A Generalized Heat Transfer Coefficient of Heat Transfer by Chang and Wang

l'ergmo,, lnt. J. Heat Mass Transfer. Vol. 40, No. 3, pp. 53~544, 1997

Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved

0017 9310/97515.00+0.00

PII: S0017-9310(96)00116--0

A generalized heat transfer correlation for louver fin geometry

YU-JUEI C H A N G and CHI-CHUAN W A N G Energy and Research Laboratories, Industrial Technology Research Institute, Hsinchu, Taiwan,

Republic of China

(Received 6 December 1995 and in final form 17 April 1996)

Abstraet--A generalized heat transfer correlation for louver fin geometry is developed with the aid of a large data bank. This data bank consists of 91 samples of louvered fin heat exchangers with different geometrical parameters, including louver angle, tube width, louver length, louver pitch, fin length and fin pitch. For the corrugated louver fin geometry, it is shown that 89.3% of the corrugated louver fin data are correlated within _+ 15% with mean deviation of 7.55%. The inclusion of the plate-and-tube louver fin data in the heat transfer correlation (equation (A1)) results in a mean deviation of 8,21%. Copyright

© 1996 Elsevier Science Ltd.

INTRODUCTION

To effectively improve the thermal performance of the air-cooled heat exchangers, it is important to reduce high air-side therrnal resistance. Therefore, extended surfaces are commonly used in the air-side of heat exchangers. The extended surface enhances the heat transfer rate by increasing the surface area and by inducing turbulent mixing of air flow. Therefore, highly interrupted surfaces are often encountered in enhanced surfaces to efficiently break up the growth of thermal bounda.ry layer from leading edge. Exam- ples of interrupted surfaces are the offset strip fin and louvered fin. Louvered fins can be manufactured by high-speed production techniques and as a result are less expensive than other interrupted flow geometry when produced in large quantities. Figure 1 shows five typical air-cooled heat exchangers that use the louver fin geometry. As seen, the air-cooled heat exchangers generally consist of multi-louver fins and flat tube. Generally, the minor diameter of the flat tube is 1.5- 5 mm. The flat tube design offers several advantages as outlined by Webb and Jung [1] :

(1) the air flow is normal to all of the louvers; (2) the wake region behind the tube does not reduce

heat transfer on downstream fin regions ; (3) it provides a higher fin efficiency; (4) the small projected area of the flat tube will

result in lower profile drag than the larger diameter round tube does.

More quantitative comparisons between the louver fin surface and other geometries are shown by several investigators. Using: the volume goodness comparison method, Sunden and Svantesson [2] concluded that the louvered surfaces are more efficient than the cor- responding smooth surface. Chang et al. [3] used vari- ous comparison methods, including area goodness factor, volume go,adness factor and performance

evaluation criteria proposed by Cowell [4] to quan- titatively study the air side of the fiat tube condenser and its round tube condenser counterpart. They found that the fiat tube geometry offers significant improve- ment as comparing to the round tube condenser. Recently, Cowell et al. [5] compared the louvered fin surface with offset-strip surface configuration. They reported that the louvered fins are capable of out- performing offset strips.

Despite the superiority of the louver fin surface, the fact is that the louvered surfaces have been in existence since the 1950s. The available performance data in the open literature are very limited. Davenport [6] reported a comprehensive study of a non-standard variant of the flat tube and louvered corrugated heat exchangers. Totally, 32 samples of louver fin samples were tested. The fin geometry tested by Davenport is shown in Fig. 1 (Type A). Note that the fin pitch studied by Davenport is larger than that presently used and the louver fin is distinctly triangular shaped channel. Davenport had proposed a correlation for Fig. IA geometry and claimed 95% of the exper- imentalj factors data had been correlated within +6%.

Achaichia and Cowell [7] were the first to present the performance data for flat tube and louvered plate fin surfaces (Fig. 1, type B). They had verified the flattening characteristics of the Stanton number at low Reynolds number previously observed by Davenport [6]. They had explained the flattening characteristics as the effective heat transfer configuration changes from 'flat plate' to 'duct flow'. A total of 15 samples were tested in their study. They also presented a cor- relation that claimed all the Stanton number data for ReLp > 75 to be within 10%.

Webb and Jung [1] presented experimental data for six brazed aluminium heat exchangers. The fin geometry of their brazed aluminium heat exchangers includes three standard corrugated fin geometry (Fig. 1, Type C) and three splitter fin geometry (Fig. 1,

533

534 Y.-J. CHANG and C.-C. WANG

NOMENCLATURE

A total surface area (Af+ At) [m 2] ReDh Af fin surface area [m 21 Ai louver surface area [m z] ReLp At external tube surface area [m 2] Dh hydraulic diameter of fin array [ram] S, Dm major diameter [mini Fp fin pitch [mm] Sz Fd fin depth [mm] St Fi fin length [mm] Tp h0 heat transfer coefficient [W m -2 K -~] Td j the Colburn factor [dimensionless] k thermal conductivity [W m - ' K -l] 1 fin length [mm] 0 L h louver height [mm] 6 L~ louver length [mm] e Lp louver pitch [mm] el rn ( ~ ) [m-q r/ N number of test data point qf Nj number of full louvers over flow

direction [dimensionless] Pr the Prandtl number [dimensionless] r ratio of the fin area at the sample sides to

the overall louver fin area [dimensionless]

Reynolds number based on hydraulic diameter [dimensioneless] Reynolds number based on louver pitch [dimensionless] non-louvered inlet and exit fin regions [mm] re-direction length [mm] the Stanton numer [dimensionless] tube pitch [mm] tube depth [mm].

Greek symbols louver angle [deg] thickness of tube wall or fin [nun] A / A , finning factor [dimensionless] At/ A [dimensionless] surface effectiveness [dimensionless] fin efficiency [dimensionless].

Subscripts 1 louvered portion 2 unlouvered portion f fin.

Type E). The brazed aluminium heat exchanger is made of multi-louver fins brazed to a flat, extruded tube, with a cross section of several independent pass- ages. They found that the standard corrugated brazed aluminium flat tube design gives a 90% higher heat transfer coefficient for only 25% higher pressure drop compared with the round tube plain plate fin design.

Rugh et al. [8] provided data on a high fin density (1960 fins m-]) louvered surface. Data were presented against Reynolds number (based on Dh) in the range of 150 and 300. The heat exchanger they tested is a corrugated louver fin with a splitter plate (Fig. 1, Type D). Comparisons were drawn relative to the plain fin, and they reported that the louver fins produce an approximately 25% increase in heat transfer coefficient and 110% increase in pressure drop.

The investigations of heat transfer and pressure drop of standard louver fin and incline louver fin were reported by Sunden and Svantesson [2, 9]. Their inves- tigations show that all the louvered surfaces are more efficient than the corresponding smooth surface, and the standard louver fin geometry reveals higher Stanton number than other inclined louver fin geometries.

Chang et aL [10] and Chang and Wang [11] pre- sented 27 samples of corrugated louvered fin heat exchangers (Fig. 1, Type C) with different geometrical parameters, including tube width, louver length, louver pitch, fin length and fin pitch. Results are pre- sented as plots of friction factor, f, and the Colburnj factor against Reynolds number based on louver pitch in the range of 100-1000. They also applied the Sah-

noun and Webb [12] and the Dillen and Webb [13] models to compare with the experimental data, and showed good agreements between the experimental data and the models. By introducing 'area ratio' par- ameters, a simpler correlation of the Colburn j factor and friction factor f were obtained. It is shown that 85% of the experimental data of heat transfer and friction data were correlated within _ 10%. Later on, Webb et al. [14] used both Davenport [6] and Chang and Wang [11] data to develop semi-analytical heat transfer and friction correlations, which predict 95% of the heat transfer coefficient data within + 20%, and are applicable to currently used copper/brass and brazed aluminium cores.

Though a few correlations are already available, the justification for proposing a new one is required. For instance, Sunden and Svantesson [9] indicated that the Achaichia and CoweU correlation [7] considerably overpredicts their fin geometry and CoweU et al. [5] argued that the use of Sunden and Svantesson's [9] correlation [7] should be very careful, since their data bank is very limited (six samples). Therefore, the objective of the present study is to propose a general heat transfer correlation that uses a much larger data bank.

THE DATA BANK

An attempt has been made to collect data from a wide range of geometric dimensions. In Table 1, a complete list has been given and the relevant definition of the geometric parameters is shown in Fig. 2. Table

Generalized heat transfer correlation 535

Type (A), Corrugated Louver With Triangular Channel

Type (B), Plate-and- Tube Louver Fin Geome, try

Triangular channel Air flow

y

Louvered plate fin

Air flow

Type (C), Louver With Channelt

Corrugated Rectangular

Air flow louver fin

Type (D), Corrugated Louver 'With Splitter Plate and Rectangular Channel

Type (E), Corrugated Louver With Splitter Plate and Tri~mgular Channel

Air flow

Triangular channel

Air flow

Fig. I. Type of louver fin heat exchangers.

Splitter plate

Splitter plate

536 Y.-J. CHANG and C.-C. WANG

Table 1. Geometric details of the louver fin heat exchangers

Louver Louver Louver Sample Core pitch length angle

Variant source type (mm) (mm) (deg)

Fin Tube Fin Fin Fin pitch depth depth length thickness (mE) (mm) (mm) (mm) (mm)

Tube Rows pitch of Dh Data (mm) tubes (ram) point

1 D(1) A 3 2 D(2) A 3 3 D(3) A 3 4 D(4) A 2.25 5 D(5) A 2.25 6 D(6) A 2.25 7 D(7) A 1.8 8 D(8) A 1.8 9 D(9) A 1.8

10 D(10) A 1.5 II D(13) A 1.8 12 D(14) A 3 13 D(15) A 2.25 14 D(16) A 2.25 15 D(17) A 2.25 16 D(18) A 2.25 17 D(19) A 2.25 18 D(20) A 3 19 D(21) A 2.25 20 D(22) A 1.8 21 D(23) A 1.5 22 D(24) A 2.25 23 D(25) A 2.25 24 D(26) A 2.25 25 D(27) A 2.25 26 D(28) A 2.25 27 D(29) A 2.25 28 D(30) A 2.25 29 D(31) A 2.25 30 D(32) A 2.25 31 C&W(1) C 1.318 32 C&W(2) C 1.318 33 C&W(3) C 1,318 34 C&W(4) C 1.42 35 C&W(5) C 1.42 36 C&W(6) C 1,42 37 C&W(7) C 1.481 38 C&W(8) C 1.481 39 C&W(9) C 1.481 40 C&W(10) C 1.534 41 C&W(ll) C 1.534 42 C&W(12) C 1.534 43 C&W(13) C 1.693 44 C&W(14) C 1.693 45 C&W(15) C 1.693 46 C&W(16) C 1.546 47 C&W(17) C 1.546 48 C&W(18) C 1.546 49 C&W(19) C 1.86 50 C&W(20) C 1.86 51 C&W(21) C 1.86 52 C&W(22) C 1.59 53 C&W(23) C 1.59 54 C&W(24) C 1.59 55 C&W(25) C 1.532 56 C&W(26) C 1.532 57 C&W(27) C 1.532 58 PSU(1) C 1 59 PSU(IO) C 1.016 60 PSU(ll) C 1.016 61 PSU(12) C 1.016 62 PSU(15) C 0.94 63 A&C(1) B 1.4 64 A&C(2) B 1.4 65 A&C(3) B 1.4 66 A&C(4) B 1.4 67 A&C(5) B 1.4

9.5 8.43 9.5 10.37 9.5 16.66 9.5 13.36 9.5 16 9.5 19.2 9.5 18.8 9.5 20.83 9.5 27.82 9.5 19.63 9.5 14.15 9.5 11.15

11.7 24.14 11 21.37 10 21.37 9 21.37 8 20.28 7.1 13.89 7.1 13.78 7.1 20.42 7.1 26.1 7.1 9.52 7.1 16.53 7.1 17.7 7.1 16 7.1 13.89 7.1 14.15 6.5 16.63 6 17.59 5 14.41

12,44 28 12,44 28 12,44 28 17.18 28 17.18 28 17.18 28 12.78 28 12.78 28 12.78 28 16.07 28 16.07 28 16.07 28 12.15 28 12.15 28 12.15 28 16.17 28 16.17 28 16.17 28 15.25 28 15.25 28 15.25 28 13.18 28 13.18 28 13.18 28 16.84 28 16.84 28 16.84 28 6.5 30 6.858 27 6.858 27 6.858 27 7.62 27 8.5 25.5 8.5 25.5 8.5 25.5 8.5 21.5 8.5 28.5

1.55 40 40 12.7 1.55 40 40 12.7 1.6 40 40 12.7 1.55 40 40 12.7 1.56 40 40 12.7 1.56 40 40 12.7 1.55 40 40 12.7 1.585 40 40 12.7 1.575 40 40 12.7 1.525 40 40 12.7 1.625 40 40 12.7 1.56 40 40 12.7 1.675 40 40 12.7 1.65 40 40 12.7 1.65 40 40 12.7 1.625 40 40 12.7 1.6 40 40 12.7 1.535 40 40 7.8 1.525 40 40 7.8 1.535 40 40 7.8 1.55 40 40 7.8 1.485 40 40 7.8 1.51 40 40 7.8 1.51 40 40 7.8 1.225 40 40 7.8 1.005 40 40 7.8 1.535 40 40 7.8 1.51 40 40 7.8 1.535 40 40 7.8 1.5 40 40 7.8 1.8 22 22 16 2 22 22 16 2.2 22 22 16 1.8 22 22 19 2 22 22 19 2.2 22 22 19 1.8 26 26 16 2 26 26 16 2.2 26 26 16 1.8 26 26 19 2 26 26 19 2.2 26 26 19 1.8 32 32 16 2 32 32 16 2.2 32 32 16 1.8 32 32 19 2 32 32 19 2.2 32 32 19 1.8 38 38 19 2 38 38 19 2.2 38 38 19 1.8 44 44 16 2 44 44 16 2.2 44 44 16 1.8 44 44 19 2 44 44 19 2.2 44 44 19 1.124 16 16 8 1.954 20.32 20.32 9.22 1.588 20.32 20.32 9.22 1.27 20.32 20.32 9.22 1.114 16.26 16.26 9.15 2.02 32 41.6 9 3.25 32 41.6 9 1.65 32 41.6 9 2.09 32 41.6 9 2.03 32 41.6 9

0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 14 0.075 9.182 0.075 9.174 0.075 9.182 0.075 9.194 0.075 9.142 0.075 9.162 0.075 9.162 0.075 8.928 0.075 8.74 0.075 9.182 0.075 9.162 0.075 9.182 0.075 9.154 0.16 21 0.16 21 0,16 21 0A6 24 0.16 24 0.16 24 0.16 21 0.16 21 0.16 21 0.16 24 0.16 24 0.16 24 0.16 21 0.16 21 0.16 21 0.16 24 0.16 24 0.16 24 0.16 24 0.16 24 0.16 24 0.16 21 0.16 21 0.16 21 0.16 24 0.16 24 0.16 24 0.157 9.6 0.0508 11.11 0.0508 11.11 0.0508 11.11 0.127 11.11 0.05 11 0.05 11 0.05 11 0.05 11 0.05 11

l 2.78 9 1 2.78 9 1 2.86 9 1 2.78 9 1 2.8 9 1 2.8 9 1 2.78 9 1 2.84 9 1 2.82 9 1 2.74 9 1 2,9 9 1 2.8 9 1 2.99 9 1 2.95 9 1 2.95 9 1 2.9 9 1 2.86 9 1 2.61 9 1 2.6 9 1 2.61 9 1 2.64 9 1 2.54 9 1 2.58 9 1 2.58 9 1 2.14 9 1 1.8 9 1 2.61 9 1 2.58 9 1 2.61 9 1 2,56 9 1 3.069 9 1 3.399 9 1 3.72 9 1 3.041 9 1 3.374 9 1 3.701 9 1 3.043 9 1 3.37 9 1 3,69 9 1 3.069 9 1 3.406 9 1 3.736 9 1 3.047 9 1 3.376 9 1 3.697 5 1 3.057 9 1 3.394 9 1 3,724 9 1 3.07 9 1 3.409 9 1 3.74 9 1 3.007 9 1 3.333 9 1 3.651 9 1 3.036 9 1 3.371 9 1 3.699 9 1 1.962 6 1 3.317 5 1 2.621 5 1 2.145 6 1 1.759 6 2 3.33 9 2 4.94 8 2 2.69 9 2 3.37 8 2 3.3 8

Generalized heat transfer correlation

Table 1--continued

537

Louver Louver Louver Fin Tube Fin Fin Fin Tube Rows Sample Core pitch length angle pitch depth depth length thickness pitch of

Variant source type (mm) (ram) (deg) ( m m ) (mm) (mm) ( m m ) ( r a m ) ( ram) tubes Dh

(mm) Data point

68 A&C(6) 13 1.4 8.5 25.5 2.15 16 20.8 9 69 A&C(7) B 1.4 8.5 25.5 1.7 16 20.8 9 70 A&C(8) 13 0.81 8.5 29 2.11 32 41.6 9 71 A&C(9) 13 0,81 8.5 29 1.72 32 41.6 9 72 A&C(10) 13 0,81 8.5 29 3.33 32 41.6 9 73 A&C(ll) 13 1.1 8.5 30 2.18 32 41.6 9 74 A&C(12) B 0.81 8.5 20 2.16 32 41.6 9 75 A&C(13) B 1.1 5.5 28 2.16 32 41.6 6 76 A&C(14) B 1.1 11.5 22 2.17 32 41.6 12 77 A&C(15) B 1.1 5.5 22 2.17 32 41.6 6 78 W&J(1) C 1.397 16.255 30 2.117 25.4 25.4 18.923 79 W&J(2) C 1.397 16.255 30 1.693 25.4 25.4 18.923 80 W&J(3) C 1.397 16.255 30 1.411 25.4 25.4 18.923 81 W&J(4) Fi 1.65 7.0987 30 2.117 25.4 25 .4 8.64 82 W&J(5) F', 1.65 7.0987 30 1.693 25.4 25 .4 8.64 83 W&J(6) F', 1.65 7.0987 30 1.411 25.4 25 .4 8.64 84 Rugh D 0.85 2.13 25 0.51 15.6 15.6 2.84

et al. 85 S&S(1) C. 1.4 10.2 22 1.5 57.4 57.4 12.5 86 S&S(2) C 1.4 10.3 18.5 2.0 57.4 57.4 12.4 87 S&S(3) C 1.3 10.0 24.5 2.0 37 37 12.4 88 S&S(4) C 1.2 6.8 24 1.8 37 37 8.6 89 S&S(5) C 1.1 6.8 25.5 1.8 50 50 9.6 90 S&S(6) C 0.5 5.0 28.5 1.9 47.8 47.8 8 91 Tanaka C 1.884 18.5 35 1.5 50 50 20

et al.(1)

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.1575 0.1575 0.1575 0.1575 0.1575 0.1575 0 . ~

0.06 0 .~ 0.06 0 .~ 0.06 0 .~ 0.16

11 11 11 11 11 11 11 8

14 8

22.99 22.99 22.99 22.99 22.99 22.99

7.51

14" 13.9" 13.9* 10.1' 11.1" 9.5* 25 +

3.47 2.76 3.38 2.81 5.02 3.49 3.45 3.14 3.66 3.16 3.505 2.82 2.337 3.073 2.515 2.134 0.824

2.609 3.400 3.426 2.972 2.984 3.058 3.928

9 6 6 8 6 8 7 8 6 9 6 4 4 6 5 6 9

12 12 12 14 11 9 6

* The major tube diameter is not given, a value of 1.5 mm is assumed, + The major tube diameter is not given, a value of 5 mm is assumed.

2 gives the detailed dimensions on the louver fin, and their corresponding definition of the geometric dimen- sions are drawn :in Fig. 3. The present data bank includes those from Davenport [6] (30 samples, Fig. 1, Type A), Tanaka et al. [15] (one sample, Fig. 1, Type C). Achaicl~La and Cowell [7] (15 samples, Fig. 1, Type B), Webb [16] (five samples, Fig. 1, Type C), Sunden and Svantesson [9] (6 samples, Fig. 1, Type C), Webb and Jung [1] (6 samples, Fig. 1, Type C and Type E), Rugh et al. [17] (1 sample, Fig. 1, Type D) and Chang and Wang [11] (27 samples, Fig. 1, Type C). The original test samples of Davenport [6] are 32. However, as depicl:ed by Davenport [6], their samples of no. 11 and no. 12 are damaged. Therefore, these two samples are not included. The present exper- imental data all use the same fin efficiency calculation (q =(tan(ml))/ml, where m = x/(2ho)/(kf6r)) except Achaichia and Cowell [7]. As indicated by Fig. 1 (Type B), the louver fin geometry of Achaichia and Cowell [7] is quite different from that of corrugated fin geometry. The calculation of the plate-and-tube louver surface efficiency consists of two surface efficiency ql,r/2, respectively, for louvered portions and unlouvered portions. Namely,

q = r / , r+r/2(1--r) , (1)

where r is the ratio of the fin area at the sample sides to the overall louver fin area.

Achaichia [18] did not give the detailed calculation of r/2.To avoid any misleading of the regression result,

their data are not included in the final regression of the corrugated geometry. However, we also present another correlation that had included the plate-and- tube data from Achaichia and Cowell [7], which is illustrated in the appendix.

The data reduction methods in the data bank are also quite different as depicted in Table 3. Davenport [6] and Tanaka et al. [15] use U A - L M T D reduction method with correction factor equal to 1, and other investigators use e-NTU method. The effect of cor- rection factor is insignificant since the corresponding capacity ratio at the highest airflows of their data is very small (a value of 0.05 is shown in the thesis of Davenport [19]), The use of different flow arrange- ment in e-NTU method is also negligible. This may be seen in a sensitivity analysis by Chang and Wang [11]. They reduced all the data using an unmixed/mixed relation and an unmixed/unmixed flow arrangement and found that the differences between unmixed/ unmixed and unmixed/mixed situations are quite small. The reason for this phenomenon is analogous to that of Davenport [19].

PREVIOUS LOUVER FIN CORRELATION

Correlation by Davenport [6] (Fig. l, Type A) is :

FL -'[1.1 j = 0.249Re£pO.42 = o . ~ . l ~ / ~o.=o

300 < Renh < 4000. (2)

538 Y.-J. CHANG and C.-C. WANG

Corrugated Louver Fin Geometry

Plate-and-Tube Louver Fin Geometry. Achaichia and Cowell [7]

o __t_

1-- Td

Fd

I I

" ,' *"- U n l o u v e r e d ! ! i i a r e a I I

Louver Tube / "

A+B=Td A B i__ _1 I_ _1

( } (c ?1 Louver I

Fig. 2. Definition of various geometric parameters.

U n l o u v e r e d a r e a

Generalized heat transfer correlation

Table 2. Geometric dimension of the louver fin

539

Sample Fin Louver S~ Si $2 $2 Variant source material Fin type number (mm) number (mm) number

1 D(1) Cu I 8 4 2 8 I 2 D(2) Cu I 8 4 2 8 1 3 D(3) Cu 1 8 4 2 8 1 4 D(4) Cu I 12 3.25 2 6.5 1 5 D(5) Cu 1 12 3.25 2 6.5 1 6 D(6) Cu I 12 3.25 2 6.5 1 7 D(7) Cu 1 16 2.8 2 5.6 1 8 D(8) Cu I 16 2.8 2 5.6 1 9 D(9) Cu 1 16 2.8 2 5.6 1

10 D(10) Cu I 20 2.5 2 5 1 11 D(13) Cu I 16 2.8 2 5.6 1 12 D(14) Cu I 8 4 2 8 1 13 D(15) Cu I 12 3.25 2 6.5 1 14 D(16) Cu I 12 3.25 2 6.5 1 15 D(17) Cu I 12 3.25 2 6.5 1 16 D(18) Cu I 12 3.25 2 6.5 1 17 D(19) Cu I 12 3.25 2 6.5 1 18 D(20) Cu I 8 4 2 8 1 19 D(21) Cu I 12 3.25 2 6.5 1 20 D(22) Cu I 16 2.8 2 5.6 1 21 D (22,) Cu I 20 2.5 2 5 1 22 D(24.) Cu I 12 3.25 2 6.5 1 23 D(25) Cu I 12 3.25 2 6.5 1 24 D(2~) Cu I 12 3.25 2 6.5 1 25 D(27) Cu I 12 3.25 2 6.5 1 26 D(28) Cu I 12 3.25 2 6.5 1 27 D(29) Cu I 12 3.25 2 6.5 1 28 D(30) Cu I 12 3.25 2 6.5 1 29 D(31) Cu I 12 3.25 2 6.5 1 30 D(32) Cu I 12 3.25 2 6.5 1 31 C&W(1) A1 I 12 1.815 2 2.55 1 32 C&W(2) AI I 12 1.815 2 2.55 1 33 C&W(3) AI I 12 1.815 2 2.55 1 34 C&W(4) AI I 10 2.78 2 2.24 1 35 C&W(5) AI I 10 2.78 2 2.24 1 36 C&W(6) A1 I 10 2.78 2 2.24 1 37 C&W(7) A1 I 12 2.39 2 3.45 l 38 C&W(8) AI I 12 2.39 2 3.45 1 39 C&W(9) A1 I 12 2.39 2 3.45 1 40 C&W(I[0) A1 I 12 2.725 2 2.14 1 41 C&W(I[1) AI I 12 2.725 2 2.14 1 42 C&WCt2) AI I 12 2.725 2 2.14 1 43 C&W(]I3) A1 IV 12 4.82 2 2.692 1 44 C&W(] 4) AI IV 12 4.82 2 2.692 1 45 C&W(] 5) A1 IV 12 4.82 2 2.692 1 46 C&W(] 6) A1 II1 12 2.8 2 2.617 3 47 C&W(I 7) A1 III 12 2.8 2 2.617 3 48 C&W(I 8) A1 III 12 2.8 2 2.617 3 49 C&W(I 9) A1 V 12 2.582 4 2.67 2 50 C&W(20) A1 V 12 2.582 4 2.67 2 51 C&W(21) AI V 12 2.582 4 2.67 2 52 C&W(22) AI I 22 3.335 2 2.35 1 53 C&W(23) AI I 22 3.335 2 2.35 1 54 C&W(24) AI I 22 3.335 2 2.35 1 55 C&W(2;5) A1 III 18 3.615 2 3.067 3 56 C&W(26) A1 III 18 3.615 2 3.067 3 57 C&W(27) AI III 18 3.615 2 3.067 3 58 PSU(1) Cu I 10 1.75 2 1.5 59 PSU(10) Cu I 10 3.4671 2 2.2098 60 PSU(11) Cu I 10 3.4671 2 2.2098 61 PSU(12) Cu I 10 3.4671 2 2.2098 62 PSU(15) AI I 10 1.3335 2 3.2512 63 A&C(I ) Cu I 20 3.8 2 6 64 A&C(2) Cu I 20 3.8 2 6 65 A&C(2,) Cu I 20 3.8 2 6 66 A&C(~.) Cu I 20 3.8 2 6 67 A&C(5) Cu I 20 3.8 2 6 68 A&C(6) Cu VI 10 3.4 2 6

540 Y.-J. CHANG and C.-C. WANG

Table 2--continued

Sample Fin Louver S~ S~ $2 $2 Variant source material Fin type number (mm) number (mm) number

69 A&C(7) Cu VI 10 3.4 2 6 0 70 A&C(8) Cu I 36 3.505 2 5.005 1 71 A&C(9) Cu I 36 3.505 2 5.005 1 72 A&C(10) Cu I 36 3.505 2 5.005 1 73 A&C(11) Cu I 26 3.65 2 5.15 1 74 A&C(12) Cu I 36 3.505 2 5.005 1 75 A&C(13) Cu I 26 3.65 2 5.15 1 76 A&C(14) Cu I 26 3.65 2 5.15 1 77 A&C(15) Cu I 26 3.65 2 5.15 1 78 W&J(1) A1 I 10 4.315 2 2.8 1 79 W&J(2) AI I 10 4.315 2 2.8 1 80 W&J(3) A1 I 10 4.315 2 2.8 1 81 W&J(4) A1 I 10 2.45 2 4 1 82 W&J(5) A1 I 10 2.45 2 4 1 83 W&J(6) AI I 10 2.45 2 4 1 84 R et al. Cu I 10 1.815 2 3.75 1 85 S&S(1) Cn II 30 3.5 2 4.2 2 86 S&S(2) Cu I 34 3.033 2 3.733 1 87 S&S(3) Cu I 22 2.55 2 3.3 1 88 S&S(4) Cu I 26 1.7 2 2.4 1 89 S&S(5) Cu I 38 2.55 2 3.1 1 90 S&S(6) Cu III 48 4.61 2 4.86 3 91 Tanaka et al. A1 I 20 3.793 2 4.734 1

Note that the equation is dimensional, the units of the characteristic length are in ram. They reported that 95% of the experimental data were correlated within 6%.

Achaichia and Cowell [7] suggested correlation for the Stanton number (St) based on experiments (Fig. 1, type B), and is given as :

F. (0.936 ReLp243 --1"76L0 +0.9950)

St = 1.554 0

/ T , \ - 0 . 0 9 [ F \ - 0 . 0 4 × ReZ°sal\Lpp/IPl ~kZ~p/][ P| ReLp > 75. (3)

They claimed all the Stanton number data to be within 10%.

Chang and Wang [11] presented Colburn j factors for brazed aluminium heat exchangers (Fig. 1, Type C) as

j = 0.436Re~ -°'559 e 0"192 el 0"0956 100 < Rerp < 1000

(4)

where

= A / A , (5)

F" 1 = AI/A. (6)

The e~ accounts for the effect of louver surface area on the heat transfer, and e is the finning factor. Equa- tion (4) can describe 85% of their experimental data within + 10%.

Sunden and Svantesson [9] proposed a heat transfer correlation for multi louvered surface (Fig. 1, Type C),

[ O \ o . 2 3 9 [ F \ o . o 2 o 6 ( F t ~ -0.285 J=a'67ReLPo"gll~ ) I~pp) k Lp,]

/ L ~0.0671/T, \ -0 .243 X Jt'~h " p .

CONSTRUCTION OF THE CORRELATION

The basic form of the correlation used is :

j = C, ReC~. (8)

It is assumed that Cl and C2 are dependent on the physical dimensions of the heat exchanger. A sep- arated linear regression was proceeded to determine all the exponents, C2, of the heat exchangers. However, it is found that no suitable correlation can correlate the exponents with an acceptable accuracy. Therefore, Cz is given as constant. The determination of C~ is analogous to Cz. After a trial and error process, the final equation form (for corrugated fin geometry and 100 < ReLp < 3000) yields :

( 0 ) 0 23 J= ReZ°"gl~) Ig ) I-~p) I-~p, ]

\T.j \T.] (9)

Figure 4 shows the comparison of the experimental data with equation (9). It is shown that 89.3% of

Generalized heat transfer correlation 541

(I)

C) I - - - - I : I I :

Fd

(n)

(III)

0 _l v_ Lp

Fa

(IV)

e i =s'=i=s'-I =I i= L,

Fd

(v) 0 Lp _t t_

( V I ) Fig. 3. Type of louvered fin geometry.

542 Y.-J. CHANG and C.-C. WANG

Table 3. Reduction process for the heat transfer data

Heat transfer Presentation of rate Reduction experimental Experimental data

Data source based on : method Flow arrangement data range

Davenport [6] Air side UA-LMTD - - Renh vsj 300 < Reoh < 4000 Chang and Wang Average e-NTU Cross flow both sides ReLp vsj 100 < ReLp < 1000

[11] unmixed Webb [16] Average e-NTU cross flow both sides Reoh vsj 200 < Reoa < 5000

unmixed Achaichia and Air side e-NTU Cross flow, tube side Reoh vs St 75 < ReDh < 8000

Cowell [7] mixed and air side unmixed

Webb and Jung [1] Average ~-NTU Cross flow both sides ReLp vsj 100 < ReLp < 2000 unmixed

Rugh et al. [17] Average e-NTU Cross flow, tube side Reoh vsj 150 < Reoh < 300 mixed, air side

unmixed Sunden and - - - - ReLp vsj I00 < ReLp < 800

Svantesson [9] Tanaka et al. [15] Air side UA-LMTD - - Vfronta I VS ~/0h0 1 m s- ' < Vfro,t~, < 5 m s-l

Table 4. Comparison of the proposed corrugated correlation with the experimental data

Present Achaichia and Chang and Sunden and Deviation correlation Davenport [6] Cowell [7] Wang [ 1 1 ] Svantesson [9]

_ 10% 75.04% 58.96% 21.90% 50.08% 39.82% _ 15% 89.28% 73.51% 31.55% 70.14% 54.98% +20% 95.10% 81.62% 40.12% 81.78% 71.98% +25% 98,01% 87.29% 50.69% 88.21% 82.39% Average deviation 0,91% 3.05% 26.98% 4.35% - 4.66% Mean deviation 7.55% 11.51% 27.62% 12.48% 15.53%

l N ' •

Average deviation = _ _ ( ~ J p r e d - - J e x p ~ >( 100%.

1 ( ~ [jp~'d -j*xp 1'} x 100%" j,x--~ , Mean deviation = /

N: number of data point.

the corrugated louver fin data are correlated within ___ 15%, and the present correlation gives a mean devi- ation of 7.55% of the corrugated louver fin data.

TESTS OF THE VARIOUS CORRELATIONS AGAINST THE DATA

In addition to the correlation proposed in this paper, several other correlations were tested against the data. These correlations include the Davenpor t [6], the Achaichia and Cowell [7], the Sunden and Svantesson [9] and the Chang and Wang [11] cor- relations.

The results of the comparison of the correlations with all the corrugated louver fin data are shown in Table 4. As seen, the mean deviation of the present correlation, the Davenpor t correlation, the Achaichia and Cowell [7] correlation, the Chang and Wang cor- relation [11], and the Sunden and Svantesson [9] correlation are 7.55%, 11.51%, 27.62%, 12.48%, and 15.53%, respectively. The average deviation of the Achaichia and Cowell correlation [7] is approximately equal to its mean deviation. This indicates that their

plate-and-tube louver fin data are considerably higher than those corrugated louver fin data. The reason for this phenomenon is not very clear at present. Further work is required to quantify this phenomenon. One possible explanation is the geometric difference between the plate-and-tube and the corrugated louver fin geometry. Regarding the correlation of heat trans- fer, the present study does not present the friction factor correlation for the louver fin geometry, because the variations of the friction factors vs the Reynolds number are over 300%. Worse, the friction factors are nonlinear in the logarithm scale plot. Therefore, it is not easy to accurately correlate the friction factor within a short time. We do not include the correlation of friction factor in this paper at this stage.

CONCLUSIONS

A generalized heat transfer correlation for louver fin geometry is proposed in the present study. A total of 91 samples of louver fin heat exchangers are used in the regression analysis. Fo r the corrugated louver fin geometry, it is shown that 89.3 % of the corrugated

¢)

2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Generalized heat transfer correlation

2 3

10 10

Fig. 4. Heat transfer error plots for the corrugated samples.

543

louver fin da ta are correlated within + 15% with mean deviat ion of 7.55%. The inclusion o f the pla te-and- tube louver fin da ta in the heat t ransfer corre la t ion (equat ion A1) results in a mean deviat ion of 8.21%.

Acknowledgements---The authors would like to express grati- tude for the Energy R&D foundation funding from the Energy Commission of the Ministry of Economic Affairs, Taiwan. The authors are indebted to Professor Ralph Webb for providing valuable suggestions and PSU radiator data.

REFERENCES

1. R. L. Webb and S. H. Jung, Air-side performance of enhanced brazed aluminium heat exchangers, ASHRAE Trans. 98, Pt 2, 3!)1-401 (1992).

2. B. Sunden and J. Svantesson, Thermal hydraulic per- formance of new multilouvered fins, in Proceedings of the 9th Int. Heat Transfer Conf., Vol. 14-HX-16, pp. 91- 96 (1990).

3. Y. J. Chang, C. C. Wang, R. J. Shyu and Y. Z. R. Hu, Performance comparison between automotive fiat tube condenser and round tube condenser, in 4th ASME/JSME Thermal Engineering Joint Conf. Vol. 4, pp. 331-336 (199.';).

4. T. A. Cowell, A general method for the comparison of compact heat transfer surfaces, ,L Heat Transfer 112, 288-294 (1990).

5. T. A. Cowell, M. R. Heikal and A. Achaichia, Flow and heat transfer in compact louvered fin surfaces, Expl. Thermal Fluid Sci. 10, 192-199 (1995).

6. C. J. Davenport, Correlation for heat transfer and flow

friction characteristics of louvered fin, AIChE Syrup. Ser. 79, 19-27 (1983).

7. A. Achaichia and T. A. Cowell, Heat transfer and pres- sure drop characteristics of flat tube and louvered plated fin surfaces, Expl. Thermal ~luid Sci. 1, 147-157 (1988).

8. J, P. Rugh, J. T. Pearson and S. Ramadhyani, A study of a very compact heat exchanger used for passenger compartment heating in automobiles, in Compact Heat Exchangers for Power and Process Industries, ASME Symp. Ser., HTD-Vol. 201, pp. 15-24. ASME, New York (1992).

9. B. Sunden and J. Svantesson, Correlation of j- and f- factors for multilouvered heat transfer surfaces, in Pro- ceedings of the 3rd UK National Heat Transfer ConS, pp. 805-811 (1992).

10. Y.J. Chang, C. C. Wang and W. R. Chang, Heat transfer and flow characteristics of automotive brazed aluminium heat exchangers, ASHARE Trans. 100, Pt 2, 643-652 (1994).

11. Y. J. Chang and C. C. Wang, Air side performance of brazed aluminium heat exchangers, J. Enhanced Heat Transfer 3, 15-28 (1996).

12. A. Shanoun and R. L. Webb, Prediction of heat transfer and friction for the louver fin geometry, J. Heat Transfer 114, 893-900 (1992).

13. E. R. Dillen and R. L. Webb, Rationally based heat transfer and friction correlations for the louver fin geometry, SAE Technical Paper Series 940504 (1994).

14. R, L. Webb, Y. J. Chang and C. C. Wang, Heat transfer and friction correlations for the louver fin geometry, in Proceedings of the Vehicle Thermal Management System, Vol. 2, pp. 533-541 (1995).

15. T. Tanaka, M. Itoh, M. Kudoh and A. Tomita, Improve- ment of compact heat exchangers with inclined louvered fins, Bull. JSME 27, 219-226 (1984).

544 Y.-J. CHANG and C.-C. WANG

16. R. L. Webb, PSU radiators test data, unpublished data for five radiators (1988).

17. J. P. Rugh, J. T. Pearson and S. Ramadhyani, A study of a very compact heat exchanger used for passenger compartment heating in automobiles, in Compact Heat Exchangers for Power and Process Industries, ASME Symp. Ser., HTD-Vol. 201, pp. 15-24. ASME, New York (1992).

18. A. Achaichia, The performance of louvered tube-and- plate fin heat transfer surfaces, Ph.D. Thesis, Brighton Polytechnic, pp. 72-73 (1987).

19. C.J. Davenport, Heat transfer and fluid flow in louvered triangular ducts, Ph.D. thesis, Coventry (Lancaster) Polytechnic, p. 38 (1987).

APPENDIX

Although there are geometric differences between plate- and-tube and corrugated louver fin geometry, we have included all the experimental data of the 91 samples in the regression which yields :

x \ ~ ) \ ~ ) \~-~p,] . (AI)

Figure A1 shows the comparison of the experimental data with equation (A1). The present correlation (equation (A1)) can predict 87.8% of the experimental data within + 15%, and a mean deviation of 8.21%. Detailed comparisons with other correlations are also depicted in Table A1. For a very quick evaluation of heat transfer coefficient in engineering application, a very simple form of the correlation is proposed as follows :

j = 0.425Reap °'496. (A2)

This simple equation can describe 88.2% of the data bank within 25%, and 70.7% of the data bank within 15%. The mean deviation of this simple equation is 12.7%.

2

1.8

1.6

1.4

1.2 O

• 0.8

0.6

0.4

0.2

0 2 3

10 10 ReLp

Fig. A1. Heat transfer error plots for the all louver fin samples.

Table A 1. Comparison of the correlation with all the experimental data

Present Achaichia and Chang and Sunden and Deviation correlation Davenport [6] Cowell [7] Wang [11] Svantesson [9]

__. 10% 71.48% 54.82% 30.60% 47.66% 35.42% + 15% 87.76% 68.88% 40.36% 66.02% 50.52% + 20% 94.01% 77.99% 48.57% 79.56% 67.19% _+ 25% 97.14% 85.42% 57.94% 78.89% 79.82%

Average deviation 1.02% 0.37% 22.73% 1.56% - 7.12% Mean deviation 8.21% 12.39% 24.43% 12.88% 16.43%