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Renewable and Sustainable Energy Reviews 43 (2015) 363–380

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

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 Faculty of Mechanical Engineering, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia c Automotive Engineering Centre, Universiti Malaysia Pahang, 26600 Pekan, Pahang, Malaysia b

art ic l e i nf o

a b s t r a c t

Article history: Received 23 November 2013 Received in revised form 29 August 2014 Accepted 22 October 2014 Available online 27 November 2014

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.

Keywords: Heat exchanger Flat tube In-line/staggered configurations Optimum spacing Thermofluids characteristics

Contents 1. 2. 3.

4. 5. 6.

7. 8.

n

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background of tubes bank. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow and geometric parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. External velocity of fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Tube diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Tube rows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Tube pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Fins pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimum spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Correlations of thermofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flat tube and other shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. In-line and staggered configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Tubes array between parallel plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Corresponding author. E-mail addresses: [email protected], [email protected] (T.A. Tahseen). 1 Tel. þ 609 424 2246; fax: þ 609 424 2202.

http://dx.doi.org/10.1016/j.rser.2014.10.070 1364-0321/& 2014 Elsevier Ltd. All rights reserved.

364 364 369 369 370 370 370 371 372 373 376 376 377 377 377

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Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

1. Introduction There has been a significant amount of research work carried out to improve the efficiency of heat exchangers. The reason for these efforts is that heat exchangers have a widespread use in industrial, transportation as well as domestic applications such as thermal power plants, means of transport, heating and air conditioning systems, electronic equipment and space vehicles [1]. Because of their extensive use, increase in their efficiency would consequently reduce cost, space and materials required drastically [1,2]. The aforementioned research work includes a focus on the choice of working fluids with high thermal conductivity, selection of their flow organization and high effective heat transfer surfaces constructed from high-conductivity materials. This paper shows a general review of the heat transfer and fluid flow characteristics of a tube banks heat exchanger and discusses the effect on the thermofluid characteristics of several parameters: the frontal velocity of fluid, tube diameter, tube configuration, tube rows, tube spacing, fin spacing, and tube shape. The optimum tube-to-tube and fin-to-fin spacing with the maximum heat transfer rate and minimum pressure drop also presented. A highlight

the most important of the correlations for heat transfer and fluid flow in a tube banks heat exchanger is provided. The other specific shapes (flat tube) and confinement of the tube between parallel plates are outlined were reviewed. The shows and describes the gaps in the research which may be considered by new studies and suggests future work. Finally, presents the significant conclusions. All sections presented for tube configuration with finned and unfined tube bundle.

2. Background of tubes bank The general configurations of un-finned and finned tube banks heat exchangers were presented in Figs. 1 and 2. Both in-line and staggered configurations of tube as well as the circular and flat tubes shape. In general, one fluid flow over the tubes array, while a other fluid at the different temperature moves through the tubes. The rows of tube at the in-line and staggered arrangements in the flow direction of fluid (i.e., inlet velocity of air u1) as shown in Fig. 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 flat tubeand (d) Staggered flat tube.

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Nomenclature a A AcF AF Ano Ar Cd CFD D Dh Do Dvh fF fT e H k NR pF PL PT tF SF W

air overall surface area of heat transfer (m) cross-section flow area (m2) surface area of fin (m2) surface area of outside tube without fin (m2) elliptic tube minor-to-major axis ratios drag coefficients computational fluid dynamics tube diameter (m) hydraulic diameter (m) outside diameter of tube (m) volumetric hydraulic diameter (m) fins friction factor tubes friction factor ellipses eccentricity e ¼b/a fin spacing (m) thermal conductivity of fluid (w/(m k)) number of tube rows in flow direction fin pitch longitudinal tube pitch transverse tube pitch fin thickness, m spacing between two fins¼ pF 1 (m) ratio of heat transfer area of a row of tubes to frontal free flow area

Dimensionless group Bi Eu

j Nu NuZ Nu Re Sc Sh Sh St Pr

365

Colburn factor Nusselt number Nusselt number predicted by Žukauskas correlation average Nusselt number Reynolds number Schmidt number Sherwood number average Sherwood number Stanton number Prandtl number

Greek symbol q~ n;m _ m ΔT per ϕf ΔP ΔpF ΔpT ρ

maximum dimensionless overall thermal conductance mass velocity (kg/m2 s) temperature increase along the periodic length dimensionless fin density in z-direction pressure drop per unit length pressure drop associated fin area in finned-and-tube heat exchanger (Pa) pressure drop associated tubes in finned-and-tube heat exchanger (Pa) density (kg/m3)

Subscribers a f o to

air fluid out tube out side

Biot number Euler number

of tube such as d, for circular tube and transverse tube diameter of flat tube as well as by the longitudinal pitch, P1 and transverse pitch, P2 the distance between centers of tube. Beale and Spalding [3] carried out a numerical investigation of transient incompressible flow in in-line square, rotated square, and staggered tube banks for the Re number range of 30rRer3000 and ratio of pitch to diameter of 2/1. The drag lift, pressure drop, and heat transfer coefficient were calculated. A calculation procedure for a 2D elliptic flow is applied to predict the pressure drop and heat transfer characteristics of laminar and turbulent flows of air across tube banks. The theoretical results of the model are compared with previously published experimental data [4]. A 2D numerical study of the laminar steady state flow in a circular tube banks heat exchanger was carried out for low Reynolds number numbers [5,6]. The flow in a bundle of elliptical cylinders was investigated both numerically and experimentally [7,8]. The momentum and energy equations have been solved by using a finite difference method. The effect of the Nusselt number on the surface of the tube was recorded by Juncu [9]. The importance of heat transfer and fluid flow appearances of tube banks 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 circular tube banks have been done previously. The numerical analysis of laminar forced convection in a 2D steady state in the circular cylinder banks of a tube in square and non-square in-line arrangements. The study shows that the highest heat transfer rate occurs at the first tube compared with the other tubes. In addition, the pressure drop increases significantly as the transverse pitch-todiameter ratio is reduced [17].

Numerical studies over a 3D multi-row plate fin heat exchanger were carried out of late by Jang et al. [18] The results showed staggered arrangement to yield a pressure drop 20–25% higher than the in-lined arrangement. The staggered arrangement also gave an average heat transfer coefficient that was 15–27% higher than the in-lined arrangement. It was the first study to have given numerical solutions and experimenting with realistic geometry and the inlet-outlet conditions for the real multi-row (1–6 rows) plate fin-and tube heat exchangers. The entire computational domain (1–6 rows) from fluid inlet to outlet was solved directly. There are certain limitations as it only takes into account the laminar flow range, where the flow is in the range of 60 rRe r900, even though the study has performed a three-dimensional simulation for a real multi-row plate-fin heat exchanger. The effect of airflow rates and average particle diameters on thermofluid characteristics in the tube banks in both in-line and staggered configurations for gas-particle flow were studied experimentally by Murray [19]. The results showed that the local and average Nusselt numbers for the flow with particles can lead to enhanced thermofluid characteristics; also the results depend on the particle size and Reynolds number for in-line and staggered arrangements. The author also found that the performance of heat transfer in the in-line configuration is more suitable compared with the staggered configuration tube bundle for most flow cases. Lu et al. [20] presented the influence of geometric parameters such as tube pitch, fin spacing, and tube diameter on the coefficient of performance (COP) and the ratio of heat transfer rate to pressure drop (Q/ΔP). The authors found the optimum value of the pressure drop by using a numerical simulation. Fiebig et al. [21] employed the finite volume technique to calculate the

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Fig. 2. The configurations of round tube banks heat exchanger (a) in-line (b) staggered, and (c) side view. (adopted from [99]).

conjugate heat transfer and flow characteristics in 3D in a flat plate finned-tube heat exchanger. Using a fixed geometry, the patterns of flow, distribution of pressure, heat flux distribution, heat transfer coefficient distribution, and fin efficiency versus the Reynolds number. The downstream fin is much less efficient than

the upstream fin. The finite conductivity in the wake behind the tube caused the reversal of heat transfer. The steady-state laminar incompressible flow across a tube bundle was investigated and the finite element method was introduced and applied to solve the 2D and 3D energy equation and Navier–Stokes equations [22,23].

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Tremendous efforts were made to develop the numerical simulations used to predict the fluid flow and heat transfer in tube banks. The many previous studies using an in-line configuration by

367

Krishne Gowda et al. [24], Mavridou and Bouris [25], a staggered configuration [26–28], and both in-line and staggered configurations [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 1 Effect of the flow and geometric parameters on the thermofluids characteristics. Researcher

Type Re number and velocity range

Tube shape

Geometric parameter

Tutar and Akkoca [43]

N

Cir

0.116r pf r 0.365

Jang and Yang [50]

Nþ E 2 m/s ru r7 m/s

600r Rer 2000

 The small effect of the number of tube rows on the coefficient of heat transfer when the number of multi-rows NR 44.  The pressure drop increased with an increase in the number of rows from 1 to 4 for both in-line and staggered configurations.

E

4  103 r Rer 1  104

Cir. Elp. Cir Cir.

Cir.

4-rows axis ratio 2.83:1

OD ¼ 10.2 mm, pf ¼ 3.5 mm

OD ¼ 18 mm, pf ¼ 3.1 mm, PL ¼34 mm, PT ¼ 42 mm

 Pressure drop reduction by 25–30%.  Heat transfer coefficient increased by 35–50%.  Heat transfer coefficient was 14–32% higher in the staggered configuration compared with the in-line configuration  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.  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.

1  103 r Rer 11  103

Hasan [54]

E

Ibrahim and Gomaa [55]

Nþ E 5.6  103 r Rer 4  104

Simo Tala et al. [56]

N

Re ¼1050, and 2100

Elp.

2r Ar r4

 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

Elp.

0.25 r Ar r1.0

 The better thermal performance with smaller Re number and Ar.  The heat exchanger employing elliptic tube arrangement contributes significantly to the energy conservation.

Cir. Elp.

e ¼1.0 (circular); e ¼0.7 and e¼ 0.5

 The increase of thermal-hydraulic performance of above 80% were obtained with a reduction in the tube ellipticity compared with a circular shaped tube.

 The reduction of the thermal and viscous irreversibilities respectively down to 15% and 50% was observed in the modified shapes when compared to circular ones.

Yan and E Sheen [57] Halici et al. E [58] Kim et al. E [59]

300r Rer 2000

Cir.

0.9 m/sr ur 4 m/s

Cir.

550 r Rer 1200

Cir

Yoo et al. [60]

7.7  103 r Rer 30.3  103

E

Cir

PL ¼19.05 mm; PT ¼ 25.4 mm; Pf ¼ 1.4, 1.69, and 2.0 Row no. ¼1–4

 The Δp~ increased with increases in the number of tube rows for the same frontal air velocity.  The increase in the number of tube rows leads to a decrease in the Colburn j and friction factors.

PL ¼27, 30, and 33 mm mm pf ¼ 7.5, 10.0, 12.5, and 15.0

 The staggered fin and tube configurations enhance the performance of heat transfer by 7% and 10%, respectively, compared

PL ¼PT ¼ 1.5, 1.75, and 2.0

 The Nu number increases by more than 30% and 65% on the second and third tubes, respectively, compared with the

to the in-line fin configuration.

 The heat transfer performance decrease with increase of tube number.

first tube.

 The local heat transfer coefficients on each tube increase except on the front part of first tube as the tube spacing decreases.  The results were shown in the form of the friction coefficient, pressure drop, and coefficient of heat transfer.

Beale and Spalding [61] Khan et al. [62].

N

100r Rer 1000

Cir

1.25 r p/D r2.0

A

1  103 r Rer 1  105

Cir

PL ¼20.5, and 34.3 mm PT ¼ 20.5, and 31.3 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.

Xie et al. [63].

N

1  103 r Rer 6  103

Cir

32 mm r PL r 36 mm, 19 mm rPT r23 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.

Ramana et al. [64]

E

200r Rer 1500

Cir

PL ¼PT ¼ 2.0

 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.

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Ay et al. [51] E 0.5 m/sr ur 7 m/s Paeng et al. Nþ E 1082 r Re r1649 [52] Tang et al. [53]

Finding

N

A: analytical study; Cir: circular tube; E: experimental study; Elp: elliptic tube; and N: numerical study.

 The heat transfer increases with increasing ellipticity of the tubes. However, the pressure drop is significantly reduced by both increasing tube ellipticity and decreasing density of fins. PL ¼35, and 38 Cir mass flow rate used in all of the models is 1.904  10  5 kg/s

 The addition of fins leads to enhanced heat transfer but causes an increase in the pressure drop. 0.4 r pf r 5.0 Cir. N

Sheui et al. [68] Erek et al. [69]

0.3 ru r2.0

 The heat transfer ratio of tube surface to fin was still o 10%.  The fin efficiency and fin temperature depend slightly on the fin parameters. Elp. N Chen et al. [67]

100r Rer 500

the maximum Nu number is the without-uniformity temperature on the wall fin and tube wall.

 The impact of transverse pitch in the higher Reynolds numbers the drafting of the traditional heat transfer.  Increase space of the longitudinal for the uniformly distributed cylinders will strengthen the total heat transfer. Otherwise, 3.0 r PT r 7.0 Cir. N Lee et al. [66]

500r Rer 2000

 For Reo 14100, the large local Nusselt number takes place at the leading edge (e.g., P/b¼ 0.0).  For Re4 14100, the maximum value of the average Nusselt number enhancement ratio is nearly about 2.0. Nþ E 4000r Rer 45570 Berbish [65]

Elp.

1.5 r PL, PT/br 4.0

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used computational fluid dynamics (CFD) to simulate the flow and thermal characteristics of plate un-finned and finned-tube heat exchangers. All of them aimed to compare the heat transfer and flow characteristics in 2D and 3D heat exchangers with finned or un-finned tubes for different geometrical parameters [31–40], and the finite-element [41] were also used. In addition, the structure of fluid flow between fins is complicated and usually difficult to study in 3D. A few researchers have reported numerical studies of 3D modeling for finned-tube heat exchangers. Romero-Méndez et al. [42] carried out a numerical and experimental study of the influence of the fin spacing on the hydrodynamics and heat transfer of the fluid flow through a 3D finned tube with a single row arrangement for the range of Reynolds numbers from 260 to 1460. A similar 3D numerical investigation was carried out by Tutar and Akkoca [43]. They predicted the vorticity distributions, average heat transfer coefficient, and pressure drop coefficient for several conditions of the fin spacing. For all of the turbulence cases, the values of these organized factors were compared with each other. Although this study provides an analysis of turbulent ranges in 3D for the flow on a finned tube, the domain employed in this study (one tube row) is not pragmatic. Normally one to six tube rows regions are used in practical applications [44]. Using the lumped capacitance technique (LCT), Kim et al. [45] measured the heat transfer coefficient in a plain finned-tube heat exchanger. The authors found that the LCT using polycarbonate displayed the same results regardless of thickness. The LCT is suitable to measure the coefficient of heat transfer for the Biot number, Bi o0.058. They claimed that this method is a good way to obtain the quantitative coefficient of heat transfer for the plate fin. Recently, many researchers suggested linking the particle image velocimetry (PIV) and infrared thermography (IR) measurements in order to evaluate each of the fields of velocity and temperature and to infer the map of the coefficient of heat transfer [46]. The used of the PIV technique for different thermal applications such as enhanced heat transfer in heat exchangers. Some of the available empirical studies for the fluid flow in a tube bundle were carried out using PIV with the wide range of Reynolds numbers [38,47,48] for a staggered configuration, Iwaki et al. [49] for both in-line and staggered configurations. The sample of results for used this technique by Bougeard [47] as presented in Fig. 3.

3. Flow and geometric parameters Flow conditions and the finning geometry primarily influence the distribution of the heat transfer coefficient over un-finned and finned-tube heat exchangers. Heat transfer and pressure drop from a un-finned and finned-tube bundle are affected by many other factors, and communication among these factors make designing problems significantly tedious. Several parameters effecting of the thermal-hydraulic characteristics of tube banks heat exchanger such as: external velocity, tube diameter, tube rows, tubes pitch and fins pitch. The general effect of the flow and geometric parameter are presented in Table 1. The more detailed the effected of these parameters will be shows as follows. 3.1. External velocity of fluid Boundary layer development and shape which varies with air velocity is one of the most important factors influencing the heat transfer performance in un-finned and finned-tube bundle. The creation of horseshoe vortices increase and the boundary layer thickness decrease as the air velocity increases. It is a general convention that the fluid velocity in the recirculation zone is lower than in the mainstream; hence, the heat transfer coefficient

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is decreased. To determine the Reynolds number for bodies in cross-flow, the selection of flow velocity is imperative. It must be noted that a characteristic dimension used to identify the Reynolds number has not been agreed upon. The researchers have used the inlet velocity, mean velocity and velocity in the smallest cross section area as reference velocity [44,70]. In most cases, the reference velocity is defined as the last one (velocity in the smallest cross section area) according to the available literature. Furthermore, air drafting technique is used for complete design of heat exchangers. Depending on the flow conditions at the bundle inlet, performance of heat transfer and pressure drop for the unfinned and finned-tube banks will vary [71]. Tang and Yang [72] performed the experimental study on the characteristics of heat transfer across the flow in a single-row finned-tube heat exchanger on both the air and water sides. They found that the total thermal resistance value on the water-side was less than 10% when the Reynolds number varied between 1200 and 6000. The air-side thermal resistance was always predominant. Furthermore, their results indicate that the thermal resistance of the air-side is almost equal to that of the water-side in the Reynolds number range of 500–1200. He et al. [73] numerically evaluated the effect of frontal air velocity in staggered finned-tube heat exchangers with the air velocity ranging between 0.646 and 4.64 m/s. Also, the effect on the Nusselt number and friction coefficient of inlet air velocities ranging between 0.4 m/s and 4 m/s was studied by Borrajo-Peláez et al. [74]. 3.2. Tube diameter Taler [75,76] numerically investigated the heat transfer on the double rows in the laminar flow region of a two-pass automobile radiator. The oval-shaped tubes had two diameters: the minor was 6.35 mm and the major 11.82 mm. They found that the zones behind the tubes contributed little to the heat exchanger performance. Their results showed wakes in front of and behind the tube at the second row, which led to the minimization of the heat transfer rate to the lowest value. The influence of tube diameter on the Nusselt number and friction factor was presented numerically by Xie et al. [77]. The Reynolds number was varied between 1000 and 6000. The diameter of the tube was varied from 16 mm to 20 mm. Their study reveals that both heat transfer and friction coefficients increase with increases in the tube diameter. The influence of tube diameter on the Nusselt number and friction coefficient with the various from 5 to 15 mm was studied by Borrajo-Peláez et al. [74]. 3.3. Tube rows Every study verified the influence of tube bundle in the direction of flow on variation of heat transfer coefficient around the fin and from row-to-row. While, it should be noted that a single tube and fewer rows yield limited results, some studies have developed row correction factors to counter this problem. There is a need to be further research by implementing four and more tube row bundles. With the staggered configuration, the main flow passes during the surfaces of the fin and tube because of the location of all rows in almost the same direction as the flow. The impact of the number of rows on the coefficient of heat transfer for an in-line configuration was higher compared with the staggered configuration when the number of rows, NR was NR Z2 [71,78]. Note that, the coefficient of heat transfer became fixed following the third row. Reductions of pressure drop up to 30% of the loss pressure coefficient (pressure drop coefficient per unit row because only the existence of the tubes) viewed in favor of elliptical arrangement. The comparison was conducted between arrangement for circular and elliptical tubes with the same area of

hindering the free flow for Reynolds number based on the fin pitch range of 200 rRer2000. The air velocity range covered the advantage for applications in air conditioning. In addition, it was noted that the reduction in loss pressure coefficient is higher when increases Reynolds number and negligible for three rows arrangements. 3.4. Tube pitch This section discuss a review of the heat transfer and pressure drop in un-finned and finned and tube heat exchangers with circular tube experimental measurements in the relevant literature. The relationship was established for the heat transfer and pressure drop. Regardless of the influence of tube diameter, the severity of the turbulence within the bundle depends on the velocity of the air and tube spacing. Thus, these parameters have a strong effect on the pressure drop in the banks of tubes. When the transverse pitch of the tube was changed, the existence of a clear influence on the pressure drop at the side-air was observed, while there was a lack of significant change in the heat transfer performance [79]. For the staggered configuration, the heat transfer coefficient is bigger for the nearer transverse pitch [79,80]. It would appear that the air velocity at the smallest channel between the fins becomes highest when the transverse pitch decreases and this impact leads to bigger values of the pressure drop and coefficient of heat transfer. On the other hand, the authors stated that an extension of the longitudinal pitch of the tube in the staggered configuration leads to decreases of the Nusslt and Euler numbers. Similar results were reported by Rabas et al. [81] for the impact of longitudinal pitch on the heat transfer performance, and the influence on the pressure drop has been confirmed by Jameson [82]. The finite element method [83,84] to solve the Navier–Stokes and energy equations of heat transfer and fluid flow over in-line and staggered configurations of tube banks at the fixed Pr number of 0.7. Wong and Chen [83] presented results for various Reynolds numbers ranging between 20 and 40 and a pitch-to-diameter ratio of 2.0. Chen and Weng [84] studied the effect of pitch-to-diameter ratio and Re number on the Nu number, pressure drag, total drag, and friction drag. The ranges of the pitch-to-diameter ratio and Re number were 1.7–2.0 and 4–40, respectively. Zdravistch et al. [85] used a finite volume technique and presented results for two pitch-to-diameter ratios of 1.5 and 2.0 with various Reynolds numbers based on the velocity of approach from 54 to 120 at a fixed Pr number of 0.7. It is boosted using the finite volume technique in a 2D [86], and 3D [87]. The laminar air flow and forced convection heat transfer in the staggered circular tube banks were studied numerically Wang et al. [88]. Three tube pitch ratios of 1.25, 1.5, and 2.0 with rotated square (RS) and equilateral triangle (ET) tube configurations with 10 tube rows for two Reynolds numbers of 100 and 300 were tested. The authors found that a decrease of the tube pitch ratio leads to a rise in the heat transfer and friction coefficients. In general, the friction and local heat transfer coefficients are less in the RS configuration compared with the ET configuration at the same tube pitch ratio. They claimed that the results can be used particularly at lower Reynolds numbers to predict the total heat transfer in tube banks. The tube bundle arrangements as shown in Fig. 4. The mass transfer and hydrodynamic characteristics for the in-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. The results were shown in the form of streamlines, temperature contours, and local Sherwood, Sh and Sh numbers. The correlation obtained for the Sh number shows good agreement with previous experimental correlations. Numerical investigations of the local coefficient of heat transfer for the tube bundle issue were carried

T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380

Fig. 4. The nomenclature staggered tube bundle configuration [88].

fin spacing compared with the larger fin spacing because the boundary layer is thicker. Small fin spacing leads to an increase in the thickness of the boundary layers. The swept the formation of a region of stagnation at the surface of the tube and the fin base through a non-turbulent flow, which was expected from the subscribe in the effective heat transfer. Hence, the allowable ranges of reduction in the space between fins depend on the velocity flow and flow turbulence in the channel between fins. In this regard, other researches were carried out to find the best design for enhanced surfaces for heat transfer [97]. Fig. 1(a and b) shows the geometry of tube banks with plain fins, four rows deep on 12.7 mm diameter tubes equilaterally spaced on 32 mm centers; Rich [98] calculated the heat transfer and friction data for this system. The tubes as well the fins were made of copper and the fins were joined together by solder to reduce resistance by contact. The thickness of all fins was kept the same at 0.25 mm thick. The fins density (1/pf) ranged from 114 fins/m to 811 fins/m but all her geometrical parameters were identical. The friction drag force is the total of the drag on a bare tube (ΔpT) and the drag caused by the fins (Δpf) as suggested by Rich [98]. The drag force on the fins is the difference between the total drag force and the drag force related to the corresponding bare tube banks. Hence, the friction factor from the fins is
2AcF  ρ f F ¼ Δp  ΔpT _ Þ2 A F ðm

Fig. 5. LES: (top) streamline of the spanwise-averaged velocity field and contour plots of the spanwise-averaged turbulent kinetic field (bottom) at several of P/D [93].

out for a wide range of transverse and longitudinal pitches, Reynolds numbers [90,91], and Prandtl numbers [50], and experimental [92]. The wall-resolved large eddy simulation (LES) with unsteady RANS was used to investigate the flow over a periodic and in-line tube bundle [93]. The researchers studied the impact of tube spacing on fluid flow with three values of the pitch-todiameter ratio (P/D) of 1.4, 1.6, and 2.0. The significant results from this study showed that the decreases of P/D led to an increase of the flow deviation. The influences of the P/D on streamlines and kinetic energy contour for all cases were which tested as is illustrated in Fig. 5. The effect of Reynolds number on the flow and conjugate heat transfer performance of in-line and a staggered arrangement of a circular tube bundle were studied. The laminar flow with thermally and developing in a 3D with Reynolds numbers in the range of 300 rRer800 [14] the influence of tube separation [94]. The results were provided in the form of temperature contours, streamline, average pressure drop, and Nu number. The effect of the longitudinal spacing on characteristics of heat transfer in the in-line tube bundle for a single phase was studied [95] with the CFD technique. The author conducted sensitivity analyses using different models of two-equation turbulence to determine the effect of the turbulence model on characteristics of the heat transfer and to identify the turbulence model that could describe the physical phenomena of concern most appropriately. The result suggested that the coefficient of heat transfer may be reduced by 37.1% from that predicted using the relationship [10], and the longitudinal pitch decreases. From the results analysis, it was found that deterioration in the heat transfer can be observed using the experimental correlation coefficient and a link and Žukauskas [10].

371

ð1Þ

The friction factor and the Colburn j-factor ðSt  Pr2=3 Þ data (smoothed curve fit) are represented in Fig. 6 as a function of Reynolds number based on Dh for the eight fin spacing tested. Entrance and exit losses are not taken into account in the friction factor and have also been subtracted from the pressure. The hydraulic diameter based of Re number does not correlate the j or f data as verified in Fig. 6. Δpt is the drag measured for the bare tube banks of the identical geometry, without fins. Both Δp drop contributions are analyzed at the same smallest area mass velocity. Fig. 7 graphically represents the fin friction factor calculated by Eq. (1) plotted against the Reynolds number on the basis of the longitudinal row pitch (PL) and the same j-factor. It can also be inferred from the graph that j-factor is essentially independent of fin 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. _ the heat transfer coefficient of With the same mass velocity ðmÞ the bare tube banks is 40% greater as compared to the finned-tube banks. With the exception of the closest fin spacing, the obtained friction correlation is convincingly good as can be seen in Fig. 7.

3.5. Fins pitch The empirical results of Rabas and Taborek [96] shows that the coefficient of heat transfer near the fin root is closer at the smaller

Fig. 6. The heat transfer and friction characteristics of a four-row plain plate heat exchanger for several fin pitches [98,99].

372

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A questionable observation is made in the friction factor data of surfaces 7 and 8 as these surfaces show smaller j/f values than the other fins spacing. The j/f ratio usually increases as the fin spacing is decreased because the fractional parasitic drag associated with the tube is lessened. Since all geometries tested maintained the same PL and tube outside diameter. Therefore, Reynolds number based on them would not have any significance. Fig. 7 is proof that the Reynolds number that is governed by hydraulic diameter will not correlate the impact of fin pitch. To determine the effect of the number of tube rows on the j-factor, Rich [100] used similar heat exchanger geometry with 551 fins/m, in a study performed later. The average j-factor (smoothed data fit) for each heat exchanger as a function of Reynolds number can be seen in Fig. 8. The number of rows in each coil is shown in the figure. The row effect varied inversely with Reynolds numbers, greatest at the low Reynolds numbers and negligible at RePL 4 5000. Many studies have been carried out on plain finned-tube heat exchangers after [50,98– 104]. Rich's observation that the j-factor shows negligible effect of fin pitch was validated by these studies, but they do show appreciable row effect at low Reynolds numbers. It was reported by Wang et al. [105] and Wang and Chi [106] that friction does not depend on a number of rows. Borrajo-Peláez et al. [107] presented a numerical study in 3D to compare both the air-to-water side and the air-side model of a finned-tube heat exchanger. In their simulations, the effect of the pitch of fins on the heat transfer and friction coefficients in the range between 0.75 and 4 mm was studied. The impact of fin pitches on the heat transfer for the

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].

discrete smooth plate fin and tube heat exchanger at the air-side was studied experimentally [108]. They used in-line and staggered fin 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 the range of 500 rRer800. The heat transfer factors (j) were around 6.0–11.6% higher in the discrete type compared with a continuous smooth plate finned-tube heat exchanger. An experimental study of thermal and flow characteristics in finned elliptic tube heat exchangers with a tube eccentricity of 0.5 [107]. The isothermal fins condition and range of flow was 200 rRer1500. The results were presented in the form of local and Nu numbers and friction and Colburn j-factors.

4. Optimum spacing The demand for an increase in energy has been rising in all facets of society. The answer to this demand is intelligent use of available energy. Utilization of available energy for optimization of industrial processes (exergy) has been the most popular research topic recently. This is owing to the extensive use of heat exchangers in industrial applications such as with tubes arrangements, finned and un-finned, refrigeration, serving as heat exchangers in air conditioners, heaters etc. Heat exchanging equipment in these devices has to be designed so they can be accommodated by the devices which enclose them. Therefore, an optimized heat exchanger 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 its performance. The design basis for choosing the spacing among the geometric advantages of a group of fixed size (such as, area or volume) like this that the overall thermal behavior between the tube array and fluid flow. Experimental investigation of heat exchangers with finned elliptical tubes, as carried out by [50,109,110], shows a relative pressure drop reduction of up to 30% with the relative heat transfer gain observed in the elliptical arrangements when weighed with the circular ones. A hybrid mathematical model for finned circular and elliptic tubes arrangements was formulated by Rocha et al. [111]. This model is based on energy conservation and heat transfer coefficients achieved from an experiment of naphthalene sublimation through a heat and mass transfer analogy [112,113]. Fin temperature and fin efficiency in one and two row elliptic tube and plate fin heat exchangers are obtained numerically. A relative fin efficiency gain of up to 18% was detected with the elliptical arrangement when fin efficiency results for plate fin and circular tube heat exchangers were compared with the outcomes of Rosman et al. [114]. The optimal plate-to-plate spacing and maximum overall heat conductance for laminar forced convection were studied by Bejan and Sciubba [115]. They used two boundary conditions applied on the surfaces of the plate: both uniform heat flux and uniform temperature. The Prandtl number was in the range of 0.71 rPrr 1000. They found that the optimized space between the plates is proportional to the pressure head (Δp) the upped to the power (  0.25), plate length L0.5, and property set (μα)0.25. The maximum overall thermal conductance is proportional to (Δp)0.5. Cooling was performed by the use of forced convection, the previous studies containing the results of optimum spacing between parallel plates [116] and plates with cylinders [42,60]. Jubran et al. [117] carried out an experimental investigation of the influence of shroud clearance, wasting pins, and fin pitch on the heat transfer coefficient with circular pin fins in both in-line and staggered configurations. The researchers found a small and a powerful influence of the wasting pins in the in-line and staggered arrangements, respectively. On the other hand, they found the optimum spacing between the fins in both

T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380

streamwise and spanwise directions regardless of which shroud clearance and arrangement type was used. Later, previous work was extended by Bejan [118], who confirmed the optimal spacing between tubes. He explained that this optimal spacing decreases with the Prandtl number as well as the pressure drop and increases with the bundle length. The experimental and numerical results for optimal spacing with the maximum thermal conductance are explained and correlated analytically by intersecting the small-spacing and large-spacing asymptotes of the thermal conductance function [119]. The optimal spacing between tubes with cooling by free convection [120]. Matos et al. [121] carried out a numerical study of the heat transfer characteristics of air flow over a circular and elliptical tube heat exchanger using the finite element method. The staggered configuration was used for the tube arrangement. The Reynolds numbers defined for the parameter of the characteristic length ranged from 300 to 800. Their results showed that there was a relative gain of 13% for the heat transfer and a pressure drop reduction of up to 25% with the elliptical tube. In addition, they reported the results of the circular and elliptical tubes with the same construction area for the flow. Matos et al. [122] extended the previous work in 3D numerical and experimental investigations. The two Reynolds numbers based on the swept length (Re) are 852 and 1065. The main results obtained by this study are that there is a gain in heat transfer (thermal conductance) of up to 19% and a reduction in relative material mass of up to 32% in the optimal elliptic tubes configuration compared with the optimal circular tubes configuration. The results of the finned tube optimization for experimental and numerical at e¼0.5 with regard to eccentricities and space between tubes, as is illustrated in Fig. 9. Fig. 10 shows the

temperature distribution on fin for plate finned-tube heat exchangers with four tube rows for circular and elliptic tube. Investigations and improvements of the traditional circular tube banks have been found by many different numerical methods and CFD codes in both the laminar and the turbulent regime. Design optimizations of heat exchangers were found for the size of tubes with spacing and arrangements by different algorithms [123–126]. Fig. 11 shows some perceptions of the temperature and flow fields of design for the optimal design number 894 [126]. Mainardes et al. [127] experimentally studied the reduction of the power pumping required to supply air over finned circular and elliptic tube banks. Their results were presented for Reynolds numbers defined in the small axis of the ellipse varying between 2650 and 10,600. Tube pitches of 0.25 rPT/2br0.6 and eccentricities ranging from 0.4 to 1.0 were used. They found a reduction in the pumping power of around 5–10% with the optimal elliptic tube configuration 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 in staggered tube banks as follows: Nu ¼ 0:33  Re0:6 Pr 1=3

ð2Þ

This correlation is used with 10 or more tube rows in the direction of flow in a staggered configuration and for 10 oReo4  104. The characteristics of heat transfer for both inline and staggered tube bank configurations were studied experimentally by Grimison [129]. Based on a correlation of the empirical results of several researchers, a correlation is given as follows: Nu ¼ C  Ren

Fig. 9. The experimental and numerical for finned configurations [122].

373

ð3Þ

Fig. 11. Perceptions of the temperature and flow fields of design 347 for ΔTper ¼ 13.48 K, ΔPshell ¼ 25.40 Pa/m [126].

Fig. 10. The temperature distribution on fin for plate fin heat exchangers with four-row tubes. (a) S/2b¼ 0.5, e¼1, ϕf ¼ 0:006 and ReL ¼ 852; (b) S/2b¼ 0.5, e ¼0.5, ϕf ¼ 0:006 and ReL ¼852 [122].

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For the empirical correlation above, only the air flow can be used; it works well for ten or more rows in a deep. For a row number of less than 10, Kays and London [109] developed its correction by giving a factor C2, defined as follows: C2 ¼

hNR h10

ð4Þ

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 NujðNR o 10Þ ¼ C 2  NujðNR Z 10Þ

ð5Þ

The 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. Grimison [129] also used the second way to obtain the following expression: Nu ¼ 0:32  F a  Re0:61 Pr 0:31

ð6Þ

and provided graphical values for the tube configuration factor (Fa) obtained by Grimison [129] with changes in the value of the Re number 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 graphic representation by Grimison [129] for the staggered configuration Nu ¼ 0:35  F a  Re0:57 Pr 0:31

ð7Þ

with F a ¼ 1 þ 0:1  P L þ

0:34 PT

ð8Þ

for in-line configuration Nu ¼ 0:34  F a  Re0:61 Pr 0:31

ð9Þ

with

)   ( 7:17 0:266 1000 1=2  6:52  0:12 F a ¼ 1 þ PL þ 2 PL Re ðP T  0:8Þ

ð10Þ

Additionally they used the isothermal boundary condition by Khan et al. [62], which was modified slightly by Grimison's equation [129] and employed the analytical solution for the heat transfer in a tube bundle; the correlation is given by Nu ¼ C a  Re1=2 Pr 1=3

ð11Þ

can be employed with for the in-line configuration P 0:285 C a ¼ ½0:25 þ expð  0:55  P L Þ  P 0:212 L T 0:61  P 0:053 P 0:091 L T ½1  2  expð  1:09  P L Þ

Generally, we want to know a Nu number for the whole tube bundle containing 16 or more rows. Žukauskas [10] suggested an empirical correlation of the form Nu ¼ C  C 1  Rem Pr n

The deviation of correlation above about 75% in the ranges of PL/D¼1.2–3.2, c/D¼ 0.18–0.16, and Re¼ 0.8  104–4  104. The end correlations are worth to the heat exchanger design of a single tube row near to the wall shell with the convection type of heat transfer. McQuiston [101], Gray and Webb [136], Kim et al. [137], and Wang et al. [138] formulated the correlations to predict the j and f factors versus Reynolds number for plain on staggered tube arrangement. Figs. 6 and 7 show the data of Rich [98,100] that the McQuistion correlation is based on, including three other studies. In addition to the data from two more researchers, the same data was used by Gray and Webb [136]. Even though the heat transfer correlations from McQuiston [102] and the Gray and Webb [136] are similar in accuracy, the friction factor from Gray and Webb [136] is far more accurate. The heat transfer from Gray and Webb [136] for four or more tube rows of staggered tube geometry is  0:031    0:502 p PT j4 ¼ 0:14  ðReD Þ  0:328 F ð14Þ Do PL The assumption made in Eq. (14) is that the fourth row stabilizes the heat transfer coefficient, so in case of more than four tube rows and less than four; the j-factor is governed by the correlation as shown on the data in Fig. 8. It is represented by: "    0:031 #0:607ð4  NR Þ jNR  0:092 N R ¼ 0:991  2:24  ðReD Þ ð15Þ j4 4 The McQuiston [101] correlation gives results similar to that of the correlation obtained from Eqs. (14) and (15) 89% of the data for 16 heat exchangers was correlated within 710%. The first of the two terms assumed by the Gray and Webb [136] friction correlation for the pressure drop to be composed of, is the drag force on the fins. While discussing Fig. 8, its model was laid down. Eq. (16) gives the friction factor of the heat exchanger    AF AF tF 1 f ¼ f F þf F 1 ð16Þ A A pF Friction factor associated with fins can be determined by  1:318 p f F ¼ 0:508  ðReD Þ  0:521 F ð17Þ Do

for the staggered configuration Ca ¼

to 4 × 104, and the clearance ratio (c) distance between wall and tube centre was varied from 0.05 to 4.0. The longitudinal pitch (PL) ratio between the centre-to-centre tube-to-tube diameter ranged from 1.2 to 4.4. The correlation of the overall Nusselt number resulted in the agreement is:    0:12  0:23 PL c Nu ¼ 0:103  Re0:74 ð13Þ D D

ð12Þ

The 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 the measurement values of the heat transfer in the empirical correlations. For both in-line and staggered configurations, Grimison [129] correlated the measurements for each test done by Huge [133] and Pierson [134]. This empirical correlation was related to the tube bundle for 10 or more tube rows in the direction of flow. The experimental study of air flow over an in-line tube near a wall was presented by Aiba [135]. The Reynolds number ranged from 0.8 × 104

Correlation for flow normal to a staggered bank of plain tubes gives the friction factor related to the tubes (ft). In order to calculate the tube contributions (Δpt) the Žukauskas [10] tube banks correlation were used by Gray and Webb [136], also presented in Incropera et al. [130]. The finned-tube exchanger _ at which ft is calculated. has the same mass of data velocity ðmÞ 95% of the data for 19 heat exchangers was correlated by Eq. (16) within 713%. The equation can be applied to any number of tube rows. 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 of Gray and Webb correlation in the ranging of 1.97 rPT/Do r 2.55, 1.7 rPL/Do r2.58, 0.08 rpf/Do r0.64, and 500 rReD r24700. In their recent work, Seshimo and Fujii [139] tested 35 heat exchangers, having methodically varied geometric parameters to give more generalized correlation for staggered banks of plain fins with

T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380

Table 2 The constant of the Eqs. (19) and (20) [99].

Table 3 The correlations constant for Eq. (25) [142].

Configuration

n

m

c1

c2

One-row Tow-row

0.38 0.47

1.07 0.89

0.43 0.83

35.1 24.7

one to five tube rows. Three tube diameters (6.35, 7.97, and 9.52 mm) were used with the multi-row designs using an equilateral triangular pitch. Four fin densities, from 454 to 1000 fins/m were considered for obtaining data. One-row designs with the different transverse tube pitch and fin depth prove that using an entrance length parameter the one-and two data may be separately correlated. Reynolds number (ReDvh ) defined in the term of the volumetric hydraulic diameter (Dvh) and was used to correlate their data. Volumetric hydraulic diameter can be computed by 4 Dvh ¼ Am L A

where AmL is the total volume of the exchanger minus the volume of the tube banks. The entrance length parameter used to correlate one-and tworow data is: χ Dþvh ffi ReDvh Pr  Dvh =L. The correlations are given by Nu ¼ 2:1  ðχ Dþvh Þn

ð19Þ

f  L  Dvh ¼ c1 þ c2  ðχ Dþvh Þ  m

ð20Þ

The constant parameters for Eqs. (19) and (20) tabulated in Table 2. Vortex shedding from the tubes proved to be an important factor as these entrance length based correlations for three or more rows failed over entire Reynolds number range 200 oReDh o800. Using conventional Nu number and Reynolds number (ReDh) and flow based on the smallest flow area, data were correlated for ReDh 4400. The one-row variant of Eqs. (19) and (20) correlated the data for one to five rows for ReDh o 400. Tube diameters as small as 5.0 mm is used in a certain window air conditioner, which goes to show that the tube diameter used in finned-tube heat exchangers is decreasing. Kim et al. [137] included data from Wang and Chi [138] for heat exchanger having 7 mm diameter tubes to revise the correlation from Gray and Webb [136]. For tube diameters larger than 7 mm, the Kim et al. [137] correlation calculated the data with comparable accuracy as obtained by Ref. [134]. It was an appreciable improvement for the 7 mm tube data. Tube diameters as small as 6.7 mm were used by Wang et al. [138] to develop another general correlation. Comparisons were drawn between Kim et al. [137] and Wang et al. [138] correlations at ReD ¼2500 for 1r NR r3, 1.3 rpf r3.0 mm. The predicted j-factor by Kim et al. [137] for heat exchangers having 9.5 mm-OD tubes, are in line with those by Wang [140] correlation within 710%. Approximately the same j-factor for NR ¼3 was obtained for the 7 mm tube configuration, for the two correlations. However, the difference varied inversely with the row number. A higher friction factor is predicted by Kim et al. [137] correlation than Wang et al. [138] correlation. For three or more tube rows, the Kim et al. [137] correlation is j3 ¼ 0:163  ðRed Þ  0:369

PT

PL

Inline configuration

Staggered configuration

c

c

pF Do

0:0138 

PT do

0:13 

PT PL

0:106 ;

NR Z 3

"    0:123  1:17    0:564 #ð3  NR Þ jN R p PT PT ¼ 1:043  ðReD Þ  0:14 F ; j3 Do Do PL

ð21Þ

N R ¼ 1; 2

ð22Þ

n

n

Sh 1.25 1.25 1.5 1.5 2.0

1.25 1.5 1.25 1.5 2.0

0.561 0.851 0.285 0.316 0.343

0.643 0.593 0.681 0.685 0.625

1.147 1.019 0.871 0.854 0.881

0.569 0.582 0.565 0.564 0.524

f 1.25 1.25 1.5 1.5 2.0

1.25 1.5 1.25 1.5 2.0

1.795 1.958 1.121 1.168 0.907

–0.162 –0.165 –0.133 –0.130 –0.127

2.310 2.377 1.949 1.837 1.519

–0.165 –0.162 –0.171 –0.155 –0.158

ð18Þ



375

f F ¼ 1:455  ðReD Þ  0:656



pF Do

  0:134 

PT Do

1:23 

PT PL

  0:347

ð23Þ

Kim et al. [137] correlation was used by Jakob [141] for the friction factor due to tubes, ft, which is shown by ( )  π 0:188 PT  0:16 0:25 þ
1 ð24Þ  fT ¼ 1:08 ðReD Þ 4 Do ðP T =Do Þ  1 The friction factor of the heat exchanger is calculated by Eq. (16). Another numerical correlation was suggested by Zhang and Li [142] for estimation of the Sherwood number and friction loss according to a wide assortment of bank geometries and working conditions. The average Sherwood number and friction factor correlation was as follows: ) Sh ¼ c  Ren Sc0:333 ð25Þ f ¼ c  Ren 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 correlations have an accuracy of more than 98% for numerical data. Xie et al. [63] presented numerical corrections for the Nusselt number and friction factor of the air-side fin-and-tube heat exchangers. The correlations were validated in the ranges of 0.67r u1 r 4.0, 16 mm rDo r20 mm, 2 mm rpf r 4 mm, 32 mm rPT r36 mm, 38 mm rPL r46 mm, and 1  103 r Rer 6  103. These correlations are more accurate and authoritative which was developed from Wang et al. [138] for extensive ranges of validation. The Nusselt number correlation is defined as     p  0:165 P T 0:0558 Nu ¼ 1:565  Re0:3414 N R  F Do PL

ð26Þ

Elsewhere, the friction factor correlation is given by Eq. (2.26)     p  0:1676 P T 0:6265 f ¼ 20:713  Re  0:3489 N R  F Do PL

ð27Þ

The mean deviation between the predicted and numerical values was around 3.7% and 6.5% in the Nu number and f correlations, respectively. Numerical and experimental methods for finding the coefficient of heat transfer in heat exchangers with extended fins were studied recently by Taler [143]. He used the non-linear regression method to determine the Nusselt number on both the water-and the air-side. On the other hand, the author used the Levenberg–Marquardt method to calculate the lower

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Table 4 Details more correlations with condition and geometry parameters. Researchers Paeng et al. [52] Xie et al. [63]

Correlations

Conditions


1=3 Nu ¼ 0:049  ðReD Þ0:784 Prf  0:0558    0:165 Nu ¼ 1:565  Re0:3414  PP 12 N R DpFo

1082 r ReD r 1649

Stagg.

Nþ E

Cir.

0.4–6.0

1  103 oReo6  103 16 mm rDo r 20 mm, 2 mm r pF r4 mm, 38 mm r P1 r46 mm, 32 mm mm rP2 r 36 mm 200r Rea r 1500

Stagg.

N

Cir.

3.7

In-lin.

N

200r Rer 1700

In-lin.

T þE

Cir.

2.5

10r Rer 4  104, NR Z 10 5  102 oReo3  104, 11:2 r Ao =At r 23:5 4.5  103 r Rer2.7  104, 0.336r H/Dr 0.516 150r Rer 350 ReZ 1  104, 0.7 r Pr r100, L/D Z 60 PL ¼1.0, 1.97r PT r 3.16, Reo 6400 Re4 6400 40r Rer 800, 0.1 rPr r 10

–

–

Gen.

–

Stagg.

E

Cir.

8.2

Stagg.

E

Cir.

5

Auto. radiator Auto. radiator

E E

Elp. Gen.

– –

Stagg.

E

Elp.

–

In-lin. Stagg. Stagg.

A

Cir.

E

Cir.

– – 5.9

In-lin.

E

Cir.

3.8

Stagg. In-lin. Stagg.

E E

Elp. Cir.

6.2 14.5 5.7

f ¼ 20:713  Re  0:3489  Taler [76] Rosman et al. [114] Colburn [128]

Nua ¼ 0:06963  ðRea Þ0:6037 ðPra Þ1=3 h i Nu ¼ 3:58 þ 8:46  10  4 Re1:24  Pr 0:4 Nu ¼ 0:33  Re0:6 Pr 1=3    0:362

Kayansayan [144]

j ¼ 0:15  Re  0:28

Chen and Ren [145]

Nu ¼ 0:191  Re0:68 Pr 0:4

Taler [143] Dittus and Boelter [146]

Nu ¼ 0:085  Re0:712 Pr 1=3 Nu ¼ 0:023  Re0:8 Pr 0:3

Merker and Hanke [147]

Sh ¼ 1:181  Re0:480

Chen and Wung [148] Wang et al. [149]

 0:6265    0:168 P1 N R DpFo P2

Ao Ato

Sh ¼ 1:212  Re0:676 Nu ¼ 0:8  Re0:4 Pr 0:37 Nu ¼ 0:78  Re0:45 Pr 0:38 Nu ¼ 1:7  NuZ Nu ¼ 1:38  NuZ

Kim and Kim [150]

j ¼ 0:710  ReDh  N R  0:141 pF 0:384

Khan et al. [151] Jacimovic et al. [152]

Nu ¼ 0:33  Re0:64 Pr 1=3
 0:65 W  0:7 f ¼ Re180 0:85 þ 0:52  Rd

NR 41, Reo 500 NR 41, 500o Reo 1000 600r ReDh r 2000, 7.5 r pF r 15, 1r NR r 4 1  104 rRer3.6  104 300o Reo 4000

Geometry parameters

Method

Tube shape

Deviation (%)

6.5

Elp.

A: analytic study; Auto: automotive;; Cir: circular tube; E: experimental study; Elp: elliptic tube; N: numerical study; In-lin: in-line configuration; S: simulation study; and Stagg: staggered configuration.

value of the sum of squares error. Further correlations which are available are summarized in Table 4.

6. Flat tube and other shapes In this section, shows the focus reviews of research in the flat tube and other tube shapes (i.e., came, wing). The flat tube has two diameters small and large diameters called are transverse and longitudinal, respectively. Both in-line and staggered configurations 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 fluid flow over the banks of flat tubes, excluding the contemporary studies of [153–157]. Bahaidarah et al. [158] carried out a numerical investigation of steady, laminar, incompressible, 2D flow over a flat tubes bundle. They used both an in-line and a staggered arrangement and calculated the best configuration from the viewpoint of the heat transfer. Benarji et al. [153] presented the results for a 2D, incompressible, and unsteady flow over the in-line and staggered flat tube arrangements under isoflux and isothermal boundary conditions. From the standpoint of heat transfer, the inline arrangement shows better performance than the staggered arrangement in most of the cases. However, the values of dimensionless pressure drop are higher in the staggered arrangement compared with the in-line arrangement. Tahseen et al. [159] have

a numerical studied of the heat transfer for air flow over a two staggered flat tube configuration. They have shown the effect of Re number on the heat transfer coefficient. They results show that the heat transfer coefficient increase with an increase of Re number always. In the following year, Tahseen et al. [160] carried out analyzed numerically the thermal and fluid characteristics of air flow in an in-line flat tube bundle configuration. They used the neuro-fuzzy inference system (ANFAS) model to predict values of heat transfer coefficient and pressure drop. They examined the transverse pitches from 1.5 to 4.5 with interval 1.0, and three longitudinal pitches are 3, 4 and 6, for the Re number ranging from 10 to 320. They results were presented in the forms Nu number, dimensionless pressure drop, streamline and temperature contours. The key results from this study that the average deviation between the numerical and ANFIS model values for Nu number is 1.9%, and the dimensionless pressure drop is 2.97%. Webb and Iyengar [161] carried out an experimental study of finned-tube heat exchangers with both oval and circular tubes and compared them from the standpoint of the air-side performance. The values of the heat transfer coefficient are approximately equal in both circular and oval tubes heat exchangers. However, the pressure drop was lower than 10% in the oval tube compared with the circular tube heat exchangers. The heat transfer and pressure drop of staggered flat tube banks were studied experimentally. Numerical studies of flow and heat transfer in a heat exchanger with staggered configuration were carried out for circular and wing-shaped tubes [162], circular, elliptic, and wing-shaped tubes, [163], and circular and elliptic tubes [164]. They used transient numerical simulations of the flow and heat transfer. The results of all studies are shown in

T.A. Tahseen et al. / Renewable and Sustainable Energy Reviews 43 (2015) 363–380

the form of the average drag coefficient (Cd) and average Stanton number (St ). They found higher values of Cd and the St number in circular tubes, whereas the difference between the values of Cd was small at a large hydraulic diameter as well as St number. Wang et al. [165] carried out numerical and experimental studies to obtain the performances of heat transfer in a finned flat tube heat exchanger. In the numerical part, they used the two boundary conditions on the fin walls. The first uniform temperature and the second conjugate numerical method. They found that the deviation in the average heat transfer coefficient obtained from the two ways of boundary conditions is higher than 5% for a fin efficiency of less than 80%, whereas the deviation is less than 5% for fin efficiency higher than 80%, but the appropriate choice is the conjugate method. They claimed that the reported results provide a standard to help researchers to select an appropriate numerical method for finding 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 the distribution of temperature and heat transfer over a series of circular tubes confined between parallel plates in a numerical study carried out by Kundu et al. [166]. Three Reynolds numbers were tested: 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, and those of L/D were 2.0, 3.0 and 6.0. They found that the bulk temperature rose almost linearly from one HEM to another HEM for an equal rate of heat transfer from all modules for the case of fully developed flow. In the same year, they studied the pressure drop and heat transfer [167]. In the following year, Kundu et al. [168] conducted an experimental study of the pressure drop and heat transfer for laminar and turbulent flow over a series of in-line circular tubes confined to a parallel plates channel within the range of 220rRer2800. They compared the numerical results with the data of laminar flow. The results presented were in reasonably good agreement. In a more recent review, Bahaidarah et al. [169] developed a numerical model of the flow past in-line tubes in circular, oval, flat, and diamond arrays between parallel plates at the range of Reynolds numbers of 25–350. Their results show that the heat transfer rate is lower in the diamond tubes for all Reynolds numbers. For Reo50, the flow and geometry were key factors influencing the heat transfer performance, while at Re450 the geometric 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 fitted coordinates (BFC) to be transformed from the physical domain to the computational domain. The Re number varies within the range is 25–300, and three longitudinal pitches of 2–4 at the Pr number taken of 0.7. Jue et al. [171] studied the flow and heat transfer characteristics of a cross-flow of three heated cylinders arranged in the form of an isosceles triangle confined between two parallel plates. They used the finite element method to solve the continuity, momentum, and energy equations. The average changes in the drag coefficient and the time Nu number around the surface of three cylinders were investigated in each cylinder. The calculation was carried out with 100rRer300 and 0.5rgap/diameterr1.25.

7. Future work Flat tubes are vital components in various technical applications like modern heat exchangers, automotive radiators, automotive air conditioning evaporators, and condensers. In comparison to the round tube heat exchangers, flat tube heat exchangers are expected to have smaller air-side pressure drop and improved air-side heat

377

transfer coefficients. For the above reasons, the optimum spacing (e. g., tube-to-tube, fin-to-fin) with the maximum overall heat conductance (heat transfer rate) and minimum pressure drop needs more focus and research in the future. In addition, more works are needed to develop the thermofluid correlations in tubes of this shape.

8. Conclusions A comprehensive literature survey on plain plate finned and un-finned tube heat exchangers with many shapes of tubes (e.g., circular, elliptic, flat) has been provided. The work focused on and presented the thermofluid characteristics of heat exchangers depending on several parameters: external fluid velocity, tube configuration (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 that    

   

the heat transfer coefficient and pressure drop increase with increased external velocity of fluid. Few studies focused on the effect of tube diameter in a circular tube while many researchers studied the effect of the axis ratio in an elliptic tube on the thermal and fluid flow characteristics. The staggered configuration shows the high heat transfer coefficient compared with the in-line configuration for finned and unfinned tube heat exchangers regardless of the tube shape. The heat transfer coefficient and pressure drop increase with increased fin density. Many researchers have shown the effect of transverse tube pitch on the heat transfer coefficient and pressure drop, and all studies show that the heat transfer and pressure drop increase as the transverse tube pitch decreases for finned and un-finned tube heat exchangers with in-line and staggered configurations. Based on this review and previous studies published in the literature, one can infer that the form of the tube and the order have a significant effect on heat transfer. This current review is very useful in terms of enhancing the thermal and fluid flow characteristics and development of the correlations for thermofluid characteristics in heat exchangers. In future works, further research needs to be carried out to develop the correlations for heat transfer and fluid flow in tube banks 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.

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