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Energy 35 (2010) 3686e3695

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Energy

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Second law analysis and heat transfer in a cross-flow heat exchanger with a newwinglet-type vortex generator

Isak Kotcioglu a, Sinan Caliskan b,*, Ahmet Cansiz c, Senol Baskaya d

aDepartment of Mechanical Engineering, Faculty of Engineering, University of Atatürk, 25240 Erzurum, TurkeybDepartment of Mechanical Engineering, Faculty of Engineering, University of Hitit, 19030 Corum, TurkeycDepartment of Electrical-Electronics Engineering, Faculty of Engineering, University of Atatürk, 25240 Erzurum, TurkeydDepartment of Mechanical Engineering, Faculty of Engineering and Architecture, Gazi University, Maltepe 06570, Ankara, Turkey

a r t i c l e i n f o

Article history:Received 7 January 2010Received in revised form5 May 2010Accepted 8 May 2010Available online 16 June 2010

Keywords:Vortex generatorsCross-flow heat exchanger3-NTUEntropy generation

* Corresponding author. Tel.: þ90 312 5823469; faE-mail address: sinancaliskan2000@yahoo.com (S

0360-5442/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.energy.2010.05.014

a b s t r a c t

In this paper a second law analysis of a cross-flow heat exchanger (HX) is studied in the presence ofa balance between the entropy generation due to heat transfer and fluid friction. The entropy generationin a cross-flow HX with a new winglet-type convergentedivergent longitudinal vortex generator(CDLVG) is investigated. Optimization of HX channel geometry and effect of design parameters regardingthe overall system performance are presented. For the HX flow lengths and CDLVGs the optimizationmodel was developed on the basis of the entropy generation minimization (EGM). It was found thatincreasing the cross-flow fluid velocity enhances the heat transfer rate and reduces the heat transferirreversibility. The test results demonstrate that the CDLVGs are potential candidate procedure toimprove the disorderly mixing in channel flows of the cross-flow type HX for large values of the Reynoldsnumber.

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1. Introduction

The second law of thermodynamics is used as a basis for eval-uating the irreversibility associated with the simple heat transferprocesses. Cross-flow heat exchangers (HXs) are generally used inair/gas heating and cooling systems and can be used for HX andventilation systems. Winglet-type convergentedivergent longitu-dinal vortex generators (CDLVGs) passively create stream-wisevortices that are adverted through the inter-winglet space, causingboundary-layer modification and enhanced bulk mixing. There aresome non-conventional ways to enhance the performance ofwinglet plate HX which contribute to the mixing and/or splittingthe fluid streams within the HX. The CDLVGs channels arefrequently used to increase heat and mass transfer in the HXswhich are commonly employed in the HX winglets/fins, regenera-tors and channels of the HXs. Mixing and/or splitting the fluid inthe channels cause an irreversibility in the HXs. Heat transferprocesses are accompanied by thermodynamic irreversibility dueto entropy generation. Adding a heat transfer enhancement devicewithin the channels will increase the heat transfer rate and reduce

x: þ90 312 2319810.. Caliskan).

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the heat transfer irreversibility. The fluid friction increases with theincrease of hydrodynamic irreversibility.

The optimal design criteria for thermal systems can be achievedin terms of by minimizing the entropy generation in the relevantsystems. The irreversibility can be identified by determining thecorresponding entropy generation. Second law and entropygeneration analysis are used as relatively newmethods to optimizevortex generators array geometry by measuring the thermo-dynamic losses which are caused by temperature differences andfluid friction. Effectiveness of the HX only indicates the relativemagnitude of the heat transfer loading in a process. In order tounderstand whether a process is efficient or not, a second lawanalysis is necessary. The effectiveness of a HX is usually expressedas a function of the number of transfer units (NTUs) and the ratio ofthe mass flow capacity rates. Various advanced energy recovery/conversion technologies will require high-performance heattransfer characteristics typical of micro/mini-channel HXs toachieve energy recovery performance targets. There are number ofpublished studies on the entropy generation and the second lawanalysis regarding the determination of the irreversibility sourcesin components and engineering flow systems. Details on theseconcepts and the thermodynamic optimizations are given byVargas et al. [1], Bejan et al. [2] and Bejan [3]. In these studies, theentropy generation and energy analysis of a cross-flow HX havealso been introduced. In addition, Bejan [3, 4] obtained

I. Kotcioglu et al. / Energy 35 (2010) 3686e3695 3687

corresponding minimum entropy generation, optimum designconditions and the second law related studies for a various HXs.These studies explain the concepts of the optimization of finnedcross-flow, minimum entropy generation in forced convection,irreversibility in HX design and entropy generation through theheat and fluid flow. Khan et al. [5] applied an entropy generationminimization (EGM) method to study the thermodynamic lossescaused by heat transfer and pressure drop for the fluid in a cylin-drical pin-fin heat sink and bypass flow regions.

Bergles [6] reported that the heat transfer enhancement atthe HXs may be achieved by many techniques, which can beclassified into the passive, active and compound groups. Theentropy generation in a heat and mass transfer processes wasinvestigated by San et al. [7,8], where the irreversibility in theprocess was attributed to flow pressure drop, heat transferthrough temperature gradient and mass diffusion throughconcentration gradient. Entropy generation rates for a HX withconstant surface temperature and constant heat flux have beendiscussed by Zimparow [9]. In that study the generalizedperformance evaluation criteria for enhanced heat transfertechniques have been obtained by means of the first-law anal-ysis. Durmus [10] studied the exergy and NTU analysis for theHXs with co-axial parallel flow and obtained empirical correla-tions. In addition, the heat transfer, pressure loss and exergyanalyses were performed for the conditions with/without tur-bulators and these analyses were compared with each other.Rosen and Dincer [11] recently examined the energy and exergyanalysis of thermal systems.

Ranganayakulu et al. [12] analyzed a cross-flow plate incompact HX by accounting for the effects of two dimensionalnon-uniform inlet fluid flow distribution on both of the hot andcold fluid sides. Soylemez [13] studied the optimization of HXarea for heat recovery by mixing and, so eliminating, all thesethermal and economical parameters except the surface area,depending on the certainty of the operating characteristics of theapplications and the most efficient operating condition of the HX.Ogulata et al. [14] investigated the heat exchange betweenstreams flowing along the passages, made from the fins. Ogulataet al. also [15] analyzed the performance of heat transfer surfacesin a variety of different ways: volume versus power consumption,frontal area versus power consumption, heat transfer coefficientas a function of pumping power per unit of heat transfer area,etc. Lucas [16] has analyzed a co-generation system on the basisof thermodynamic laws.

Gomez et al. [17] have carried out by applying a newnumerical procedure for the study of thermal performance ofmulti-pass parallel cross-flow and counter-cross-flow HXs. Theproposed procedure constitutes a useful research tool both fortheoretical and experimental studies of the thermal performanceof the cross-flow HXs. Shang et al. [18] mentioned that the designof ultra-compact HXs of the entropy generation number eitherincreases or decreases with increasing flow channel size varia-tions, depending on the operating conditions. Fakheri [19]showed that for parallel flow, counter flow, and shell and tubeHX the efficiency is only a function of a single non-dimensionalparameter called Fin Analogy Number. Satapathy [20] carried outsecond law analysis of thermodynamic irreversibility in a coiledtube HX for the optimum values. San and Jan [21] performeda second law analysis of a wet cross-flow HX for various weatherconditions. Wu et al. [22] defined an exergy transfer effectivenessto evaluate the performance of HXs operating above/below thesurrounding temperature with/without finite pressure drop. Itwas discussed systemically that the effects of heat transfer unitnumber and the ratio of the heat capacity of cold fluids on exergytransfer effectiveness of HXs.

As can be recognized from the above investigations, the exis-tence of a better mixing of the flow in the channel is always relatedto an increase of the heat transfer coefficient for the channelgeometry. The objective of this study is to determine the thermalefficiency for cross-flow HX with convergentedivergent longitu-dinal plate type winglets based on the second law of thermody-namics, and how they contribute to the advancement of the state-of-the- art of heat exchange devices. In addition, we examined theheat transfer characteristics and entropy generation of a newlydeveloped HX with winglet-type vortex generator by using thethermal performance and friction results to assess the effectivenessof the vortex generators for the HX. The effectiveness and secondlaw efficiency of the HX configuration is calculated by usingexperimental data for the inlet conditions of working fluids flowingthrough HX. This study includes the analysis of the minimumentropy generation number, effectiveness, NTU, optimum flow pathlength and dimensionless mass velocity of the HX. The minimumentropy generation number is taken into consideration in terms ofthe second law of thermodynamics for the HX. Following, thesecond law performance of a cross-flow HX is experimentallyevaluated for various operating conditions. The investigation wascarried out in the flow direction of the winglets respect to theincoming flow for bh¼ 30� for the exhaust fluid and bc¼ 60� forsupply fluid.

2. Experimental apparatus and procedure

The experimental apparatus with the winglet-type CDLVG isshown in Fig. 1. The test sections and the main dimensions of theplate type winglet vortex generators used in the experiment areshown in Fig. 2(a) and (b). The major components of the experi-mental setup include an air filter, a supply fan unit, cross-flowcompact HX core (at dimensions La/Lc¼ 1 as seen in Fig. 2(a)),hydrodynamic entrance section, flexible PVC pipe, orifice plates(compatible with ASME standards and recommendations), pres-sure measurement units, inclined tube alcohol micro manometer,thermocouples, AC574 air conditioning laboratory unit for airsupply and data acquisition system.

The experimental mechanism was constructed with thefollowing subsequent procedures. While exhaust flow rate wascontrolled by an exhaust centrifugal fan, the supply flow rate wasadjusted by digital fan speed controller. As a working fluid thesupply air and exhaust air are used. Both exhaust and supply air inthe test section flow perpendicularly respect to each other. The flowrate of the exhaust air flow was controlled by adjusting the clackvalve at the intended turbulence intensity. The pressure drop ismeasured by pressure probes with an accuracy of�0.3% of the fullscale. The test section and the connections of the piping systemwere designed in such a way that the associated parts can bechanged ormodified easily. The outer surface of the test sectionwasinsulated (k¼ 0.27 Wm�1 K�1) with a layer of glass wool to preventheat loss and to obtain a uniform heat flux at the same time. Inorder to obtain a linear velocity distribution related to the fluid flowin the system the wire sieves were placed into the channels.Experimental tests were performed at the different clack intervalswith a blow out-mode. For the fluid flow and heat transfer tests,surface temperatures, inlet and outlet temperatures, pressure dropacross the test section were recorded.

The experimental setup was manufactured by the stainless steelplates and experiments were conducted in square duct of200� 200mm span in the width and length. The location of theCDLVGs are oriented parallel to the fluid flow pattern between 18horizontal plates, which are spaced at 10 mm distance. There aretotal of 64 winglet-type vortex generators between the steel plates.The vortex generators were longitudinally inserted through the

Fig. 1. A schematic display of the experimental setup. (1) Fan-speed controller; (2) thermometer; (3) thermometer (wet-dry); (4) evaporator; (5) fan; (6) weather heaters;(7) supply flow in; (8) supply flow out; (9) exhaust flow in; (10) exhaust flow out; (11) U-manometer; (12) pipe line; (13) test section; (14) thermocouples; (15) data acquisitioncard; (16) inclined manometer; (17) computer; (18) tank; (19) condenser; (20) vapor connection; (21) main water inlet; (22) water heater; (23) compressor; (24) vapor connection;(25) flow meter; (26) filter drier; (27) pressure indicator; and (28) thermostatic extension valve.

I. Kotcioglu et al. / Energy 35 (2010) 3686e36953688

plates in the vertical direction in eighteen-row, which is defined asa newwinglet-type HX. The trailing edge of thewinglet was locatedat a distance of x¼ 5 mm from the inlet. The vortex generators aremade of rectangular stainless steel with the dimensions of 10 mmlength (l), 1.5 mm thick (tw) and 10 mm height of channels exhaustand supply (bh¼ bc¼ 10 mm). The inclination angle of wingletswith the flow direction of exhaust fluid is fixed at bh¼ 30�, and theinclination angle of winglets with the flow direction of supply fluidwas fixed at bc¼ 60�. As seen in Fig. 2(a), in order to increase theeffect on the secondary flows and renewable boundary layer in thestructure of new type winglets, the channel geometry is formed asnozzle and diffuser. The axes of rotation of the winglets parallel tothe main flow direction are called as longitudinal vortices. On theother hand, the axes of rotation of the winglets normal to the mainflow direction are called as transverse vortices. Because the longi-tudinal vortices consist of strong swirling around the axis, which isaligned essentially with the main flow direction, this leads a heavyfluid mixing between the core and the region near the wall.Generally, less energy is needed to turn the flow around the axisaligned with the main flow direction than to generate the swirlaround an axis perpendicular to the main flow direction. There isa region situated between diverging and converging channelswhere the velocity is not high enough to enable the resolution ofthe flow direction. As the convergent/divergent longitudinalvortices act as plates in the flowing fluid, each new edge startsa new boundary layer which is very thin, thus a high heat transfercoefficients can be obtained.

The resistance, pressure and flow measurements were taken ata fixed flow rates in the loop within the winglets. To measure thepressure drop resulting from the presence of the winglet pairs,3 mm diameter static pressure taps of 8 (two orifice meter wereinstalled before the inlet heaters to control the pressure of the air atthe inlet, two exhaust air and two supply air at the inlet/outlet ofthe test section channels) were placed at the various locations.During the experiments, the pressure drop was measured bypressure taps with an accuracy of�0.1 mmH2O. The supply air flowrate was adjusted by a digital fan speed controller and thetemperatures were measured by thermocouples.

During the experiments, the temperature difference betweenthe mainstream and the heating surface is kept constant and theheat flux is varied in the range of 484e1458 W/m2. The inlet andoutlet mainstream temperatures are measured by averaging thetemperatures of the four thermocouples positioned at the middleof the inlets and the outlets of the HX, as shown in Fig. 1. Thesethermocouples are T-type coppereconstantan coated with Teflonin the 0.25 mm diameter and provide the measurements at fourlocations in the same cross-section. An additional thermocoupleis also used to measure the surrounding temperature. Accuracyof the thermocouples is within �0.15%. All of the flow propertiesare determined at the average bulk temperature. After thesystem is started to work, it is allowed to run until steady-stateconditions prevailed. Once the temperature of the test sectionreached to the steady-state condition, the corresponding powerand the temperature difference between the ambient and thetest section is recorded for a period of 300 s at a sampling rate of2 s. The measured heat losses for the current experiment werefound to be less than �6% for all experimental conditions. Forthe temperature measurements, a standard deviation of 0.16 �C isobtained between the individual data points and the calibrationcurve. The resulting calibration curve is then used during thedata reduction to find the average temperature of the system.National Instrument Multifunction data acquisition system (DAQBoard, AT-MIO 16) of 100 kS/s sampling rate and Lab Viewsoftware version 5 are used to record the temperatures. Havinga capacity of 40 channels data acquisition system is used tocollect data. The effect of thermal radiation for internal flow isignored during the experiments due to low temperature differ-ences between the walls and winglets. In this experimentalstudy, we mainly focused on the temperature and pressure dropmeasurements of supply and exhaust air flows at the inlet andoutlet to the system. Effectiveness of the HX unit is determinedfor various inlet flow conditions. The experiments are performedfor various temperatures and Reynolds numbers in the rangebetween 3000 and 39,000, based on the mainstream velocity andthe hydraulic diameter of the duct, under constant heat fluxconditions.

Fig. 2. (a) The geometric features of the cross-flow heat exchanger (HX) ventilatormatrix. (b) Top view of geometry and placement of winglets in rectangular channel.

I. Kotcioglu et al. / Energy 35 (2010) 3686e3695 3689

The conditioning of the air takes place in a square fiber glassduct which is 200 mm long, and it is mounted on a steel framewith castors. Air is drawn into the duct by a variable speedcentrifugal fan and wet and dry thermometers are placed at theinlet. Air is pre-heated by two 1kW finned electrical heaters. Thesupply air flows through the evaporator of the refrigeration plant,where it is cooled in the de-humidifier, releasing some of itsmoisture content as liquid. Two 0.5 kW finned electrical heatingcoils are used for re-heating. The final condition of the supply airis determined by thermocouples and the mass flow rate deter-mined from the differential pressure transducer. The installedseven heaters (two pre-heat, two re-heat, three boilers) areindividually controlled. The steam is provided by an atmosphericboiler with three heating elements, which create various rates ofsteam production, as shown in the Fig. 1. The water level iscontrolled by a float valve and observed through a sight glass.The compressor draws R134a vapor from the evaporator anddischarges into an air-cooled condenser.

3. Thermodynamic optimization

In the optimization procedure of the HXs, for the minimumentropy generation, the optimized number of variables and selectedparameters for operating conditions based on the system propertiesshould be considered. These variables have been selected such thattheflexibility in themodelingandoptimizationprocess ismaximized.Detailed information about these optimization procedures can befound in the literature surveys written by Vargas et al. [1], Soylemez[13] and Mohagheghi et al. [23]. Generally, an optimization problemconsists of an objective function and constraints for decision or

dependent variables. Thus, the optimization of the system is of greatimportance to increase the most efficient operating condition of theHX recovery with winglet-type vortex generator.

In this study we investigated the effectiveness of the winglet-type vortex generators inserted into plates in terms of parameterssuch as entropy generation number, optimum dimensionless massvelocity, pressure drop, effectiveness, NTU, dimensionless heattransfer area and optimum flow length. Data collection during theexperiments was carefully monitored and controlled. For the setupgeometry, the channel dimensions determined as shown in theFig. 2(a) and (b), where La, Lb and Lc are width, height and length,respectively (La¼ Lb¼ Lc¼ L¼ 0.20 m) and the channel flat platethickness (tw) is 0.0015 m. The heights of each exhaust air (bh) andsupply air (bc) channels in exchanger are 0.0085 m, as shown inFig. 2(a). For this HX system, the number of exhaust and supply airchannels in the test region was calculated as 18.

3.1. Heat transfer and second law analysis

In general, there is a trade off between the heat transfer areaand pressure drops. Based on this trade off we can determineoptimal geometric features such that the total entropy generationrate of the HX is minimized. Minimum entropy generation rate isdetermined in a way that the thermodynamic performance of thecross-flow HX is improved by increasing the stream-to-streamcontact area or the NTU. The convective heat transfer processesare characterized by two types of losses: one is due to the fluidfriction and the other is due to the heat transfer across a finitetemperature difference. These losses are the indication of theirreversibility quantity. The total irreversibility of a HX includesboth operational irreversibility and irreversibility due to use ofthe material.

EGM is used as a thermodynamic optimization method invarious engineering applications. EGM, which is a process to designbetter heat transfer equipment method, is the minimization ofthermodynamic irreversibility or the minimization of destructionof useful energy in actual devices. The second law of thermody-namics uses the exergy balance, which is defined as the degrada-tion of the energy, for the design of thermal systems. Degradationof energy is due to the irreversibility of real processes. The amountof exergy flowing out in the system is smaller than that of theflowing in, since the exergy is consumed within the system toproduce entropy. These processes are accompanied by entropygeneration, which is an indicator of undesirable thermodynamicirreversibility that reduces the thermal performance. The mini-mized entropy generation is one of the important component in theoverall cost estimation. The EGM is a measure of the system leveland the degree of thermodynamic irreversibility of the system. Thetotal entropy generation rate of the system is the sum of entropygeneration rate of both exhausts and supply air flowð _Sgen ¼ _Sgen;e þ _Sgen;sÞ. Entropy generation rate per unit length

ð _S0gen ¼ d _Sgen=dxÞ can be written based on the informationincluded in the usual correlations for average heat transfer and fluid

friction. There is trade off (an optimal geometry) where _S0gen is

minimum. It is possible to determine the optimal channel geometryor Reynolds number, which leads to minimum irreversibility.According to the second law of thermodynamics, when the energyquality gets poorer the losses always occur in real cycles because ofirreversibility. The entropy generation rate for the exhausts and thesupply air is given as below.

_S0gen;e ¼

�_S0gen;e

�DT

þ�_S0gen;e

�DP

(1a)

I. Kotcioglu et al. / Energy 35 (2010) 3686e36953690

_S0gen;s ¼

�_S0gen;s

�DT

þ�_S0gen;s

�DP

(1b)

Entropy generation rate for a cross-flow HX is given by

_S0gen ¼ _mCpln

Te;oTe;i

þ _mCplnTs;oTs;i

� _mRlnPe;oPs;i

� _mRlnPs;oPs;i

(2)

where _mCp term denotes the heat capacities of the fluids, R is thegas constant, T is the temperature and P is the pressure ofthe exhaust and the supply of air fluids. For the outlet pressurePe;o ¼ Pe;i � DPe and Ps;o ¼ Ps;i � DPs relations are valid. The outletpressure is lower than that of the pressure inlet. The entropygeneration rate is positive as soon as a pressure drop takes placesbetween inlet and outlet (Pe;i � Pe;o and Ps;i � Ps;o). The first twoterms on the right-hand side of Eq. (2) represent the entropy

generation rate ð _S0gen;DT Þ, which account for the heat transfer irre-versibility, and the last two term represent the entropy generation

rate ð _S0gen;DPÞ, which account for the fluid friction irreversibility [14].The relative importance of the two irreversibility mechanisms

with respect to each other is defined by fluid flow irreversibility/heattransfer irreversibility; namely the irreversibility distribution ratio,

f ¼ _S0gen;DP=

_S0gen;DT . The entropy generation rate is generally used in

the dimensionless form. The entropy generation number is widelyused for evaluating performance of the two-fluid HXs. The irrevers-ibility distribution rate increases as the friction irreversibility contri-bution increases. In order tominimize lossesdue to the irreversibility,the most frequently used entropy generation number (Ns), which isobtained by dividing the entropy generation rate by the minimumheat capacity flow rate ðC* ¼ _mCpÞ, proposed by Bejan [3] as,

Ns ¼_S0gen�_mCp

�min

(3)

where _m is the mass flow rate. The minimal heat capacity rate isdefined as the product of themass flowand specific heat capacity ofthe fluids for each Reynolds number. The heat capacity of exhaustair side is very high compared to the supply air side. The value ofthis entropy generation number may vary in the range betweenzero and infinity. Limiting the entropy generation number to zero(Ns/ 0) implies that these losses approach to zero and increaseswith increasing Ns value. Similarly, Ns term varies in terms of theReynolds number for which f changes in between zero and infinity.As the Reynolds number increases, the entropy generation numberalso increases with it. Whether the calculatedNs represent a high ora low entropy generation rate it does depend on the various factors.The entropy generation rate can bewritten for a balanced the cross-flow HX (fluid flow heat capacity C*¼ 1) when temperaturedifferences and frictional pressure drops are not negligible. Basedon this case, by using the HX efficiency (3), one can calculate Ns asa function of only the inlet fluid stream temperatures and theentropy generation number as

Ns ¼ ð1� 3Þ�Ts;i � Te;i

�2Te;iTs;i

þ RCp

��DPP

�eþ�DPP

�s

(4)

where the inlet pressure is given as the sum of the ambient pres-sure P and the pressure drop DP in the HX. A limit of engineeringimportance is the nearly ideal HX limit in which (1� 3) and (DP/P)are considerably smaller than unity. In this limit the entropygeneration number can be linearized to read as given in Eq. (4). Theeffectiveness of HX (3) is a main factor determining the ability ofheat transfer. The effectiveness of the cross-flow HX depends on C*

and NTU parameters given by Bejan [3]. The heat capacity (C*) isdefined as the rate of the Cmin to Cmax. While evaluating the

effectiveness of each of the individual passages, both of the parti-tions were considered as equal since the convective heat transfercoefficient was assumed uniform throughout the HX. The heatcapacities were also assumed as equal. The exhaust and supplyflows were unmixed due to the vortex generators. An 3-NTUmethod was then used to analyze the HX’s performance. The term(1� 3)in Eq. (4) is can be rewritten as below.

1� 3 ¼ 0:477ðNTUÞ�0:4 (5)

Following, Eq. (4) is rewritten in a new equation with the defi-nition of dimensionless temperature difference DT* and the totalpressure drop ðDP=PÞe;s, as below.

Ns ¼ 0:477ðNTUÞ�0:4�DT*2

�þ RCp

�DPP

�e;s

(6)

As it is expected, the fluid friction irreversibility disappearswhen the pressure drops to zero on the two sides of the surface. Theheat transfer irreversibility disappears when the area is very large(NTU/N). The dimensionless temperature difference and thetotal pressure drop are written, respectively, as below.

�DT*

�¼ jTs;i � Te;ijffiffiffiffiffiffiffiffiffiffiffiffiffi

Te;iTs;ip (7a)

DPe;s ¼�DPP

�eþ�DPP

�s

(7b)

Since the entropy generation number should be minimized todecrease the heat transfer losses, the effects of the constructiondimensions should be considered for any HX design. Thus, theentropy generation of Eq. (6) is rewritten as Eq. (7a) and (7b) byusing following equations [2],

DPP

¼ f4LDh

G2

2rP(8)

where f is the friction factor, G is the mass velocity and L is the flowpath length of HX. The number of heat transfer units is used intraditional first-law analyses of the HXs. NTU depends on Stantonnumber (St ¼ h=CpG, where h is the average heat transfer coeffi-cient), the length of HX and the duct hydraulic diameter (Dh), whichis defined as below.

NTU ¼ 4LDh

St (9)

where the dimensionless mass velocity (G*), Stanton number,friction factor are explained in references of [14,16]. The entropygeneration number can be rewritten as,

Ns ¼0:477

�DT*

�2ð4L=DhÞ0:4ðStÞ0:4

þ RCp

f�4LDh

�G*2 (10)

where the friction factor is found as 0.0447 in terms of the experi-mental results. The duct hydraulic diameter of the HX is taken as0.0163 m. The total entropy generation rate was able to express asthe sumof contributionsdue toeach sideof theheat transfer surface.

3.2. The optimum flow path length

The optimum flow path length ð4L=DhÞopt, which minimizes theentropy generation number, is given as below.

�4LDh

�opt

¼240:191

�DT*

�2Cp

St0:4fRG*2

35

11:4

(11)

I. Kotcioglu et al. / Energy 35 (2010) 3686e3695 3691

By using the identical hydraulic diameters, the dimensionlesstemperature difference (DT*) can be reduced by increasing the flowpath length, which in turnwill cause viscous properties to increase.The optimum flow length for minimum irreversibility decreases asthe dimensionless mass velocity increases. The opposite trend ofthis will lead to the existence of an optimum flow path length,where the total irreversibility will be a minimum. For this optimumflow path length, the minimum entropy generation number isobtained by substituting Eq. (11) into Eq. (10), given as below.

Ns;min ¼0:477

�DT*

�2ð4L=DhÞ0:4optðStÞ0:4

þ RCp

f�4LDh

�opt

G*2 (12)

The minimum entropy generation number (Ns,min) is directlyproportional to the mass velocity, which is also a function of Dh, fand St.

3.3. The heat transfer area

In order to obtain realistic yield and accurate results, the datacollection during the experiments wasmonitored and controlled bya computer. Regarding the setup configuration of this study, thechannel dimensions are defined as shown in the Fig. 2(a) and (b).For this particular design, there are number of 18 channel plates(Np) where the channel flat plate thickness (tw) is 0.0015 m. Thehydraulic diameters of supply air flow and the exhaust air flow areequal to each other and defined as Dh¼ 0.0163 m. In this case, thedimensionless heat transfer areaðA*

heatÞ, which was introduced byBejan et al. [2], given by the following equation.

A*heat ¼ 4L

DhG*(13)

The entropy generation number given in Eq. (12) can berewritten as below.

Ns ¼0:477

�DT*

�2ðStÞ0:4A*0:4

heatG*0:4

þ RCp

fA*heatG

*3 (14)

The optimum dimensionless mass velocity ðG*optÞ, which mini-

mizes the entropy generation number, can be defined with thefollowing relation.

G*opt ¼

240:191

�DT*

�23A*1:4

opt ðStÞ0:4ðR=CpÞf

35

13:4

(15)

By using Eq. (15), the minimum entropy generation number isdetermined as below.

Ns;min ¼0:477

�DT*

�2ðStÞ0:4A*0:4

opt G*0:4opt

þ RCp

fA*optG

*3opt (16)

The minimum entropy generation number that can be achievedon one side of the heat transfer surface is governed by the optimumdimensionless mass velocity selected for that side.

3.4. The heat transfer volume

In order to minimize the entropy generation number, the effectsof the heat transfer volume (which is taken as V¼ 0.008 m3) andoptimum mass velocity can be used. Thus, the dimensionless heattransfer volume (V*), whichwas introduced by Bejan et al. [2], givenas below.

V* ¼ 4LDh

ReG*2opt

(17)

By using Eqs. (16) and (17), the entropy generation numbergiven in Eq. (10) can be rewritten with the following equation.

Ns ¼0:477

�DT*

�2St0:4V*0:4G*0:8

opt

þ RCp

fV*

ReG*4opt (18)

The optimum dimensionless mass velocity that minimizes theentropy generation number is given as below.

G*opt ¼

240:095

�DT*

�2Re1:4Cp

V*1:4RðStÞ0:4f

35

14:8

(19)

As can be inferred from above analysis, if both of the heattransfer area (A) and heat transfer volume (V) are fixed, Reynoldsnumber can be optimized for minimum entropy generation rate.

4. Experimental uncertainties

In order to use the exact values of the experimental results anuncertainty analysis of experimental measurements is performed.For this reason, it is necessary to analyze the uncertainties associ-ated with the measured and/or calculated values. In addition, it isalso very important to evaluate the uncertainties which areinherent during the experimental operation. The errors anduncertainties in the experiments may arise from instrumentselection, instrument condition, instrument calibration, environ-ment, observation, reading and test planning. The uncertainties inthe combination of the experimental and predicted values wereestimated to be approximately less than �5%. The maximumuncertainties of the investigated non-dimensional parameterswere found to be; �3.75% for Reynolds number, �8.47% for Nusseltnumber and �13.2% for f. In addition, the percentage of the relativeuncertainties were around�2.3% in the mass flow rate (the error inthe measurement of channel area is less than �0.35%), �5% in themass velocity, �3.2% in the effectiveness, �2.83% in the heattransfer coefficient and �3% in the pressure loss. The inlet air wastypically heated from 20 �C to 90 �C. Depending on bulb size,response time, velocity of air flow and thermocouple calibrationpolynomials, the total uncertainty associated with temperaturemeasurements was estimated to be �0.382. This value is applicablewhen the temperature measurements are between 0 and 100 �Ctemperature range. The uncertainties were estimated as a referenceaccording to the standard procedure proposed by Kline andMcClintock [24,25]. Generally, the % error was found to be within�5%. Thus, we concluded that the heat loss to the surroundings wasreasonably small. The effect of the uncertainty in the measurementis given as,

dRXi¼ vG

vXidXi (20)

where the several independent variables are used in any givenfunction of R, the individual terms are combined by root-sumsquare method as,

dR ¼(XN

i¼1

�vG

vXidXi

�2)1=2

(21)

where Xi represents the corresponding measurement uncertainty.In Eq. (21), N is the number of experimental data and G denotes theuncertainty for ith experimental datum. Considering the relative

y = 11,399e0,0877x

R2 = 0,9953

y = 11,086e0,0972x

R2 = 0,9896

y = 10,67e0,1041x

R2 = 0,9938

y = 11,084e0,107

R2 = 0,997

20

40

60

80

100

120

140

11 13 15 17 19 21 23Mass Velocity G (kg/s)

Pres

sure

Dro

p P

(Pa

)

Supply air outlet

Exhaust air outlet

Supply air inlet

Exhaust air inlet

Fig. 3. Variation of pressure drop as a function of mass velocity for exhaust flow andsupply flow.

I. Kotcioglu et al. / Energy 35 (2010) 3686e36953692

errors in the individual factors denoted by xn, the error estimationcan be given by following equation.

wðk;h;f ;D;i.Þ ¼nðx1Þ2þðx2Þ2þ.þ ðxnÞ2

o�1=2(22)

During the measurements of the parameters, the individualcontributions to the uncertainties of each measured physicalproperty were given in Table 1, while the uncertainty associatedwith the derived quantities was obtained by using the propagationof uncertainty analysis.

5. Results and discussion

The results obtained from the experiments were analyzed byusing the graphics of each parameter.

5.1. Validation of the pressure drop and mass velocity results

Themeasured pressure drop variation as a function of mass flowrate by using the CDLVGs presented in Fig. 3. The uncertainty in themeasurements varies from3% to 28.6% over themass velocity range.Using the 95% confidence interval and standard error-propagationanalysis, the relative uncertainty in the convection coefficient, thepressure loss and the mass flow rate is estimated to be less than�2.83%, �3% and �2.3%, respectively. Clearly, it is seen from Fig. 3that the pressure drops increase with increasing the mass velocity.Although themass velocity is same for the supply and exhaustflows,the pressure drop difference is higher for the inlet and outlet of theexhaust flow. Thismeans that the pressure changes according to thetemperature and density of the exhaustflow. As previously reportedbyKotcioglu et al. [26,27], the pressure drop increases as thewingletangle increases. In these studies, the correlations of channel heightand length together with the winglet angle and length fora diverging and converging rectangular duct were presented.

5.2. (3-NTU) effectiveness and transfer unit number

The heat transfer and fluid flow thermodynamic irreversibilitiesdetermine the effectiveness of the cross-flow HX in terms of theturbulent supply and exhaust air flow as a working fluid for thedifferent mass flow rates, pre-heater and re-heater conditions. Inthis study, the construction dimensions of the setup, which mini-mize the entropy generation number, is taken into consideration. Inorder to decrease the heat transfer losses and the frictional pressuredrop and also to increase the effectiveness of the HX, the entropygeneration number must be minimized. 3-NTU technique was usedto evaluate the performance of the HX with winglet-type vortexgenerator. NTUs varies between 1.920 and 3.050. The calculatedeffectiveness results are shown in Fig. 4. As seen in this figure, the

Table 1Typical uncertainties for relevant variables.

Variable Notation Uncertainty �(%)

Air velocity V 5Air density (from tables) r 0.2Mass flux G 3,8Mass flow rate _m 2.3Mean air temperature T 0.39Hydraulic diameter of the duct Dh 1.0Dynamic viscosity of the air (from tables) m 0.046Current I 0.75Pressure P 3Thermal conductivity of the air (from tables) k 0.4Heat flux q00 1.35Hear transfer coefficient h 2.83

experimental effectiveness (3-NTU) values for balanced cross-flowarrangement (C*¼ 1) are confirmed with the theoretical andexperimental values of Ogulata et al. [14,15]. These results indicatethat the HX should be operated at the effectiveness greater thanthat of the theoretically expected value. In addition, the betteroperating conditions will be achieved when 3 approaches to unity,where the low irreversibility is expected. The results also show thata higher value of channel and vortex generator such as height,length, number and angle will increase the fluid friction irrevers-ibility and will increase the total entropy generation number.Therefore, this type of HX with CDLVGs effectiveness is higher evenif the sizes are smaller for the same working conditions. From thefin geometry of isosceles triangle profile point of view, the effec-tiveness of the HX with CDLVGs fin profile given in this study ishigher than that of the ones in Ogulata et al. [15], as shown in Fig. 4.

Fig. 5 shows the variation of the minimum entropy generationnumber (Ns,min) with the dimensionless heat transfer area ðA*

heatÞ.As seen in this figure, when the dimensionless heat transfer areaincreases the minimum entropy generation number decreases. Tominimize the entropy generation number, its effect on the heattransfer area and mass velocity (G*) can be analyzed by using Eq.(16). The relationship between the non-dimensional heat transferarea and the minimum entropy generation number given by Eq.(16) and the measured values are given in Fig. 5 for a small massvelocity range. In order to increase the effectiveness of the HX, theentropy generation number should beminimized by decreasing thelosses of heat transfer and the frictional pressure drop.

5.3. Optimum flow path length, the dimensionless heat transferarea and the dimensionless mass velocity

Fig. 6 shows the variation of the optimum flow path length((4L/D)opt)with the dimensionlessmass velocity (G*). The variation of

Fig. 4. Variation of effectiveness as a function of number of transfer unit (NTU).

y = 72417x-6,8196

R2 = 0,981

0,001

0,0015

0,002

0,0025

0,003

0,0035

0,004

0,0045

0,005

0,0055

11,2 11,7 12,2 12,7 13,2Dimensionless Heat Transfer Area(A*x1000)

Min

imum

Ent

ropy

Gen

erat

ion

Num

ber(

Ns,

min

.)

Fig. 5. Variation of minimum entropy generation number as a function of dimen-sionless heat transfer area.

y = 0,0751x-1,1831

R2 = 0,97

0,0035

0,0036

0,0037

0,0038

0,0039

0,004

0,0041

0,0042

0,0043

0,0044

11,1 11,5 11,9 12,3 12,7 13,1Dimensionless Heat Transfer Area(A*x1000)

Opt

imum

Dim

ensi

onle

ss M

ass

Vel

ocity

(G*o

pt.)

Fig. 7. Variation of optimum dimensionless mass velocity as a function of dimen-sionless heat transfer area.

I. Kotcioglu et al. / Energy 35 (2010) 3686e3695 3693

optimum flow path length ((4L/D)opt) in Eq. (11) with the dimen-sionless mass velocity (G*) was determined by considering thedimensionless temperature DT* such that by increasing the flowlength in the same hydraulic diameters can reduce dimensionlesstemperatureDT*. Otherwise, the trendwill lead to the existence of anoptimum length, where the total irreversibility will be aminimum. Itcan be seen that the increase in the dimensionless mass velocity orincrease in the dimensionless temperature difference providessmaller optimum flow path length for the heat transfer and pressuredrop. This is because, with decreasing the HX optimum flow length,both types of the irreversibilities are less noticeable. This means thatthe chosen HX unit needs to be very small.

In order to ensure the minimum entropy generation the heattransfer area should be investigated. For this reason, the variation ofthe dimensionless heat transfer area with the optimum dimen-sionless mass velocity was investigated. As can be seen from theexperimental results shown in Fig. 7, the optimum dimensionlessmass velocity (G*)opt and the hydraulic diameters of both of thesupply air flow and the exhaust air flow decrease when thedimensionless heat transfer area (A*) increases. As a consequence ofthis, the pressure drop decreases in the HX. It can be concluded thatthe chosen hydraulic diameter is important in terms of channel andpassage number designed in the form of nozzle and venture fromthe given frontal area point of view. In the light of these comments,one can conclude that the dimensionless temperature differenceand the geometrical features are effective parameters.

Fig. 8 shows the variation of the minimum entropy generationnumber with the optimum flow path length. The entropy genera-tion rate ð _S0genÞ decreases with decreasing the optimum flow pathlength and the dimensionless irreversibility rate increases withdecreasing the optimum flow path length. According to the secondlaw of thermodynamics _S

0gen � 0 relation is valid; therefore, the

y = 0,1646x-1,5333

R2 = 0,9956

18

19

20

21

22

23

24

0,0395 0,0405 0,0415 0,0425 0,0435 0,0445 0,0455 0,0465

Dimensionless Mass Velocity(G*)

Opt

imum

Flo

w P

ath

Len

gth(

4L/D

)opt

.

Fig. 6. Variation of optimum flow path length as a function of dimensionless massvelocity.

entropy generation is a measure of the strength of the inequality oran indicator of the degree of thermodynamic irreversibility of thesystem. Higher optimum flow path length ensures a lower entropygeneration number because of less pressure drop in the ducts.According to Eqs. (8) and (15), higher values of the optimum flowpath length (L) and the hydraulic diameter (Dh) cause an increase inthe dimensions of the HX for a finite temperature difference,however. Consequently, it can be said that the increase in (4L/D)optcauses frictional irreversibility and while the decrease in (4L/D)optleads heat transfer irreversibility. It has been observed that entropygeneration number due to the heat transfer is decreased when Re isincreased and the entropy generation number due to fluid frictionis increased as Re increased. For this reason, vortex generatorgeometry has a balance between thermal contact irreversibility andfluid drag irreversibility, which leads to an overall minimum rate ofentropy generation for the vortex generator.

The variation of the minimum entropy generation number withthe optimum dimensionless mass velocity is shown in Fig. 9. Asshown in this figure, the increase in the optimum dimensionlessmass velocity leads to an increase in the minimum entropygeneration number because of the increase in the frictional pres-sure drop. For this reason, small values of G*

opt should be chosen.While the size and weight of the HX can be chosen as high as it isdesired, the small values of G*

opt require high volume and surfacearea. This suggests an increase in the cost of the system construc-tion. As a result, as shown in Figs. 5, 8 and 9 the entropy generationnumber (Ns) varies between 0.0015 and 0.005. Comparing with theliterature, the value of this entropy generation number can vary inthe range between zero and infinity. Limiting the entropy genera-tion number to zero (Ns/ 0) implies that the losses from theirreversibilities approach to zero and they increases with increasing

y = 74277x-5,6454

R2 = 0,993

0,001

0,0015

0,002

0,0025

0,003

0,0035

0,004

0,0045

0,005

0,0055

18,3 18,8 19,3 19,8 20,3 20,8 21,3 21,8 22,3 22,8 23,3

Optimum Flow Path Length (4L/D)opt.

Min

imum

Ent

ropy

Gen

erat

ion

Num

ber(

Ns,

min

.)

Fig. 8. Variation of minimum entropy generation number as a function of optimumflow path.

y = 1E+14x6,9331 R2 = 0,9964

0,0010

0,0015

0,0020

0,0025

0,0030

0,0035

0,0040

0,0045

0,0050

0,0055

0,0036 0,0037 0,0038 0,0039 0,0040 0,0041 0,0042 0,0043 0,0044

Optimum Dimensionless Mass Velocity (G*opt.)

Min

imum

Ent

ropy

Gen

erat

ion

Num

ber(

Ns,

min

)

Fig. 9. Variation of minimum entropy generation number as a function of optimumdimensionless mass velocity.

I. Kotcioglu et al. / Energy 35 (2010) 3686e36953694

the Ns value. The condition of being Ns< 1 indicates that theexisting experimental system has advantages and applicabilityfrom the thermodynamic point of view. This is due to the fact thatdecreasing the degree of the irreversibility of the HX in terms of thisratio it is concluded that an advantageous result is obtained fromthe point of further increase of the heat transfer. The variation ofthe minimum entropy generation number in term of the dimen-sionless heat transfer area, the dimensionless mass velocity and theoptimum flow path length are examined for the present HX system.Finally, the importance of second law based thermodynamic opti-mization of the HXs is emphasized.

6. Conclusions

In this study the estimation of the entropy generation rate isused for the thermodynamic optimization of the HXs. In order todetermine the performance of the HXs the entropy generation ratewas evaluated. With this aim the influence of the HX flow pathlength, the dimensionless heat transfer area and the mass velocityon the entropy generation rate were investigated. For the estima-tion of the flow geometry optimization regarding the thermalperformance of the HX with CDLVGs, the key findings may besummarized as follows.

� At the low Reynolds number, the entropy generation numberwas influenced by the heat transfer while at the high Reynoldsnumber, it was influenced by the pressure drop. The experi-mental data were represented by the given correlations withinthe uncertainty of 3.75% for the Re number; 8.47% for the Nunumber and 13.2% for f. If compared to HX’s without vortexgenerators, the present vortex generator shows an increase inthe heat transfer enhancement from 15% to 30% and also anincrease in the pressure-loss penalty from 20% to 30%, ina comparisonwith and without vortex generators, respectively.

� The mean uncertainties are around �0.15% in the temperature,�9.5% in the mass flow rate and �5% in the mass velocity. Themaximum deviation percentage from the experimental andproposed correlation values of above parameters was found tobe �1% for the convergentedivergent vortex generator datacurve. The causes of the errors between the theoretical andexperimental values may be attributed to the setting andmeasurements on the system in the laboratory conditions.

� With the e-NTU technique related to the performance of thewinglet-type vortex generator array systems, it was deter-mined that the NTUs varies between 1.920 and 3.050. Theeffectiveness values of the HX with and without the CDLVGgenerators containing gaps for the passage of fluid into thechannel was obtained up to 68e80%, compared to a HX withempty tubes in cross-flow.

� In this experimental design a new structure is introduced to theflow region such that the vortex angle plays an important rolein both of the separation of flows. Because the CDLVGs profile isformed as nozzle the venture causes a clear turbulence in thestream-wise flow acceleration or deceleration throughout thechannels. The main reason for turbulence may be attributed tothe behavior of pressure rise at the end of diverging channeland the pressure drop at the converging channel resulting in anenhanced mixing in the winglet-type CDLVGs.

� The measurements showed that air flow velocity has a signifi-cant effect on the efficiency of the HX. The HX efficiencydecreased with increasing the air flow velocity. It was observedthat increasing the cross-flow fluid velocity will enhance theheat transfer rate and will reduce the heat transfer irrevers-ibility. It was also found that the pressure loss reduces as thevelocity increases; nevertheless the reduction is rather small.Due to the irreversibility, the motion of mixed fluid in thechannels, the number of channels and the vortex generatorsurface affect the variation on the HX that increases heattransfer area on both exhaust air and supply air sides, leadingto a higher heat transfer and pressure drop and also increasingthe entropy generation number.

In conclusion, the dimensionless mass velocity, for the minimumirreversibility, as the dimensionless mass velocity increases theoptimum flow path length decreases.When inspecting the optimumdimensionless mass velocity and the dimensionless heat transferarea, as the dimensionless heat transfer area increases the optimumdimensionless mass velocity tends to decrease. In addition, wheninspecting the relation of the minimum entropy generation numberwith the dimensionlessmass velocity, as the optimumdimensionlessmass velocity increases the minimum entropy generation numberalso increases. Based on all of these results, the low entropy genera-tion levels can be controlled by the dimensionless mass velocity.Because the fluid flow pair flowing only in the low dimensionlessmass velocities, passes through theheat transfer area bycontacting ina long time of duration periods due to the requirement of wingletgeometry, being theminimumentropygenerationnumber in the lowenough levels, it was emphasized that this HX is very important fromthe practical applicability point of view.

Acknowledgements

This project was supported by Atatürk University BAP-1997/37.The author gratefully acknowledges Professor Teoman Ayhan fromthe University of Bahrain for valuable suggestions and stimulatingdiscussions on this work.

Nomenclature

A*heat dimensionless heat transfer area

b height of channels exhaust and supply (m)C* heat capacity of fluid (WK�1)Cp specific heat at constant pressure (J kg�1 K�1)Dh duct hydraulic diameter (m)f friction factor (e)G mass velocity (kg s�1m�2)G* dimensionless mass velocityk thermal conductivity (Wm�1 K�1)La width of duct (m)Lc length of duct (m)Lb height of duct (m)l length of winglets (m)_m mass flow rate (kg s�1)

I. Kotcioglu et al. / Energy 35 (2010) 3686e3695 3695

Ns entropy generation number (e)NTU number of transfer units (e)Q rate of heat transfer (W)q00 heat flux (Wm�2)P pressure (Pa)R ideal gas constant (J kg�1 K�1)Re Reynolds number (e)_Sgen entropy generation rate (WK�1)_Sgen;DP entropy generation rate due to friction (WK�1)_Sgen;DT entropy generation rate due to heat transfer across

a finite temperature difference (WK�1)_S0gen entropy generation rate per unit length (Wm�1 K�1)St Stanton number (e)tw thickness of winglets (m)T absolute temperature (K)G uncertainty for i-th experimentalV* dimensionless heat transfer volume

Greek symbolsDP pressure drop (Pa)DT temperature difference (K)DTL logarithmic mean temperature difference (K)DT*¼ s dimensionless temperature differenceb inclination angle of winglets3 heat transfer effectiveness (e)r mean density of fluid (kgm�3)

Subscriptse exhausts supplyc cold fluidh hot fluidi inleto outletl lossmax maximummin minimum

Superscript* dimensionless

References

[1] Vargas JVC, Bejan A. Thermodynamic optimization of finned cross flow heatexchangers for aircraft environmental control systems. Int J Heat Fluid Flow2001;22:657e65.

[2] Bejan A, Poulikakos D. Fin geometry for minimum entropy generation inforced convection. J Heat Transfer 1982;104:616e23.

[3] Bejan A. Entropy generation through heat and fluid flow. New York: Wiley;1982.

[4] Bejan A. The concept of irreversibility in heat exchanger design: counter flowheat exchangers for gas-to-gas applications. ASME J Heat Transfer 1977;99:374e80.

[5] Khan WA, Culham JR, Yovanovich MM. Optimization of pin-fin heat sinks inbypass flow using entropy generation minimization method. ASME J ElectronPackag 2008;130:7.

[6] Bergles AE. Heat transfer enhancement-the encouragement and accommo-dation of high heat fluxes. J Heat Transfer (Trans ASME) 1997;119:8e19.

[7] San JY, Worek MW, Lavan Z. Entropy generation in convective heat transferand isothermal convective mass transfer. ASME J Heat Transfer 1987;109:647e52.

[8] San JY, Worek MW, Lavan Z. Entropy generation in combined heat and masstransfer. Int J Heat Mass Transfer 1987;30:1359e69.

[9] Zimparov V. Extended performance evaluation criteria for enhanced heattransfer surface. Heat transfer through ducts with constant wall temperature.Int J Heat Mass Transfer 2000;43:3137e55.

[10] Durmus A. Heat transfer and exergy loss in a concentric heat exchanger withsnail entrance. Int Commun Heat Mass Transfer 2002;29:303e12.

[11] Rosen MA, Dincer I. Effect of varying dead-state properties on energy andexergy analyses of thermal systems. Int J Therm Sci 2004;43(2):121e33.

[12] Ranganayakulu CH, Seetharamu KN, Sreevatsan KV. The effects of inlet fluidflow on uniformity on thermal performance and pressure drops in cross flowplate-fin compact heat exchangers. Int J Heat Mass Transfer 1997;40:27e38.

[13] Soylemez MS. On the optimum heat exchanger sizing for heat recovery.Energy Convers Manage 2000;41:1419e27.

[14] Ogulata RT, Doba F, Kucuk A. Plate type waste heat recovery system. J Ther-modyn 1995;33:67e9.

[15] Ogulata RT, Doba F, Yilmaz T. Irreversibility analysis of cross flow heatexchangers. Energy Convers Manage 2000;41:1585e99.

[16] Lucas K. On thermodynamics of cogeneration. Int J Therm Sci 2000;39:1039e46.

[17] Gomez LC, Navarro HA, Jabardo JMS. Thermal performance of multipassparallel and counter-cross-flow heat exchangers. ASME J Heat Transfer2007;129:282e90.

[18] Shang W, Besant RW. Effects of manufacturing tolerances on regenerativeexchanger number of transfer units and entropy generation. ASME J Eng GasTurbines Power 2006;128:585e98.

[19] Fakheri A. Thermal efficiency of the cross flow heat exchangers. In: ASMEinternational mechanical engineering congress and exposition (IMECE2006),vol. 1; 2006. p. 645e651.

[20] Satapathy AK. Thermodynamic optimization of a coiled tube heat exchangerunder constant heat flux condition. Energy 2009;34:1122e6.

[21] San JY, Jan CL. Second-law analysis of a wet cross flow heat exchanger. Energy2000;25:939e55.

[22] Wu SY, Yuan XF, Li YR, Xiao L. Exergy transfer effectiveness on heat exchangerfor finite pressure drop. Energy 2007;32:2110e20.

[23] Mohagheghi M, Shayegan J. Thermodynamic optimization of design variablesand heat exchangers layout in HRSGs for CCGT, using genetic algorithm. ApplTherm Eng 2009;29:290e9.

[24] Kline SJ, McClintock FA. Describing uncertainties in single sample experi-ments. Mech Eng 1955;75:3e8.

[25] Editorial JHT. Journal of heat transfer policy on reporting uncertainties inexperimental measurements and results. J Heat Transfer 1993;115:5e6.

[26] Kotcioglu I, Ayhan T, Olgun H, Ayhan B. Heat transfer and flow structure ina rectangular channel with wing-type vortex generator. Tr J Eng Environ SciTUBITAK 1998;22:185e95.

[27] Kotcioglu I, Caliskan S. Experimental investigation of a cross-flow heatexchanger with wing-type vortex generators. J Enhance Heat Transfer2008;15:113e27.