Heat Transfer and Thermal Performance Analysis of a Surface With Hollow Rectangular Fins

8/8/2019 Heat Transfer and Thermal Performance Analysis of a Surface With Hollow Rectangular Fins

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Heat transfer and thermal performance analysis of a surfacewith hollow rectangular fins

Ugur Akyol a, Kadir Bilen b,*

a Department of Mechanical Engineering, Faculty of Corlu Engineering, University of Trakya, 59860 Corlu/Tekirdag, Turkeyb Department of Mechanical Engineering, Faculty of Engineering, University of Ataturk, 25240 Erzurum, Turkey

Received 14 April 2004; accepted 19 May 2005Available online 5 August 2005

Abstract

An experimental study was conducted to investigate the heat transfer and friction loss characteristics in a horizontal rectangularchannel having attachments of hollow rectangular profile fins over one of its heated surface. The Reynolds number based on the flowaveraged inlet velocity and the hydraulic diameter, ranged from 3000 to 32,000. The hollow rectangular profile fins in 10 cm heightand a b = 2 cm 4 cm dimensions with a thickness of 0.2 cm were mounted on a heating surface vertically. Reynolds number, finarrangement and fin pitch in the flow direction were the experimental parameters. Both in-line and staggered fin arrangements werestudied for one-fixed spanwise (Sx/a = 3) and four different streamwise (Sy/b = 1.5, 1.875, 2.5 and 3.75) distances. Correlation equa-tions for Nu, f and thermal performances were determined for fin configurations and the straight channel case without fins. 2005 Elsevier Ltd. All rights reserved.

Keywords: Finned surfaces; Heat transfer enhancement; Thermal performance; Hollow rectangular fins; Forced convection heat transfer

1. Introduction

It is well known that a straight fin with a concave par-abolic profile provides maximum heat dissipation for agiven profile area [1]. Since the concave parabolic shapeis difficult and costly to manufacture, the rectangularprofile is preferred even though it does not utilise thematerial most efficiently [2]. For example, in a study per-formed by Tahat et al. [3], pin fins were employed on the

heating surface in a rectangular channel; and Bilen et al.[4] investigated the heat transfer and friction loss charac-teristics of a surface with cylindrical fins arranged bothin-line and staggered in a channel having rectangularcross-section. The maximum amount of the heat trans-fer occurred at Sy/D = 2.94.

A thermal performance analysis is also worthwhilefor the evaluation of the net energy gain. One of theways to evaluate the heat transfer performance is thecomparison of the heat transfer coefficients at a constantpumping power [46].

Many studies have been done for different types of finarrays, for example the one reported in [7], but still thereis lack of knowledge of the forced convection heat trans-fer from a surface with vertical hollow rectangular pro-

file fins. The array employed in the present studyconsists of vertically mounted hollow rectangular profilefins on a surface. The experiments were performed forin-line and staggered fin arrangements. Heat transferexperiments without fins were also conducted, for effi-ciency comparison. Furthermore, friction loss was deter-mined by measuring pressure drop along the test section.In calculations, two different areas, which were calledthe total surface area and the projected area, were em-ployed for the average Nusselt number.

1359-4311/$ - see front matter 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.applthermaleng.2005.05.014

* Corresponding author. Tel.: +90 442 231 4864; fax: +90 442 2360957.

E-mail address: [email protected] (K. Bilen).

www.elsevier.com/locate/apthermeng

Applied Thermal Engineering 26 (2006) 209216
mailto:[email protected]:[email protected]


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2. Experimental rig

An experimental set up was installed to study the heattransfer performance and friction factor of hollow rect-

angular profile fins (Fig. 1). Air was the working fluid.The test facility was consisted of a wooden channel seton the suction side of a fan. The cross-section of thechannel was rectangular in each section; 10 cm in heightand 18 cm in width with a wall thickness of 1.8 cm, totallength of the channel was 200 cm. The test section wasmounted at the bottom surface. The aluminum hollowrectangular profile fins were placed on an aluminumplate in dimensions of 30 cm length, 18 cm width and0.2 cm thickness. A plate heater with a 1500 W maxi-mum power, which was approximately the same dimen-sions as the aluminum plate, heated the lower horizontal

wall of the test section to supply a constant heat. The

amount of the heat given to the test section was con-trolled by a variac and a voltage regulator. To reducethe contact resistance to heat flow, a sink compoundof high thermal conductivity was applied both between

the heater and the test surface and between the test sur-face and the fins. The backsides of the heater and of theother walls were insulated with glasswool, in order tominimize the heat losses.

Seven copperconstantan thermocouples were in-stalled along the test section centerline, to measure thesteady state temperature of the base surface of the finarray. The average of these readings was taken as aver-age temperature of the test surface at steady state. Ana-log signals from the experimental system were fed to thedata acquisition card (HG 818 advantech), then thesesignals were amplified and converted to digital signals

and both saved and displayed on the computer screenas real temperature values. The temperatures were usedthe average of ten values collected for a single thermo-couple location in two-minute interval at steady state

Nomenclature

A heat transfer area (m2)a, b fin length in spanwise and streamwise direc-

tion, respectively

Dh hydraulic diameter of the channel (m)f friction factorh mean heat transfer coefficient (W m2 K1)H fin and channel height (m)k thermal conductivity of air (W m1 K1)L test surface length (m)N number of finNu Nusselt number for finned surfaceNus Nusselt number for smooth channel_Q heat transfer rate (W)

Re Reynolds numberS distance between the adjacent fins (m)T steady state temperature (K)

V mean inlet velocity (m s1)W channel or test plate width (m)

Greek symbols

DP static pressure difference (N m2)g performance efficiency

m kinematic viscosity of air (m2 s1)q air density (kg/m3)

Subscriptsa finnedaxi axialbac backcon convectionf filmin inlet, in-lineloss lossesnet netout outpro projectedrad radiations mean surface, smooth

stag staggeredtot totalvol voltx, y spanwise and streamwise directions, respec-

tively

Inclined

manometer

Fin

Anemometer

FanMixer Flow

straightener

Insulation

HeaterTest

surfaceComputerVoltage

regulator

Fig. 1. Schematic diagram of experimental apparatus.

Table 1Distance between fins and the number of rectangular profile fins for

a b = 2 4 cm2 and Sx/a = 3

Sy/b 1.5 1.875 2.5 3.75Ny 5 4 3 2

Nx 3 3 3 3Ntot (in-line) 15 12 9 6

Ntot (staggered) 13 10 8 5

210 U. Akyol, K. Bilen / Applied Thermal Engineering 26 (2006) 209216


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conditions. The inlet temperature of the air stream wastaken as the average readings of two copperconstantanthermocouples located after the flow straightener. Simi-larly the outlet temperature of the air stream was takenas the average reading of four copperconstantan ther-

mocouples located in the downstream region of the insu-lated channel. Moreover, one thermocouple was usedfor the outer surface temperature of the heating sectionand one for the ambient temperature. The coppercon-stantan thermocouples were calibrated in a thermostatwithin 0.1 C deviation before being used in the experi-ments. The average velocity in the channel was deter-mined by averaging the 11 velocities in perpendiculardirection and 19 in spanwise direction to flow by an ane-mometer. The pressure drop within the test section ofthe channel was measured by using two static pressuretapings installed on the roof of the test section, whichwere connected to an inclined manometer. In the experi-ments, the duration to reach steady state conditions wasabout 12 h, depending upon experimental conditions.The hollow rectangular profile fins with a cross-sectionof 2 cm (in the spanwise direction) by 4 cm (in thestreamwise direction) and 10 cm height, the same heightas that of the channel, were attached on the upper sur-face of the base plate. The fin number and the distancebetween the fins are given in Table 1, and the arrange-ment of the fins on the test section is illustrated in Fig. 2.

3. Calculation of the heat transfer rate and the friction

factor

The net heat transfer rate _Qnet is the heat given to theflow, by convection at the steady state conditions andcan be calculated based on the following energy balanceequation:

_Qnet _Qvol _Qloss 1

_Qloss _Qbac _Qrad _Qaxi 2

where _Qvol is the total power input to the test section,_Qbac is the conduction heat loss from the backside to

the environment, _Qrad is radiative heat loss from the test

surface to its surroundings, and _Qaxi is the axial conduc-tion heat loss through the channel wall, which isreported that this loss is less than 3.2% of the totalpower input [8], and it was assumed to be nominally3% for the present case due to the similarity of the sys-

tems. The conduction heat loss_Qbac from the down wall

of the test section to the environment was calculated byapplying the natural convection correlation betweenwall and atmosphere using the related correlation [9].The radiative loss was estimated from a simplified modelwhere the heated surface was treated as a plate surfacesurrounded by a large environment. The results sug-gested that the radiative losses with an emissivity valueof 0.05 for polished aluminum were less than 1% of_Qvol. The electric energy supplied to the test surface is

not exactly equal to the convective energy loss from thissurface. It becomes equal after subtracting the losses,

_Qnet _Qcon 3

The steady state rate of the convection heat transferfrom the test surface with fins can be calculated by

_Qcon hAtot Ts Tout Tin

2

!4

where Tout is the outlet temperature of air flow that wasdetermined by averaging the temperatures measured atfour locations at the exit section of the test surface, Tinis the inlet temperature of air that was determined byaveraging the temperatures at two locations at the en-trance of the test section, Ts is the average temperature

of seven locations in the centerline of the surface andAtot is the total surface area. Either the projected orthe total surface can be taken as the surface area inthe calculations. The total surface area, Atot, and theprojected area, Apro, can be expressed on the followingequations, respectively:

Atot Apro 2a bHNtot abNtot 5

Apro WL 6

where a and b are the length of the fins in spanwise andstreamwise directions, H is the height of the fins, Ntot isthe number of fins, W is the width of the base plate and

a b

Fig. 2. The arrangements of fins on plate: (a) in-line array, (b) staggered array.

U. Akyol, K. Bilen / Applied Thermal Engineering 26 (2006) 209216 211


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L is the length of the base plate, respectively. The aver-age convective heat transfer coefficient based on thetotal heat transfer surface area (surface + fins) can becalculated by combining Eqs. (3) and (4),

h _Qnet

Atot Ts ToutTin

2 7

Also, the average convective heat transfer coefficientbased on the projected area can be evaluated from,

hpro _Qnet

Apro Ts ToutTin

2

8The average Nusselt number definitions based on the

total surface and the projected area are as the following:

Nu hDh

k9

Nupro hproDh

k10

The Reynolds number based on the averaged flowinlet velocity and the channel hydraulic diameter is givenby

Re VDh

m11

The friction factor was determined from the mea-sured values of pressure drop, DP; across the test lengthL = 30 cm using the equation,

f DP

LDh q

V2

2

12

In Eqs. (11) and (12) Vis the averaged velocity in the en-trance of the test section and DP measured by using theinclined manometer is the static pressure differencealong the top wall of the test section, and Dh is thehydraulic diameter of the channel. The values ofthe thermophysical properties of air were evaluated atthe averaged fluid temperature, Tf= (Tin + Tout)/2.

The maximum air velocity was changed in a rangefrom 0.5 m/s to 4 m/s for the smooth channel. Theexperiments were conducted at a nominal power of50 0.6 W ( _Qvol). By using the estimation method ofMoffat [10], the maximum uncertainties of the investi-gated non-dimensional parameters are found to be asfollows: Re, 8.3%; Nu, 6.1%; f, 8.7% for the channelswith fins and Nus, 12.3%; fs, 16.4% for the channel with-out fins. The maximum uncertainties ofNu, and f are ofacceptable values for the channel with fins. The value offs, is only a little high for the channel without fins, whileNus, is also of acceptable value. When the average valueoffs is taken for all Reynolds numbers, it is found to be11.5%. The individual contribution to these uncertain-ties is pressure drop (DP), 2.7%; (DP)s, 5.2%, meanstream temperature (T), 0.2 C hydraulic diameter ofchannel (Dh), 1.2%.

4. Experimental results and discussion

4.1. Validation of data

In the literature, there have been data for different finand channel configurations and dimensions, therefore,

to make a comparison, it is chosen the data for channelwithout fins. The experimental results for smooth chan-nel are compared with the correlation for turbulent flow,reported in the literature [9] in Fig. 4. The comparisonvalidates the experimental results, although the presentresults have some discrepancy from the correlation givenin literature. The present results are obtained for entryregion, while the correlation in literature is for fullydeveloped flow. Therefore it is expected that the Nusseltnumber for entry region is of a little higher than thosefor fully developed region due to the thinner thermalboundary layer. Finally, the validation of the experi-ments with respect to the correlation given in literature

is reasonable.

4.2. Experimental results

The experiments were performed in a channel withhollow rectangular profile fins that attached either in-line or staggered to the plate, as well as in a channelwithout fins. The rectangular profile fins were mountedvertically on the test surface to give Sy/b values of 1.5,1.875, 2.5 and 3.75 in the streamwise direction, whilekeeping Sx/a = 3 constant in the spanwise direction.Reynolds number was ranging from 3000 to 32,000

based on the channel hydraulic diameter and the aver-age velocity at the entrance of the test section. Fromthe experimental results, variation of Nusselt numbersand pressure losses with Reynolds number and differentfin distances were presented graphically for both in-lineand staggered fin arrangements in this section.

The results correlated with Nusselt number and fric-tion factor for smooth channel are as follows,respectively:

Nus 0.419 Re0.565s 13

fs 0.002 Re0.4s 14

The mean deviations of the predicted Nusselt numberand friction factor are 3.2% and 11.7%, respectively.Nusselt number for the surface with fins calculated onthe basis of projected area represents the effect of thevariation in the surface area, as well as that of distur-bances in the flow due to the fins on the heat transferenhancement. However, Nusselt number based on thetotal surface area represents only the effect of distur-bances in the flow. Fig. 3 indicates the variation of theaverage Nusselt number based on the total surface areawith Reynolds number for various pitch values instreamwise direction for both in-line (Fig. 3a) and stag-



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gered arrays (Fig. 3b). The average Nusselt number in-creases with fin pitch value in streamwise direction andhas a maximum value at Sy/b ffi 3.75 that correspondsto the largest pitch value for both arrangements. On

the other hand, the variation of the average Nusseltnumber with Sy/b is quite small for the staggered finarray (Fig. 3b). This situation can be explained by theoccurrence of insufficient flow mixing between the finsfor the in-line array. For the staggered arrangement,Nusselt number is higher for all fin pitch values in com-parison to the in-line one. This enhancement may beoriginated from the increasing intensity of the turbu-lence and better mixing.

Change of Nusselt number based on the projectedarea, with respect to the Reynolds number is given inFig. 4a and b. The averaged Nusselt number decreaseswith increasing fin pitch values in streamwise direction

and has a maximum value at Sy/b ffi 1.5. The sequenceof fin pitch values for Nusselt number based on the projected area is reversed according to that based on thetotal surface area. Since the Nusselt number based onthe total surface area is independent of the changes inthe heat transfer surface area, it may increase due toonly the increasing intensity of the turbulence. However,the enhancement in Nusselt number based on the pro-jected area includes the increase of the turbulence as wellas that of the surface area related to the fin number. The

Fig. 4a and b illustrate also the smooth channel case fora comparison.

The correlations for the Nusselt number and the fric-tion factor are as the follows:

For the in-line array based on the total surface area,Nu 1.116Re0.45Sy=b

0.31 15

Based on the projected area,

Nupro 6.32Re0.44Sy=b

0.32 16

Friction factor for the in-line array,

f 0.703Re0.09Sy=b0.45 17

For the staggered array based on the total surfacearea,

Nu 1.717Re0.44Sy=b0.05 18

Based on the projected area,

Nupro 8.791Re0.43Sy=b

0.58 19

Friction factor for staggered array,

f 3.782Re0.04Sy=b1.53 20

The variation of the friction factors, with respect tothe fin spacing and Reynolds number, calculated fromthe measured pressure drop values, is presented inFig. 5a and b, for in-line and staggered arrangements.

Re10-3

Nu

0

40

80

120

160

0 5 10 15 20 25 30

in-lineSy/b

1.5

1.875

2.5

3.75

Re10-3

Nu

0

40

80

120

160

0 5 10 15 20 25 30

staggered

Sy/b

1.5

1.875

2.5

3.75

a b

Fig. 3. Variation of Nusselt number based on the total surface area with Reynolds number: (a) for the in-line array, (b) for the staggered array, Sx/

a = 3.

Re10-3

Nupro

0

150

300

450

600

0 5 10 15 20 25 30

Eq. (13)Nu=0.036Re

0.8(Dh/L)

0.055

Re10-3

Nupro

0

150

300

450

600

0 5 10 15 20 25 30

Eq. (13)Nu=0.036Re

0.8(Dh/L)

0.055

a b

in-line Sy/b

1.5

1.875

2.5

3.75

Smooth

Nusselt [9]

stag.Sy/b1.5

1.875

2.5

3.75

Smooth

Nusselt [9]

Fig. 4. Variation of Nusselt number based on the projected surface area with Reynolds number, and comparison of data with correlation for smoothchannel: (a) for the in-line array, (b) for the staggered array, Sx/a = 3.



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Since the pressure drop increases with decreasing of thefin spacing, the corresponding value of the friction fac-tor increases. It is considered that this behavior can beoriginated from increasing of the blockage effect of finswith fin number. Pressure drop values or the friction fac-

tors for the in-line array were always less than those forthe staggered one.

4.3. Performance criteria

For a constant pumping power, it is useful to deter-mine the effectiveness of heat transfer enhancement ofa heat transfer promoter in comparison with smoothsurface such that [11]

_VsDPs _VaDPa 21

where _Vs and _Va are the volumetric flow rates over the

plate, and DPa and DPs are the pressure drops withand without fins, respectively. Using the Darcy equation(Eq. (12)) and Reynolds number for each configuration,Eq. (21) may be written as

fsRe3s faRe

3a 22

The heat transfer enhancement efficiency for a con-stant pumping power may be expressed as follows[7,11,12]:

g ha=hsP 23

where ha and hs are the convective heat transfer coeffi-cients with and without fins, respectively, and index Pdenotes pumping power.

Using Eqs. (14), (17), (20), and (22) the Reynoldsnumber for the smooth surface (Res) can be written as

a function of the Reynolds number for in-line and stag-gered arrays (Rea).

For the in-line array

Res 5.675Re0.885a Sy=b

0.132 24

For the staggered array

Res 9.308Re0.894a Sy=b

0.45 25

Using Eqs. (13), (15), and (24) the heat transferenhancement efficiency based on the total surface areafor the in-line array can be written as

g

in

ha=hsP

0.995Re0.05

a

Sy=b0.385

26

In the same way, the following expression based onthe total surface area is obtained for the staggered arrayfrom Eqs. (13), (18) and (25):

gstag ha=hsP 1.162Re0.065a Sy=b

0.30427

Similarly, the heat transfer enhancement efficiencybased on the projected area can be determined for bothin-line and staggered fin arrays. For the in-line array, theexpression based on the projected area,

Rex10-3

f

1e-4

0.001

0.01

0.1

1

10

4 10 16 22 28

in-lineSy/b

1.5

1.875

2.5

3.75

Smooth

Eq. (14)

Rex10-3

f

1e-4

0.001

0.01

0.1

1

10

4 10 16 22 28

staggered

Sy/b

1.5

1.875

2.5

3.75

Smooth

Eq. (14)

a b

Fig. 5. Variation of friction factor with Reynolds number and the various distances between fins: (a) for the in-line array, (b) for the staggered array,Sx/a = 3.

Rex10-3

0.00

0.25

0.50

0.75

1.00

1.25

0 5 10 15 20 25 30

in-lineSy/b

1.5

1.875

2.5

3.75

Rex10 -3

0.00

0.25

0.50

0.75

1.00

1.25

0 5 10 15 20 25 30

staggeredSy/b

1.5

1.875

2.5

3.75

a b

Fig. 6. Variation ofg with Reynolds number based on the total area: (a) for the in-line array, (b) for the staggered array, Sx/a = 3.

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gin ha=hsP 5.657Re0.06a Sy=b

0.245 28

and for the staggered array based on the projectedarea,

gstag

ha=hsP

5.95Re0.075a

Sy=b0.326 29

can be written. Fig. 6a and b illustrate the change ofheat transfer performance based on the total surfacearea with respect to the Reynolds number for variousspaces in streamwise direction between fins, for in-lineand staggered fin arrays. As seen from Fig. 6a, g basedon the total area is greater than 1 (gP 1) only for in-linearrangement of Sy/b = 3.75. Heat transfer efficiency isless for lower fin spacing values. The performance coef-ficient decreases with increasing Reynolds number forall fin spaces. The variation of heat transfer performancebased on the projected area with increasing Reynolds

number and at various spaces in streamwise directionbetween fins, for in-line and staggered fin arrays are alsopresented in Fig. 7. It is seen that, g is greater than 1(gP 1) for both fin arrangements and all Reynoldsnumber values.

5. Conclusion

An experimental investigation of heat transferenhancement has been studied for four streamwise dis-tances of fins and two fin arrangements (in-line and stag-gered) and various Reynolds numbers. According to theexperimental data obtained for the surface equippedwith hollow rectangular profile fins, the conclusionscan be summarized as follows:

Both in-line and staggered fin arrangements signifi-cantly enhanced the heat transfer in comparison tothe surface without fins.

Nu number increased with increasing Re numberboth on the basis of the total surface area and theprojected area for in-line and staggered arrange-ments, since increasing Reynolds number decreasesthe boundary layer over the surface.

A slightly better heat transfer was achieved for thestaggered array than for the in-line arrangement onthe basis of total surface area due to the increase ofthe turbulence and better mixing of the flow. How-ever for staggered arrangement, increase in Reynolds

number increased the pressure drop and correspond-ing friction factor, because the staggered arrangementhas much more blockage effect in fluid flow.

For the staggered array, the dependence of the varia-tion of Nu number with fin spacing was smaller thanthe in-line arrangement on the basis of total surfacearea, because more space between fins was neededto provide a better mixing of the flow for in-linearrangement.

For the in-line array, the dependence of the variationof f with fin spacing was smaller than the staggeredarrangement, due to the decrease of the blockage

effect of fins. In the calculation of performance efficiency based on

the total surface area, g was greater than unity only atSy/b = 3.75 for the in-line array, and the values of gwere less than 1 for the remaining ratios and botharrangements.

For both in-line and staggered arrangements basedon the projected area, the performance efficiency gwas greater than 1 for all fin spacings and Reynoldsnumbers. It is recommended to use these types offin arrangements based on the projected area.

In order to gain more information about the heattransfer mechanism for this type of the finned system,it is suggested that heat transfer enhancement with re-spect to various cross-sections of the fin, different fin dis-tances in spanwise directions, and the gap effect betweenthe fin top and the upper surface of the channel shouldbe studied in future.

Acknowledgements

This work was funded by the Ataturk UniversityResearch Foundation under 1997/43.

Re10-3

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 5 10 15 20 25 30

in-lineSy/b

1.5

1.8752.5

3.75

Re10-3

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 5 10 15 20 25 30

staggered

Sy/b

1.5

1.8752.5

3.75

a b

Fig. 7. Variation of g with Reynolds number based on the projected area: (a) for the in-line array, (b) for the staggered array, Sx/a = 3.



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Heat Transfer and Thermal Performance Analysis of a Surface With Hollow Rectangular Fins

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