An overview on thermal and fluid flow characteristics in a plain plate finned and un-finned tube banks heat exchanger Tahseen Ahmad Tahseen a,b,n , M. Ishak b,c,1 , M.M. Rahman b,c,1 a Department of Mechanical Engineering, College of Engineering, Tikrit University, Tikrit, Iraq b Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia c Automotive Engineering Centre, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia article info Article history: Received 23 November 2013 Received in revised form 29 August 2014 Accepted 22 October 2014 Available online 27 November 2014 Keywords: Heat exchanger Flat tube In-line/staggered configurations Optimum spacing Thermofluids characteristics abstract The heat exchangers have a widespread use in industrial, transportation as well as domestic applications such as thermal power plants, means of transport, air conditioning and heating systems, electronic equipment and space vehicles. The key objectives of this article are to provide an overview of the published works that are relevant to the tube banks heat exchangers. A review of available and display that the heat transfer and pressure drop characteristics of the heat exchanger rely on many parameters. Such parameters as follows: external fluid velocity, tube configuration (in-line/staggered, series), tubes rows, tube spacing, fin spacing, shape of tubes, etc. The review also shows the finned and un-finned tube configurations heat exchangers. The important correlations for thermofluids in tube banks heat exchangers also discussed. The optimum spacing of tube-to-tube and fin-to-fin with fixed size (i.e., area, volume) with the maximum overall heat conductance (heat transfer rate) were summarized in this review. In addition, the few studies show the effect of tube diameter in a circular shape compared with elliptic tube shape. Overall, the heat transfer coefficient and pressure drop increases with increasing fluid velocity regardless the arrangement and shape of the tube. In the meantime, the other shape of tubes (such as flat or flattened) for finned and un-finned with the optimum design needs more research and investigation due to have lesser air-side pressure drop and improved air-side heat transfer coefficients. They have putted some the significant conclusions from this review. & 2014 Elsevier Ltd. All rights reserved. Contents 1. Introduction ........................................................................................................ 364 2. Background of tubes bank............................................................................................. 364 3. Flow and geometric parameters ........................................................................................ 369 3.1. External velocity of fluid ........................................................................................ 369 3.2. Tube diameter ................................................................................................ 370 3.3. Tube rows ................................................................................................... 370 3.4. Tube pitch ................................................................................................... 370 3.5. Fins pitch .................................................................................................... 371 4. Optimum spacing ................................................................................................... 372 5. Correlations of thermofluids ........................................................................................... 373 6. Flat tube and other shapes ............................................................................................ 376 6.1. In-line and staggered configurations .............................................................................. 376 6.2. Tubes array between parallel plates ............................................................................... 377 7. Future work ........................................................................................................ 377 8. Conclusions ........................................................................................................ 377 Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/rser Renewable and Sustainable Energy Reviews http://dx.doi.org/10.1016/j.rser.2014.10.070 1364-0321/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: [email protected], [email protected](T.A. Tahseen). 1 Tel. þ609 424 2246; fax: þ609 424 2202. Renewable and Sustainable Energy Reviews 43 (2015) 363–380
Transcript
An overview on thermal and fluid flow characteristics in a plain platefinned and un-finned tube banks heat exchanger
Tahseen Ahmad Tahseen a,b,n, M. Ishak b,c,1, M.M. Rahman b,c,1
a Department of Mechanical Engineering, College of Engineering, Tikrit University, Tikrit, Iraqb Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysiac Automotive Engineering Centre, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia
a r t i c l e i n f o
Article history:Received 23 November 2013Received in revised form29 August 2014Accepted 22 October 2014Available online 27 November 2014
The heat exchangers have a widespread use in industrial, transportation as well as domestic applicationssuch as thermal power plants, means of transport, air conditioning and heating systems, electronicequipment and space vehicles. The key objectives of this article are to provide an overview of thepublished works that are relevant to the tube banks heat exchangers. A review of available and displaythat the heat transfer and pressure drop characteristics of the heat exchanger rely on many parameters.Such parameters as follows: external fluid velocity, tube configuration (in-line/staggered, series), tubesrows, tube spacing, fin spacing, shape of tubes, etc. The review also shows the finned and un-finned tubeconfigurations heat exchangers. The important correlations for thermofluids in tube banks heatexchangers also discussed. The optimum spacing of tube-to-tube and fin-to-fin with fixed size (i.e.,area, volume) with the maximum overall heat conductance (heat transfer rate) were summarized in thisreview. In addition, the few studies show the effect of tube diameter in a circular shape compared withelliptic tube shape. Overall, the heat transfer coefficient and pressure drop increases with increasing fluidvelocity regardless the arrangement and shape of the tube. In the meantime, the other shape of tubes(such as flat or flattened) for finned and un-finned with the optimum design needs more research andinvestigation due to have lesser air-side pressure drop and improved air-side heat transfer coefficients.They have putted some the significant conclusions from this review.
There has been a significant amount of research work carriedout to improve the efficiency of heat exchangers. The reason forthese efforts is that heat exchangers have a widespread use inindustrial, transportation as well as domestic applications such asthermal power plants, means of transport, heating and air con-ditioning systems, electronic equipment and space vehicles [1].Because of their extensive use, increase in their efficiency wouldconsequently reduce cost, space and materials required drastically[1,2]. The aforementioned research work includes a focus on thechoice of working fluids with high thermal conductivity, selectionof their flow organization and high effective heat transfer surfacesconstructed from high-conductivity materials.
This paper shows a general review of the heat transfer and fluidflow characteristics of a tube banks heat exchanger and discussesthe effect on the thermofluid characteristics of several parameters:the frontal velocity of fluid, tube diameter, tube configuration, tuberows, tube spacing, fin spacing, and tube shape. The optimumtube-to-tube and fin-to-fin spacing with the maximum heat tra-nsfer rate and minimum pressure drop also presented. A highlight
the most important of the correlations for heat transfer and fluidflow in a tube banks heat exchanger is provided. The other specificshapes (flat tube) and confinement of the tube between parallelplates are outlined were reviewed. The shows and describes thegaps in the research which may be considered by new studies andsuggests future work. Finally, presents the significant conclusions.All sections presented for tube configuration with finned and un-fined tube bundle.
2. Background of tubes bank
The general configurations of un-finned and finned tube banksheat exchangers were presented in Figs. 1 and 2. Both in-line andstaggered configurations of tube as well as the circular and flattubes shape. In general, one fluid flow over the tubes array, while aother fluid at the different temperature moves through the tubes.The rows of tube at the in-line and staggered arrangements in theflow direction of fluid (i.e., inlet velocity of air u1) as shown inFig. 2(a and b). The characteristics of configuration by the diameter
Fig. 1. The configurations of finned round and flat tube heat exchanger. (adopted from [99]). (a) In-line classic tube shape, (b) Staggered classic tube shape, (c) In-line flattubeand (d) Staggered flat tube.
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of tube such as d, for circular tube and transverse tube diameter offlat tube as well as by the longitudinal pitch, P1 and transversepitch, P2 the distance between centers of tube. Beale and Spalding[3] carried out a numerical investigation of transient incompres-sible flow in in-line square, rotated square, and staggered tubebanks for the Re number range of 30rRer3000 and ratio of pitchto diameter of 2/1. The drag lift, pressure drop, and heat transfercoefficient were calculated. A calculation procedure for a 2Delliptic flow is applied to predict the pressure drop and heattransfer characteristics of laminar and turbulent flows of air acrosstube banks. The theoretical results of the model are comparedwith previously published experimental data [4]. A 2D numericalstudy of the laminar steady state flow in a circular tube banks heatexchanger was carried out for low Reynolds number numbers[5,6]. The flow in a bundle of elliptical cylinders was investigatedboth numerically and experimentally [7,8].
The momentum and energy equations have been solved byusing a finite difference method. The effect of the Nusselt numberon the surface of the tube was recorded by Juncu [9]. Theimportance of heat transfer and fluid flow appearances of tubebanks in the design of heat exchangers is well known [10].Comprehensive experimental [11,12], numerical studies [4,13,14]and both experimental and numerical studies [15,16] of circulartube banks have been done previously. The numerical analysis oflaminar forced convection in a 2D steady state in the circularcylinder banks of a tube in square and non-square in-line arrange-ments. The study shows that the highest heat transfer rate occursat the first tube compared with the other tubes. In addition, thepressure drop increases significantly as the transverse pitch-to-diameter ratio is reduced [17].
Numerical studies over a 3D multi-row plate fin heat exchangerwere carried out of late by Jang et al. [18] The results showedstaggered arrangement to yield a pressure drop 20–25% higherthan the in-lined arrangement. The staggered arrangement alsogave an average heat transfer coefficient that was 15–27% higherthan the in-lined arrangement. It was the first study to have givennumerical solutions and experimenting with realistic geometryand the inlet-outlet conditions for the real multi-row (1–6 rows)plate fin-and tube heat exchangers. The entire computationaldomain (1–6 rows) from fluid inlet to outlet was solved directly.There are certain limitations as it only takes into account thelaminar flow range, where the flow is in the range of 60rRer900, even though the study has performed a three-dimensionalsimulation for a real multi-row plate-fin heat exchanger. The effectof airflow rates and average particle diameters on thermofluidcharacteristics in the tube banks in both in-line and staggeredconfigurations for gas-particle flow were studied experimentallyby Murray [19]. The results showed that the local and averageNusselt numbers for the flow with particles can lead to enhancedthermofluid characteristics; also the results depend on the particlesize and Reynolds number for in-line and staggered arrangements.The author also found that the performance of heat transfer in thein-line configuration is more suitable compared with the stag-gered configuration tube bundle for most flow cases.
Lu et al. [20] presented the influence of geometric parameterssuch as tube pitch, fin spacing, and tube diameter on thecoefficient of performance (COP) and the ratio of heat transferrate to pressure drop (Q/ΔP). The authors found the optimumvalue of the pressure drop by using a numerical simulation. Fiebiget al. [21] employed the finite volume technique to calculate the
Nomenclature
a airA overall surface area of heat transfer (m)AcF cross-section flow area (m2)AF surface area of fin (m2)Ano surface area of outside tube without fin (m2)Ar elliptic tube minor-to-major axis ratiosCd drag coefficientsCFD computational fluid dynamicsD tube diameter (m)Dh hydraulic diameter (m)Do outside diameter of tube (m)Dvh volumetric hydraulic diameter (m)fF fins friction factorfT tubes friction factore ellipses eccentricity e¼b/aH fin spacing (m)k thermal conductivity of fluid (w/(m k))NR number of tube rows in flow directionpF fin pitchPL longitudinal tube pitchPT transverse tube pitchtF fin thickness, mSF spacing between two fins¼pF�1 (m)W ratio of heat transfer area of a row of tubes to frontal
free flow area
Dimensionless group
Bi Biot numberEu Euler number
j Colburn factorNu Nusselt numberNuZ Nusselt number predicted by Žukauskas correlationNu average Nusselt numberRe Reynolds numberSc Schmidt numberSh Sherwood numberSh average Sherwood numberSt Stanton numberPr Prandtl number
Greek symbol
~qn;m maximum dimensionless overall thermal conductance_m mass velocity (kg/m2 s)ΔTper temperature increase along the periodic lengthϕf dimensionless fin density in z-directionΔP pressure drop per unit lengthΔpF pressure drop associated fin area in finned-and-tube
heat exchanger (Pa)ΔpT pressure drop associated tubes in finned-and-tube
heat exchanger (Pa)ρ density (kg/m3)
Subscribers
a airf fluido outto tube out side
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conjugate heat transfer and flow characteristics in 3D in a flat platefinned-tube heat exchanger. Using a fixed geometry, the patternsof flow, distribution of pressure, heat flux distribution, heattransfer coefficient distribution, and fin efficiency versus theReynolds number. The downstream fin is much less efficient than
the upstream fin. The finite conductivity in the wake behind thetube caused the reversal of heat transfer. The steady-state laminarincompressible flow across a tube bundle was investigated and thefinite element method was introduced and applied to solve the 2Dand 3D energy equation and Navier–Stokes equations [22,23].
Fig. 2. The configurations of round tube banks heat exchanger (a) in-line (b) staggered, and (c) side view. (adopted from [99]).
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Tremendous efforts were made to develop the numerical simula-tions used to predict the fluid flow and heat transfer in tube banks.The many previous studies using an in-line configuration by
Krishne Gowda et al. [24], Mavridou and Bouris [25], a staggeredconfiguration [26–28], and both in-line and staggered configura-tions [29,30]. Seventeen works among the previous researches
Fig. 3. The finned-two-tube rows (left to right the flow direction). (a) Total energy exchanged, (b) energy exchanged for conduction, (c) energy exchanged by radiation,(d) temperature integration and (e) convection coefficient distribution [47].
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Table 1Effect of the flow and geometric parameters on the thermofluids characteristics.
Researcher Type Re number and velocity range Tubeshape
Geometric parameter Finding
Tutar andAkkoca[43]
N 600rRer2000 Cir 0.116rpfr0.365 � The small effect of the number of tube rows on the coefficient of heat transfer when the number of multi-rows NR44.� The pressure drop increased with an increase in the number of rows from 1 to 4 for both in-line and staggered
configurations.
Jang andYang [50]
NþE 2 m/srur7 m/s Cir.Elp.
4-rows axis ratio 2.83:1 � Pressure drop reduction by 25–30%.� Heat transfer coefficient increased by 35–50%.
Ay et al. [51] E 0.5 m/srur7 m/s Cir � Heat transfer coefficient was 14–32% higher in the staggered configuration compared with the in-line configurationPaeng et al.[52]
NþE 1082rRer1649 Cir. OD¼10.2 mm, pf¼3.5 mm � The deviation between these experimental results and previous work is in the range of 7–32.4%.� The error range in the correlation of 16.5–31.4% with compared previous correlation.
Tang et al.[53]
E 4�103rRer1�104 Cir. OD¼18 mm, pf¼3.1 mm,PL¼34 mm, PT¼42 mm
� The characteristics of air-side heat transfer and friction coefficients.� The heat exchanger with slit fin has better performance than that with vortex-generator fin, especially at high Reynolds
numbers.
Hasan [54] E 1�103rRer11�103 Elp. 2rArr4 � High values of the Nu number in oval compared with circular tube.� The drag coefficient, was better in the oval tubes compared with circular tubes
Ibrahim andGomaa[55]
NþE 5.6�103rRer4�104 Elp. 0.25rArr1.0 � The better thermal performance with smaller Re number and Ar.� The heat exchanger employing elliptic tube arrangement contributes significantly to the energy conservation.
Simo Talaet al. [56]
N Re¼1050, and 2100 Cir.Elp.
e ¼1.0 (circular); e¼0.7 ande¼0.5
� The increase of thermal-hydraulic performance of above 80% were obtained with a reduction in the tube ellipticitycompared with a circular shaped tube.
� The reduction of the thermal and viscous irreversibilities respectively down to 15% and 50% was observed in the modifiedshapes when compared to circular ones.
Yan andSheen [57]
E 300rRer2000 Cir. PL¼19.05 mm; PT¼25.4 mm;Pf¼1.4, 1.69, and 2.0
� The Δ ~p increased with increases in the number of tube rows for the same frontal air velocity.
Halici et al.[58]
E 0.9 m/srur4 m/s Cir. Row no.¼1–4 � The increase in the number of tube rows leads to a decrease in the Colburn j and friction factors.
Kim et al.[59]
E 550rRer1200 Cir PL¼27, 30, and 33 mmmmpf¼7.5, 10.0, 12.5, and 15.0
� The staggered fin and tube configurations enhance the performance of heat transfer by 7% and 10%, respectively, comparedto the in-line fin configuration.
� The heat transfer performance decrease with increase of tube number.
Yoo et al.[60]
E 7.7�103rRer30.3�103 Cir PL¼PT¼1.5, 1.75, and 2.0 � The Nu number increases by more than 30% and 65% on the second and third tubes, respectively, compared with thefirst tube.
� The local heat transfer coefficients on each tube increase except on the front part of first tube as the tube spacing decreases.
Beale andSpalding[61]
N 100rRer1000 Cir 1.25rp/Dr2.0 � The results were shown in the form of the friction coefficient, pressure drop, and coefficient of heat transfer.
Khan et al.[62].
A 1�103rRer1�105 Cir PL¼20.5, and 34.3 mm � The Nu numbers depend on the transverse, longitudinal pitches and Reynolds number.� For staggered configuration, the heat transfer coefficient is higher compared with the in-line configuration.PT¼20.5, and 31.3 mm
Xie et al.[63].
N 1�103rRer6�103 Cir 32 mmrPLr36 mm,19 mmrPTr23 mm
� The decrease in the transverse pitch causes an increase flow velocity, which in turn enhances the heat transfer.� The heat transfer and flow friction of the presented heat exchangers are correlated in the multiple forms.
Ramanaet al. [64]
E 200rRer1500 Cir PL¼PT¼2.0 � The high Reynolds number enhancement of the heat transfer is 100% with the staggered arrangement.� The pressure drop in an in-line arrangement decrease by about 18% compared to configurations without the porous
medium.
T.A.Tahseen
etal./
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ableand
SustainableEnergy
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s43
(2015)363
–380368
used computational fluid dynamics (CFD) to simulate the flow andthermal characteristics of plate un-finned and finned-tube heatexchangers. All of them aimed to compare the heat transfer andflow characteristics in 2D and 3D heat exchangers with finned orun-finned tubes for different geometrical parameters [31–40], andthe finite-element [41] were also used.
In addition, the structure of fluid flow between fins is compli-cated and usually difficult to study in 3D. A few researchers havereported numerical studies of 3D modeling for finned-tube heatexchangers. Romero-Méndez et al. [42] carried out a numericaland experimental study of the influence of the fin spacing on thehydrodynamics and heat transfer of the fluid flow through a 3Dfinned tube with a single row arrangement for the range ofReynolds numbers from 260 to 1460. A similar 3D numericalinvestigation was carried out by Tutar and Akkoca [43]. Theypredicted the vorticity distributions, average heat transfer coeffi-cient, and pressure drop coefficient for several conditions of the finspacing. For all of the turbulence cases, the values of theseorganized factors were compared with each other. Although thisstudy provides an analysis of turbulent ranges in 3D for the flowon a finned tube, the domain employed in this study (one tuberow) is not pragmatic. Normally one to six tube rows regions areused in practical applications [44]. Using the lumped capacitancetechnique (LCT), Kim et al. [45] measured the heat transfercoefficient in a plain finned-tube heat exchanger. The authorsfound that the LCT using polycarbonate displayed the same resultsregardless of thickness. The LCT is suitable to measure thecoefficient of heat transfer for the Biot number, Bio0.058. Theyclaimed that this method is a good way to obtain the quantitativecoefficient of heat transfer for the plate fin. Recently, manyresearchers suggested linking the particle image velocimetry(PIV) and infrared thermography (IR) measurements in order toevaluate each of the fields of velocity and temperature and to inferthe map of the coefficient of heat transfer [46]. The used of the PIVtechnique for different thermal applications such as enhanced heattransfer in heat exchangers. Some of the available empiricalstudies for the fluid flow in a tube bundle were carried out usingPIV with the wide range of Reynolds numbers [38,47,48] for astaggered configuration, Iwaki et al. [49] for both in-line andstaggered configurations. The sample of results for used thistechnique by Bougeard [47] as presented in Fig. 3.
3. Flow and geometric parameters
Flow conditions and the finning geometry primarily influencethe distribution of the heat transfer coefficient over un-finned andfinned-tube heat exchangers. Heat transfer and pressure drop froma un-finned and finned-tube bundle are affected by many otherfactors, and communication among these factors make designingproblems significantly tedious. Several parameters effecting of thethermal-hydraulic characteristics of tube banks heat exchangersuch as: external velocity, tube diameter, tube rows, tubes pitchand fins pitch. The general effect of the flow and geometricparameter are presented in Table 1. The more detailed the effectedof these parameters will be shows as follows.
3.1. External velocity of fluid
Boundary layer development and shape which varies with airvelocity is one of the most important factors influencing the heattransfer performance in un-finned and finned-tube bundle. Thecreation of horseshoe vortices increase and the boundary layerthickness decrease as the air velocity increases. It is a generalconvention that the fluid velocity in the recirculation zone islower than in the mainstream; hence, the heat transfer coefficient
Berbish
[65]
NþE
4000r
Rer
4557
0Elp.
1.5r
P L,P
T/br
4.0
�Fo
rRe
o14
100,
thelargelocalNusseltnumbe
rtake
splace
atthelead
inged
ge(e.g.,P/b¼0.0).
�Fo
rRe
414
100,
themax
imum
valueof
theav
erag
eNusseltnumbe
ren
han
cemen
tratiois
nea
rlyab
out2.0.
Leeet
al.
[66]
N50
0r
Rer
2000
Cir.
3.0r
P Tr
7.0
�Th
eim
pactof
tran
sverse
pitch
inthehigher
Reyn
oldsnumbe
rsthedraftingof
thetrad
itional
hea
ttran
sfer.
�Increa
sesp
aceof
thelongitudinal
fortheuniformly
distributedcy
linderswill
strengthen
thetotalh
eattran
sfer.O
therwise,
themax
imum
Nunumbe
ris
thewithou
t-uniformitytemperature
onthewallfinan
dtube
wall.
Chen
etal.
[67]
N10
0r
Rer
500
Elp.
�Th
ehea
ttran
sfer
ratioof
tube
surfaceto
finwas
still
o10
%.
�Th
efinefficien
cyan
dfintemperature
dep
endslightlyon
thefinparam
eters.
Sheu
iet
al.
[68]
N0.3r
ur
2.0
Cir.
0.4r
p fr
5.0
�Th
ead
ditionof
finslead
sto
enhan
cedhea
ttran
sfer
butcausesan
increa
sein
thepressure
drop.
Erek
etal.
[69]
Nmassflow
rate
usedin
allof
the
mod
elsis
1.90
4�10
�5kg
/sCir
P L¼35
,and38
�Th
ehea
ttran
sfer
increa
seswithincrea
singellip
ticity
ofthetube
s.How
ever,thepressure
dropis
sign
ificantlyreducedby
both
increa
singtube
ellip
ticity
anddecreasingden
sity
offins.
A:an
alytical
study;
Cir:circulartube
;E:
experim
entalstudy;
Elp:ellip
tictube
;an
dN:numerical
study.
T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380 369
is decreased. To determine the Reynolds number for bodies incross-flow, the selection of flow velocity is imperative. It must benoted that a characteristic dimension used to identify the Reynoldsnumber has not been agreed upon. The researchers have used theinlet velocity, mean velocity and velocity in the smallest crosssection area as reference velocity [44,70]. In most cases, thereference velocity is defined as the last one (velocity in thesmallest cross section area) according to the available literature.Furthermore, air drafting technique is used for complete design ofheat exchangers. Depending on the flow conditions at the bundleinlet, performance of heat transfer and pressure drop for the un-finned and finned-tube banks will vary [71].
Tang and Yang [72] performed the experimental study on thecharacteristics of heat transfer across the flow in a single-rowfinned-tube heat exchanger on both the air and water sides. Theyfound that the total thermal resistance value on the water-sidewas less than 10% when the Reynolds number varied between1200 and 6000. The air-side thermal resistance was alwayspredominant. Furthermore, their results indicate that the thermalresistance of the air-side is almost equal to that of the water-sidein the Reynolds number range of 500–1200. He et al. [73]numerically evaluated the effect of frontal air velocity in staggeredfinned-tube heat exchangers with the air velocity ranging between0.646 and 4.64 m/s. Also, the effect on the Nusselt number andfriction coefficient of inlet air velocities ranging between 0.4 m/sand 4 m/s was studied by Borrajo-Peláez et al. [74].
3.2. Tube diameter
Taler [75,76] numerically investigated the heat transfer on thedouble rows in the laminar flow region of a two-pass automobileradiator. The oval-shaped tubes had two diameters: the minor was6.35 mm and the major 11.82 mm. They found that the zonesbehind the tubes contributed little to the heat exchanger perfor-mance. Their results showed wakes in front of and behind the tubeat the second row, which led to the minimization of the heattransfer rate to the lowest value. The influence of tube diameter onthe Nusselt number and friction factor was presented numericallyby Xie et al. [77]. The Reynolds number was varied between 1000and 6000. The diameter of the tube was varied from 16 mm to20 mm. Their study reveals that both heat transfer and frictioncoefficients increase with increases in the tube diameter. Theinfluence of tube diameter on the Nusselt number and frictioncoefficient with the various from 5 to 15 mm was studied byBorrajo-Peláez et al. [74].
3.3. Tube rows
Every study verified the influence of tube bundle in thedirection of flow on variation of heat transfer coefficient aroundthe fin and from row-to-row. While, it should be noted that asingle tube and fewer rows yield limited results, some studies havedeveloped row correction factors to counter this problem. There isa need to be further research by implementing four and more tuberow bundles. With the staggered configuration, the main flowpasses during the surfaces of the fin and tube because of thelocation of all rows in almost the same direction as the flow. Theimpact of the number of rows on the coefficient of heat transfer foran in-line configuration was higher compared with the staggeredconfiguration when the number of rows, NR was NRZ2 [71,78].Note that, the coefficient of heat transfer became fixed followingthe third row. Reductions of pressure drop up to 30% of the losspressure coefficient (pressure drop coefficient per unit rowbecause only the existence of the tubes) viewed in favor ofelliptical arrangement. The comparison was conducted betweenarrangement for circular and elliptical tubes with the same area of
hindering the free flow for Reynolds number based on the fin pitchrange of 200rRer2000. The air velocity range covered theadvantage for applications in air conditioning. In addition, it wasnoted that the reduction in loss pressure coefficient is higherwhen increases Reynolds number and negligible for three rowsarrangements.
3.4. Tube pitch
This section discuss a review of the heat transfer and pressuredrop in un-finned and finned and tube heat exchangers withcircular tube experimental measurements in the relevant litera-ture. The relationship was established for the heat transfer andpressure drop. Regardless of the influence of tube diameter, theseverity of the turbulence within the bundle depends on thevelocity of the air and tube spacing. Thus, these parameters have astrong effect on the pressure drop in the banks of tubes. When thetransverse pitch of the tube was changed, the existence of a clearinfluence on the pressure drop at the side-air was observed, whilethere was a lack of significant change in the heat transferperformance [79]. For the staggered configuration, the heattransfer coefficient is bigger for the nearer transverse pitch[79,80]. It would appear that the air velocity at the smallestchannel between the fins becomes highest when the transversepitch decreases and this impact leads to bigger values of thepressure drop and coefficient of heat transfer. On the other hand,the authors stated that an extension of the longitudinal pitch ofthe tube in the staggered configuration leads to decreases of theNusslt and Euler numbers. Similar results were reported by Rabaset al. [81] for the impact of longitudinal pitch on the heat transferperformance, and the influence on the pressure drop has beenconfirmed by Jameson [82]. The finite element method [83,84] tosolve the Navier–Stokes and energy equations of heat transfer andfluid flow over in-line and staggered configurations of tube banksat the fixed Pr number of 0.7. Wong and Chen [83] presentedresults for various Reynolds numbers ranging between 20 and 40and a pitch-to-diameter ratio of 2.0. Chen and Weng [84] studiedthe effect of pitch-to-diameter ratio and Re number on the Nunumber, pressure drag, total drag, and friction drag. The ranges ofthe pitch-to-diameter ratio and Re number were 1.7–2.0 and 4–40,respectively. Zdravistch et al. [85] used a finite volume techniqueand presented results for two pitch-to-diameter ratios of 1.5 and2.0 with various Reynolds numbers based on the velocity ofapproach from 54 to 120 at a fixed Pr number of 0.7. It is boostedusing the finite volume technique in a 2D [86], and 3D [87]. Thelaminar air flow and forced convection heat transfer in thestaggered circular tube banks were studied numerically Wanget al. [88]. Three tube pitch ratios of 1.25, 1.5, and 2.0 with rotatedsquare (RS) and equilateral triangle (ET) tube configurations with10 tube rows for two Reynolds numbers of 100 and 300 weretested. The authors found that a decrease of the tube pitch ratioleads to a rise in the heat transfer and friction coefficients. Ingeneral, the friction and local heat transfer coefficients are less inthe RS configuration compared with the ET configuration at thesame tube pitch ratio. They claimed that the results can be usedparticularly at lower Reynolds numbers to predict the total heattransfer in tube banks. The tube bundle arrangements as shown inFig. 4. The mass transfer and hydrodynamic characteristics for thein-line circular tube configuration were examined numerically[89]. The ratios of pitch to diameter of tube are 1.45, 1.50, 1.75,1.85, and 2.00 with a low Reynolds number of Reo200. Theresults were shown in the form of streamlines, temperaturecontours, and local Sherwood, Sh and Sh numbers. The correlationobtained for the Sh number shows good agreement with previousexperimental correlations. Numerical investigations of the localcoefficient of heat transfer for the tube bundle issue were carried
T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380370
out for a wide range of transverse and longitudinal pitches,Reynolds numbers [90,91], and Prandtl numbers [50], and experi-mental [92]. The wall-resolved large eddy simulation (LES) withunsteady RANS was used to investigate the flow over a periodicand in-line tube bundle [93]. The researchers studied the impact oftube spacing on fluid flow with three values of the pitch-to-diameter ratio (P/D) of 1.4, 1.6, and 2.0. The significant results fromthis study showed that the decreases of P/D led to an increase ofthe flow deviation. The influences of the P/D on streamlines andkinetic energy contour for all cases were which tested as isillustrated in Fig. 5. The effect of Reynolds number on the flowand conjugate heat transfer performance of in-line and a staggeredarrangement of a circular tube bundle were studied. The laminarflow with thermally and developing in a 3D with Reynoldsnumbers in the range of 300rRer800 [14] the influence of tubeseparation [94]. The results were provided in the form of tem-perature contours, streamline, average pressure drop, and Nunumber. The effect of the longitudinal spacing on characteristicsof heat transfer in the in-line tube bundle for a single phase wasstudied [95] with the CFD technique. The author conductedsensitivity analyses using different models of two-equation turbu-lence to determine the effect of the turbulence model on char-acteristics of the heat transfer and to identify the turbulencemodel that could describe the physical phenomena of concernmost appropriately. The result suggested that the coefficient ofheat transfer may be reduced by 37.1% from that predicted usingthe relationship [10], and the longitudinal pitch decreases. Fromthe results analysis, it was found that deterioration in the heattransfer can be observed using the experimental correlationcoefficient and a link and Žukauskas [10].
3.5. Fins pitch
The empirical results of Rabas and Taborek [96] shows that thecoefficient of heat transfer near the fin root is closer at the smaller
fin spacing compared with the larger fin spacing because theboundary layer is thicker. Small fin spacing leads to an increase inthe thickness of the boundary layers. The swept the formation of aregion of stagnation at the surface of the tube and the fin basethrough a non-turbulent flow, which was expected from thesubscribe in the effective heat transfer. Hence, the allowableranges of reduction in the space between fins depend on thevelocity flow and flow turbulence in the channel between fins. Inthis regard, other researches were carried out to find the bestdesign for enhanced surfaces for heat transfer [97]. Fig. 1(a and b)shows the geometry of tube banks with plain fins, four rows deepon 12.7 mm diameter tubes equilaterally spaced on 32 mm cen-ters; Rich [98] calculated the heat transfer and friction data for thissystem. The tubes as well the fins were made of copper and thefins were joined together by solder to reduce resistance by contact.The thickness of all fins was kept the same at 0.25 mm thick. Thefins density (1/pf) ranged from 114 fins/m to 811 fins/m but all hergeometrical parameters were identical. The friction drag force isthe total of the drag on a bare tube (ΔpT) and the drag caused bythe fins (Δpf) as suggested by Rich [98]. The drag force on the finsis the difference between the total drag force and the drag forcerelated to the corresponding bare tube banks. Hence, the frictionfactor from the fins is
f F ¼ Δp�ΔpT� �2AcF � ρ
_mð Þ2AF
ð1Þ
The friction factor and the Colburn j-factor ðSt � Pr2=3Þ data(smoothed curve fit) are represented in Fig. 6 as a function ofReynolds number based on Dh for the eight fin spacing tested.Entrance and exit losses are not taken into account in the frictionfactor and have also been subtracted from the pressure. Thehydraulic diameter based of Re number does not correlate the jor f data as verified in Fig. 6. Δpt is the drag measured for the baretube banks of the identical geometry, without fins. Both Δp dropcontributions are analyzed at the same smallest area mass velocity.Fig. 7 graphically represents the fin friction factor calculated byEq. (1) plotted against the Reynolds number on the basis of thelongitudinal row pitch (PL) and the same j-factor. It can also beinferred from the graph that j-factor is essentially independent offin spacing and is a function of velocity in the minimum flow area.For all of the test geometry, the row pitch (PL) is kept constant.With the same mass velocity ð _mÞ the heat transfer coefficient ofthe bare tube banks is 40% greater as compared to the finned-tubebanks. With the exception of the closest fin spacing, the obtainedfriction correlation is convincingly good as can be seen in Fig. 7.
Fig. 6. The heat transfer and friction characteristics of a four-row plain plate heatexchanger for several fin pitches [98,99].
Fig. 5. LES: (top) streamline of the spanwise-averaged velocity field and contour plotsof the spanwise-averaged turbulent kinetic field (bottom) at several of P/D [93].
Fig. 4. The nomenclature staggered tube bundle configuration [88].
T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380 371
A questionable observation is made in the friction factor data ofsurfaces 7 and 8 as these surfaces show smaller j/f values than theother fins spacing. The j/f ratio usually increases as the fin spacingis decreased because the fractional parasitic drag associated withthe tube is lessened. Since all geometries tested maintained thesame PL and tube outside diameter. Therefore, Reynolds numberbased on themwould not have any significance. Fig. 7 is proof thatthe Reynolds number that is governed by hydraulic diameter willnot correlate the impact of fin pitch. To determine the effect of thenumber of tube rows on the j-factor, Rich [100] used similar heatexchanger geometry with 551 fins/m, in a study performed later.The average j-factor (smoothed data fit) for each heat exchanger asa function of Reynolds number can be seen in Fig. 8. The number ofrows in each coil is shown in the figure. The row effect variedinversely with Reynolds numbers, greatest at the low Reynoldsnumbers and negligible at RePL 45000. Many studies have beencarried out on plain finned-tube heat exchangers after [50,98–104]. Rich's observation that the j-factor shows negligible effect offin pitch was validated by these studies, but they do showappreciable row effect at low Reynolds numbers. It was reportedby Wang et al. [105] and Wang and Chi [106] that friction does notdepend on a number of rows. Borrajo-Peláez et al. [107] presenteda numerical study in 3D to compare both the air-to-water side andthe air-side model of a finned-tube heat exchanger. In theirsimulations, the effect of the pitch of fins on the heat transferand friction coefficients in the range between 0.75 and 4 mm wasstudied. The impact of fin pitches on the heat transfer for the
discrete smooth plate fin and tube heat exchanger at the air-sidewas studied experimentally [108]. They used in-line and staggeredfin alignments. The fin spacing was varied from 7.5 mm to 15 mm,the number of tube rows was 2–4, and the Re number was in therange of 500rRer800. The heat transfer factors (j) were around6.0–11.6% higher in the discrete type compared with a continuoussmooth plate finned-tube heat exchanger. An experimental studyof thermal and flow characteristics in finned elliptic tube heatexchangers with a tube eccentricity of 0.5 [107]. The isothermalfins condition and range of flow was 200rRer1500. The resultswere presented in the form of local and Nu numbers and frictionand Colburn j-factors.
4. Optimum spacing
The demand for an increase in energy has been rising in allfacets of society. The answer to this demand is intelligent use ofavailable energy. Utilization of available energy for optimization ofindustrial processes (exergy) has been the most popular researchtopic recently. This is owing to the extensive use of heat exchan-gers in industrial applications such as with tubes arrangements,finned and un-finned, refrigeration, serving as heat exchangers inair conditioners, heaters etc. Heat exchanging equipment in thesedevices has to be designed so they can be accommodated by thedevices which enclose them. Therefore, an optimized heat exchan-ger would provide maximum heat transfer for a given space [70].Such equipment should strike a balance between reduction in size,or in volume taken and maintenance or enhancement of itsperformance.
The design basis for choosing the spacing among the geometricadvantages of a group of fixed size (such as, area or volume) likethis that the overall thermal behavior between the tube array andfluid flow. Experimental investigation of heat exchangers withfinned elliptical tubes, as carried out by [50,109,110], shows arelative pressure drop reduction of up to 30% with the relative heattransfer gain observed in the elliptical arrangements whenweighed with the circular ones. A hybrid mathematical modelfor finned circular and elliptic tubes arrangements was formulatedby Rocha et al. [111]. This model is based on energy conservationand heat transfer coefficients achieved from an experiment ofnaphthalene sublimation through a heat and mass transfer ana-logy [112,113]. Fin temperature and fin efficiency in one and tworow elliptic tube and plate fin heat exchangers are obtainednumerically. A relative fin efficiency gain of up to 18% was detectedwith the elliptical arrangement when fin efficiency results forplate fin and circular tube heat exchangers were compared withthe outcomes of Rosman et al. [114]. The optimal plate-to-platespacing and maximum overall heat conductance for laminarforced convection were studied by Bejan and Sciubba [115]. Theyused two boundary conditions applied on the surfaces of the plate:both uniform heat flux and uniform temperature. The Prandtlnumber was in the range of 0.71rPrr1000. They found that theoptimized space between the plates is proportional to the pressurehead (Δp) the upped to the power (�0.25), plate length L0.5, andproperty set (μα)0.25. The maximum overall thermal conductance isproportional to (Δp)0.5. Cooling was performed by the use offorced convection, the previous studies containing the results ofoptimum spacing between parallel plates [116] and plates withcylinders [42,60]. Jubran et al. [117] carried out an experimentalinvestigation of the influence of shroud clearance, wasting pins,and fin pitch on the heat transfer coefficient with circular pin finsin both in-line and staggered configurations. The researchersfound a small and a powerful influence of the wasting pins inthe in-line and staggered arrangements, respectively. On the otherhand, they found the optimum spacing between the fins in both
Fig. 7. The graphing of the j factor and fin friction with RePL [98,99].
Fig. 8. The mean coefficients of heat transfer for plain plate-finned tubes (571 fins/m) having on to six rows. Same geometry dimensions as Fig. 6 [99,100].
T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380372
streamwise and spanwise directions regardless of which shroudclearance and arrangement type was used. Later, previous workwas extended by Bejan [118], who confirmed the optimal spacingbetween tubes. He explained that this optimal spacing decreaseswith the Prandtl number as well as the pressure drop andincreases with the bundle length. The experimental and numericalresults for optimal spacing with the maximum thermal conduc-tance are explained and correlated analytically by intersecting thesmall-spacing and large-spacing asymptotes of the thermal con-ductance function [119]. The optimal spacing between tubes withcooling by free convection [120]. Matos et al. [121] carried out anumerical study of the heat transfer characteristics of air flow overa circular and elliptical tube heat exchanger using the finiteelement method. The staggered configuration was used for thetube arrangement. The Reynolds numbers defined for the para-meter of the characteristic length ranged from 300 to 800. Theirresults showed that there was a relative gain of 13% for the heattransfer and a pressure drop reduction of up to 25% with theelliptical tube. In addition, they reported the results of the circularand elliptical tubes with the same construction area for the flow.Matos et al. [122] extended the previous work in 3D numerical andexperimental investigations. The two Reynolds numbers based onthe swept length (Re) are 852 and 1065. The main results obtainedby this study are that there is a gain in heat transfer (thermalconductance) of up to 19% and a reduction in relative materialmass of up to 32% in the optimal elliptic tubes configurationcompared with the optimal circular tubes configuration. Theresults of the finned tube optimization for experimental andnumerical at e¼0.5 with regard to eccentricities and spacebetween tubes, as is illustrated in Fig. 9. Fig. 10 shows the
temperature distribution on fin for plate finned-tube heat exchan-gers with four tube rows for circular and elliptic tube. Investiga-tions and improvements of the traditional circular tube banks havebeen found by many different numerical methods and CFD codesin both the laminar and the turbulent regime. Design optimiza-tions of heat exchangers were found for the size of tubes withspacing and arrangements by different algorithms [123–126].Fig. 11 shows some perceptions of the temperature and flow fieldsof design for the optimal design number 894 [126]. Mainardeset al. [127] experimentally studied the reduction of the powerpumping required to supply air over finned circular and elliptictube banks. Their results were presented for Reynolds numbersdefined in the small axis of the ellipse varying between 2650 and10,600. Tube pitches of 0.25rPT/2br0.6 and eccentricities ran-ging from 0.4 to 1.0 were used. They found a reduction in thepumping power of around 5–10% with the optimal elliptic tubeconfiguration compared with the circular tube configuration.
5. Correlations of thermofluids
Based on the relevant data available until 1933, Colburn [128]suggested a simple correlation for flow and heat transfer instaggered tube banks as follows:
Nu¼ 0:33� Re0:6Pr1=3 ð2ÞThis correlation is used with 10 or more tube rows in the
direction of flow in a staggered configuration and for10oReo4�104. The characteristics of heat transfer for both in-line and staggered tube bank configurations were studied experi-mentally by Grimison [129]. Based on a correlation of the empiri-cal results of several researchers, a correlation is given as follows:
Nu¼ C � Ren ð3Þ
Fig. 10. The temperature distribution on fin for plate fin heat exchangers with four-row tubes. (a) S/2b¼0.5, e¼1, ϕf ¼ 0:006 and ReL¼852; (b) S/2b¼0.5, e¼0.5, ϕf ¼ 0:006and ReL¼852 [122].
Fig. 11. Perceptions of the temperature and flow fields of design 347 forΔTper¼13.48 K, ΔPshell¼25.40 Pa/m [126].Fig. 9. The experimental and numerical for finned configurations [122].
T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380 373
For the empirical correlation above, only the air flow can beused; it works well for ten or more rows in a deep. For a rownumber of less than 10, Kays and London [109] developed itscorrection by giving a factor C2, defined as follows:
C2 ¼hNR
h10ð4Þ
where hNR and h10 are the coefficient of heat transfer for NR rows(fewer than 10) and 10 or more rows; thus the rewritten equation(3) gives
Nuj NR o10ð Þ ¼ C2 � Nuj NR Z10ð Þ ð5ÞThe correlation constants of C, C2, and n are contained in the
form of tables in most textbooks on heat transfer (e.g.,[44,129,130]) for both in-line and staggered configurations. Gri-mison [129] also used the second way to obtain the followingexpression:
Nu¼ 0:32� Fa � Re0:61Pr0:31 ð6Þand provided graphical values for the tube configuration factor (Fa)obtained by Grimison [129] with changes in the value of the Renumber for dimensionless longitudinal and transverse pitches.A slight modification of the above Eq. (4) was done by Hausen [131],who offered a new correction for Fa in place of the graphicrepresentation by Grimison [129] for the staggered configuration
Nu¼ 0:35� Fa � Re0:57Pr0:31 ð7Þwith
Fa ¼ 1þ0:1� PLþ0:34PT
ð8Þ
for in-line configuration
Nu¼ 0:34� Fa � Re0:61Pr0:31 ð9Þwith
Fa ¼ 1þ PLþ7:17PL
�6:52� �
0:266
PT �0:8ð Þ2�0:12
( )1000Re
� �1=2
ð10Þ
Additionally they used the isothermal boundary condition byKhan et al. [62], which was modified slightly by Grimison'sequation [129] and employed the analytical solution for the heattransfer in a tube bundle; the correlation is given by
Nu¼ Ca � Re1=2Pr1=3 ð11Þcan be employed with for the in-line configuration
Ca ¼ 0:25þexp �0:55� PLð Þ½ � � P0:212L P0:285
T
for the staggered configuration
Ca ¼0:61� P0:053
L P0:091T
1�2� exp �1:09� PLð Þ½ �Generally, we want to know a Nu number for the whole tube
bundle containing 16 or more rows. Žukauskas [10] suggested anempirical correlation of the form
Nu ¼ C � C1 � RemPrn ð12ÞThe correlation constants C, m, and n, and the parameter C1 are
contained, in the form of tables, in most textbooks on heat transfer(e.g., [129,130]) for both in-line and staggered configurations.Further information can be found in Ref. [132]. They displayed themeasurement values of the heat transfer in the empirical correla-tions. For both in-line and staggered configurations, Grimison [129]correlated the measurements for each test done by Huge [133] andPierson [134]. This empirical correlation was related to the tubebundle for 10 or more tube rows in the direction of flow. The experi-mental study of air flow over an in-line tube near a wall was pre-sented by Aiba [135]. The Reynolds number ranged from 0.8 × 104
to 4 × 104, and the clearance ratio (c) distance between wall andtube centre was varied from 0.05 to 4.0. The longitudinal pitch (PL)ratio between the centre-to-centre tube-to-tube diameter rangedfrom 1.2 to 4.4. The correlation of the overall Nusselt numberresulted in the agreement is:
Nu¼ 0:103� Re0:74PL
D
� ��0:12 cD
� �0:23ð13Þ
The deviation of correlation above about 75% in the ranges ofPL/D¼1.2–3.2, c/D¼0.18–0.16, and Re¼0.8�104–4�104. The endcorrelations are worth to the heat exchanger design of a singletube row near to the wall shell with the convection type of heattransfer.
McQuiston [101], Gray and Webb [136], Kim et al. [137], andWang et al. [138] formulated the correlations to predict the j and ffactors versus Reynolds number for plain on staggered tubearrangement. Figs. 6 and 7 show the data of Rich [98,100] thatthe McQuistion correlation is based on, including three otherstudies. In addition to the data from two more researchers, thesame data was used by Gray and Webb [136]. Even though theheat transfer correlations from McQuiston [102] and the Gray andWebb [136] are similar in accuracy, the friction factor from Grayand Webb [136] is far more accurate.
The heat transfer from Gray and Webb [136] for four or moretube rows of staggered tube geometry is
j4 ¼ 0:14� ReDð Þ�0:328 pFDo
� �0:031 PT
PL
� ��0:502
ð14Þ
The assumption made in Eq. (14) is that the fourth rowstabilizes the heat transfer coefficient, so in case of more thanfour tube rows and less than four; the j-factor is governed by thecorrelation as shown on the data in Fig. 8. It is represented by:
jNR
j4¼ 0:991� 2:24� ReDð Þ�0:092 NR
4
� ��0:031" #0:607� 4�NRð Þ
ð15Þ
The McQuiston [101] correlation gives results similar to that ofthe correlation obtained from Eqs. (14) and (15) 89% of the data for16 heat exchangers was correlated within 710%. The first of thetwo terms assumed by the Gray and Webb [136] friction correla-tion for the pressure drop to be composed of, is the drag force onthe fins. While discussing Fig. 8, its model was laid down. Eq. (16)gives the friction factor of the heat exchanger
f ¼ f FAF
Aþ f F 1�AF
A
� �1� tF
pF
� �ð16Þ
Friction factor associated with fins can be determined by
f F ¼ 0:508� ReDð Þ�0:521 pFDo
� �1:318
ð17Þ
Correlation for flow normal to a staggered bank of plain tubesgives the friction factor related to the tubes (ft). In order tocalculate the tube contributions (Δpt) the Žukauskas [10] tubebanks correlation were used by Gray and Webb [136], alsopresented in Incropera et al. [130]. The finned-tube exchangerhas the same mass of data velocity ð _mÞ at which ft is calculated.95% of the data for 19 heat exchangers was correlated by Eq. (16)within 713%. The equation can be applied to any number of tuberows. Although a fiction correlation was developed by McQuiston[101] for the same data, it has significantly high error limits, þ167/–12%. The dimensionless parameter employed in the develop ofGray and Webb correlation in the ranging of 1.97rPT/Dor2.55,1.7rPL/Dor2.58, 0.08rpf/Dor0.64, and 500rReDr24700. Intheir recent work, Seshimo and Fujii [139] tested 35 heat exchan-gers, having methodically varied geometric parameters to givemore generalized correlation for staggered banks of plain fins with
T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380374
one to five tube rows. Three tube diameters (6.35, 7.97, and9.52 mm) were used with the multi-row designs using an equi-lateral triangular pitch. Four fin densities, from 454 to 1000 fins/mwere considered for obtaining data. One-row designs with thedifferent transverse tube pitch and fin depth prove that using anentrance length parameter the one-and two data may be sepa-rately correlated. Reynolds number (ReDvh
) defined in the term ofthe volumetric hydraulic diameter (Dvh) and was used to correlatetheir data. Volumetric hydraulic diameter can be computed by
Dvh ¼4AAmL ð18Þ
where AmL is the total volume of the exchanger minus the volumeof the tube banks.
The entrance length parameter used to correlate one-and two-row data is: χþ
Dvhffi ReDvh
Pr � Dvh=L. The correlations are given by
Nu¼ 2:1� ðχþDvh
Þn ð19Þ
f � L� Dvh ¼ c1þc2 � ðχþDvh
Þ�m ð20Þ
The constant parameters for Eqs. (19) and (20) tabulated inTable 2.
Vortex shedding from the tubes proved to be an importantfactor as these entrance length based correlations for three ormore rows failed over entire Reynolds number range 200oReDho800. Using conventional Nu number and Reynolds number(ReDh) and flow based on the smallest flow area, data werecorrelated for ReDh4400. The one-row variant of Eqs. (19) and(20) correlated the data for one to five rows for ReDho400. Tubediameters as small as 5.0 mm is used in a certain window airconditioner, which goes to show that the tube diameter used infinned-tube heat exchangers is decreasing. Kim et al. [137]included data from Wang and Chi [138] for heat exchanger having7 mm diameter tubes to revise the correlation from Gray andWebb [136]. For tube diameters larger than 7 mm, the Kim et al.[137] correlation calculated the data with comparable accuracy asobtained by Ref. [134]. It was an appreciable improvement for the7 mm tube data. Tube diameters as small as 6.7 mm were used byWang et al. [138] to develop another general correlation. Compar-isons were drawn between Kim et al. [137] and Wang et al. [138]correlations at ReD¼2500 for 1rNRr3, 1.3rpfr3.0 mm. Thepredicted j-factor by Kim et al. [137] for heat exchangers having9.5 mm-OD tubes, are in line with those by Wang [140] correlationwithin 710%. Approximately the same j-factor for NR¼3 wasobtained for the 7 mm tube configuration, for the two correlations.However, the difference varied inversely with the row number. Ahigher friction factor is predicted by Kim et al. [137] correlationthan Wang et al. [138] correlation. For three or more tube rows,the Kim et al. [137] correlation is
j3 ¼ 0:163� Redð Þ�0:369 pFDo
� �0:0138 PT
do
� �0:13 PT
PL
� �0:106
; NRZ3 ð21Þ
jNR
j3¼ 1:043� ReDð Þ�0:14 pF
Do
� ��0:123 PT
Do
� �1:17 PT
PL
� ��0:564" # 3�NRð Þ
; NR ¼ 1;2
ð22Þ
f F ¼ 1:455� ReDð Þ�0:656 pFDo
� ��0:134 PT
Do
� �1:23 PT
PL
� ��0:347
ð23Þ
Kim et al. [137] correlation was used by Jakob [141] for thefriction factor due to tubes, ft, which is shown by
f T ¼π
40:25þ 0:188
ðPT=DoÞ�1� �1:08 ReDð Þ�0:16
( )� PT
Do�1
� ð24Þ
The friction factor of the heat exchanger is calculated byEq. (16).
Another numerical correlation was suggested by Zhang and Li[142] for estimation of the Sherwood number and friction lossaccording to a wide assortment of bank geometries and workingconditions. The average Sherwood number and friction factorcorrelation was as follows:
Sh ¼ c � RenSc0:333
f ¼ c � Ren
)ð25Þ
The correlation parameters c and n are tabulated in Table 3.The number of tube rows is more than 10 and the range of
Reynolds numbers of these correlations is 100–500. These correla-tions have an accuracy of more than 98% for numerical data. Xieet al. [63] presented numerical corrections for the Nusselt numberand friction factor of the air-side fin-and-tube heat exchangers.The correlations were validated in the ranges of 0.67ru1r4.0,16 mmrDor20 mm, 2 mmrpfr4 mm, 32 mmrPTr36 mm,38 mmrPLr46 mm, and 1�103rRer6�103. These correla-tions are more accurate and authoritative which was developedfrom Wang et al. [138] for extensive ranges of validation. TheNusselt number correlation is defined as
Nu¼ 1:565� Re0:3414 NR �pFDo
� ��0:165 PT
PL
� �0:0558
ð26Þ
Elsewhere, the friction factor correlation is given by Eq. (2.26)
f ¼ 20:713� Re�0:3489 NR �pFDo
� ��0:1676 PT
PL
� �0:6265
ð27Þ
The mean deviation between the predicted and numericalvalues was around 3.7% and 6.5% in the Nu number and fcorrelations, respectively. Numerical and experimental methodsfor finding the coefficient of heat transfer in heat exchangers withextended fins were studied recently by Taler [143]. He used thenon-linear regression method to determine the Nusselt number onboth the water-and the air-side. On the other hand, the authorused the Levenberg–Marquardt method to calculate the lower
Table 3The correlations constant for Eq. (25) [142].
T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380 375
value of the sum of squares error. Further correlations which areavailable are summarized in Table 4.
6. Flat tube and other shapes
In this section, shows the focus reviews of research in the flattube and other tube shapes (i.e., came, wing). The flat tube has twodiameters small and large diameters called are transverse andlongitudinal, respectively. Both in-line and staggered configura-tions of finned flat tube heat exchanger are presented in Fig. 1(c)and (d).
6.1. In-line and staggered configurations
There is a little previous literature on the heat transfer and fluidflow over the banks of flat tubes, excluding the contemporarystudies of [153–157]. Bahaidarah et al. [158] carried out a numer-ical investigation of steady, laminar, incompressible, 2D flow overa flat tubes bundle. They used both an in-line and a staggeredarrangement and calculated the best configuration from the view-point of the heat transfer. Benarji et al. [153] presented the resultsfor a 2D, incompressible, and unsteady flow over the in-line andstaggered flat tube arrangements under isoflux and isothermalboundary conditions. From the standpoint of heat transfer, the in-line arrangement shows better performance than the staggeredarrangement in most of the cases. However, the values of dimen-sionless pressure drop are higher in the staggered arrangementcompared with the in-line arrangement. Tahseen et al. [159] have
a numerical studied of the heat transfer for air flow over a twostaggered flat tube configuration. They have shown the effect of Renumber on the heat transfer coefficient. They results show that theheat transfer coefficient increase with an increase of Re numberalways. In the following year, Tahseen et al. [160] carried outanalyzed numerically the thermal and fluid characteristics of airflow in an in-line flat tube bundle configuration. They used theneuro-fuzzy inference system (ANFAS) model to predict values ofheat transfer coefficient and pressure drop. They examined thetransverse pitches from 1.5 to 4.5 with interval 1.0, and threelongitudinal pitches are 3, 4 and 6, for the Re number ranging from10 to 320. They results were presented in the forms Nu number,dimensionless pressure drop, streamline and temperature con-tours. The key results from this study that the average deviationbetween the numerical and ANFIS model values for Nu number is1.9%, and the dimensionless pressure drop is 2.97%. Webb andIyengar [161] carried out an experimental study of finned-tubeheat exchangers with both oval and circular tubes and comparedthem from the standpoint of the air-side performance. The valuesof the heat transfer coefficient are approximately equal in bothcircular and oval tubes heat exchangers. However, the pressuredrop was lower than 10% in the oval tube compared with thecircular tube heat exchangers. The heat transfer and pressure dropof staggered flat tube banks were studied experimentally. Numericalstudies of flow and heat transfer in a heat exchanger with staggeredconfiguration were carried out for circular and wing-shaped tubes[162], circular, elliptic, and wing-shaped tubes, [163], and circularand elliptic tubes [164]. They used transient numerical simulationsof the flow and heat transfer. The results of all studies are shown in
Table 4Details more correlations with condition and geometry parameters.
T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380376
the form of the average drag coefficient (Cd) and average Stantonnumber (St). They found higher values of Cd and the St number incircular tubes, whereas the difference between the values of Cd wassmall at a large hydraulic diameter as well as St number. Wang et al.[165] carried out numerical and experimental studies to obtain theperformances of heat transfer in a finned flat tube heat exchanger.In the numerical part, they used the two boundary conditions onthe fin walls. The first uniform temperature and the secondconjugate numerical method. They found that the deviation in theaverage heat transfer coefficient obtained from the two ways ofboundary conditions is higher than 5% for a fin efficiency of lessthan 80%, whereas the deviation is less than 5% for fin efficiencyhigher than 80%, but the appropriate choice is the conjugatemethod. They claimed that the reported results provide a standardto help researchers to select an appropriate numerical method forfinding the fin style in a more reliable and efficient way.
6.2. Tubes array between parallel plates
A Heat Exchanger Module (HEM) was used to obtain thedistribution of temperature and heat transfer over a series ofcircular tubes confined between parallel plates in a numerical studycarried out by Kundu et al. [166]. Three Reynolds numbers weretested: 50, 200, and 500, with three pitches between plates (H/D)and tube pitches (L/D). The values of H/D were 1.5, 2.0, and 3.0, andthose of L/D were 2.0, 3.0 and 6.0. They found that the bulktemperature rose almost linearly from one HEM to another HEMfor an equal rate of heat transfer from all modules for the case offully developed flow. In the same year, they studied the pressuredrop and heat transfer [167]. In the following year, Kundu et al.[168] conducted an experimental study of the pressure drop andheat transfer for laminar and turbulent flow over a series of in-linecircular tubes confined to a parallel plates channel within the rangeof 220rRer2800. They compared the numerical results with thedata of laminar flow. The results presented were in reasonably goodagreement. In a more recent review, Bahaidarah et al. [169]developed a numerical model of the flow past in-line tubes incircular, oval, flat, and diamond arrays between parallel plates at therange of Reynolds numbers of 25–350. Their results show that theheat transfer rate is lower in the diamond tubes for all Reynoldsnumbers. For Reo50, the flow and geometry were key factorsinfluencing the heat transfer performance, while at Re450 thegeometric shape has a significant influence on the performance.Similar numerical study for flat tube carried out by Tahseen et al.[170] using the finite volume method for solve the continuity,momentum and energy equations with the used body fittedcoordinates (BFC) to be transformed from the physical domain tothe computational domain. The Re number varies within the rangeis 25–300, and three longitudinal pitches of 2–4 at the Pr numbertaken of 0.7. Jue et al. [171] studied the flow and heat transfercharacteristics of a cross-flow of three heated cylinders arranged inthe form of an isosceles triangle confined between two parallelplates. They used the finite element method to solve the continuity,momentum, and energy equations. The average changes in the dragcoefficient and the time Nu number around the surface of threecylinders were investigated in each cylinder. The calculation wascarried out with 100rRer300 and 0.5rgap/diameterr1.25.
7. Future work
Flat tubes are vital components in various technical applicationslike modern heat exchangers, automotive radiators, automotive airconditioning evaporators, and condensers. In comparison to theround tube heat exchangers, flat tube heat exchangers are expectedto have smaller air-side pressure drop and improved air-side heat
transfer coefficients. For the above reasons, the optimum spacing (e.g., tube-to-tube, fin-to-fin) with the maximum overall heat conduc-tance (heat transfer rate) and minimum pressure drop needs morefocus and research in the future. In addition, more works are neededto develop the thermofluid correlations in tubes of this shape.
8. Conclusions
A comprehensive literature survey on plain plate finned andun-finned tube heat exchangers with many shapes of tubes (e.g.,circular, elliptic, flat) has been provided. The work focused on andpresented the thermofluid characteristics of heat exchangersdepending on several parameters: external fluid velocity, tubeconfiguration (in-line/staggered, series), tube spacing, fin spacing,shape of tube, and so on.
The main conclusions of this review are summarized as follows:
� All studies (analytic, numerical, and experimental) show thatthe heat transfer coefficient and pressure drop increase withincreased external velocity of fluid.
� Few studies focused on the effect of tube diameter in a circulartube while many researchers studied the effect of the axis ratioin an elliptic tube on the thermal and fluid flow characteristics.
� The staggered configuration shows the high heat transfer coeffi-cient compared with the in-line configuration for finned and un-finned tube heat exchangers regardless of the tube shape.
� The heat transfer coefficient and pressure drop increase withincreased fin density.
� Many researchers have shown the effect of transverse tube pitchon the heat transfer coefficient and pressure drop, and all studiesshow that the heat transfer and pressure drop increase as thetransverse tube pitch decreases for finned and un-finned tubeheat exchangers with in-line and staggered configurations.
� Based on this review and previous studies published in theliterature, one can infer that the form of the tube and the orderhave a significant effect on heat transfer.
� This current review is very useful in terms of enhancing thethermal and fluid flow characteristics and development of thecorrelations for thermofluid characteristics in heat exchangers.
� In future works, further research needs to be carried out todevelop the correlations for heat transfer and fluid flow in tubebanks heat exchangers with the flat tube shape.
� Finally, the optimum design (tube-to-tube and fin-to-fin spacing)in a flat tube heat exchanger needs more work and more focus.
Acknowledgments
The authors would like to gratefully acknowledge the UniversitiMalaysia Pahang for the financial support under Project no.RDU120103.
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