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International Journal of Thermal Sciences 79 (2014) 183e193

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International Journal of Thermal Sciences

journal homepage: www.elsevier .com/locate/ i j ts

Role of channel shape on performance of plate-fin heat exchangers:Experimental assessment

M. Khoshvaght-Aliabadi a, F. Hormozi a,*, A. Zamzamian b

a School of Chemical, Petroleum, and Gas Engineering, Semnan University, Semnan 35131-19111, IranbMaterials and Energy Research Center (MERC), Karaj, Iran

a r t i c l e i n f o

Article history:Received 13 June 2013Received in revised form6 January 2014Accepted 6 January 2014Available online 18 February 2014

Keywords:Plate-fin heat exchangerPlate-fin channelComparative evaluationPerformance evaluation criteriaVortex-generator

* Corresponding author. Tel.: þ98 9123930495; faxE-mail addresses: mkhaliabadi@gmail.com

fhormozi@semnan.ac.ir (F. Hormozi), azamzamian@m

1290-0729/$ e see front matter � 2014 Elsevier Mashttp://dx.doi.org/10.1016/j.ijthermalsci.2014.01.004

a b s t r a c t

A comparative evaluation of seven common configurations of channels used in plate-fin heat exchangersis presented. All the channels, including plain, perforated, offset strip, louvered, wavy, vortex-generator,and pin, are fabricated and tested experimentally. The working fluid is water, and Reynolds numberrange is from 480 to 3770. To evaluate the performance of these channels and also select an optimumplate-fin channel, three mostly used energy-based performance evaluation criteria are employed. Theresults are presented as plots of dimensional and non-dimensional parameters. In comparison with all ofthe studied channels, the vortex-generator channel shows a significant enhancement in the heat transfercoefficient and a proper reduction in the heat exchanger surface area. Therefore, it can be applied as ahigh quality interrupted surface in the plate-fin heat exchangers. Moreover, the wavy channel displays anoptimal performance at low Reynolds numbers.

� 2014 Elsevier Masson SAS. All rights reserved.

1. Introduction

1.1. Plate-fin heat exchanger specifications

Process intensification (PI) usually pertains to chemical engi-neering instruments and methods. The plate-fin heat exchanger(PFHE) as a multi-functional device and heat transfer augmentationtechniques in this heat exchanger can be a popular issue from the PIpoint of view. A PFHE consists of a block with alternating layers ofextended surfaces as plate-fins. These layers are separated byparting sheets and restrained by side bars. A large heat transferarea, light weight per unit volume, high thermal performance,possibility of heat exchange among several streams, and closetemperature on channels are the advantages which make the PFHEone of the popular type of heat exchangers. Based on differentapplications, various types of plate-fin channels such as plain,perforated, offset strip, louvered, wavy, vortex-generator, and pinare used in the PFHEs. Each of these channels enhances the heattransfer with special techniques. The PFHEs are employed over awide range of temperatures and pressures for gasegas, gaseliquid,and multi-phase duties, such as cryogenics for separation andliquefaction of air (Coldbox system), production of petrochemicals

: þ98 2313354136.(M. Khoshvaght-Aliabadi),erc.ac.ir (A. Zamzamian).

son SAS. All rights reserved.

and large refrigeration systems, and natural gas processing andliquefaction. To make the PFHEs as compact as possible in theseapplication, the complex plate-fin channels, i.e., perforated, offsetstrip, louvered, wavy, vortex-generator, and pin, can be replacedinstead of plain one.

1.2. Literature review

The great advantages and different applications of the PFHEs arethe factors that motivate many investigators to study the perfor-mance of these heat exchangers. Therefore, numerous experi-mental and numerical studies have been conducted oncharacteristics of each plate-fin channel. The experimental andnumerical thermal-hydraulic data of the PFHEs with differentchannels are given for perforated [1,2], offset strip [3e9], louvered[10e15], wavy [16e26], vortex-generator [27e33], and pin [33e38]. Nevertheless, studies which focus on the comparison of thethermal-hydraulic performance of different channels are verylimited. A review of the prominent comparative studies [39e43] ispresented here.

A comparative assessment of five different channels, namelyplain with the rectangular and triangle cross sections, offset strip,louvered, and vortex-generator, to operate in compact heat ex-changers was experimentally conducted by Brockmeier et al. [39],when air operated as the working fluid. They reported that thevortex-generator surface has the best performance, and it can

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193184

reduce the heat transfer surface area up to 76% for the fixed heatduty and pumping power. A thermodynamic analysis was per-formed by Tagliafico and Tanda [40] to compare the performance ofa number of the PFHE surfaces. The comparisons were done underconstraints, including the fixed heat transfer duty, mass flow rate,and lengthewidth of the heat exchanger. In another study, fourbasic channels of the PFHEs, namely the rectangular plain, stripoffset, perforated, and wavy, were simulated at the laminar flowregime by Zhu and Li [41]. The major purposes of this study werethe heat transfer behaviors in both the developing and the devel-oped regions and local Nusselt number variations along the flowdirection. Correlations for the thermal entry length were also ob-tained. In all of the previous comparative studies, the surface of oneside of the heat exchanger was considered. A study on both sides ofthe heat exchanger surfaces was conducted by Khalil et al. [42].Dong et al. [43] recently used of the VG-I criteria which measuresthe possible reduction of the surface area to compare five plate-fins.They considered the air as coolant on the gas side of a flat-tube heatexchanger.

Because of differences in geometrical parameters, workingfluids, and data reductionmethodswhichwere adopted in differentliterature, a comprehensive assessment of the common plate-finchannels is not possible. Also, in most previous comparativestudies, the air was considered as working fluid. To the best of ourknowledge, no experimental study has compared the thermal-hydraulic performance of different plate-fin channels when aliquid such as thewater was used in the PFHE asworking fluid. Also,a detailed performance evaluation of all the channel shapes was notconsidered in the comparisons. Therefore, this motivates us toevaluate a PFHE performance with different plate-fin channels.Seven common channel shapes, including plain, perforated, offsetstrip, louvered, wavy, vortex-generator, and pin, were fabricatedand tested by using a proper experimental procedure at the con-stant temperature boundary condition. The thermal-hydraulicspecifications in these channels were obtained and presented inthe dimensional and non-dimensional forms. Three extensivelyused energy-based performance evaluation criteria (PEC), includingthe j/f1/3 ratio, JF factor, and VG-I criterion, were used for theappraisal.

2. Experiments and measurements

2.1. Experimental test loop

A schematic diagram of the designed and fabricated experi-mental test loop is shown in Fig. 1. The main sections of theexperimental rig are; (1) transmission fluid state, (2) measurementequipment, (3) constant temperature bath system, and (4) coolingunite. The basic components along with their model are numberedand introduced in the schematic. This setup was designed tomeasure the heat transfer and pressure drop characteristics of theworking fluid flowing over the length of different plate-finchannels.

As shown in Fig. 1, the flow rate was controlled by two adjust-able ball valves; one after the pump and by-pass three-way and theother one at the by-pass line. The accurate flow adjustment wasconducted by a rotameter. The main flow measuring device was ahigh sensitive ultrasonic flow meter. Two high precise T-typethermocouples were used to measure the inlet and outlet tem-peratures of the fluid by putting them into the flow line. Nine K-type thermocouples were mounted on the external and differentpositions of the test section surfaces to measure the wall temper-ature distribution and ensure the uniformity of the surface tem-perature along the test section. The pressure drop was found bysubtracting the measured local pressure values at the inlet and

outlet of the test section. To achieve a high accuracy, two verysensitive pressure transmitters were utilized. Authenticity of theestimated pressure drop was examined by using two glass pipes asdifferential pressure manometer.

The constant temperature bath system consists of a two-phasechamber and temperatureepressure control systems. The two-phase chamber was made of 2 mm thick stainless steel sheets.The dimensions of the chamber were 20 cm � 60 cm � 30 cm(Width � Length � Height). The temperature of the chamber wascontrolled by a 2 kWelectrical heater as heat source, a temperaturecontroller, a power controller, and a calibrated T-type bulk tem-perature sensor. This control systemmaintained the operating fluidat its boiling point. The pressure of the chamber was controlled by asmall size-high accurate pressure control digital sensor and a steamelectrical pressure valve boarded on the chamber.

The cooling unit system consists of a brazed PFHE, a flat tube-and-plate fin heat exchanger along with an air fan, a calibratedbulk K-type temperature sensor, and a temperature controller.While the working fluid was cooled circa the reservoir temperaturein the brazed PFHE, the supplementary cooling to achieve thestringent temperature of the reservoir was done in the second heatexchanger by crossing the air over its flat tubes. The signal obtainedfrom the temperature sensor located at the outlet of this heatexchanger was used in the temperature controller which com-manded the oneoff status of the air fan. Some detail, includingmodel, range, and accuracy, about all the measuring instrumentsare presented in Table 1.

For all the experimental tests, the data were logged by a com-puter whenever the steady-state condition was achieved, usuallywithin 10e15 min from the beginning of each experiment. In thepresent study, the steady-state condition was defined as all themeasurement quantities and operation factors remained constant.Then, the working fluid flow rate was increased, and the new datawere recorded. To reduce themeasuring errors as much as possible,the decreasing fluid flow rate trend was also utilized. All the factorswere measured six times; half for the increasing trend and half forthe decreasing trend, and the most centralized four of them werechosen to calculate the average values used in the data reductionsection.

2.2. Test sections

To create a physically meaningful and reliably comparativestudy and also to assess relative advantages of different plate-finchannels, three comparative constraints, namely comparablegeometrical parameters, similar operating conditions, and equalthermo-physical properties of the working fluid, were consideredhere.

The geometrical constraints encompass the following cases,

� A similar frontal flow area,� A similar channel length,� A similar fin thickness,� And similar values of specific geometrical parameters.

The first three constraints produce an equal external heattransfer area attaching with the saturated steam except the wavychannel due to its special geometry. The frontal flow area, channellength, and fin thickness of 3�10�4 m2, 0.4m, and 4�10�4 mwerechosen, respectively.

The other constraint was selected from the operating conditionspoint of view,

� A same volumetric flow rate,� A same inlet temperature,

Fig. 1. Schematic diagram of experimental test loop.

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193 185

� A same thermal condition on the external surfaces of thechannels.

The above factors relate the range of Reynolds number (from480 to 3770 according to the channel hydraulic diameters), theinlet working fluid temperature (298.15 K), and the temperatureof the saturated steam attaching with the external surfaces of thetest sections (368.15 K), respectively. It should be noted thatmost of the industrial PFHEs in the same scale of the studiedchannels in the present work have capability in the range of100e400 lph (i.e., 1.66e6.66 lpm), which it is very close to therange of the present work. Also, condensation is one of the

Table 1Model, range, and accuracy of measuring instruments.

Instrument Measure Model

Ultrasonic flow meter Flow rate FlownInlet & outlet thermocouples Bulk temperature PT-10Surface thermocouples Temperature OmegPressure transmitters Local pressure PSCH0

application areas of the PFHEs, which exactly pertains to thecurrent condition.

The test sections consist of a plate-fin channel, two cover plates(or parting sheets), and two side bars. A conoid shape header wasfabricated at the beginning of the test sections to provide relativelyuniform flow distribution. A similar structure was made as thenozzle to collect the flow at the end of the test sections. Theseparate parts of the test section and assembled form of test sec-tion, when the plain channel is as core surface, are shown in Fig. 2.The geometrical configurations of different channels are depictedin Fig. 3. The detailed dimensions are also summarized in Table 1.All the components were made of copper. The plate-fin channel,

Range Accuracy

etix� 100series� 0e25 lit min�1 �0.05 lit min�1

0 T-type �50 to 200 �C �0.1 �Ca K-type �73 to 260 �C �0.2 �C.05BCIA 0e5000 Pa �1.0 Pa

Fig. 2. Separate parts and assembled form of test section.

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193186

cover plates, and side bars were constructed of 0.4, 0.7, and 1.0 mmthick sheets, respectively.

3. Theory

3.1. Data processing

The thermal-hydraulic performance of a plate-fin heatexchanger is in terms of the heat transfer and pressure drop per-formance characteristics. The equation of the experimentalconvective heat transfer rate was used to compute the heat transfercoefficient,

_Qconv: ¼ _mCP�Tf ;out � Tf ;in

�(1)

where _m, CP, Tf,out and Tf,in represent the mass flow rate, specificheat, inlet and outlet bulk temperatures of the working fluid. Theeffective heat transfer coefficient was estimated from the ratio ofthe convective heat transfer rate to the total surface area and

Fig. 3. Plate-fin channels: (a) plain (b) perforated (c) offset

logarithmic mean temperature difference between the wall and theworking fluid,

h ¼_Qconv:

Ach:f

�Tw � Tf

�LMTD

(2)

�Tw � Tf

�LMTD

¼�Tw � Tf ;in

���Tw � Tf ;out

�logh�

Tw � Tf ;in�.�

Tw � Tf ;out�i (3)

where Tw is the wall temperature which is the average of the ninemeasured temperatures on the external wall of the test sections.The thermal performance can be illustrated in a non-dimensionalform, namely Colburn factor,

j ¼ Nu

RePr1=3(4)

where Nu is the Nusselt number, Re is Reynolds number, and Pr isPrandtl number. Reynolds number can be calculated based on massvelocity as follows,

Re ¼ GDhm

(5)

The generalized relation of the hydraulic diameter for the plate-fin channels is given by Refs. [44],

Dh ¼ 4AcLAch:f

(6)

where Ac is the minimum free flow area, L is the flow length, andAch.f is the total heat transfer area. The hydraulic diameter relationsfor the tested channels are obtained and given in Table 3 based onEq. (6).

The Fanning friction factor of the test samples were estimatedfrom the pressure drop values using the following equation,

f ¼ 2rDhDPLG2 (7)

where r is the working fluid density, DP is the pressure drop, and Gis the mass velocity.

strip (d) louvered (e) wavy (f) vortex-generator (g) pin.

Table 4Constants of different properties correlations.

G a b c d

r �19.906 2.061 � 10�1 �6.766 � 10�4 7.392 � 10�7

m �3.027 2.999 � 10�2 �9.897 � 10�5 1.088 � 10�7

k 27.168 �2.277 � 10�1 6.230 � 10�4 �5.334 � 10�7

Table 2The detailed dimensions of the test sections (�10�3 m).

PFC type Legend (Fp) (Fh) (L) (t) Specific geometricalparameters

Plain 10 10 400 0.4 e

Perforated 10 10 400 0.4 dh ¼ 5 & S ¼ 20 &f ¼ 7% open

Offset strip 10 10 400 0.4 Lo ¼ 20

Louvered 10 10 400 0.4 Lh ¼ 5 & Lp ¼ 5 & La ¼ 90�

Wavy 10 10 400 0.4 Lw/2 ¼ 20 & A ¼ 5

Vortex 10 10 400 0.4 Vh ¼ 5 & Vl ¼ 20 & Vt ¼ 10

Pin 10 10 400 0.4 0.4dp ¼ 5 & Sl ¼ 20 & St ¼ 10

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193 187

3.2. Thermo-physical properties of working fluid

High thermal conductivity, low viscosity, and low cost are theconsiderable advantages of a perfect liquid as working fluid orcoolant. The most commonworking fluid, which was considered inthe current work, is water. To obtain accurate results, the thermo-physical properties of the water as working fluid were experi-mentally measured under the range of the operating temperature(298.15e313.15 K). The transient hot-wire method was utilized tomeasure the thermal conductivity by using a thermal propertiesanalyzer, KD2 Pro system (Decagon Devices). It is discovered thatthis property increases with the temperature. The rheological be-haviors were studied by using an accurate rheometer (Physica MCR301, Anton Paar). The results explained that the dynamic viscositydecreases with the temperature. The measured results depictedthat the sensitivity of the dynamic viscosity to the temperature islower than the thermal conductivity. The density was evaluated byusing of the weighing a known volume of the working fluid with aset of precise digital-electronic balance (CPA 1003S, Sartorius) andpycnometer. Similar to the dynamic viscosity, this property de-creases with the temperature. The specific heat capacity wasmeasured by using a differential scanning calorimeter (C80D,Setaram). No significant variations were observed with the tem-perature in the studied range for this property. It should be notedthat a repeated measures method was performed for every case,and the average value of the centralized data was used in this work.

Then, based on the measured properties and following format,empirical correlations were developed for each property,

G ¼ aþ bT þ cT2 þ dT3 (8)

In the above equation, the general variable G represents the r, m,or k; T is the operating temperature (298.15e313.15 K); and a, b, c,and d are the correlation constants which are presented in Table 4.

The correlations developed here can satisfactorily predict thethermo-physical properties of the water at the range of the oper-ating temperature. The mean deviations between the experimentalmeasurements and the computed results of the density, viscosity,

Table 3Hydraulic diameters of different plate-fin channels.

Channel type Hydraulic diameter (Dh)

Perforated Dh ¼ ð4LFpFhÞð4þ nhpdhtÞ=2LFp þ 2LFh � nppd2hOffset strip Dh ¼ ð2FpFhÞð2LoÞ=ðFp þ Fh þ FhtÞLouvered Dh ¼ LFpFh=LFp þ LFh þ 2nlLhtWavy Dh ¼ 2LFpFh=LzðFp þ FhÞVortex-generator Dh ¼ 12LFpFh=6LFp þ 2LFh þ 3ntVht þ 2ntV2

hPin Dh ¼ ð12LFpFhÞð2þ 2LFh þ nppdpFhÞ=ð6LFp � nppd2pÞ

and thermal conductivity correlations are about 0.1%, 1.1%, and0.15%, respectively.

3.3. Uncertainty of experimental data

The experimental uncertainties of the obtained parametersfrom the data reduction section were calculated by using the Klineand McClintock method [45] and the following equation,

dR ¼24XM

j¼1

vRvXj

dXj

!2351=2 (9)

where j, M, dR, and dXj are the specific parameter counter, numberof the independent variables, uncertainties associated with thedependent, R, and independent, Xj, variables. Eqs. (10) and (11)present the relations obtained from Eqs. (4) and (7) based on Eq.(9) to estimate the uncertainties of the j factor and f factor.

dj¼"�

1

RePr1=3dNu

�2

þ�

Nu

Re2Pr1=3dRe

�2

þ�

Nu

3RePr4=3dPr�2#1=2

(10)

df ¼"�

DhDP2LG2 dr

�2

þ�rDP2LG2 dDh

�2

þ�rDh

2LG2 dDP�2

þ�rDhDP2L2G2 dL

�2 þ �rDhDPLG3 dG

�2�1=2 ð11Þ

Similar relations were obtained for the Nusselt, Reynolds, andPrandtl numbers, but they are not presented here due to the spacerestriction. Themean uncertainties of the estimated parameters arepresented in Table 5 based on the uncertainty equations andTable 2.

4. Results and discussion

Heat transfer and pressure drop measurements of differentplate-fin channels are presented in the current section. The effectsof the channel configuration on dimensional and non-dimensionalthermal-hydraulic parameters are discussed. For each plate-finchannel, the results were obtained at various volumetric flowrates in the range of 2e5 lpm. The result of the plain channel wasconsidered to establish a baseline for comparison.

Table 5Main parameters and their uncertainties.

Parameter Uncertainty

Convective heat transfer rate 2.90%Effective heat transfer coefficient 0.31%Reynolds number 0.97%Nusselt number 2.12%Prandtl number 1.02%Colburn factor 1.79%Fanning friction factor 3.30%

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193188

4.1. Heat transfer results

Interrupted and indirect channels are normally used to enhancethe heat transfer. The result of the convective heat transfer coeffi-cient is an important parameter for heat exchanger designers. Acomparison of the convective heat transfer coefficient variationswith the volumetric flow rate for various channel shapes is shownin Fig. 4. The results indicate that the heat transfer coefficient in-creases with raising the flow rate. This figure depicts that the plainchannel has the lowest values in the entire tested range, since theheat transfer coefficient in the other channels enhances by thermalboundary layers interruption with holes, strips, louvers, corruga-tions, wings, and pins. The highest values were found for thevortex-generator channel. In the vortex-generator channel, thelongitudinal, transverse, and normal swirl flows may be generatedbehind the wings and the flow becomes more disturbed. The swirlflows make a heavy exchange of core and wall fluid, leading to theenhancement of heat transfer between the flowing fluid and thechannel walls. The generation of the longitudinal swirl flows, whichexchange the core fluid in the hot walls (cover plates) direction, isthe main reason of this drastic heat transfer enhancement in thevortex-generator channel. However, the possibility of the longitu-dinal swirl flows generation in the other tested channel is veryweak. It can be seen that the vortex-generator gives higher andhigher values, as the flow rate increases. For instance in the graph ofthis channel, the enhancement of the heat transfer coefficient withincreasing flow rate from 2.0 to 5.0 lpm is about 34.6%. A possiblemechanism for this appreciable heat transfer coefficient enhance-ment is due to increasing number and size of swirl flows in thischannel, because the strength of such promoted cells depends onthe flow rate.

After the vortex-generator channel, the wavy channel has thegreatest values. This is attributed to lengthen of the flow path andpresence of transverse and normal swirl flows accompanied withcorrugations corners of this channel [46]. It can be concluded thatthe swirl flows are the important mechanism in the heat transferenhancement of the PFHEs.

Likewise, the heat transfer coefficient curve in case of the offsetstrip channel places between those of the wavy and pin channels atthe flow rates higher than 3.5 lpm, but at the lower flow rates, theheat transfer coefficient of this channel is found to be lower thanthat of the pin channel. This illustrates that the flow separation by

Fig. 4. Heat transfer coefficient e Reynolds number for different plate-fin channels.

pins in the pin channel are more effective than the boundary layersregeneration by strips in the offset strip channel at the lower flowrates. Similar to the vortex-generator channel results, the discrep-ancies between the heat transfer coefficient for flow in the offsetstrip channel and those in the plain channel one become biggerwith increasing the flow rate.

Using non-dimensional parameters provides flexibility andgenerality to compare different heat exchangers. However, thethermal-hydraulic specifications of the PFHEs are usually demon-strated in the non-dimensional forms as the j factor and f factor. Fora further comparison of the thermal performance, the tested resultsof the considered channel configurations are plotted in the term ofthe ji/jplain ratio versus Reynolds number as depicted in Fig. 5. Itshould be noted that according to Eq. (6) and Table 3, the hydraulicdiameter differs for each channel in the same frontal area andchannel length. For the sake of comparison, Fig. 6 demonstrates thetotal heat transfer area and hydraulic diameter of different chan-nels. The vortex-generator and pin channels have the highest hy-draulic diameters due to their lower total heat transfer areas, seeEq. (6). Therefore, it causes Reynolds number for these channelsbecome higher at the same volumetric flow rates and similarproperties of the working fluid (i.e., density and viscosity).

As depicted in Fig. 5, the ji/jplain values of all the channels arehigher than one. The enhancement in the ji/jplain ratio with thevortex-generator channel is obvious compared to the other chan-nels. Also, over the tested range of Reynolds number, the average jfactor of the vortex-generator enhances by a factor of above 2 timesthat of the plain channel. For the wavy and pin channels, the ji/jplainratio values are very close to each other and lower than those of thevortex-generator. The figure also presents that in contrast with theji/jplain ratio values of the perforated, louvered, wavy, and pinchannels, those values of the offset strip and vortex-generatorchannels enhance with increasing Reynolds number. Thisenhancement of the vortex-generator channel from the lowest tothe highest Reynolds numbers is higher than that of the offset stripchannel (about 5.8% for the vortex-generator and 2.2% for the offsetstrip). It illustrates that at the high Reynolds numbers the vortex-generator and offset strip channels reinforce the heat transferaugmentations and can be a better selection as core surface ofPFHEs from the heat transfer point of view. Note that the heattransfer augmentation of the wavy channel is comparativelyeffective at the lower Reynolds numbers, but relatively marginal

Fig. 5. ji/jplain ratio values e Reynolds number for different plate-fin channels.

Fig. 6. Total heat transfer area and hydraulic diameter of different plate-fin channels.

Fig. 7. Pressure drop e volumetric flow rate for different plate-fin channels.

Fig. 8. fi/fplain ratio values e Reynolds number for different plate-fin channels.

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193 189

enhancement is seen compared to the other channels in the higherReynolds numbers.

The ji/jplain ratio generally gets little higher values with theperforated channel than those of the plain channel. This is attrib-uted to the holes which have two opposite effects on the j factor;when the working fluid flow approaches a hole, there is an increasein the j factor because the flow and thermal boundary layer areinterrupted there; then the j factor drops rapidly through that holedue to the local heat transfer area reduced by the hole [41]. As aresult, the perforated channel does not enhance the overall ji/jplainratio as much as the other mentioned channels. A similar argumentmay be true for the louvered channel due to the presence of thelouvers in this channel.

Over the tested range of Reynolds number, the j factor values ofthe perforated, offset strip, louvered, wavy, vortex-generator, andpin channels averagely increase by about 16.4%, 30.1%, 9.0%, 44.8%,111.2%, and 30.4% higher than those of the plain channel, respec-tively. Also, themaximum enhancement of the ji/jplain ratio is 1.22 atRe ¼ 1390 for the perforated, 1.31 at Re ¼ 2540 for the offset strip,1.14 at Re ¼ 1080 for the louvered, 1.56 at Re ¼ 970 for the wavy,2.19 at Re¼ 3770 for the vortex-generator, and 1.39 at Re¼ 1500 forthe pin.

4.2. Pressure drop results

The pressure drop is the other parameter which is important forheat exchanger designers. Fig. 7 shows the pressure drop valuesversus the volumetric flow rate for different plate-fin channels.Similar to the convective heat transfer coefficient, this parameter ismainly affected and enhanced by the flow rate. Over the testedrange of the flow rate, the pressure drop values of the perforatedand louvered channels seems to have a little bit higher values thanthat of the plain channel. In the same time, the pin and wavychannels get higher values, respectively. Likewise, the curve in caseof the vortex-generator places between those of the pin channeland thewavy channel at the flow rate lower than 3.5 lpm, but at thehigher flow rates, the pressure drop of the vortex-generator isfound to be the maximum. Blocking the working fluid flow by thepins and wings along with periodic separation of the boundarylayer and enlarging the flow path along with periodic variation ofthe flow direction are the main reasons of the higher pressure dropvalues of the pin, vortex-generator, and wavy channels, respec-tively. This illustrates that the enhancement of heat transfer isusually penalized by the increase in the pressure drop.

Themeasured flow pressure drops along the tested channels arealso used for the friction factor predictions described in Eq. (7). Thevariations of the evaluated fi/fplain with Reynolds number ofdifferent plate-fin channels are shown in Fig. 8. The fi/fplain ratiovalues of all the channels are higher than one. It is found that thefriction factor of the pin and vortex-generator channels is muchhigher than that of the plain channel. This is mainly attributed tothe high hydraulic diameters of these channels according to Eq. (7),where the friction factor is proportional to Dh. Promotion of un-stable mode for formed vortices in the core of flow associated withthese channels which leads to a significant increase of pressuredrops (see Fig. 7) is the other reason.

In all of the tested channels, it can be observed that the fi/fplainratio gradually decreases up to a crucial Reynolds number, afterwhich it tends to increase. The noticed increase in the friction factormay be attributed to the undeveloped flow in the short core lengthof the tested channels. The disruption of the main flow in thetransitional region results in a significant increase in the pressuredrop leading to an increase of friction factor. At Reynolds numbershigher than that of the crucial values, the fully developed flows

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193190

might occur, and the friction factor tends to decrease. The resultsshow that this crucial Reynolds number occurs for the wavychannel at the lower Reynolds number than that of the otherchannels, about 1650, and the offset strip and louvered channelscome in the second and third, about 1800 and 1900, respectively.

The f factor values for the perforated, offset strip, louvered,wavy, vortex-generator, and pin channels averagely increase byabout 7.9%, 11.7%, 8.9%, 22.2%, 113.1%, and 116.3% higher than thoseof the plain channel, respectively. A similar trend of the j factor and ffactor was numerically reported by Zhu and Li [41] for four com-mon plate-fin channels, namely plain, perforated, offset strip, andwavy, with 0.306 m length of channels.

Finally, the mean deviations of the convective heat transfercoefficient and pressure drop values between each channel and theplain one are summarized in Table 6, according to the followingdefinition,

Mean deviation ð%Þ ¼ 1N

X�����fi � fplain

fplain

�����!

� 100% (12)

From the tabulated results, the vortex-generator channel showsa significant enhancement in the heat transfer coefficient comparedto the pressure drop, whereas the pin channel exhibits a reversemanner. This ratio related to the louvered, wavy, and offset stripchannels is not noticeable. It is interesting to note that, while theperforated channel has the maximum ratio of the heat transfercoefficient enhancement to the pressure drop enhancement, itsheat transfer coefficient enhancement is not significant in com-parison with the other channels.

4.3. Performance evaluation criteria analyses

As mentioned earlier, an improvement in the heat transferperformance is associated with an increase in the pressure drop.Consequently, it is significant to evaluate the net profits by usingsuch channels. There are several performance evaluation criteria(PEC) such as the j/f ratio, j/f1/3 ratio, and JF factor in the compactheat exchangers to select the optimum geometry with a larger jfactor and smaller f factor. Bhowmik and Lee [6] demonstrated thatthe j/f ratio criterion could not be considered as a suitable perfor-mance criterion for fluids with high Prandtl number, and theappropriate performance criterion for fluids with Prandtl numberaround 7 was found to be the JF criterion. Nevertheless, the per-formance evaluation criteria used in this comparative assessmentconsist of a component criterion, i.e., the ji/fi1/3 ratio [47], and acomparative criterion, i.e., the thermal-hydraulic performancefactor, the JFi factor [48]. Also, the VG-I criterion of the Webb [49]was considered to measure the possible reduction of the surfacearea relative to each channel compared to the plain one, i.e., the Ai/Aplain ratio. The definitions of the JFi factor and Ai/Aplain ratio, whichdescribe the performance benefits of a plate-fin channel comparedto the plain one, are presented in Eqs. (13) and (14),

JFi ¼�ji=jplain

��fi=fplain

�1=3 (13)

Table 6Mean deviations of heat transfer coefficient and pressure drop between eachchannel and plain one.

PFC type Perforated Offset strip Louvered Wavy Vortex Pin

h 16.39% 30.13% 9.01% 44.76% 111.18% 30.42%DP 7.27% 21.51% 11.72% 39.63% 56.26% 57.92%

Ai

Aplain¼�jplainji

�3=2 fifplain

!1=2

(14)

where the subscripts ‘i’ and ‘plain’ mean a type of the plate-finchannel and plain one as the reference channel or baseline,respectively.

A comparison among the ji/fi1/3 ratio values versus Reynoldsnumber for different channels is displayed in Fig. 9. The high valuesof the ji/fi1/3 ratio propose a heat exchanger with a good heattransfer and pressure drop performance. An overall scrutiny on thefigure discloses that the ji/fi1/3 ratio values of all the channelsdecrease with Reynolds number. It is depicted that under thestudied Reynolds number range, the highest and lowest values arefound for the vortex-generator and plain channels, respectively.The ji/fi1/3 ratio of the wavy and offset strip channels are close at thesmaller Reynolds numbers (i.e., Re < 1500), and the wavy channelhas the higher values in this regime, while at the Re > 1500, theoffset strip channel gets the higher values.

As depicted in Table 6, whereas the pin channel has the greatestpressuredropamong thestudiedchannels, this channel shapeshowsconsiderable high values of the ji/fi1/3 ratio. This is attributed to thepower of the friction factor (i.e., 1/3) in the denominator of the ji/fi1/3

ratio, which reduces the effect of the friction factor or pressure droponthis ratio. It is interesting tonote thatbasedonFigs.4 and7, thepinchannel has theweakest performance from the ji/fi criterion point ofview. Moreover, the ji/fi1/3 ratio curve of the pin channel places be-tween thoseof thewavyandoffset strip channels at Re>2250, but atthe lower Reynolds numbers, the ji/fi1/3 ratio of this channel is foundtobe thehigher than thoseof thewavyandoffset strip channels.Overthe tested range of Reynolds number, the ji/fi1/3 ratio generally getsthe slightly higher valueswith the perforated and louvered channelsas compared to the plain channel particularly at the higher Reynoldsnumbers. From Fig. 9 and above discussion, it can be said that theeffect of channel configuration on the ji/fi1/3 ratio for tested channelsis changeable and relates to the Reynolds number.

Taking a step beyond a component performance evaluationcriterion is consideration a comparative criterion, namely thermal-hydraulic performance factor (JFi). Similar to the ji/fi1/3 ratio, thiscriterion is a ‘the larger the better’ parameter, and a high value ofthis criterion indicates a heat exchanger with a superior thermal-hydraulic performance. In Fig. 10, the JFi factor values against

Fig. 9. j/f1/3 ratio values e Reynolds number for different plate-fin channels.

Fig. 10. JF factor values e Reynolds number for different plate-fin channels. Fig. 11. Possible reduction of surface area values e Reynolds number for differentplate-fin channels.

Table 7Average and maximum enhancement values of studied performance evaluationcriteria for different plate-fin channels compared to plain one.

Criterion type Perforated Offsetstrip

Louvered Wavy Vortex-generator

Pin

ji/fi1/3

ratioAverage 13.5% 25.8% 6.0% 35.6% 64.4% 1.7%Maximum 17.1% 31.2% 7.7% 39.8% 73.4% 5.1%

JFifactor

Average 13.5% 25.8% 6.0% 35.6% 64.4% 1.7%Maximum 17.1% 31.2% 7.7% 39.8% 73.4% 5.1%

VG-I Average 17.2% 28.8% 8.2% 36.6% 52.4% 2.8%Maximum 21.1% 33.5% 13.4% 39.5% 56.2% 7.2%

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193 191

Reynolds number for different plate-fin channels are comparedrespect to the plain one. An overall inspection on this figure ex-poses that this factor for all the channel shapes is higher than thatof the plain one except the pin channel at the high Reynoldsnumbers. As clarified in the figure, a better thermal-hydraulicperformance is found for the vortex-generator channel, and thewavy and offset strip channels come in the second and third.Similar to the ji/jplain ratio curves (see Fig. 5), the vortex-generatorand offset strip are the channels which their JF factor curvescontinually become larger with increasing Reynolds number. Also,the high ratio of the convective heat transfer coefficient to thepressure drop of the perforated channel (see Table 6) causes thatthis channel has the greater JF factor values than that of the pinchannel.

As another comparative criterion which considers the possiblereduction of the surface area for fixed values of pumping power,heat duty, and temperature difference is the VG-I criterion. Thepossible reduction of surface area values as a function of Reynoldsnumber for different plate-fin channels are given in Fig. 11. Thisfigure clarifies that this criterion almost has the samemanner to theJF factor curves for all the channels. The vortex-generator also re-duces the maximum amount of the surface area. After the vortex-generator, the wavy, offset strip, perforated, and louvered chan-nels take the first to the fourth ranks in the reduction of surfacearea, respectively.

Finally, the average and maximum enhancement values of thestudied performance evaluation criteria for different plate-finchannels compared to the plain one are presented in Table 7. Asexpected, the tabulated results explain that the ji/fi1/3 ratio, as acomponent criterion, and JF factor, as a comparative criterion, havethe same enhancement values for all the channels.

4.4. Final remarks

From the plotted and tabulated results, there is no doubt thatthe vortex-generator channel with the highest values of the heattransfer coefficient (see Fig. 4) and ji/jplain ratio (see Fig. 5) has thebest performance from the ji/fi1/3 ratio and JFi factor point of views.As depicted, the exchanging of the working fluid from the walls tothe core regions of the flow, disrupting of boundary layers, andcreating of swirl flows are the main reasons of the high heattransfer coefficient values in this channel. Moreover, this channel

shape provides the maximum saving of the heat exchanger surfacearea and thus in the heat exchanger volume.

The pin channel has the noticeable j factor and f factor values.The pressure drop enchantment due to the blocking of the flow bypins is more notable than the heat transfer coefficient enchantmentdue to the separating of the boundary layers by pins. Therefore, thisdesign of the plate-fin channels proposes the maximum ji/fi ratioamong all the channels after the vortex-generator channel for aPFHE at the studied range of Reynolds number.

The wavy channel with the greatest heat transfer area and thelongest flow path in the fixed length of a PFHE has the highestvalues of the heat transfer coefficient and j factor after the vortex-generator channel. From the obtained results by the ji/fi1/3 ratio andJFi factor, this scheme of the plate-fin channels has an optimumperformance at low Reynolds numbers among all the channels.Moreover, thewavy channel has the second rank in the reduction ofsurface area.

The offset strip channel increases the heat transfer by enlargingthe surface area and regenerating thermal boundary layer in eachcolumn. This shape of the plate-fin channels has the fourth state ofthe j and f factor values at the range of studied Reynolds number. Ithas the third state of the thermal-hydraulic performance andreduction of the surface area.

In contrast to the condition that the air works as working media,the results show that the louvered channel has a weak thermal-hydraulic performance when a liquid like the water is as workingfluid. This channel along with the perforated channel has approx-imately comparable values of the j factor and f factor values, andthereby there are not sensible variations in the studied perfor-mance evaluation criteria.

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193192

Further, since thermo-hydraulic design of a PFHE is stronglydependent upon the performance of plate-fin channels [50], thecurrent study can provide the great values to select the optimumplate-fin channel for use in the PFHEs based on their specific ap-plications and expectations in the industries, such as aerospace,automobile, cryogenic, food, and chemical.

5. Conclusion

An experimental comparative study on the performance of aplate-fin heat exchanger (PFHE) with different plate-fin channels iscarried outwhenwater is used asworking fluid. The commonplate-fin channels, including plain, perforated, offset strip, louvered,wavy, vortex-generator, and pin, are fabricated and evaluated.Various performance evaluation criteria, namely the ji/fi1/3 ratio,thermal-hydraulic performance factor, JFi, and VG-I criterion, Ai/Aplain, are adopted to appraise the performance of the PFHE withdifferent channels. The conclusions related to the current work canbe summarized as:

� The highest values of the heat transfer coefficient and j factor areobtained by the vortex-generator, wavy, pin, offset strip,perforated, louvered, and plain channels, respectively. Also, thegreatest values of the pressure drop and f factor are acquired bythe pin, vortex-generator, wavy, offset strip, louvered, perfo-rated, and plain channels, respectively.

� A better heat transfer in comparison to the pressure drop fromthe ji/fi1/3 ratio point of view is obtained by the vortex-generator,wavy, offset strip, pin, perforated, louvered, and plain channels,respectively.

� A good thermal-hydraulic performance, the highest value of theJFi factor, in comparison to the plain one is presented by thevortex-generator, wavy, offset strip, perforated, louvered, pin,and plain channels, respectively.

� The vortex-generator, wavy, offset strip, perforated, louvered,and pin channels have respectively the maximum ability toreduce the surface area of the PFHE in comparison to the plainone.

Finally, some changes such as the scale of the PFHE and the typeof the working fluid might alter some of the above conclusions.

Acknowledgments

The authors would like to express their thanks to University ofSemnan and Materials and Energy Research Center for theirfinancial supports through the set-up fabrication and researchimplementation.

NomenclatureA wavy fin amplitude, mAc minimum free flow area, m2

Ach.f total surface area in contact with working fluid, m2

Cp specific heat, J kg�1 K�1

Dh hydraulic diameter, mdh radius of perforations, mdp radius of pins, mFh fin height, mFp fin pitch, mG mass velocity, kg m�2 s�1

h effective heat transfer coefficient, W m�2 K�1

L fin length, mLa louver angle, �

Lh louver height, mLo lance length, m

Lp louver pitch, mLw wave length, mLz wavy fin passage length, mM number of the independent variables_m mass flow rate, kg s�1

nh number of perforationsnl number of louversnp number of pinsnt number of tabs_Qconv: convective heat transfer rate, WS distance between two perforations, mSl longitudinal pin spacing, mSt transverse pin spacing, mT temperature, Kt fin thickness, mVh vortex height, mVl longitudinal vortex spacing, mVt transverse vortex spacing, mDP pressure drop, PaR dependent variableDT temperature difference, KX independent variables

Greek symbolsr density, kg m�3

m dynamic viscosity, Pa sk thermal conductivity, W m�1 K�1

Superscript. ratee effective

Subscriptsconv. convectivef fluidf,in fluid inletf,out fluid outleti a plate-fin channel typej specific parameter counterLMTD logarithmic mean temperature differenceplain plain plate-fin channelw wall

Dimensionless groupsAi/Aplain VG-I criterion ¼ (jplain/ji)3/2/(fi/fplain)1/2

j Colburn factor ¼ Nu/RePr1/3

ji/fi surface flow area goodness factor ¼ ji/fiji/fi1/3 betterheat transfer in comparison topressuredrop¼ ji/fi1/3

JF Thermal-hydraulic performance factor ¼ (ji/jplain)/(fi/fplain)1/3

f Fanning friction factor ¼ 2rDhDP/LG2

Nu Nusselt number ¼ hDh/kPr Prandtl number ¼ mCp/kRe Reynolds number ¼ GDh/mSt Stanton number ¼ h/GCp

AcronymsPEC performance evaluation criteriaPFHE plate-fin heat exchangerPI process intensification

M. Khoshvaght-Aliabadi et al. / International Journal of Thermal Sciences 79 (2014) 183e193 193

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