International Journal of Heat and Mass Transfer 54 (2011) 1743–1751

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Numerical study on a slit fin-and-tube heat exchanger with longitudinalvortex generators

Jiong Li a, Shuangfeng Wang a,⇑, Jinfang Chen a, Yong-Gang Lei b

a Key Lab. of Enhance Heat Transfer and Energy Conversion, Ministry of Education, South China University of Technology, Guangzhou 510640, Guangdong, PR Chinab State Key Laboratory of Multiphase Flow in Power Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China

a r t i c l e i n f o

Article history:Received 28 July 2010Received in revised form 12 January 2011Accepted 13 January 2011Available online 12 February 2011

Keywords:Slit finLongitudinal vortexField synergy principleHeat transferComputational fluid dynamics (CFD)

0017-9310/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2011.01.017

⇑ Corresponding author. Tel.: +86 20 22236929.E-mail address: sfwang@scut.edu.cn (S. Wang).

a b s t r a c t

A 3-D numerical simulation is performed on laminar heat transfer and flow characteristics of a slit fin-and-tube heat exchanger with longitudinal vortex generators. Heat transfer enhancement of the novel slitfin mechanism is investigated by examining the effect of the strips and the longitudinal vortices. Thestructure of the slit fin is optimized and analyzed with field synergy principle. The result coincides withthe guideline ‘front coarse and rear dense’. The heat transfer and fluid flow characteristics of the slit fin-and-tube heat exchanger with longitudinal vortex generators are compared with that of the heat exchan-ger with X-shape arrangement slit fin and heat exchanger with rectangular winglet longitudinal vortexgenerators. It is found that the Colburn j-factor and friction factor f of the novel heat exchanger withthe novel slit fin is in between them under the same Reynolds number, and the factor j/(f1/3) of the novelheat exchanger increased by 15.8% and 4.2%, respectively.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Fin-and-tube heat exchangers have been used extensively inrefrigeration and air conditioning. Enhanced fins including wavyfin and interrupted fin are widely used to improve the performanceof fin-and-tube heat exchangers. As an interrupted fin, the slit finhas been studied by many investigators [1–6]. It enhances heattransfer by renewing the boundary layer and reducing the thick-ness of the boundary layer [1]. The first study in literature on theslit fin and round tube heat exchanger was performed by Nakayamaand Xu [2]. They reported that the heat exchanger of 2 row,staggered arrangements with the slit fin, which used 9.5 mm tubediameter, 0.2 mm fin thickness and 2 mm slit width, showed ahigher heat transfer coefficient by about 78% than that of the planefin. Hiroaki et al. [3] experimentally studied the effect of strip loca-tion of X-arrangement on the heat transfer and pressure drop char-acteristics. A representative case was proposed by Kang and Kim[4]. It had the X-shaped pattern of slits and a 7 mm round tube.They reported accomplishing a 1.6 times heat transfer performanceand two-third compactness over the existing results. Numericalsimulations have also been widely used to investigate the flowand heat transfer details of the slit fin. Yun and Lee [5] analyzedthe effect of various design parameters on the heat transfer andpressure drop characteristics of the heat exchanger with a slit

ll rights reserved.

fin. The airside performance of fin-and-tube heat exchangershaving slit geometry was experimentally investigated by Wanget al. [6]. A total of 12 samples were tested and compared. Effectsof fin pitch and the number of tube row were examined. A generalcorrelation was proposed to describe the airside performance ofthe slit fin configuration. Tao et al. [7] and Qu et al. [8] investigatedthe slit fin with three-dimensional numerical computation to ana-lyze the type and location of the strips. They conducted some anal-ysis on the heat transfer enhancement mechanism with fieldsynergy principle and found out that strip located in the down-stream part had better heat transfer performance than that locatedin the upstream part.

For enhanced fins, vortex generator is a promising flow manip-ulator, which introduces vortices into the flow passage causingheat transfer enhancement. It has three mechanisms for passiveheat transfer enhancement: (1) developing boundary layers; (2)swirling; (3) flow destabilization. This enhancement method hasthe important advantage of low cost and ease of implementation,with a usually modest pressure drop penalty [9–13]. There aremany commonly employed vortex generators [14], delta-wing vor-tex generators and rectangular winglet vortex generators.

In this paper, a slit fin-and-tube heat exchanger with longitudi-nal vortex generators is proposed. Compared with the traditionalslit fin, the structure of the strip is improved and similar to thatof rectangular winglet longitudinal vortex generators. In addition,the number of strips decreased to develop the longitudinal vorticesmore fully. Thus, the novel slit fin has the heat transfer and flowcharacteristics of both the traditional slit fin and the longitudinal

Nomenclature

A total heat transfer surface area (m2)Ac minimum flow area (m2)Cp specific heat at constant pressure (J kg�1 K�1)D tube outer side diameter (mm)Dh hydraulic diameter, Dh ¼ 4Ac L

A (mm)f fanning friction factorFp fin pitch (mm)gm air flux at the minimum cross-section of the flow area

(kg m�2 s�1)h heat transfer coefficient (W m�2 K�1)H height of the strip (mm)J Colburn factork thermal conductivity (W m�1 K�1)L length parameters about the strip (mm)M module productionN the number of control volume or pointNu average Nusselt numberP pressure (Pa)DP pressure drop (Pa)P bulk average pressure (Pa)Pr Prandtl numberQ heat transfer capacity (W)Re Reynolds number based on hydraulic diameter

S distance parameters between the tubes (mm)T temperature (K)

T bulk average temperature (K)Uc velocity at the minimum cross sectional area (m s�1)

U!

velocity vector (m s�1)u, v, w x, y, z velocity components (m s�1)x, y, z Cartesian coordinates

Greek symbolsa angles of attack (�)d thickness (mm)l dynamic viscosity of air (Pa s)q density (kg m�3)h the local intersection angle (�)

Subscriptsin inlet parametersw wall conditionout outlet parameters

AbbreviationLVG longitudinal vortex generator

1744 J. Li et al. / International Journal of Heat and Mass Transfer 54 (2011) 1743–1751

vortex generators. The new type of slit fin enhances heat transferfrom two aspects: (1) the interrupted fin with the strips, (2) longi-tudinal vortices generated by the strips.

Computational fluid dynamics (CFD) method is performed onheat transfer and fluid flow characteristics of the novel heat ex-changer. The effect of the strips and the vortices generating ofthe new type of slit fin is analyzed in detail. The strips location isinvestigated and optimized from the point view of the field syn-ergy principle. The heat transfer and flow characteristics of the slitfin-and-tube heat exchanger with longitudinal vortex generatorsare compared with that of heat exchanger with the X-shapearrangement slit fin and heat exchanger with rectangular wingletlongitudinal vortex generators.

2. Numerical simulation

2.1. Physical model

The schematic diagram of a slit fin-and-tube heat exchangerwith longitudinal vortex generators is shown in Fig. 1. The tubeis usually made of copper and the fins are made of aluminum.The slit fin is alike that some pieces of strips are punched fromthe base sheet. Fig. 2 gives the top view of the computation domainof the slit fin and tube heat exchanger with longitudinal vortexgenerators. Due to the symmetric and periodic arrangement, theshadow section of the heat exchanger shown in Fig. 2 is selectedas the computing domain. The neighboring two fins’ middle sur-faces are selected as the upper and lower boundary of the compu-tational element, respectively. The side surface of the fin and thetubes’ middle surface are selected as the front and back boundaryof the computational element, respectively. Because of the finthickness, the air velocity profile is not uniform at the entranceof the channel formed by the fins’ middle surfaces. The computa-tional domain is extended upstream 0.5 times of the original heattransfer zone to ensure the velocity distribution uniform at the in-let of domain. The computational domain is also extended down-stream 1 time of the original heat transfer zone so that fully

developed boundary condition can be used at the outlet [15,16].The elementary computational domain is presented in Fig. 3, inwhich x, y, z are stream wise, span wise and normal coordinates,respectively.

2.2. Grid generation

The computational meshes are generated using Gambit, whichis packaged with FLUENT software. It is difficult to use a singlestructured quadrilateral mesh in the whole computational domain.The computational domain is divided into three parts in the flowdirection: the upstream-extended region, the fin coil region andthe downstream-extended region. Structured meshes are used inthe upstream-extended and downstream-extended region, whileunstructured meshes are employed in the fin coil region shownin Fig. 4. A very large difference in cell volume between adjacentcells is avoided and a very high quality of mesh has been ensuredthroughout the computational domain.

2.3. Governing equations and boundary conditions

The CFD software FLUENT is used for the numerical simulation.The air flow between the neighboring fins is laminar owing to thelow velocity and the small fin pitch. In the computation, theReynolds number based on the inlet average velocity (1–5 m/s)and flow passage hydraulic diameter is below 2500. The flow issteady and incompressible [15,16]. The governing equationsinclude continuity, momentum and energy equations for fluidregion, conduction equation for solid region. The equations areexpressed as follows [15,16]:

Continuity equation :@ðquiÞ@xi

¼ 0: ð1Þ

Momentum equation :@

@xiðquiukÞ ¼

@

@xil @uk

@xi

� �� @p@xk

; ð2Þ

Fig. 1. Schematic diagram of core region of a slit fin-and-tube heat exchanger with longitudinal vortex generators.

Fig. 2. Computational domain and geometric dimensions.

Fig. 3. Definition of the computational domain and coordinate system.

J. Li et al. / International Journal of Heat and Mass Transfer 54 (2011) 1743–1751 1745

Energy equation :@ ðquiTÞ ¼

@ k @T� �

: ð3Þ

@xi @xi Cp @xi

Governing equations are discreted by means of the control volumemethod, and the convection term is discreted by adopting thepower-law scheme [17]. The coupling between pressure and

Fig. 4. Mesh topology: (a) detail of the grid on the strip and (b) irregular meshing of the fin coil region.

1746 J. Li et al. / International Journal of Heat and Mass Transfer 54 (2011) 1743–1751

velocity is conducted by the SIMPLE algorithm calculating theregional. Fin thickness and heat conduction in the fins are taken intoaccount. The temperature distribution for the fins can be deter-mined by solving the conjugate heat transfer problem in the com-putational domain. Similar treatments can be found in references[15,16]. The convergence criterion is that the normalized residualsare less than 10�6 for the flow equations and 10�8 for the energyequation.

The boundary conditions are described as follows:At the inlet, velocity-inlet boundary condition: u = uin, T = Tin,

m = x = 0.At the upper and lower surface of the wind tunnel region (x–y

planes), periodic boundary conditions:

@u@z¼ @t@z¼ 0; x ¼ 0;

@T@z¼ 0 ðextended regionÞ;

u ¼ v ¼ x ¼ 0;@T@z¼ 0 ðfin regionÞ:

At the front and back surface of the wind tunnel region(x-z planes),symmetry boundary condition:

@u@y¼ @x@y¼ 0; v ¼ 0;

@T@y¼ 0:

At the outlet boundary, outflow boundary condition:

@u@x¼ @v@x¼ @x@x¼ @T@X¼ 0:

Fin surface region, interface: u ¼ v ¼ x ¼ 0; @T@y ¼ 0.

Tube region: u = v = x = 0, T = Tw.Geometric size and computational condition are listed in

Table 1.

Table 1Geometric dimension for the studied heat exchanger.

Dimension Value

Fin collar outside diameter D (mm) 7.6Transverse pitch S1 (mm) 11.6Longitudinal pitch S2 (mm) 18.8Fin pitch Fp (mm) 1.4Fin thickness d (mm) 0.105Angles of attack a (�) 45Height of strip H (mm) 1Width of strip L (mm) 1.8Position of strip (L1, L2, L3) (mm) 3, 8, 4.6Wall temperature (K) 333.15Inlet temperature of air (K) 308Frontal velocity (ms�1) 1–5

2.4. Parameter definition

In compact heat exchanger, the performance parameters de-pend on the geometry and flow conditions. The flow conditioncan be characterized by Reynolds number base on the hydraulicdiameter. Colburn j-factor and friction factor f are used to describethe heat transfer and pressure drop of heat exchangers. To improvethe model to be easily understood, Reynolds number, Colburn fac-tor j, Fanning friction factor f are defined as follows:

Re ¼ qUcDh

lj ¼ h

gmcp� Pr

23 f ¼ 2DP

qU2c

Dh

L: ð4Þ

The mean temperature, pressure and Nusselt number of a cross-sec-tion are defined as:

T ¼RR

AuTdARRAudA

p ¼RR

ApdARRAdA

Nu ¼RR

NudxdyRRdxdy

: ð5Þ

The total heat transfer, pressure loss and log-mean temperature dif-ference are defined as:

Q ¼ _mcpðTin � ToutÞ DP ¼ pin � pout

DT ¼ ðTw � TinÞ � ðTw � ToutÞln ðTw � TinÞ=ðTw � ToutÞ� � : ð6Þ

The heat transfer coefficient is defined as:

h ¼ Q=ADT: ð7Þ

3. Results and discussion

3.1. Grid independence test and model validation

Before any computational result can be deemed enough to illu-minate the physical phenomenon, the computational results mustbe justified through the grid independence test. In order to validatethe solution independence of the grid number, four different gridnumbers are studied. The grid numbers are 60,600, 122,200,244,400 and 362,800, respectively. The average Nusselt numberof the fourth grid system differs from that of the third by less than0.5%. Hence, computation is based on the third grid system 244,400at this condition. Similar examinations are also conducted for theother cases in this work.

In order to validate the reliability of the numerical methodbeing used, the heat transfer and flow characteristics of the slitfin heat exchanger are compared with the available experimentalresults published in literature. The geometric parameters for theheat exchanger are presented in [6]. The Reynolds number is below2500. The predicted results are compared with the experimental

1000100

0.01

0.1

j

Re

Experimental Numerical

Fig. 5. Comparison of factor j and factor f between numerical and experimentalresults.

Fig. 6a. Vector-plots and streamlines generated by LVGs in four y

Fig. 6b. Temperature distribution in four y–z sections

J. Li et al. / International Journal of Heat and Mass Transfer 54 (2011) 1743–1751 1747

result from Wang et al. [6]. The Colburn j-factor and friction factor fare shown in Fig. 5. As can be seen from the figures, the averagediscrepancy between the predicted factor j and the experimentalvalues is less than 4.6% and the average discrepancy between thepredicted factor f and the experimental values is less than 8.1%.The agreement between the predicted and experimental resultsindicates that the numerical model is reliable to predict heat trans-fer and flow characteristics in these compact heat exchangers.Thus, this method is employed to simulate air-side performanceof the slit fin-and-tube heat exchanger with longitudinal vortexgenerators in the present work.

3.2. Heat transfer enhancement principle of the novel slit fin

The new type of slit fin has been described above. It has the heattransfer and flow characteristics of both the traditional slit fin andthe rectangular winglet longitudinal vortex generators. It can beseen from Fig. 6a, the longitudinal vortices structure carried by slitfin is presented on the surface of S1/S2/S3/S4. As flow separationoccurs on the leading edge of the slit fin, swirling motion is gener-ated by flow separation along the side edge of the slit fin due to the

–z sections (S1/S2/S3/S4) for the novel slit fin at Re = 1051.3.

(S1/S2/S3/S4) for the novel slit fin at Re = 1051.3.

Fig. 7a. Velocity vectors of a x–z section (S5) for the novel slit fin at Re = 1051.3.

Fig. 7b. Temperature distribution in a x–z section (S5) for the novel slit fin at Re = 1051.3.

1748 J. Li et al. / International Journal of Heat and Mass Transfer 54 (2011) 1743–1751

pressure difference between the upstream and downstream sides.The effect of these vortices distorts the temperature field in a chan-nel and serves ultimately to bring about augmentation of heattransfer between the fluid and its neighboring surface. The temper-ature distributions in four y–z planes (S1/S2/S3/S4) at Re = 1051.3are presented in Fig. 6b. From the figure we can see that the tem-perature profiles are distorted by the stream wise vortices. It isindicated that the longitudinal vortices have significant influenceon the temperature distribution of the cross-sections and thechange of the thermal boundary layer thickness near the wall.These vortices take the cooler fluid from the mid region to thehot channel wall, the thermal boundary layer becomes thinner,and the temperature gradient near the wall is increased, the heattransfer is enhanced.

So far, heat transfer enhancement mechanism of the strips forthe slit fin has been studied little by numerical simulation. In thepresent work, it is analyzed as following. The velocity vector of sur-face S5 is shown in Fig. 7a. The air flow is disturbed to accelerate atthe edge of the strips, which is the basic heat transfer enhancementmethod. Fig. 7b shows the corresponding temperature field of thesurface S5. On the one hand, the thermal boundary layer is brokenand becomes thinner as strips disturb the air flow. As a result, theheat transfer is enhanced. On the other hand, strips in the fin canenhance convective heat transfer as it interrupts the flow boundarylayer to reduce its thickness by repeatedly recreation of new ther-mal boundary layers, and increases the disturbance in the flowfield. A relatively thinner boundary layer serves positively to en-hance heat transfer.

Fig. 8. Comparison of span-average Nusselt number on the x–y plane between theplain fin and the slit fin at Re = 1051.3.

3.3. Analysis of local heat transfer characteristics of the novel slit fin

Fig. 8 presents the distribution of span-average Nusselt numberalong the length of the fin-and-tube heat exchanger with plain finand slit fin with longitudinal vortex generators. For both of thebase line (plain fin) and enhanced configuration (slit fin), theNusselt number is very large at the inlet region and decreasesgradually along the flow direction until the first strip. It is becausethe temperature gradient is the maximum at the leading edge ofthe fin bottom for the first time, and then both the velocity andthermal boundary layers develop along the flow direction and

result in decrease of heat transfer. In front of the first tube, thespan-average Nusselt number abruptly increases due to the forma-tion of horseshoe vortices, which brings about better mixing andenhances heat transfer in this region. For the slit fin, the enhancedheat transfer effect of strips leads the span-average Nusselt num-ber larger than the plain fin in this region. A little peak occurs atthe downstream of the first strip as the effect of the longitudinalvortices. The trends of the span-average Nusselt number for thetwo configurations beyond the location of the second strip becomequite different. For the plain fin geometry, the Nusselt number islow in the wake region behind the tube where fluid recirculationwith low velocity causes poor heat transfer. Nevertheless, for theenhanced configuration, the values of the span-average Nusseltnumber are higher than that of the baseline configuration. The vor-tex generator creates an acceleration flow and longitudinal vortex,which lead the stream flow into the wake region and enhance themixing of the hot and cold fluid. This is the reason why the localNusselt number behind the delta winglet is greatly improved. Atthe downstream of the second strip, heat transfer is enhanced by

Fig. 9a. Four types of slit fin with the strips at different locations.

J. Li et al. / International Journal of Heat and Mass Transfer 54 (2011) 1743–1751 1749

longitudinal vortices. For the second row, the trends of the span-average Nusselt number for the two configurations is the sameas the first row, but the span-average Nusselt number is lower thanthat of the first row as the temperature gradient increases.

3.4. Effect of the locations of the strips

In the present study, some changes are made for the location ofthe strips: the strips are mainly located in the upstream half withfew strips being in the downstream for the fin C, and vice versa forfin D. Fig. 9a shows the fin configuration details of the four striparrangement patterns. Fin A is the whole plain plate fin. Fin B pos-sess uniformly distributed strips arranged over the entire fin. Thesimulation conditions are the same as above. The numerical resultsare analyzed from the point of field synergy principle.

For the analysis in terms of the field synergy principle, the fol-lowing formula is introduced: M ¼

PjU!jjgradTj=N, where: N is the

total number of the control volume covering the fin region. Whenthe intersection angle between velocity and temperature gradientbecomes zero, the production of velocity vector and temperaturegradient, jU!jjgradTj, is the largest. The value of M will be calledmodule production for simplicity. The local intersection angle isdetermined by the following equation:

h ¼ arccosU!�rT

jU!jjrTj

!hm ¼

PhiV iPVi

:

400 800 1200 1600 200060

65

70

75

80

85

90

Re

M×1

04 (K

s-1)

Inte

rsec

tion

angl

e θ

(°)

θ

1

2

3

4

5

6

7

8 M

Fin AFin BFin CFin D

Fig. 9b. Influence of the strips location on averaged intersection angle and moduleproduction.

From the local intersection angle, the average intersection angle ofthe computation domain of the fin area can be obtained by usingnumerical integration [7].

The numerical results for the average intersection angle areplotted in Fig. 9b. From the figure, it can be seen that the intersec-tion angle of fin D is the smallest, while that of fin A is the largest,with a difference about 5 deg at the same Reynolds number. It isespecially interesting to note that the averaged intersection angleof fin D is always less then that of fin C. It indicates fin D has abetter heat transfer performance than fin C. The trend and charac-teristics of module production is the same as the averaged inter-section angle.

To have better understanding of this point of view, we exam-ined some computational results of the velocity vector and iso-therm distributions in the middle plane between the twoadjacent fin surfaces for the fin A and fin D situation. These resultsare presented in Fig. 9c. It can be seen that in the upstream part ofthe fin, the temperature contours are almost perpendicular to thevelocity vector, this implies that the fluid temperature gradientare almost in the same direction as the velocity, the synergy be-tween velocity and temperature gradient is very good. Hence, inthis part of the fin, there is no need to create the interruption with-in the fluid; however, in the downstream part of the fin, the tem-perature contours are almost parallel to the velocity vector in the

Fig. 9c. Distributions of isothermals and streamlines for baseline case (Fin A) andmodified case (Fin D) at Re = 1320.8: (1) isothermal for baseline case; (2) streamlinefor baseline case; (3) isothermal for modified case; (4) streamline for modified case.

1750 J. Li et al. / International Journal of Heat and Mass Transfer 54 (2011) 1743–1751

major part of the region. It is at this place that enhancement tech-niques are needed in order to improve the synergy between veloc-ity and the temperature gradient. Fin D are made with less strips inthe upstream and more strips in the downstream. It can be seenthat in the downstream part of the fin D, the temperature contoursare not parallel to the velocity vector as that of Fin A, the temper-ature contours are almost perpendicular to the velocity vector atsome places, this implies the synergy between velocity and tem-perature gradient becomes better. This is the further understand-ing why the heat transfer performance of fin D is better than thatof fin C. The results is the same as the guideline ‘front coarse andrear dense’ [8].

3.5. Heat transfer and fluid flow comprehensive performance of thenovel slit fin

The novel slit fin has the characteristics of both the traditionalslit fin and the rectangular winglet longitudinal vortex generator,so it’s necessary to compare the heat transfer and flow characteris-tics of the slit fin-and-tube heat exchanger with longitudinal vor-tex generators to that of the traditional slit fin heat exchangerand the heat exchanger with rectangular winglet longitudinalvortex generators. The heat transfer and pressure drop perfor-mance of three heat exchangers are shown in Fig. 10a. In the figure,Fin A is slit fin with longitudinal vortex generators, Fin B is theX-Arrangement slit fin, and Fin C is the rectangular winglet

0 1 2 3 4 5 6-30

0

30

60

90 Fin A Fin B Fin C

v (m/s)

h (W

/m2 k

)

20

40

60

80

100

ΔP (Pa)

h

ΔP

Fig. 10a. Comparison of the heat transfer coefficient and pressure drop versusfrontal air velocity of three heat exchangers with different fins.

0 500 1000 1500 2000

0.014

0.021

0.028

0.035 Fin A Fin B Fin C

j / f (

1/3)

Re

Fig. 10b. Comparison of j/f(1/3) of three heat exchangers with different fins.

longitudinal vortex generators. The tube diameter of them is thesame. Geometry dimensions of Fin B refer to the specific literature[6]. The height and the length of the rectangular winglet (Fin C) areequal to that of the strips (Fin A). A qualitative comparison forenhanced heat transfer surface is an important issue in evaluatingthe performance improvement by taking some enhancement tech-nique. j/f(1/3) factor is adopted simply because its simplicity andclearness in concept. It is used to investigate comprehensive capa-bility of heat exchanger through examining the heat transfer per-formance and flow resistance. Fig. 10b shows Fin B has the bestheat transfer performance as frequent interruption of the flowcreated by the high-density strips, but its pressure drop is thelargest. For Fin C, the structure is relatively simple, the blockingeffect on the air flow is the least, and pressure drop is the smallest,then the heat transfer effect is the worst. The heat transfer perfor-mance and pressure drop of Fin A is between Fin B and Fin C, as thenumber of strips of Fin A is less than that of Fin B, but the structureis more complex than Fin C. It is shown in Fig. 10b slit fin withlongitudinal vortex generators heat exchanger has the best heattransfer and fluid flow comprehensive performance. As Reynoldsnumber ranges from 250 to 2500, j/f(1/3) factor of slit fin withlongitudinal vortex generator heat exchanger is 15.8% and 4.2%larger than that of heat exchanger with X-Arrangement slit finand heat exchanger with rectangular winglet longitudinal vortexgenerators, respectively. It can be seen that the slit fin with longi-tudinal vortex generators is a type of fin with good performance. Inaddition, its processing technology is mature and simple, so the slitfin-and-tube heat exchanger with longitudinal vortex generatorshas a good promise.

4. Conclusions

In this paper, a 3-D numerical simulation is employed to inves-tigate the heat transfer and fluid flow characteristics of the slit finheat exchanger with longitudinal vortex generators. Heat transferenhancement mechanism of it is studied in depth, and the struc-ture is analyzed and optimized from the point view of the field syn-ergy principle. The air-side heat transfer and flow characteristics ofthe slit fin-and-tube heat exchanger with longitudinal vortex gen-erators is compared with that of the heat exchanger with the tra-ditional slit fin and the heat exchanger with rectangular wingletlongitudinal vortex generators. The major conclusions are drawnas follows:

1. For the novel slit fin, longitudinal vortices can be generated bythe strips, which can improve the heat transfer performance.The new type of the slit fin has combined the heat transferand flow characteristics of both the traditional slit fin and lon-gitudinal vortices generators. It can significantly enhance heattransfer performance of fin-and-tube heat exchangers withthe modest pressure drop penalty.

2. Detailed analysis on the location of the strips is carried out fromthe point view of the field synergy principle. It indicates that thestrips located in the downstream part more and less in theupstream part has better heat transfer performance than theother type of arrangement.

3. The heat transfer performance and pressure drop of slit fin withlongitudinal vortex generators heat exchanger is in betweenheat exchanger with the traditional slit fin and heat exchangerwith rectangular winglet longitudinal vortex generators. AsReynolds number ranges from 250 to 2500, j/f(1/3) factor of slitfin-and-tube heat exchanger with longitudinal vortex generatoris 15.8% and 4.2% larger than that of heat exchanger withX-Arrangement slit fin and heat exchanger with rectangularwinglet longitudinal vortex generators, respectively.

J. Li et al. / International Journal of Heat and Mass Transfer 54 (2011) 1743–1751 1751

Acknowledgments

The authors acknowledge the financial support of funding fromGuangdong Provincial International Cooperation Funding (GrantNo. 2009B050400002), funding from NSFC (Grant No. 50876033),and NSFC-United Fund of Guangdong Province (Grant No.U0834002). The authors also wish to thank Dr. Zhang and Dr. Shenfor providing valuable advice.

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