) (4)

where Ao = Af + Ab, Af, and Ab are the areas of the fi n and base surface, respectively. h is calculated by the approximation method described by Schmidt [29]

h w w= tanh( )/( )mr mrc c (5)

where

m h= 2 o f f/( )l d (6)

w = − +( / )[ . log ( / )]R r R req c e eq c1 1 0 35 (7)

R

r

X

r

X

Xeq

c

M

c

L

M

= −1 27 0 3 0 5. ( . ) . (8)

X P PL t= +( / ) /2 2212 (9)

X PM t= /2 (10)

The air-side heat transfer coeffi cient ho and the surface effi ciency ho can be acquired by solving eqns (5)–(10) using an iterative method.

The heat transfer and friction characteristics of the heat exchanger are presented in the following dimensionless forms:

Nu h D= o c /l (11)

Re v DD cc

= r mmax / (12)

j Nu Re Pr= /( )D

1/3c

(13)

f pD L v= ( max2 2Δ c )/( )r (14)

where vmax is the velocity at the minimum free fl ow area, vmax = vfr/σ. The term σ is the ratio of the minimum fl ow area to frontal area.

Figures 3 and 4 show Nu, Δp, j factor and f factor with air frontal velocity for various fi n patterns. In these fi gures, ‘P12’ stands for plain fi n with ‘N = 12’, ‘S12’ stands for slit fi n with ‘N = 12’, ‘V12’ stands for vortex-generator fi n with ‘N = 12’, ‘VSM12’ stands for mixed fi n with front 6-row vortex-generator fi n and rear 6-row slit fi n with ‘N = 12’, and ‘SP12’ stands for spiral fi n with ‘N = 12’, respectively. Both Nusselt number and Δp increase with increasing air frontal velocity, and both j factor and f factor decrease with the increase of air frontal velocity. In Fig. 3, the Nusselt number of SP12 is the highest among the fi ve fi ns at the same frontal velocity, and that of S12 takes the second place, while that of P12 is the lowest. By contrast, Fig. 5 shows that j factor of SP12 is the highest among these fi ns at the



same frontal velocity, and that of P12 is the lowest. From Fig. 3, Δp of SP12 is the highest, while Δp of P12 is the lowest. The f factor of SP12 is obviously the high-est among these fi ns at the same frontal velocity in Fig. 4. In a sense, these results can be expected, because the enhancement of heat transfer is usually penalized by the increase of pressure drop.

The correlations for heat transfer and friction factors can be expressed as follows:

Nu c Re= 1 D

cc

2 f c Re= 3 Dcc

4 (15)

Figure 3: Nu and Δp for 12-row tested samples.

Figure 4: j and f for 12-row tested samples.



The corresponding correlations for fi ve different fi n patterns in the present study are shown in Tables 2 and 3. These correlations can be referred to engineering applications or further researches such as optimization or prediction.

The heat exchanger with crimped spiral fi n provides the highest Nusselt number associated with the highest pressure drop. Accordingly, it is essential to compare

Table 2: The correlations of Nusselt number.

Name Range of ReDc Nu = f(Re) Maximum relative error

P12 4,000–10,000 Nu = 0.080ReDc0.71 6.4%

S12 4,000–10,000 Nu = 0.057ReDc0.77 4.6%

V12 4,000–10,000 Nu = 0.094ReDc0.71 4.0%

VSM12 4,000–10,000 Nu = 0.076ReDc0.74 3.6%

SP12 4,000–10,000 Nu = 0.069Re0.76 1.6%

Table 3: The correlations of friction factor.

Name Range of ReDc f = f(Re) Maximum relative error

P12 4,000–10,000 f = 12.83 ReDc−0.36 4.9%

S12 4,000–10,000 f = 13.28 ReDc−0.35 2.5%

V12 4,000–10,000 f = 10.68 ReDc−0.34 3.3%

VSM12 4,000–10,000 f = 6.15 ReDc−0.27 2.9%

SP12 4,000–10,000 f = 4.31 Re–0.13 1.1%

Figure 5: Fin patterns for fl at tube: (a) fi n with punched vortex generators and (b) fi n with punched rhombic formation.



the heat transfer enhancement performance of the test heat exchangers. In the present study, the identical mass fl ow rate criteria, the identical pumping power criteria, and the identical pressure drop criteria are used. These criteria were suc-cessfully adopted by Yu and Tao [30] and Wang et al. [31]. Based on the constant properties assumption, the formulations of these criteria are given as:

a. Identical mass fl ow rate criteria:

( / ) ( / )ReA D ReA Dc c c p= (16)

b. Identical pumping power criteria:

( / ) ( / )fRe A D fRe A Dc c

3c

3p

4 4= (17)

c. Identical pressure drop criteria:

( / ) ( / )fRe D fRe Dc c

2c

2p

3 3= (18)

where the subscripts of ‘p’ and ‘c’ refer to plain fi nned tube (P12) and enhanced fi nned tubes (S12 V12 VSM12, or SP12), respectively. Under the condition of same temperature difference between the fl uid and the wall, the ratio of heat trans-fer rate between the enhanced fi nned tubes and the plain fi nned tube may be for-mulated as follows:

ΦΦ

c

p

c c

c p

=⎡⎣ ⎤⎦⎡⎣ ⎤⎦

Nu Re A D

Nu Re A D

( ) /

( ) / (19)

where Nu(Re) represents the experimental correlation of Nusselt number versus Reynolds number.

The comparison results are shown in Fig. 6, where the Reynolds number of plain fi n heat exchanger is taken as the x coordinate. It can be clearly seen that S12, V12, and VSM12 have better heat transfer performances than P12, while SP12 has worse performance than P12. V12 offers the best heat transfer performance when ReDc is less than about 4,500 under identical mass fl ow rate criteria, or when ReDc is less than about 4,500 under identical pumping power criteria, or when ReDc is less than about 5,000 under identical pressure drop criteria. However, when ReDc is larger than about 4,500 under identical mass fl ow rate criteria, or when ReDc is larger than about 6,000 under identical pumping power criteria, or when ReDc is larger than about 6,700 under identical pressure drop criteria, the performance of S12 is the best. At low Reynolds numbers, the boundary layer of airfl ow is thick. The structure of winglet-type VGs makes VGs be able to destroy the boundary layer more effectively and provide better airfl ow mixed than the slit fi n, and there-fore, the winglet-type VGs perform better at low Reynolds numbers. However, at high Reynolds numbers, the boundary layer of airfl ow becomes thin, and the slit fi n disturbs the airfl ow stronger and provides better airfl ow mixed than that of the winglet-type VGs. Therefore, with the increase of Re, the ratio Fc/Fp for vortex generator decreases, while that for slit fi n is quite the opposite.



Table 4: Geometric dimensions of fi n-and-tube heat exchangers.

Name Type a Tp S1 S2 B H R δ α N

V1 Vortex generators 2 2 16 22 18 1.6 – 0.08 30 3R2 Rhombic formation 2 2 16 22 18 – 1.89 0.08 120 3

Figure 6: Φc/Φp comparisons for 12-row.

For the slit fi n, the fi n with delta-wing vortex generators, and the mixed fi n (front vortex-generator fi n and rear slit fi n) at hand, the mixed fi n has better per-formance than the fi n with delta-wing vortex generators, and the slit fi n offers best heat transfer performance at high Reynolds numbers.

3 Heat Transfer Performances of the Fin Patterns for Flat Tube

In this section, the fi n-side heat transfer performances of two fi n patterns as shown in Fig. 5 for circular tube are summarized. The geometrical details of these fi n pat-terns are presented in Table 4.

These fi n patterns are manufactured, and then assembled into a kind of heat exchangers shown in Fig. 7 with the same fi n space (having the same fi n numbers, thus having the same heat transfer area).



The heat transfer performances of these heat exchangers were obtained by exper-imental method reported in [28]. The experimental results of Nu and f on the fi n side are shown in Fig. 8. The correlations of the data are presented in Tables 5 and 6.

In order to compare the heat transfer performances of V1 and R2, the identical mass fl ow rate criteria, the identical pumping power criteria, and the identical pressure drop criteria as mentioned in above section are used. The results are pre-sented in Fig. 9.

Figure 7: Heat exchangers of fl at tube bank fi n used in experiments.

Figure 8: Heat exchangers of fl at tube bank fi n used in experiments.



It is easy to see that V1 is much better than R2 at three identical conditions. For the same mass fl ow rate, the heat transfer of V1 is larger than that of R2 with an amount of 2%, but the pressure drop decreases 30%. At the same pumping power, the heat transfer of V1 is larger than that of R2 with an amount of 10%. Under the condition of the pressure drop, the heat transfer of V1 is larger than that of R2 with 15%.

It is very hard to manufacture the fi n patterns having variable parameters, and thus we used naphthalene heat mass transfer analogy method [32] in the model as

Table 5: The correlations of Nusselt number.

Name Range of Rea Nu = f(Rea) Maximum relative error

V1 1,360–2,450 Nu = 0.2960Rea0.5325 6.4%

R2 1,330–2,250 Nu = 0.1562Rea0.6194 4.6%

Table 6: The correlations of friction factor.

Name Range of Rea f = f(Rea) Maximum relative error

V1 1,360–2,450 f = 2.6089Rea–0.3542 4.9%

R2 1,330–2,250 f = 2.9836Rea–0.3448 2.5%

Figure 9: Comparisons of heat transfer performances of V1 and R2 exchangers.



shown in Fig. 10 to obtain the correlations of fl at tube bank fi n with vortex gen-erators [7–8, 23, 33–38].

As shown in Fig. 10a, the fl ow passages walled with fl at tube and plates (to model the fi ns) mounted with VGs are presented. Two plates with 6 mm thickness shown in Fig. 10b and one plate with same thickness shown in Fig. 10c are used in test channel. On the plate shown in Fig. 10b, there is a void region marked with abcd on which we put the experimentally measured plates, which are presented in

Figure 10: Experimental setup: (a) fl ow passages; (b) measured plate supporting; (c) plate constructing fl ow passage; (d) fi n surface I; (e) fi n surface II; (f) fl at tube cast from naphthalene.



Fig. 10d named with ‘fi n surface I’ and Fig. 10e named with ‘fi n surface II’. One of the surfaces of experimentally measured plates is cast from naphthalene. The depth of naphthalene is about one half of the plate thickness. VGs are mounted on the fi n surface I and the back surface of fi n surface II. Fin surfaces I and II are arranged face to face, as Fig. 10a shows, so that fi n surface II can be used for mod-eling the back side surface of the fi n mounted with VGs. The stakes with 8 mm width and 4, 5, and 6 mm heights are used to set up the fi n spacing (Tp). Two fl at tubes cast from naphthalene shown in Fig. 10f are put in the regions labeled with B in Fig. 10a to measure the sublimation of fl at tubes. Other fl at tubes and plates except the parts of fi n surface I and fi n surface II serve only to model the fl uid mechanics of the tubes and fi ns in a fi n and tube heat exchanger, and do not par-ticipate directly in the mass transfer process.

The geometrical parameters are S1 = 40 mm, S2 = 55 mm, b = 46.3 mm, and a = 6.3 mm. As shown in Fig. 5a, the leading points of fi rst VG pair are on the line tangent to the fl at tube and two tube widths apart. The leading points of second VG pair are located on the mid line of the fl at tube with the same width apart as that of the fi rst pair. The geometry of VG is a delta winglet as shown Fig. 5a with the base-side edge length twice the trailing edge length.

Experiments are carried out for parameter combinations of three attack angles (a = 25°, 35°, and 45°), three relative heights of VG (H/Tp = 0.6, 0.8, and 0.975), three types of fi n spacing (Tp = 4, 5, and 6 mm), and including three types of tube arrangement. The preparation of naphthalene plates is as follows: First, the naph-thalene plates (fi n surfaces I and II) are cast in a specially designed mold. The surface of the cast plates had a high quality of fl atness and smoothness. Second, VGs are manufactured with copper plate of 0.8 mm thickness by a line milling method, and then the VGs are mounted at the given positions on the fi n surface I and fi n surface II by quick-drying glue. With special care, ensure the use of this glue does not damage the naphthalene surface. Finally, each cast plate is sealed in a special glass container and placed in a temperature-controlled experimental room having temperature fl uctuation less than ± 0.1°C for a period of about 24 hours before a test run. Measurements of the surface contour of the naphthalene plates before and after a test run are made with a sensitive dial gauge with the resolution of 1 μm. The dial gauge is mounted on a fi xed strut that hangs over a movable coordinate table. The coordinate table enables the surface to be indepen-dently traversed in two directions in the horizontal plane. The traversing is con-trolled by a micrometer head and can be read with a resolution of 0.05 mm. The sublimation depth on the plate is measured on the entire surface and a symmetrical mass transfer is obtained in some pre-test experiments. In the formal experiments, only half of fi n surfaces I and II are measured (hatched areas in Fig. 10d and e) due to symmetry. The total measured points are 3,300 on the half fi n surface I or II. The interval of any two neighboring points is 1 mm in both the streamwise direc-tion (y) and spanwise direction (x). The average mass transfer is measured with a precision balance capable of discriminating to within 0.1 mg for specimens having a mass up to 200 g. A volumetric fl ow meter is used to measure the fl ow with pre-cision of 0.1/3,600 m3/s. The temperature of air entering the test section is sensed



by a precision grade laboratory thermometer, which can be read to 0.1°C. A digital timer is used to measure the duration of a test run as well as the time required for setting up the experiment and for executing the surface contour measurements. The pressure drops are measured by a micropressure gauge with a precision of 0.2 mm water column. More details analysis of experimental uncertainty are discussed in [7, 8].

The results obtained by the experiments are local and averaged Sherwood num-bers, which indicate the mass transfer characteristics. Thus, after obtaining the local and average Sherwood number [7], the analogy between heat and mass trans-fers is used to determine the local and average Nusselt number by

Nu = Sh(Pr/Sc)n (20)

where Sc and Nu are defi ned as

Sc T= ( )−0.15262 28 298 10. . (21)

Nu D= ⋅a l/ (22)

According to the suggestion of Goldstein [32] n = 0.4 is adopted in this study. The Reynolds number and the friction factor are defi ned as follows:

Re u D= ⋅ ⋅r mmax / (23)

f pD L v= Δ ( / )maxr 2 2 (24)

where v Q Amax min= and D S a T S a Tp p= − − +4 2 21 1( ) ( ( ) ).

The more detailed reports of serials investigations can be found in Gao et al. [33] for the effect of the height of vortex generators, Ke et al. [34] for the effect of the attack angle of vortex generators, Shi et al. [35] for the effect of the fi n space, and Zhang et al. [36, 37] for the effect of vortex generator position. Here, we only introduce the effect of transversal tube pitch on the local heat transfer and average heat transfer characteristics [38].

The local Nua distributions on the surface II for three different S1/S2 values are presented in Fig 11a–c, respectively. These fi gures reveal that ahead of the second row of VGs, Nua is small. This characteristic means that the vortices generated by the fi rst row of VGs mounted on the surface I will need space to develop. These vortices can reach the fi n surface II and have some effect on Nua of the surface II. Starting from the second row of VGs, there is a region with large Nua around the tube. This indicates that the vortices near the surface II is intensifi ed by the second row VGs. The stream-wise axis of the core of vortices is nearly in line with the second row of tube for case of S1/S2 = 0.582, the region with large Nua is broken by this tube, see Fig. 11a. Nua on the surface II is small around the second row of tube indicates the interactions of vortices generated by the tube and VGs of fi rst and second rows decrease the heat transfer enhancement around this tube for the



case of S1/S2 = 0.582. For this confi guration, heat transfer enhancement is deteriorated around the third row tube because of the intensifi ed unfavorable inter-actions of the vortices generated by VGs, the tubes upstream, and the VGs down-stream. Here the interactions between vortices mean the vortices generated at different positions increase or decrease the amplitude of the same velocity compo-nent in a given point. If more rigorous defi nition is used, interactions mean the increase or decrease of the cross-averaged absolute vortex fl ux in main fl ow direc-tion. Unfavorable interactions of vortices mean they decrease the amplitude of velocity components. It is found that unlike for the case of S1/S2 = 0.582, for cases of S1/S2 = 0.969 and S1/S2 = 0.727, starting from the second row VGs, there are clear regions with large Nua beside the tubes, see Figs 11b and c. The width of the region with large Nua is increased with increasing of S1/S2.

As shown in Figs 12a–c, on fi n surface I, the heat transfer enhancement is appreciable, especially around the tube. The heat transfer enhancement becomes weak in the region far from the tube for S1/S2 = 0.969. The distributions of Nua around the fi rst tube row are similar for three cases of S1/S2. In the region of the second tube row, it is found that the effect of the vortices generated upstream on Nua can penetrate far downstream. It is found that the vortices generated by VGs located around the fi rst tube row has counter rotation direction as the vortices generated by the VGs located around the second tube row. If the tube center lining the main fl ow direction of the fi rst-tube row and the second-tube row are too close,

Figure 11: Comparison of local Nua distribution on fi n surface I:(a) Rea = 1,119, S1/S2 = 0.528, (b) Rea = 1,121, S1/S2 = 0.727, (c) Rea = 1,090, S1/S2 = 0.969.



the interactions of these vortices with counter rotation direction reduce the ampli-tude of velocity components and hence deteriorate heat transfer enhancement. Because of increase in the intensity of vortices interactions with counter rotation direction for small S1/S2, there is no clear region with large Nua near the end of the third tube row. For large S1/S2, for example S1/S2 = 0.969, with less interactions of vortices, two clear regions in which the Nua is enhanced are observed.

At different S1/S2, the comparison of span-averaged Nua distribution in the stream direction on fi n surfaces I and II is presented in Fig. 13. In this experiment, we used the same size of VG, considering the fi n with different S1/S2 will have different area of heat transfer, and in this fi gure we added the span-averaged Nua of smooth fi n for reference. The heat transfer enhancement can be compared with these reference data. As shown in Fig. 13a, for S1/S2 = 0.582, it is clear that VGs can enhance heat transfer effi ciently, in most regions, Nua on surface I is larger than that on surface II. When S1/S2 = 0.727, within relative large region, Nua on II is larger than Nua on I around the fi rst and the second tube rows. However, when S1/S2 = 0.969, Nua on II is larger than Nua on I around the third tube row.

Interactions of vortices will decrease heat transfer enhancement for small S1/S2 case. For the case of S1/S2 = 0.969, there is enough space for vortices generated upstream to develop, and there is less intensity of interactions between vortices, the Nua on II has a larger value than Nua on I downstream. If we refer to Fig. 13c, because the centerlines in main fl ow direction of the fi rst tube row and the second tube row are far away, it is clear that the vortices generated by VGs around the fi rst row are unlikely to interact with vortices generated by VGs around the second row

Figure 12: Comparison of local Nu distribution on fi n surface II: (a) Rea = 1,119, S1/S2 = 0.528, (b) Rea = 1,121, S1/S2 = 0.727, (c) Rea = 1,090, S1/S2 = 0.969.



tube. If compared with the reference data, from Fig. 13, the heat transfer enhance-ment by VGs is different for the three cases studied. The larger heat transfer enhancement comes from the case of S1/S2 = 0.969. The smaller heat transfer enhancement occurred for a case of S1/S2 = 0.582. These results can be explained by the interactions of vortices generated by VGs explained previously. The interac-tions of vortices affect the heat transfer on surfaces with and without VGs.

The average Nua and fa for parameters at a = 35°, Tp = 5 mm, and H = 4 mm is presented as a function of Rea for various transversal tube pitch in Fig. 14. Nua increases with increasing Rea for all cases of different transversal tube pitch. The friction factor decreases with increasing Rea.

Figure 13: Comparison of span-averaged Nua on the fi n surfaces I and II for different S1/S2.



For different S1/S2, it is clear that the large value of S1/S2 will have small value of Nua and fa at the same Rea. If all of data obtained by the experiments are cor-related with considering of Tp, θ, H, and S1/S2, the following correlations can be obtained:

Nu ReT

a

H

T

S

Sp

pa a

. . . . .. ( ) ( ) ( ) ( )= 0 28245

0 631 0 527 0 241 0 180 1

2

0 87ao

11 (25)

f ReT

a

H

Tp

pa a

.

. . .

.=⎛

⎝⎜⎞

⎠⎟⎛

⎝⎜

⎞

⎠⎟

⎛⎝⎜

⎞⎠⎟

−8 48245

0 515

0 527 0 647 0 31a 991

2

S

S

⎛⎝⎜

⎞⎠⎟

−0.592

(26)

500 < Rea < 4,100, 25° ≤ q ≤ 45°, 0.528 ≤ Tp/a ≤ 0.952

The maximum deviation of data is 12.3%. The maximum deviations are 7.6% and 8.3% for Nusselt number and friction factor, respectively.

The correlation obtained through mass transfer, that is, eqns (25) and (26), are validated through the experimental method carried out in [28], and the difference between mass transfer and real heat exchanger performance is shown in Fig. 15.

Figure 14: Effects of S1/S2 on average Nua and fa at different Rea.



Comparing the air-side average Nusselt number and the friction factor obtained by the naphthalene sublimation technique with that obtained by the experiments of the real heat exchanger, one can note that small differences exist for both Nua∼Rea and fa∼Rea, as shown in Fig. 15. The experimental results of naphtha-lene sublimation technique via the heat/mass transfer analogy is in a good agree-ment with experimental data of the real heat exchanger on the air side. The maximal difference for Nua is 6.63%, and for fa is 4.48%. This indicates that although two kinds of experiments have different thermal boundary conditions, one is an isothermal condition and the other is a mixed condition, yet, at the Reyn-olds numbers studied, the results indicate that the heat/mass transfer coeffi cient obtained using the naphthalene sublimation technique at an isothermal condition can be applied to the mixed thermal boundary condition. Our further studies show the reason is that at the present confi guration and the fi n material, the fi n effi -ciency is larger than 0.8, and thus the thermal boundary effect is only limited below 5% [39].

The aforementioned facts show correlations (25) and (26) have a required accuracy.

Up to now, for fl at-tube bank fi n heat exchangers, the heat transfer performance of the fan with vortex generators have not been compared with the louver fi n pat-tern thoroughly. Fortunately, Allison and Dally [26] carried out investigations in comparing a special fi n with one par vortex generators to a special louver fi n of fl at tube bank fi n heat exchanger. It was found that the test of a full-scale coil with fl ow-up delta-winglet geometry exhibited 87% of the capacity of the louver fi n surface. By contrast, it showed a substantially lower pressure drop to approxi-mately 53% of the louver surface. Allison and Dally claimed that the confi guration studied appears to be the best arrangement yet published in the literature, and in many applications the capacity defi cit can be compensated for by an increase in coil face area, and the resulting fan energy consumption is only 54% of that of the equivalent louver fi n surface.

Figure 15: Effects of S1/S2 on average Nua and fa at different Rea.



4 Conclusion

Based on limited data available on various fi n patterns that can be used for tube bank fi n heat exchangers, a brief summary of heat transfer performances of these fi n patterns is provided in this chapter. The main conclusion remarks are as fol-lows:

1. For the circular tube bank fi n heat exchangers, with the Reynolds number rang-ing from 4,000 to 10,000, at high Reynolds numbers, the slit fi n offers best heat transfer performance.

2. For the fl at tube bank fi n heat exchangers, the fi n with vortex generators has a better heat transfer performance than the fi n punched rhombic formation and the louver fi n.

3. Naphthalene heat mass transfer analogy method can be used to screen the fi n pattern with a required accuracy.

4. For the circular tube bank fi n heat exchangers, further optimization and experi-mental comparisons of the fi n pattern with vortex generators to the slit fi n pat-tern should be carried out to make sure it has better heat transfer performance.

Acknowledgments

This work is supported by National Natural Science Foundation of China (Grant Nos. 51230603 and 51025623) and the National Basic Research Program of China (973 Program, No. 2012CB720402).

Nomenclature

a a width of fl at tube, mmA area, m2

Afr air frontal area, m2

Amin minimum fl ow area, m2

Ao total surface area, m2

B length of fl at tube, mmc1, c2, c3, c4 coeffi cient of formulationD hydraulic diameter of fi n side channel, mmDc fi n collar outside diameter, Dc = Do+2d, mmDi inside diameter of tube, mmDo outside diameter of tube, mmFp fi n pitch, mmFs fi n spacing, mm

f, fafriction factor f pD v L= 2 2Δ c max/( )r , f pD v La max= 2 2Δ /( )r

H heat transfer coeffi cient, W.m−2.K−1



H height of vortex generator, mmj Colburn factorL length of fi n, mmm mass fl ow rate, kg.s−1

N number of tube rowsn constantNu,Nua Nusselt number, Nu=h Dc/λ, Nua=h De/λP12 abbreviation of plain fi n with N=12Pl longitudinal tube pitch, mmPt transverse tube pitch, mmQ heat transfer rate, W, or volume fl ow rate, m3/s R length of rhombic formations, mmR2 fi n pattern with punched rhombic formationrc fi n collar outside radius, Dc/2, mm

Re, ReDc, ReaReynolds number, Re=r v Do/µ, ReDc =r v Dc/µ, ReDc =r v D/µ

S1 longitudinal tube pitch, mmS2 transverse tube pitch, mmS12 abbreviation of slit fi n with N = 12Sc Schmidt numberSh Sherwood numbersl length of slit , mmsh height of slit or spiral fi n, mmsw width of slit, mmT temperature, KTp fi n spacing, mmU overall heat transfer coeffi cient, W.m−2.K−1

V velocity, m.s-1

V1 fi n pattern with punched vortex generatorsV12 abbreviation of vortex-generator fi n with N = 12vfr air frontal velocity, m.s−1

Vh height of vortex generator, mmVl length of vortex generator, mm

VSM12abbreviation of mixed fi n with front 6-row vortex-generator fi n and rear 6-row slit fi n

Greek symbolsΔt logarithmic mean temperature difference, KΔp pressure drop, PaF heat transfer rate, Wd fi n thickness, mma angle of attack, deg



h fi n effi ciencyho surface effi ciencyl thermal conductivity, W m–1 K–1

m dynamic viscosity of fl uid, kg m–1 s–1

r density, kg m–3

s contraction ratio of the fi n array

Subscriptsa air sideave average valueb base surfacec compared fi nf fi n surfacei tube insidein air side inletmax maximum valueo tube outsideout air side outletp plain fi nr reference fi ns saturated steamw tube wall

References

[1] Kays, W.M. & London, A.L., Compact Heat Exchangers, McGraw-Hill: New York, 1994.

[2] McQuiston, F.C., Correlation of heat, mass and momentum transport coef-fi cients for plate fi n-and-tube heat transfer surfaces with staggered tubes. ASHRAE Transactions, 84, pp. 294–308, 1978.

[3] Gray, D.L. & Webb, R.L., Heat transfer and friction correlations for plate fi n-and-tube heat exchangers having plain fi ns. 8th. International Heat Trans-fer Conference, San. Francisco, California, pp. 2745–2750, 1986.

[4] Wang, C.C., Chang, Y.J., Hsieh, Y.C. & Lin, Y.T., Sensible heat and friction characteristics of plate fi n-and-tube heat exchangers having plain fi ns. Inter-national Journal of Refrigeration, 19, pp. 223–230, 1996.

[5] Wang, C.C., Lin, Y.T. & Lee, C.J., An air side correlation for plain fi n-and-tube heat exchangers in wet conditions. International Journal of Heat and Mass Transfer, 43, pp. 1869–1872, 2000.

[6] Wang, C.C., Chi, K.Y. & Chang, C.J., Heat transfer and friction characteris-tics of plate fi n-and-tube heat exchangers, part II: correlation. International Journal of Heat and Mass Transfer, 43, pp. 2693–2700, 2000.



[7] Wang, L.B., Zhang, Y.H., Su, Y.X. & Gao, S.D., Local and average heat /mass transfer over fl at tube bank fi n mounted in-line vortex generators with small longitudinal spacing. Journal of Enhanced Heat Transfer, 9, pp. 77–87, 2002.

[8] Wang, L.B., Ke, F., Gao, S.D. & Mei, Y.G., Local and average characteristics of heat/mass transfer over fl at tube bank fi n with four vortex generators per tube. ASME, Journal of Heat Transfer, 124(3), pp. 546–552, 2002.

[9] Kylikof, U.A., The Cooling System of Diesel Locomotive, Moscow: Machine Manufacturing (in Russian), 1988.

[10] Matos, R.S., Laursen, T.A., Vargas, J.V.C. & Bejan, A., Three dimensional optimization of staggered fi nned circular and elliptic tubes in forced convec-tion. International Journal of Thermal Sciences, 43, pp. 477–487, 2004.

[11] Saboya, F.E.M. & Sparrow, E.M., Experiments on a three-row fi n and tube heat exchangers. Journal of Heat Transfer, 98, pp. 520–522, 1976.

[12] Jacobi, A.M. & Shah, R.K., Heat transfer surface enhancement through the use of longitudinal vortices: a review of recent progress. Experimental Ther-mal and Fluid Science, 11, pp. 295–309, 2002.

[13] Nuntaphan, A., Kiatsiriroat, T. & Wang, C.C., Heat transfer and friction char-acteristics of crimped spiral fi nned heat exchangers with dehumidifi cation. Applied Thermal Engineering, 25, pp. 327–340, 2005.

[14] Nuntaphan, A., Kiatsiriroat, T. & Wang, C.C. Air side performance at low Reynolds number of cross-fl ow heat exchanger using crimped spiral fi ns. International Journal of Heat and Mass Transfer, 32, pp. 151–165, 2005.

[15] Nakayama, W. & Xu, L.P., Enhanced fi ns for air-cooled heat exchangers-heat transfer and friction correlations. 1st ASME/JSME Thermal Engineering Joint Conference, Honolulu, Hawaii, pp. 495–502, 1983.

[16] Wang, C.C., Tao, W.H. & Chang, C.J., An investigation of the air side per-formance of the slit fi n-and-tube heat exchangers. International Journal of Refrigeration, 22, pp. 595–603, 1999.

[17] Wang, C.C., Lee, W.S. & Sheu, W.J., A comparative study of compact enhanced fi n-and-tube heat exchangers. International Journal of Heat and Mass Transfer, 44, pp. 3565–3573, 2000.

[18] Du, Y.J. & Wang, C.C., An experimental study of the air side performance of the superslit fi n-and-tube heat exchangers. International Journal of Heat and Mass Transfer, 43, pp. 4475–4482, 2000.

[19] Kwak, K.M., Torli, K. & Nishino, K., Heat transfer and fl ow characteristics of fi n–tube bundles with and without winglet-type vortex generators. Experi-ments in Fluids, 33, pp. 696–702, 2002.

[20] Torli, K., Kwak, K.M. & Nishino, K., Heat transfer enhancement accom-panying pressure-loss reduction with winglet-type vortex generators for fi n-tube heat exchangers. International Journal of Heat and Mass Transfer, 45, pp. 3795–3801, 2002.

[21] Leu, J.S., Wu, Y.H. & Jang, J.Y., Heat transfer and fl uid fl ow analysis in plate-fi n and tube heat exchangers with a pair of block shape vortex generators. International Journal of Heat and Mass Transfer, 47, pp. 4327–4338, 2004.



[22] Pesteei, S.M., Subbarao, P.M.V. & Agarwal, R.S., Experimental study of the effect of winglet location on heat transfer enhancement and pressure drop in fi n-tube heat exchangers. Applied Thermal Engineering, 47, pp. 1684–1696, 2005.

[23] Zhang, Y.H., Wu, X., Wang, L.B., Song, K.W., Dong, Y.X. & Liu, S., Comparison of heat transfer performance of tube bank fi n with mounted vor-tex generators to tube bank fi n with punched vortex generators. Experimental Thermal and Fluid Science, 33, pp. 58–66, 2008.

[24] Xie, G.N., Wang, Q.W. & Sunden, B., Application of a genetic algorithm for thermal design of fi n-and-tube heat exchangers. Heat Transfer Engineering, 29, pp. 597–607, 2008.

[25] Fiebig, M., Vortex generators for compact heat exchangers. Enhanced Heat Transfer, 2(1–2), pp. 43–61, 1995.

[26] Allison, C.B. & Dally, B.B., Effect of a delta-winglet vortex pair on the per-formance of a tube–fi n heat exchanger. International Journal of Heat and Mass Transfer, 50, pp. 5065–5072, 2007.

[27] Tang, L.H., Zeng, M.A. & Wang, Q.W., Experimental and numerical inves-tigation on air-side performance of fi n-and-tube heat exchangers with vari-ous fi n patterns. Experimental Thermal and Fluid Science, 33, pp. 818–827, 2009.

[28] Wang, L.B., Yang, L.F., Lin, Z.M., Dong, Y.X., Liu, S. & Zhang, Y. H. Comparisons of performances of a fl at tube bank fi n model mounted vortex generators and the real heat exchanger. Experimental Heat Transfer, 22(3), pp. 198–251, 2009.

[29] Schmidt, T.E., Heat transfer calculations for extended surfaces. Refrigerating Engineering, 57, pp. 351–357, 1949.

[30] Yu, B. & Tao, W.Q., Pressure drop and heat transfer characteristics of turbu-lent fl ow in annular tubes with internal wave-like longitudinal fi ns. Heat and Mass Transfer, 40, pp. 643–651, 2004.

[31] Wang, L.B., Tao, W.Q. & Wang, Q.W., Experimental study of developing turbulent fl ow and heat transfer in ribbed convergent/divergent square ducts. International Journal of Heat and Fluid Flow, 22, pp. 603–613, 2001.

[32] Goldstein, R.J. & Cho, H.H., A review of mass transfer measurements using naphthalene sublimation. Experimental Thermal and Fluid Science, 10, pp. 416–434, 1995.

[33] Gao, S.D., Wang, L.B., Zhang, Y.H. & Ke, F. The optimum height of winglet vortex generators mounted on three-row fl at tube bank fi n. Journal of Heat Transfer, 125, pp. 1007–1016, 2003.

[34] Ke, F., Wang, L. B., Hua, L., Gao, S. D. & Su, Y.X., The optimum angle of attack of delta winglet vortex generators on heat transfer performance of fi nned fl at tube bank with considering non-uniform fi n temperature. Experi-mental Heat Transfer, 19, pp. 227–249, 2006.

[35] Shi, B.Z., Wang, L.B., Gen, F. & Zhang, Y.H., The optimal fi n spacing for three-row fl at tube bank fi n mounted with vortex generators. Heat Mass Transfer, 43, pp. 91–101, 2006.



[36] Zhang, Y.H., Wang, L.B., Ke, F., Su, Y.X. & Gao, S.D., The effects of span position of winglet vortex generator on local heat/mass transfer over a three-row fl at tube bank fi n. Heat Mass Transfer, 40, pp. 881–891, 2004.

[37] Zhang, Y.H., Wang, L.B., Su, Y.X. & Gao, S.D., Effects of the pitch of in-line delta winglet vortex generators on heat transfer of a fi nned three-row fl at tube bank. Experimental Heat Transfer, 17, pp. 69–90, 2004.

[38] Liu, S., Wang, L.B., Fan, J.F., Zhang, Y.H., Dong, Y.X. & Song, K.W., Tube transverse pitch effect on heat / mass transfer characteristics of fl at tube bank fi n mounted with vortex generators. Journal of Heat Transfer, 130(June), pp. 064501–064503, 2008.

[39] Wang, Y., Wang, L.C., Lin, Z.M., Yao, Y.H. & Wang, L.B., The condition requiring conjugate numerical method in study of heat transfer character-istics of tube bank fi n heat exchanger. International Journal of Heat Mass Transfer, 55, pp. 2353–2364, 2012.


chapter 7 air-side heat transfer and friction ......air-side heat transfer and friction...

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