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the convective heat transer coefficient along the ribs axeswithin a limited range o rib geometries, indicated that itsmagnitude and prole were highly inuenced by the amounto clearance above the ribs. Lower heat transer coefficientsensued that a clearance gap was introduced above the ribwhich varies rom constant value to a maximum value at the

rib. El-Sayed et al. [] changed the n height, n width, nsspace, number o ns, and the distance o n tips rom theshroud to investigate the perormance o plate-n heat sink;their conclusions were as ollows: () the pressure drop ratioincreased as Reynolds number and n increased or decreasedwith increasing intern space and n width, () increasedthe clearance between the n tips and the shroud, and woulddecrease the mean o Nusselt number, () the mean o Nusseltnumber increases as Reynolds number, n width and spacebetween ns increases or decreasing n height. Ducted owhappened in which the air was orced to ow through achannel which ts tightly over the heat sink. It made surethat all o the air went through the channels ormed by thens o the heat sink. When the air ow is not ducted, acertain percentage o air ow would bypass the heat sink.Flow bypass was ound to increase n density and clearance,while remaining relatively insensitive to inlet duct velocity[]. El-Sayed et al. [] studied the heat transer and uidow o a plate-n heat sink or the cases o parallel ow,impinging ow, and reversed impinging ow; a parallel owwould yield the greatest rate o heat transer and the leastpressure drop ratio. For all cases, the local Nusselt numberincreased rom the base to the tip in the vertical direction;its value increased with increasing Reynolds number andwith increasing distance rom the leading edge o the n inthe stream-wise direction. Te n efficiency or parallel owwas greater than that or the other two cases in the coreregion. Elshaei [] assessed the thermal uid perormanceo a plate-n heat sink under cross-ow conditions, bothexperimentally and theoretically, through parameters or themainstream velocity, n density, and clearance between tipand shroud; their effects on the bypass ow, the pressuredrop ratio, and the thermal perormance were discussed.Te mean heat-transer coefficient decreased with increasingclearance between tip and shroud, but the effect o thisclearance on the mean heat-transer coefficient decreased asReynolds number increased. In order to enhance the heattranser o n in rectangular ow channel, Li et al. [] applieda CFD numerical method; the inuence o n width, nheight, number o ns, and Reynolds number was assessed

without and with a shield. Te research discovered that theplace o back plate and ront plate could reduce bypass effectand orced the uid to enter plate-n to enhance the heatconduction, but the pressure drop ratio would also increase.Wirtz et al. [] studied the effects o ow bypass on theperormance o ducted longitudinal heat sinks. It is indicatedthatthe value oow bypass was ound upto %andresultedin a reduction o the overall heat transer rate. Quantiyingthe effect o coolant bypass on the thermal perormanceo the heat sink element was also reported. sai et al. []investigated the effect o the angle o inclination o a plateheat shield on the thermal and hydraulic perormance o aplate-n heat sink. Te research discovered that the sloping

baffle was unable to reduce the thermal resistance but couldactually reduce the pressure drop effectively. Vortices weredetermined by the specic base ow and vortex generator.Developing and ully developed channel ows have been con-sidered base ow. Different wing types have been consideredas vortex generators. Tey could easily be incorporated into

heat transer suraces by embossing, stamping, or attachingthem as ns to primary heat transer suraces. Wing-typevortex generators allowed us to control the type and enlargethe generated vortices by the orm, area, and angle o attacko the wings. Vortices increased the rate o kinetic energyux and dramatically changed transition Reynolds number,temperature prole, and their gradients at the wall. Teyenhanced riction and heat transer [].

A vortex generator was an aerodynamic surace, com-prising a small vane or bump that created a vortex. o studythe effect o vortex generator, many scholars conducted theresearch using the experiment or the numerical simulationways. Sohankar [] set a channel with two angled ribs asa vee-shaped vortex generator to augment heat transer bythe numerical simulation. Discusses the Reynolds numberand the rib included angle regarding the ow eld andheat inuence o the transer perormance, its conclusionindicated that increased vortex generator was possible topromote the heat transer effect in the ow channel butwould also create pressure losses. Sohankar and Davidson[] used the numerical simulation way, laying aside inclinesmassive vortex generator in the rectangular ow channel,and discussed the three-dimensional unsteady ow and theheat transer phenomenon. Tis research changed vortexgenerator thickness, place angle, and upstream length andhereafer ound that Reynolds number was smaller than; ow started and appeared stable. But the Reynoldsnumber is bigger than ; then ows started and appearedstable. Moreover, the Nusselt number and the riction actorincreased along with the angle and the Reynolds number,the increment o riction actor came to ast than the Nusseltnumber did. o increase vortex generator the thickness,would let leading edges o vortexgenerator resultin the biggerNusselt number and would produce the strong turbulentow in the downstream and then had the higher Nusseltnumber and would increase along with the Reynolds numberll-out. Wu and ao [] presented the inuences o mainparameters o LVGs on the heat transer enhancement andow resistance in a rectangular channel. Tese parametersincluded the location o LVGs in the channel, geometric

sizes, and shape o LVGs. Numerical results showed that theoverall Nusselt number o channels would decrease with theLVGs location away rom the inlet o the channel and woulddecrease as the space o the LVG pair is decreasing. Henze etal. [] experimentally investigated the velocity eld and wallheat transer distributions or internal ows in the presenceo longitudinal vortices. And ian et al. [,] studied theeffects o two different shaped LVGs, rectangular wingletpair (RWP) and delta winglet pair (DWP) with two differentcongurations, common-ow-down and common-ow-up.Te rectangular wing as well as the delta, respectively, by CFUand the CFD structure disposition, could accelerate the uidmix and strengthen the heat transer.

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Outlet

Heat sink

Winglet

Inlet

F : Schematic geometric model.

In this study, we changed the ow structure to enhanceheat transer effect by utilizing the delta winglet pair longitu-dinal vortex generator which was set in ront o the radiatorto mix the air surrounding radiator and the ns. Most o thecurrent scholars used to change the n shape to improve theperormance o plate-n heat sink and vortex generator orthe multi-n-tube heat exchanger. Only ew studies installed

vortex generator or plate-type heat sink to enhance heattranser effect. Tis study was intended to develop a designwith low thermal resistance and to provide a new designdirection or the present plate-n heat sink cooling moduledesign.

2. Analysis

Te geometry o the theoretical model and the boundaryconditions was illustrated and shown in Figure . Te dimen-sions o the theoretical model were m . m .m( ). In order to save the computation duration,applied symmetric geometry, the real calculation eld o

volume was m . m .m.Figure was the schematicdiagram and showed the parameters o the computationaluid dynamics model. Te thermal and ow elds werecalculated numerically with FLUEN ., according to theollowing assumptions.

() Te system was a steady state.

() Te ow was incompressible and turbulent.

() Te uid and the solid properties were constant.() Te effects o gravity and thermal radiation are

neglected.

() Te effect o turbulence on the ow eld was includedby application o the RNG - turbulence model [].

Te Reynolds number was dened as

Re=o

. ()

was hydraulic diameter which was calculated by times o duct cross-sectional area and divided by the wet-ted perimeter; the value is . m. Besides heater area

L

H

B

CFU CFD

a

X

Z

Y

X

HfHw

Lg

Lw

F : Parameter diagram.

(. m . m), the base o heat sink was heat insulation,and the thermal conductivity o heat sink was W/mk.

Hybrid meshing was used in the study; the grid construc-tion was adopted tetrahedron mesh and hexahedral meshcomplex ways. Heat sink area and rectangular channel hadhexahedral mesh construction, and vortex generators andsurrounding area was used tetrahedron mesh construction.Te pressure term was treated with a standard approach,but the pressure-velocity coupling solved with the SIMPLEalgorithm [], which was used to solve uid ow and heattranser problems. Te convergence criterion to terminatethe

computation was dened as 8 or the scaled residual o

the energy equation or 5 or the scaled residual o otherequations.

Te thermal resistance thwas dened as ollows:

th =ave in

, ()

whereavewas the surace temperature o heat sink base, was total heat rate into the heat sink, and in stands or theinlet temperature which was K. Pressure drop () wasdened as

= in out, ()

where inwas pressure o inlet and outwas pressureo outlet.Te overall perormance was dened as (th,re

/th)/(/,re). o veriy the accuracy o physical modeland numerical method, using grid independence correctionmethod simulated LVGs on the ront tip o heat sink ( = 0, = 3 ), attack angle is degree in CFU, with . mthickness and . m height o plate-n heat sink in ,Reynolds number.

3. Results and Discussion

Te applied grid system was certied under conditions o aheat sink with = 0.002 m and = 0.045 m and a

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Mathematical Problems in Engineering

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.70.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

Rth

/Rth,ref

P

/P,ref

CFD,Rth Rth,ref/

CFU,P/P,refCFD,P/P,ref

a/H

CFU,Rth /Rth,ref

F : Te inuence o owcongurations on thermalresistanceratio and pressure drop ratio ( = 0.002 m, = 0.045 m, =

0.045 m, = 0, = 15, and Re= 10,000).

vortex generator o angle = 15 at Re = 10,000 and wasmeshed with our different grid numbers o ,, ,,,, and,,. Te computational results o the meansurace temperature o the heat sink varied rom .%to .% deviation. Deducing the thermal resistance, thenumber o grids increased rom , to ,,. Tecomputational result o the mean surace temperature othe heat sink was varied within .%, with a deduced.% deviation in thermal resistance, as the number ogrids increased rom , to ,,. In order to save

computing time without penalizing the accuracy, the modelwith , grids was selected or this research.

.. Comparison of CFU and CFD. Figure showed theinuence o ow congurations on thermal resistance ratioand pressure drop ratio at = 15. It was ound that theheat transer was more intensive when the transverse distancebetween the winglet pair became less. Te temperature con-tours on the symmetric plane along the main ow directionor the different congurations at = 15 were shown inFigure . It could be seen that the longitudinal vortices hadsignicant inuence on the temperature distribution o thesymmetry and the change o the thermal boundary layer

thickness near the ns. For the CFU conguration, the owbrought the uid closer to the heat sink and decreased thetemperature o the heat sink than those in CFD congurationdid. Te thermal boundary layer was thinner in CFU thanin CFD. Te ow took the cool uid rom the midregion tothe hot heat sink, and thereore CFU had higher temperaturegradient near the heat sink and better heat transer thanthose in CFD. We applied CFU ramework to study the ideallocation or erecting vortex generator in the ow channel inthis study.

.. Minimum ransverse Distance between Winglet Pair. Tevariation o the thermal resistance ratio and pressure drop

ratio under minimum transverse distance between wingletpair was shown inFigure . Decreasing the transverse spacebetween the winglet pair (decreasing the value o) causeda great increase in upstream pressure o the plate-n heatsink and also caused many impacts on the thermal resistance.Te rear o the LVGs touched on plate-n heat sink and

small minimum transverse distance between winglet paircould provide the best overall perormance among all theconditions. Te LVGs enhanced the heat transer o the chan-nel. Te top view showed the strong three-dimensionality othe ow eld. Te decreasing value o minimum transversedistance between winglet pair showed that the increase in thecoolant uid was orced to impact the leading edges o theplate-n heat sink. As a result, the shorter distance betweenwinglet pair caused high speed uid ow into the n-to-nchannel to enhance thermal perormance. However, we couldnd that the backow o the LVG had directly effects on theow behind the heat sink, and the case with = 0.777had the largest effect among all the cases. Tis was becausethe upper air drove the middle uid to ow and that couldproduce stronger up-wash vortex. I we increased , theefficiency o thermal resistance will rise. Tis was becausemoving vortex generator near the heat sink would cause thehighest pressure drop ratio and decrease ow perormanceand would not effectively inuence the backow o the plate-n heat sink. Decreasing distance between winglet pair wouldenhance the heat transer o the n channel and increase thepressure drop ratio, but the increase in the heat transer islarger than the amount decreased in the pressure drop ratio.Te transer o heat by the heat sink became worse whenthe minimum transverse distance between winglet pair o the

vortex generators was too small and that would affect theentry o the ow into the heat sink [].

.. Te Distance between the Vortex Generator and Heat Sink.Figure showed the effect o the distance between the vortexgenerator and heat sink on the thermal resistance ratio andpressure drop ratio o heat sink. Optimal overall perormanceoccurred when the distance between the vortex generatorandheat sink was equal to zero and that could be seen in Figure .When thevortex generatorwas close to the plate-n heat sink,it could cause small thermal resistance. Tat is, as the trailingedge o vortexgenerator touched theleading edge o theplate-n heat sink ( = 0), it produced strong vortex. But, as = 2changed to = 3, it reduced thermal resistance

andthe slope wasgradually smooth. An operative range o thedistance between the vortex generator and heat sink was 0 3. Meanwhile,Figure displayed smallest pressuredrop ratio at = 0.5, which enhanced uid perormance,but the other position as = 0and = 3would causemuch drag with increased pressure drop ratio. Contours o

vorticity magnitude in various cross-sections along the mainow direction or the different distance between the vortexgenerator and heat sink or Re = 10, 000 were shown inFigures (without displaying plate-n heat sink, =0.002 m, = 0.045 m, = 0.045 m, = 0.777,

= 15, and Re = 10, 000). It could be ound thatvorticity intensity behind the heat sink gradually decreases

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X = 0.08

X = 0.01

X = 0.09

X = 0.19

X = 0.29

(m)

XYZ

1.00e + 02

9.50e + 01

9.00e + 01

8.50e + 01

8.00e + 01

7.50e + 01

7.00e + 01

6.50e + 016.00e + 01

5.50e + 01

5.00e + 01

4.50e + 01

4.00e + 01

3.50e + 01

3.00e + 01

2.50e + 01

2.00e + 01

1.50e + 01

1.00e + 01

5.00e + 00

0.00e + 00

(1/s)

F : Contours o vortices magnitude in various cross-sections along the main ow direction (

= 0.002 m,

= 0.045 m,

=

0.045 m, = 0.777, = 0, = 15, and Re = 10,000, without displaying plate-n heat sink).

XYZ

1.00e + 02

9.50e + 01

9.00e + 01

8.50e + 01

8.00e + 01

7.50e + 01

7.00e + 01

6.50e + 01

6.00e + 01

5.50e + 01

5.00e + 01

4.50e + 014.00e + 01

3.50e + 01

3.00e + 01

2.50e + 01

2.00e + 01

1.50e + 01

1.00e + 01

5.00e + 00

0.00e + 00

(1/s)

X = 0.17

X = 0.08

X = 0.01

X = 0.09

X = 0.19

X = 0.29

(m)

F : Contours o vortices magnitude in various cross-sections along the main ow direction ( = 0.002 m, = 0.045 m, =

0.045 m, = 0.777, = 2, = 15, and Re= 10, 000, without displaying plate-n heat sink).

vortex generator would greatly increase -direction backowvelocity gradient o the trailing edge o heat sink.

Te effect o attack angle o vortex generator on theoverall perormance o plate-n heat sink in comparison tonumerical and experimental results was shown inFigure .Increasing the attack angle would cause the increase in theblockage o the channel and enhances overall perormance.Part o the uid entered through the n-to-n channel toperorm heat transer, but the other accelerated rom theside o the heat sink with strong vortices. Te importance othe attack angle o vortex generator on pressure drop ratiowas great and should be considered, especially at small n

height and more ns numbers. When attack angle = 15,inlet zone had the smallest pressure among the three cases.Similarly, increasing attack angle would also increase inletzone pressure and enhanced pressure drop ratio o channel.Tese results were consistent with previous discussion andmet an optimal design rule.

Figures and showed the trend o the pressure dropratio andoverall perormance o heat sink (triangle up)whichwere in a goodagreement with the experimental data [].Butthermal resistance ratio was quite different rom each other,because cooling area o heat sink was larger on experimentalmodel.

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Mathematical Problems in Engineering

XYZ

1.00e + 02

9.50e + 01

9.00e + 01

8.50e + 01

8.00e + 01

7.50e + 01

7.00e + 01

6.50e + 016.00e + 01

5.50e + 01

5.00e + 01

4.50e + 01

4.00e + 01

3.50e + 01

3.00e + 01

2.50e + 01

2.00e + 01

1.50e + 01

1.00e + 01

5.00e + 00

0.00e + 00

(1/s)X = 0.15

X = 0.25

X = 0.08

X = 0.01

X = 0.09

X = 0.19

X = 0.29

(m)

F : Contours o vortices magnitude in various cross-sections along the main ow direction (

= 0.002 m,

= 0.045 m,

=

0.045 m, = 0.777, = 3, = 15, and Re= 10, 000, without displaying plate-n heat sink).

1.88e + 00

1.79e + 00

1.69e + 00

1.60e + 00

1.50e + 00

1.41e + 00

1.32e + 00

1.22e + 00

1.13e ++

00

0.00e + 00

(m/s)

1.03e 009.40e 01

8.46e 017.52e 01

6.58e 015.64e 01

4.70e 01

3.76e 01

2.82e 01

1.88e 019.40e 02

XY

Z

Lg = 0 m Lg = 0.045 m Lg = 0.27 m

F : Flow structures around LVG and heat sink at the distance between the vortex generator and heat sink; = 0, = 0.5, and

= 3 (= 0.002 m, = 0.045 m, = 0.045 m, = 0.777, = 15, and Re= 10, 000).

.. Fins Number and Fin Height. Figure showed thermalresistance ratio and pressure drop ratio with the distancebetween vortex generator and heat sink when ns numberequaled ten and twenty. Te pressure drop ratio caused bythe nsnumber would increase with increasing n height andattachment o vortex generator and that would reinorce thistendency. When ns number and n height were increased,the blockage effect would enorce more uid concentratedon the plate-n sink. And, thereore, the ow on side oheat sink region would be more obvious than that on theterminal region. Most o the ow visualization around theheat sink would illustrate this ow behavior. But, in the caseo ns with more total cooling area o plate-n heat sink,

it was noticed that (see Figure ) most o the ow escapesrom intern region to tip ns area and quickly enters romthe ceiling region to terminate ns direction. Tis producedthermalboundary layer would be thin on the terminal region.Consequently, the value o thermal resistance was lower thanns number = 10 case. Generally, increasing number o nscould enhance the thermal perormance, but this inuencewas insignicant or the height o a high n.

4. Conclusion

Te inuenceso main parameters o longitudinal vortex gen-erator and plate-n heat sink on heat transer enhancement

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Mathematical Problems in Engineering

10 20 30 40 50 60 700.72

0.74

0.76

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0.92

1.0

1.1

1.2

1.3

1.4

1.5

1.6

Attack angle,(deg)

R

th/Rth,re

f

P/P,re

f

n = 20, experimental (Chen, 2012)

n = 20, experimental (Chen, 2012)

n = 10, numerical

n = 10, numerical

F : Termal resistance ratio and pressure drop ratio distributions or attack angle o vortex generator between the computed resultsand experimental data ( = 0.002 m, = 0.045 m, = 0.045 m, = 0.777, = 0, and Re= 10, 000).

10 20 30 40 50 60 700.92

0.94

0.96

0.98

1.00

1.02

1.04

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

Numerical

Experimental (Chen, 2012)

Attack angle,(deg)

(

Rth

/

Rth,re

f

)(P/P,re

f),n=

10

(P/P,re

f),n=

20

(

Rth

/

Rth,re

f

)

F : Variation o overall perormance with the attack angle between the computed results and experimental data ( = 0.002 m,= 0.045 m, = 0.045 m, = 0.777, = 0, and Re= 10, 000).

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.56

0.58

0.60

0.62

0.64

0.66

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.10

1.11

1.12

1.13

1.14

1.15

1.16

1.17

1.04

1.05

1.06

1.07

1.08

1.09

P/P

,ref

(n=

10)

P/P

,ref

(n

=

20)

Rth/Rth

,ref

(n

=

10)

Rth/Rth

,ref

(n

=

20)

Lg/H

n = 10,P/P,ref

n = 20,P/P,ref

n = 10,Rth /Rth,ref

n = 20,Rth /Rth,ref

F : Te effects o the distance between the vortex generator and heat sink or ns numbers = 10, and attack angle = 30 on thethermal resistance ratio and pressure drop ratio o heat sink ( = 0.002 m, = 0.045 m, = 0.045 m, = 0.777, and Re= 10,000).

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Mathematical Problems in Engineering

and ow resistance were numerically computed and analyzedin the present paper. So the ollowing could be concluded.

() Te LVG would increase the pressure drop ratio othe uid ow in the channel. Te thermal resistanceo heat sink with LVG was lower than that without

LVG, and the thermal resistance o heat sink withcommon-ow-down conguration was larger thanthat o common-ow-up conguration.

() Using longitudinal vortex generator could effectivelychange ow conguration o channel; it also agitatedbackow o plate-n heat sink and enhanced heattranser perormance with accelerating the coolingprocess by decreasing the minimum transverse dis-tance between winglet pair and distance between

vortex generator and heat sink.

() Regarding a balance between thermal resistanceand ow perormance, minimum transverse distancebetween winglet pair = 0.777 and distancebetween vortex generator and heat sink = 0with

attack angle = 30 were an optimal design.

Increasing the ns number would enhance the perormanceo the heat sink. Oppositely, as the number o ns andthe height o the n are increased, the heat dissipationperormance would decrease signicantly. Increasing the nheight and ns number could decrease ow area o channel.In this study, installing vortex generator would decreasethermal resistance as ns number = 20is evidently betterthan the ns number = 10.

Conflict of InterestsTe authors declare that there is no conict o interestsregarding the publication o this paper.

References

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[] S. El-Sayed, S. M. Mohamed, A. M. Abdel-lati, and A.-H. E.Abouda, Investigation o turbulent heat transer and uid owin longitudinal rectangular-n arrays o different geometriesand shrouded n array, Experimental Termal and FluidScience, vol. , no. , pp. , .

[] S. Prstic, M. Iyengar, and A. Bar-Cohen, Bypass effect in highperormance heat sinks, in Proceedings of the InternationalTermal Science Seminar, pp. , Bled, Slovenia, June .

[] S. A. El-Sayed, S. M. Mohamed, A. M. Abdel-Lati, and A.E. Abouda, Experimental study o heat transer and uidow in longitudinal rectangular-n array located in differentorientations in uid ow, Experimental Termal and FluidScience, vol. , no. , pp. , .

[] E. A. M. Elshaei, Effect o ow bypass on the perormance o ashrouded longitudinal n array,Applied Termal Engineering,vol. , no. , pp. , .

[] H.-Y. Li, G.-L. sai, M.-H. Chiang, and J.-Y. Lin, Effect o ashield on the hydraulic and thermal perormance o a plate-n heat sink,International Communications in Heat and Massransfer, vol. , no. , pp. , .

[] R. A. Wirtz,W. Chen, andR. Zhou, Effects oow bypasson theperormance o longitudinal n heat sinks,Journal of ElectronicPackaging, vol. , no. , pp. , .

[] G.-L. sai, H.-Y. Li, and C.-C. Lin, Effecto theangleo inclina-tion o a plate shield on the thermal and hydraulic perormanceo a plate-n heat sink, International Communications in Heatand Mass ransfer, vol. , no. , pp. , .

[] M. Fiebig, Embedded vortices in internal ow: heat transerand pressure loss enhancement,International Journal of Heatand Fluid Flow, vol. , no. , pp. , .

[] A. Sohankar, Heat transer augmentation in a rectangularchannel with a vee-shaped vortex generator, InternationalJournal of Heat and Fluid Flow, vol. , no. , pp. , .

[] A. Sohankar and L. Davidson, Effect o inclined vortex gen-erators on heat transer enhancement in a three-dimensionalchannel, Numerical Heat ransfer A: Applications, vol. , no.

, pp. , .[] J. M. Wu and W. Q. ao, Numerical study on laminar

convection heat transer in a channel with longitudinal vortexgenerator. Part B: parametric study o major inuence actors,International Journal of Heat and Mass ransfer, vol. , no. -, pp. , .

[] M. Henze, J. von Wolersdor, B. Weigand, C. F. Dietz, and S. O.Neumann,Flow and heattranser characteristics behindvortexgeneratorsa benchmark dataset, InternationalJournalof Heatand Fluid Flow, vol. , no. , pp. , .

[] L.-. ian, Y.-L. He, Y.-G. Lei, and W.-Q. ao, Numericalstudy o uid ow and heat transer in a at-plate channelwith longitudinal vortex generators by applying eld synergyprinciple analysis,International Communications in Heat and

Mass ransfer, vol. , no. , pp. , .[] L. ian, Y. He, Y. ao, and W. ao, A comparative study on the

air-side perormance o wavy n-and-tube heat exchanger withpunched delta winglets in staggered and in-line arrangements,International Journal of Termal Sciences, vol. , no. , pp., .

[] FLUEN Incorporated, FLUEN . Users Guide, Fluent Incor-porated, Lebanon, NH, USA, .

[] H. Y. Li, C. L. Chen, S. M. Chao, and G. F. Liang, Enhancingheat transer in a plate-n heat sink using delta winglet vortexgenerators,International Journal of Heat and Mass ransfer, vol., pp. , .

[] C. L. Chen,Heat transfer enhancement of plate-n heat sink bydelta winglet vortex generators [M.S. thesis], Huaan University,New aipei, aiwan, .

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