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 CCHHEEMMIICCAALL  EENNGGIINNEEEERRIINNGG  TTRRAANNSSAACCTTIIOONNSS  
 

VOL. 39, 2014 

A publication of 

 
The Italian Association 

of Chemical Engineering 

www.aidic.it/cet 
Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Peng Yen Liew, Jun Yow Yong  

Copyright © 2014, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-30-3; ISSN 2283-9216 DOI: 10.3303/CET1439150 

 

Please cite this article as: Li L., Ma T., Xu X., Zeng M., Wang Q., 2014, Study on heat transfer and pressure drop 

performances of airfoil-shaped printed circuit heat exchanger, Chemical Engineering Transactions, 39, 895-900  

DOI:10.3303/CET1439150 

895 

Study on Heat Transfer and Pressure Drop Performances 

of Airfoil-Shaped Printed Circuit Heat Exchanger 

Lei Li, Ting Ma, XiangYang Xu, Min Zeng, QiuwWang Wang* 

Key Laboratory of Thermal-fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, 

Shaanxi, 710049, P. R. China 

wangqw@mail.xjtu.edu.cn 

Printed circuit heat exchanger (PCHE) is one of the most promising micro-channel heat exchangers for 

very high temperature and high pressure conditions. In the present study, PCHE has four channel 

configurations: straight, zigzag, s-shaped fin and airfoil-shaped fin. In this paper, we investigate the effects 

of parameters such as Reynolds number, the number of fin rows, fin transverse pitch and longitudinal pitch 

on the pressure drop and heat transfer by means of CFD code. It is found that the heat transfer and fluid 

flow approach fully developed conditions when the number of tube rows is greater than 9, and both of the f 

and Nu decrease with the increase of fin transverse pitch and longitudinal pitch. The f and Nu correlations 

are obtained. 

1. Introduction 

Compactness and efficiency are used as the essential tools to evaluate a heat exchanger. A High 

Temperature Gas-cooled Reactor (HTGR) and a Very High Temperature Reactor (VHTR) designs have 

generated considerable interest in selecting a good heat exchanger for an intermediate heat exchanger 

(IHX) and a remunerator to utilize high temperature heat for high thermal efficiency and hydrogen 

production. Therefore, many previous works were focused on the importance of the IHX and selection of 

the heat exchanger type (Wang et al., 2002).Printed circuit heat exchanger is a promising candidate for 

compact heat exchangers because it can provide a large amount of heat transfer area in a small volume. 

Typically, two technologies are applied to manufacture the PCHE: photo-etching and diffusion bonding. 

For plate fin heat exchangers, compactness is usually expressed by using the Colburn j factor, given as: 

2
3Pr

4

h
D

j N
L


 

(1)

 

0
( ) /

i LMTD
N T T T  

 
(2) 

Where: Dh is the hydraulic diameter, L is the length of the heat exchanger, N is the number of thermal 

units. As shown in Eq(1) and Eq(2) (Hesselgreaves,2001), Reduction of the hydraulic diameter engenders 

a decreased active length or heat exchanger size at the same Colburn j factor, Pr, and N conditions. By 

the means of photo-etching, small flow channels are achieved easily. And another technology, diffusion 

bonding, maintains the parent material strength because of no flux, braze or filler exist in the heat 

exchanger core. That provides a high capability of corrosion and temperature resistance. 
 



 
896 

 

 

 

Figure 1: Airfoil-shaped fin  

2. Simulation Model 

2.1 Physical Model 

The airfoil-shaped PCHE with three fin rows is selected as the numerical model, as shown in Figure1. The 

fin is shaped into NACA airfoil-shape (NACA0021 model), the maximum airfoil thickness is 0.84 mm, the 

chord length is 4 mm, the height is 1 mm. The simulation is performed in the turbulence region with 

3,627<Re<8,161, with the corresponding velocity ranged from 40 m/s to 90 m/s. In this model, the fluid is 

helium and it is assumed to be steady state, incompressible flow and constant properties. 

2.2 Governing Equations and Numerical Methods 

Simulation calculations are carried out using the software FLUENT. The governing equations are including 

continuity, momentum and energy equations: 

  0U 
 

(3) 

   U U p U     
 

(4) 

   p fU c T T    
 

(5) 

In this paper, Re is range from 3,687 to 8,161, so turbulence is taken into account by the k-ω SST model, 

neglecting the user-defined source terms, equations for the turbulent kinetic energy k and the specific heat 

dissipation rate ω can be obtained from Eq(6) and Eq(7), all equations are solved by second-order upwind 

discretization for convection. The Semi Implicit Method Pressure Linked Equation (SIMPLE) algorithm is 

used to resolve coupling of velocity and pressure. 



 
897 

( ) ( ) ( )
i

i i j

u G Y
t x x x

  


 

   
    

     
(6) 

( ) ( ) ( )
i

i i j

u G Y D
t x x x

   


 

   
     

     
(7) 

The uniform velocity inlet and pressure outlet boundary conditions available in FLUENT are used at the 

inlets and outlets, the top and bottom boundary conditions are constant temperature at 500 K, the left and 

right are given a symmetry boundary condition. 

In this paper, the Reynolds number, Nusselt number and friction factor characteristics are calculated by 

Eq(8) to Eq(11). 

i h
u D

Re



  (8) 

h
hD

Nu


  (9) 

m

Q
h

A T



 (10) 

2

2
h

i

pD
f

u L


  (11) 

Where ui is the inlet velocity, Dh is twice the height of the fin (Dh=2S). 

2.3 Grid independence 

Before examining the effects of geometrical parameters on the performance of heat transfer and flow 

friction, it is necessary to adopt an appropriate grid system for computations in turn leading to a correct 

physical understanding. Only one row fin of the model was studied in the grid independence. Five sets of 

grid were chosen: 27,786 hexas, 38,500 hexas, 54,378 hexas, 89,433 hexas and 141,588 hexas, and the 

computations are performed for a case with Reynolds number being 3,267. The results are shown in Fig. 

2(a). Comparing the results on the finest grid with the third grid, the deviations of Nu and f are 0.14 % and 

0.33 %.Because the structure of the model is similar to the tube-fin heat exchanger. The method is 

performed to examine the applicability by comparing with experiment (Tang et al., 2009) and the 

comparisons are shown in Figure 2(b). The deviation of Nusselt number using k-ω SST method between 

numerical and experimental results is less than 8.9 % and the deviation of f factor is less than 11.5 

%.According to the above comparison, the method is reliable. 

30000 60000 90000 120000 150000
0.20

0.25

0.30

0.35

0.40

0.45

0.50

 

grid

f

27

28

29

30

Grid system used for computations

 Nu

 

4000 5000 6000 7000 8000 9000 10000 11000
0.0

0.2

0.4

0.6

0.8

20

30

40

50

f

k-w SST model
Experiment

Nu

Re

 

 

 

Figure 2: The results of grid independence tests 



 
898 

 

3000 4000 5000 6000 7000 8000 9000
0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

f

Re

 1 row

 2 row

 3 row

 4 row

 5 row

 6 row

 7 row

 8 row

 9 row

 10 row

 

 

 

3000 4000 5000 6000 7000 8000 9000
20

25

30

35

40

45

Nu

Re

 1 row

 2 row

 3 row

 4 row

 5 row

 6 row

 7 row

 8 row

 9 row

 10 row

 

 

 

Figure 3: Effect of Re and fin rows number on f and Nu (a) Effect of Re and fin rows number on f (b) Effect 

of Re and fin rows number on Nu 

3. Result and Discussion 

3.1 Fin rows 

The numerical results of Nu and f with different Re and fin rows number are shown in Figure 3. With the 

increase of Re number, the Nu number increases while f decreases. It also can be seen that the Nu and f 

decrease with the increasing of the fin row, that because the enhanced phenomenon at the inlet region. 

But the Nu and f are almost identical when the row number is larger than 9. So there is no need to 

compute the model with more rows.  

3.2 Fin transverse pitch and longitudinal pitch 

The numerical results of Nu and f with different fin transverse pitch and longitudinal pitch are shown in 

Figure 4. The transverse pitch are 1.5 mm, 1.6 mm, 1.7 mm, 1.8 mm and 1.9 mm; the longitudinal pitch 

are 4 mm, 5 mm, 6 mm, 7 mm and 8 mm. The characteristics may be summarized as follows. Both Nu and 

f decrease with the increasing of transverse pitch, that because if it has a same velocity at the inlet, the 

flow channel with a larger transverse pitch has a smaller velocity at the minimum free flow cross-section, 

then the flow turbulence is reduced, witch lead to a small Nusselt number and friction factor. And the Nu 

number and f decrease with the increasing of the longitudinal pitch, that is because, when the channel has 

larger longitudinal pitch, it can create a larger flow area that will decrease the flow resistance. From Figure 

4, it can be seen the transvers pitch has more effect on heat transfer and pressure drop than the 

longitudinal pitch, which is similar to Xie et al. (2009). 

1.5 1.6 1.7 1.8 1.9
0.20

0.25

0.30

0.35

 

 f

 Nu

P
t
(mm)

f

20

21

22

23

24

25

Nu

 

4 5 6 7 8
0.15

0.20

0.25

0.30
 

  f

   Nu

P
l
（ mm）

f

20

21

22

23

24

 Nu

 

Figure 4: Effect of transverse and longitudinal pitch number on f and Nu (a) Transverse pitch (Pt), (b) 

Longitudinal pitch (Pl) 

3.3 Multiple correlations 

Based on the principle of similarity theory, the present data can be extrapolated or interpolated to other 

conditions by established correlations. For this reason, it is useful to try to obtain suitable correlations. The 

forms for correlations may be diversified, however, in order to reduce the difficulty involved in correlating 

the data and to refer to previous forms, the following forms are assumed:  



 
899 

31 2 4

0
Re ( ) ( )

CC C C

t l

h l
f C N

P P


 
(12) 

31 2 4

0
Re ( ) ( )

CC C C

t l

h l
Nu C N

P P


 
(13) 

Base on the foregoing numerical data and 1stopt15PRO code. The five coefficients are determined. Then 

the correlations become Eq(10) and Eq(11) (3,627 <Re<8,161): 

0.35035 0.49475 1.033682 0.726493
47.00654 Re ( ) ( )

t l

h l
f N

P P

 


 
(14) 

0.10518 0.615001 0.268556 0.155274
0.20756 Re ( ) ( )

t l

h l
Nu N

P P




 
(15) 

It is again noted that the valid range for the parameters. The Re ranged from 3,627 to 8,161; the 

transverse pitch ranged from 1.5 mm to 1.9 mm; the longitudinal pitch ranged from 4 mm to 9 mm, the 

predicted results and numerical data are compared as shown in Figure 5. Almost deviations are within 5 

%, which indicate that the heat transfer and pressure drop correlations are of sufficient accuracy. 

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45
0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

 f
  

p
re

d
ic

te
d

 f  numerical data

+10%

-10%

+5%

-5%

 

 

 

10 15 20 25 30 35 40 45 50
10

15

20

25

30

35

40

45

50

N
u

 p
r
e
d

ic
te

d

Nu numerical data

+5%

-5%

 

 

 

Figure 5: Comparison between predicted results and numerical data  

4. Conclusions 

3D-computations on fluid-side turbulence flow and heat transfer of air-foil shaped fin heat exchangers 
are conducted to reveal the effects of Reynolds number, the number of tube rows, fin transvers pitch and 
longitudinal pitch on the overall Nusselt number and friction factor. Base on the numerical results, the heat 
transfer and flow friction correlations are established. Few experiments have been done of PCHE with air-
foil shaped fin, but that are necessary to verify the simulation results and study on the new configuration 
heat exchanger. And the major findings are summarized as follows: 
1) With the increase of Re number, the Nu number increases while f decreases, the Nu and f are almost 

identical to those of rows number being 9 when the rows number larger than 9. 

2) Both Nu and f are decrease with the increase of transverse pitch, as well as longitudinal pitch. That is 

because, when the channel has larger transverse pitch or longitudinal pitch, it can create a larger flow 

area that will decrease the flow resistance.  

3) Multiple correlations of the Nu number and f factor have been established, and the correlations are of 
sufficient accuracy 

Acknowledgement 

This work is financially supported by the International Cooperation and Exchanges Project of NSFC of 

China (Grant No. 51120165002), National Natural Science Foundation of China (Grant No. 51025623, 

51306139) and Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant 

No. 20130201120061). 



 
900 

 
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