A review on the two-phase heat transfer characteristics in helically coiled tube heat exchangers

International Journal of Heat and Mass Transfer 95 (2016) 551–565

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Review

A review on the two-phase heat transfer characteristics in helically coiled tube heat exchangers Andrew Michael Fsadni ⇑, Justin P.M. Whitty University of Central Lancashire, School of Engineering, Rm. KM124, Preston PR2 8AJ, UK

a r t i c l e

i n f o

Article history: Received 29 July 2015 Received in revised form 14 December 2015 Accepted 16 December 2015

Keywords: Two-phase flow Curved tubes Heat transfer Boiling Nanofluids

a b s t r a c t Helically coiled tube heat exchangers are the most widely used from the family of coiled heat exchangers. This is due to their compact design, ease of manufacture and enhanced heat transfer efficiency. The purpose of this review is to summarise and critically review the published studies on the heat transfer characteristics of two-phase flow in helically coiled tubes. The first section presents the experimental and theoretical results for the boiling heat transfer characteristics reported by several authors whilst the second section focuses on the results for the heat transfer characteristics with nanofluids. Therefore, this review provides researchers in academia and industry with a practical summary of the relevant correlations for the calculation of the two-phase heat transfer coefficient. A significant scope for further research was also identified in the field of two-phase flow at non-boiling conditions and in the application nanofluids. Ó 2015 Elsevier Ltd. All rights reserved.

Contents 1. 2.

3.

4. 5.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Research methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boiling heat transfer coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Steam and water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. R-134a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nanofluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Experimental studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Numerical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scope for further research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Due to their compact design, ease of manufacture and heat transfer efficiency, helically coiled tube heat exchangers are the most common type of curved tube heat exchangers. Their use has long been established in a number of industries and processes such as in the food, nuclear and power generation industries and in heat recovery, refrigeration, space heating and air-conditioning

⇑ Corresponding author. Tel.: +44 1772893812. E-mail address: [email protected] (A.M. Fsadni). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.12.034 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

551 553 556 556 558 559 559 561 562 563 563 564

processes. Helically coiled heat exchangers are known to yield enhanced heat transfer characteristics when compared to straight tube heat exchangers due to the secondary flow, perpendicular to the axial fluid direction, which results in an improved fluid mixing, thus reducing the thickness of the thermal boundary layer. Goering et al. [1] estimated the secondary flow to account for 16–20% of the mean fluid flow velocity. This phenomenon finds its origins in the centrifugal force due to the curvature of the coil structure and is more evident with laminar flow due to the limited fluid mixing in straight tube laminar flow [2,3]. In applications with particles suspended in the fluid, such as is the case with nanofluids, Brownian motion is also known to enhance the heat transfer

552

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

Nomenclature A Bo cp C1&2 CHF d D De Di E f F FB FR Fe G He h⁄

hst htp ilg ID k K L m _ m M N Ncb Nu OD p pr P PI Pr Pr  P DP⁄

DPst q Q r rd R

cross-sectional area of tube (m2) Boiling number (–) specific heat (J/kg K) empirical constants (–) critical heat flux (kW/m2) tube diameter (m) helix diameter (m) Dean number (–) diameter of nanoparticle (m) corrugation height (m) pulsation frequency (s
1) correction factor (–) body forces (N) filling ratio (–) enhancement factor (–) mass flux (kg/m2 s) helical coil number (–) mean heat transfer coefficient after applying enhancement techniques (Nanoparticles and helical coils) (W/m2 K) mean heat transfer coefficient inside a straight tube with base fluid only two-phase heat transfer coefficient (W/m2 K) latent heat evaporation (J/kg) inner tube diameter (m) thermal conductivity (W/m K) relative heat conductivity (–) heated length (m) mass flux (kg/m2) mass flow rate (kg/s) molecular weight (mol/g) Avogadro number (mol
1) convective boiling number (–) Nusselt number (–) outside tube diameter (m) corrugation pitch (m) pitch ratio (–) system pressure (–) performance index (–) Prandtl number (–) reduced pressure (P/Pcritical) mean pressure (Pa) mean pressure drop after applying enhancement techniques (nanoparticles and helical coils) (Pa) mean pressure drop inside a straight tube with base fluid only (Pa) heat flux (kW/m2) heating power (kW) tube radius (m) radius of nanoparticle (m) helix coil radius (m)

characteristics [4]. A number of active and passive methods have also been applied to helically coiled tube heat exchangers to further enhance their performance. Typical passive methods are fluid additives, the variation of the coil and tube design, [5], the use of propellers, [6], fins [7] and internal springs [8]. Active methods include the application of induced pulsation [9] and pipe rotation [10]. The performance of helical coils is also a function of the geometry and design parameters such as the tube diameter and the pitch (Fig. 1). Most of these methods were designed to enhance the fluid mixing, thus improving the convective coefficient of heat transfer at the wall.

Re Re⁄ S T VC VF WC Wo x y

Reynolds number (–) modified Reynolds number (–) boiling suppression factor (–) temperature (°C) volume concentration as fraction (–) volumetric void fraction (–) mass concentration as fraction (–) Wo number (–) steam quality (–) latent heat of vaporisation (J/kg)

Greek symbols d curvature ratio: Internal tube radius di/mean coil radius D (–) j Boltzmann constant (J/K) l dynamic viscosity (Pa/s) q density (kg/m3) r surface tension (N/m) s sheer stress (N/m2) g performance index (–) u volume concentration (%) / dissipation term (m2/s3) vtt Martinelli parameter for the case where the liquid and vapour phases are turbulent (–) Subscripts b bulk bf base fluid cb convective boiling eff effective eq equivalent g gas properties it inner tube l liquid properties lf liquid film m mixture n nth nb nucleate boiling nf nanofluid np nanoparticle of outer fluid osc oscillatory ot outer tube sat saturation conditions slo superficial for total liquid flow st single-phase conditions TP two-phase conditions tt turbulent liquid and vapour flow v vapour w wall

Therefore, the open literature, presents a considerable amount of studies on the single-phase flow and heat transfer characteristics in helically coiled tube heat exchangers. A lesser number of studies have investigated the two-phase flow and heat transfer characteristics in helically coiled tubes. When compared to single-phase flow, two-phase heat transfer characteristics are significantly more complex whilst being more relevant to real-life engineering systems. A number of studies investigated the flow and boiling heat transfer characteristics [11,12] whilst more recently a number of authors investigated the application of nanofluids [13,14] in helical coils. Intriguingly, there are no studies that investigated the heat transfer

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

553

knowledge and controversies in literature. The current study will also identify areas for further research.

1.1. Research methods

Fig. 1. Geometry and design parameters of helically coiled tube heat exchangers.

characteristics for two-phase air/water bubbly flow at non-boiling conditions. As reported in a study co-authored by the author of the present study [15], such a phenomenon is typical to a number of systems such as central heating and power generation cooling systems. There is also a gap in the open literature on the liquid–s olid–gas/vapour three-phase heat transfer characteristics in helically coiled tube heat exchangers. Literature also presents some controversy in the field of nanofluid applications in helically coiled tube heat exchangers with some authors reporting an enhancement whilst other authors suggested a reduction in the heat transfer characteristics. Berger et al. [16] and Shah and Joshi [17], Naphon and Wongweis [18] and Pawar et al. [19] presented reviews on the single-phase fluid flow and heat transfer characteristics in helically coiled tube heat exchangers. Naphon and Wongweiss also briefly reviewed the two-phase flow and heat transfer characteristics. Howeverß their review was principally focused on the singlephase flow characteristics and hence failed to adequately review the relevant literature for two-phase flow. Therefore, to the best of the authors’ knowledge there are no comprehensive reviews on the heat transfer characteristics of two-phase flow in helically coiled tube heat exchangers. The current study will therefore present a review of the existing literature on the two-phase heat transfer characteristics in helically coiled tube heat exchangers. It is the authors’ hope that this review will be useful to academics and industry based engineers through the provision of a comprehensive report on the current

The heat transfer characteristics in helically coiled pipes were investigated through experimental and numerical methods. Some authors complemented their heat transfer research with the investigation of the two-phase flow characteristics, principally, the flow regime and pressure drop [20–22]. Fig. 2 presents a schematic diagram of the test facility developed by Chung et al. [12] for the investigation of the flow boiling heat transfer coefficient in helically coiled tubes at varying system pressures. This setup is typical for most experimental studies in this field of study. The uncertainty for the measured heat transfer coefficient was calculated to be in the range of 15–22%. As illustrated in Fig. 2, the typical experimental setup for the investigation of the flow boiling heat transfer characteristics in helical tubes, included two pumps, one for maintaining the system pressure and another for maintaining the system mass flow rate. A filter, installed downstream from the pump, was used to keep the test section clean. Before entering the test section, the working fluid was heated to a subcooled state through the use of the preheater. The system bulk fluid flow rates were typically controlled by the system circulation pump. However, some researchers [43] have also used a needle valve and a by-pass line to ensure an accurate control of the mass flow rate at the pump outlet. Inconel 690 [12,23] and stainless steel [11,24,25] were used for the test section, which was thermally insulated to minimise the heat losses to the environment. All the studies reviewed in this paper used the electrical direct heating method to heat the test section whilst, armoured K-type thermocouples were typically used to measure the bulk fluid temperature along the test section. Some studies [11] have also assumed that the temperature gradient of the bulk fluid over the heated length is linear and therefore, the bulk fluid temperature at different axial positions was calculated by interpolation (using the inlet and outlet temperatures). K-type thermocouples, welded to the outside surface of the tube, were also used to measure the tube wall temperature. These thermocouples were electrically insulated in order to avoid the effects of the heating electrical currents on it. A water cooled condenser also

Fig. 2. Schematic diagram of the experimental test rig for the investigation of the flow boiling heat transfer in helically coiled tubes (Chung et al. [12], Fig. 1).

554

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

Table 1 Review of the experimental studies on the flow boiling heat transfer characteristics of steam/water in helically coiled tubes. Authors

Heat exchanger type/flow regime

Principal experimental parameters

Steam quality

Proposed correlation and mean error

Correlations derived from the widely used straight tube two-phase flow boiling heat transfer correlations i.e. Chen, Schrock and Grossman (P < 3.5 MPa and d P 12 mm) 0:79 0:45 0:49 k c q Owhadi et al. (1968) (Chen’s 15.9 mm OD 12.5 mm ID 0.024 < d < 0.05 0.5 < x < 1 0:8 0:4 kl 0:75 F htp ¼ 0:00122 0:5l 0:29p 0:24l 0:24  T 0:24 sat  psat S þ 0:023Rel Pr l d r ll ilg qg correlation for straight 250 < D < 527 P = 0.1 MPa where; tubes) [34] Vertical 60 < q < 256 1 S¼ 80 < G < 315 1þ2:53x10
6 F 1:25 Re l

Nariai et al. (1982) (Schrock and Grossman’s correlation for straight tubes) [36]

14.3 and 20 mm ID D = 595 mm Vertical

0.024 < d < 0.034 2 < P < 3.5 MPa 0.7E5 < q < 1.8E5 150 < G < 850

0.1 < x < 0.9

F ¼ 1:0 for v1 6 0:1 tt
0:736 for v1 > 0:1 F ¼ 2:35 v1 þ 0:213 tt tt (±15%) k 0:8 1   hTP ¼ 170 d Re Pr 3 Bo þ 1:5E
4v
0:67 tt where; Bo ¼ Giqlg (±30%)

Correlations for low steam quality regions i.e. x < 0.1 and high system pressures based on the correlation for straight tubes by Steiner and Taborek (P < 7 MPa; 88.4 < G < 531; 30 < q < 1145) h i1=3 3 0 < x < 0.8 0.0093 < d < 0.020 Hwang et al. [23] 12 mm ID 3 hTP ¼ hnb F nbf þ ðhF TP Þ 1 < P < 6 MPa 606 mm < D < 1290 mm where; 30.0 < q < 1145 Vertical

0:8
0:1e1:75Pr 3:7 q 88.4 < G < 530.5 1:7 þ 3:4 þ 1
P F nbf ¼ 2:816P 0:45 7 Pr r qof r 
 
0:4 2r ð0:377 þ 0:199 ln ð M Þ þ 2:8427E
5M2 d ref


0:35 1:1 F TP ¼ ð1
xÞ1:5 þ 1:9x0:6 qql v

qof ¼ 150E3 kW=m2

Chung et al. [12]

12 mm ID 577,937,1297 mm = D Vertical

Correlations for low steam quality regions i.e. x < 0.1 Kozeki et al. [24] 21.7 mm OD 628 < D < 682 mm Vertical Campolunghi et al. [39]

15.5 mm ID D = 835 mm Vertical

Guo et al. [25]

15 mm ID D = 256 mm Horizontal/ 45° upward and downward incline/vertical

0.0093 < d < 0.021 1 < P < 7 MPa 82 < q < 200 177 < G < 531 _ < 0.06 0.02 < m

0 < x < 0.8

0.032 < d < 0.035 0.5 < P < 2.1 MPa 151 < q < 348 161 < G < 486 d = 0.019 8 < P < 17 MPa 0.1E5 < q < 3E5 1000 < G < 2500 d = 0.059 0.4 < P < 3 MPa 0 < q < 540 0 < G < 2400

0
dref ¼ 0:01 m (±29%) h i1=3 3 3 hTP ¼ hnb F nbf þ ðhF TP Þ


0:75 ¼ 2:5 v1 tt (±20%) hTP hst



0
hTP ¼ 11:226q0:6 e0:0132P (Dimensional formula) (±30%)

0.05 < x < 1

Nucleate boiling region
0:105
0:386 hTP P ¼ 4:28 v1 Pcr hst tt

Forced convection evaporation region
0:727
0:577 hTP P ¼ 7:51 v1 Pcr hst tt

Post dryout region:

0:248 hTP ¼ 26:5 v1 hst tt

where; 0:1

0:021kRe0:8 Pr0:4 ðRr Þ 2r

hst ¼ (±15%) General correlation based on the Lockhart–Martinelli parameter Crain and Bell [41] 15.64 and 16 mm ID Turbulent

0.137 < P < 0.234 MPa 35 < q < 85 29 < G < 34

Transient convective heat transfer under pressure drop type oscillations d = 0.059 Guo et al. [42] 15 mm ID 0.4 < P < 3.5 MPa D = 256 mm 0 < q < 540 Horizontal 200 < G < 2200 0.03 < fosc < 0.05 25,000 < Re < 125,000

0.7 < x < 1

 tp h hv

¼ v1

tt

where;  0:9
qg 0:5
ll 0:1 vtt ¼ 1
x x ql lg  0:1 Nuv ¼ 0:023Re0:85 Pr0:4 Rr 0
1st pressure drop oscillation  h osc  h slo

0:748

¼ 21:4 ð1000BoÞ 0:97 Wo

N d 0:125 Ap 1:4 x0:42

2nd pressure drop oscillation  osc h  h slo

¼ 0:051Wo0:16 Bo0:075 De0:37

555

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565 Table 1 (continued) Authors

Heat exchanger type/flow regime

Principal experimental parameters

Steam quality

Proposed correlation and mean error

where;  ¼ 0:023 h slo

k 0:8 Pr 0:4 2r Re

h  0:1 i Re0:05 Rr

where; ffi Wo ¼ p2R2ffiffiffiffi pf l

Bo ¼ Giqlg (±15%) Correlations for small tube diameters (d < 12 mm and x > 0.1) Kubair [40] 6.4 and 6.5 mm ID 110 < D < 177 Laminar and turbulent Vertical Bai and Guo [43]

Yi et al. (2003) [44] q < CHF

Yi et al. [44] q > CHF

Zhao et al. [11]

11 mm ID D = 255 mm Turbulent Horizontal 4 mm ID 64.2 < D < 100.2 Laminar Vertical

4 mm ID 64.2 < D < 100.2 Laminar and turbulent Vertical

9 mm ID D = 292 mm Laminar Horizontal

0.037 < d < 0.056 8 < P < 16 kPa 6 < q < 80 _ < 0.016 0.0028 < m 1300 < Re < 5200 d = 0.043 0.5 < P < 3 MPa 230 < q < 500 200 < G < 2500 0.04 < d < 0.062 5 < q < 39 977 < Wo < 1322 0.5691 < Bo < 1.5584 0.89 < Pr < 2.71 221 < Re < 1749 0.04 < d < 0.062 10 < q < 62 616 < Wo < 2044 0.5691 < Bo < 1.5584 0.89 < Pr < 3.103 3393 < Re < 4694 d = 0.031 0.5 < P < 3.5 MPa 0 < q < 900 236 < G < 943 10,000 < Re < 80,000

0.2 < x < 0.8

0.7 < x < 1

Owahadi et al. [34] and Crain and Bell [41] correlations

hTP hst hTP hst

0.11 < FR < 0.18


0:3 ¼ 1 þ 2:21 v1 ; v1 < 1:2 tt tt
0:47 1 ¼ 3:06 v ; v1  1:2 tt

tt


 Nu ¼ 10
5:7602 Re3:5939 Pr
0:8809 Bo2:235 Wo
4:1044 FR
9:4881 where; ffi Wo ¼ p2Rffiffiffiffi 2p f l

(±19%) 0.11 < FR < 0.18


 Nu ¼ 15:3188Re
0:0373 Pr
2:9680 Bo1:6674 Wo
3:7535 FR2:2973 where; ffi Wo ¼ p2Rffiffiffiffi 2p f l

(±12%) 0.1 < x < 0.2

hTP hst


0:74 ¼ 1:6 v1 þ 1:83E5Bo1:46 tt

where; Bo ¼ Giqlg (±12%)

Fig. 3. Variation of the local heat transfer coefficient with vapour quality, mass and heat flux (Hwang et al. [23], Figs. 5 and 6).

condenses the steam or refrigerant vapour after the test section. The signals from the measuring sensors for the mass flow rate, pressure, temperature of the tube wall and the bulk fluid and the heating power of the test section and pre-heaters were channelled to a data acquisition system for monitoring and processing purposes. The two-phase heat transfer coefficient was calculated through the use of Eq. (1).

hTP ¼

q ðT w
T b Þ

ð1Þ

where Tw is the circumferentially-averaged inner wall temperature, q is the heat flux at the inner wall, calculated through Eq. (2) [11], and Tb is the bulk fluid temperature.

q¼

GAcp ðT out
T in Þ pdL

ð2Þ

where G is the mass flux, A is the tube cross-sectional area, cp is the bulk fluid specific heat capacity, Tout and Tin are the bulk fluid temperatures at the flow and return ends of the test section, d and L are the tube diameter and the heated length respectively. Numerical studies were developed through the use of commercially available computational fluid dynamics packages such as FLUENT [26] and ANSYS CFX [27] and through the use of programming languages such as FORTRAN [28]. The majority of authors validated their experimental and numerical methods through the comparison of the single-phase data for heat transfer with widely used correlations. In their study on the convective boiling heat

556

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

transfer inside small helically coiled tubes, Zhao et al. [11] compared their single-phase data to the predictions given by the correlations for the Nusselt number and friction factor presented by Xin and Ebadian [29] and Seban and McLaughlin [30] respectively. Jamshidi et al. [31] adopted a similar approach for the validation of their numerical model by comparing their Nusselt number results to the predictions calculated through the correlations presented by Xin and Ebadian [29], Salimpour [32] and Dravid et al. [33].

2. Boiling heat transfer coefficient 2.1. Steam and water The open literature presents a number of correlations for the flow boiling heat transfer coefficient in helical coils for a wide range of system parameters. Table 1 summarises the reviewed correlations based on the key parameters governing their application. The latter are principally the tube size, system pressure, steam quality and the mass and heat flux. The coil orientation and the curvature ratio do not appear to be key parameters in the selection of the adequate correlation. The first experimental study to investigate the flow boiling heat transfer characteristics in helically coiled tubes was done by Owhadi et al. [34]. They reported that for most of the higher regions of steam quality, the principal mode of heat transfer was through convection whereas at lower regions of steam lower quality (x < 0.1), the nucleate boiling component was also present. Therefore the mechanism of forced flow boiling at higher regions of steam quality is considered as a forced convection evaporation, where the nucleate boiling regime is suppressed by the high vapour velocity. Owhadi et al. reported that the correlation presented by Chen [35], which is widely used to predict the flow boiling characteristics in straight tubes, could be used to predict the heat transfer characteristics in helically coiled tubes with sufficient accuracy. According to this model, the local heat transfer coefficient is a function of the steam quality, pressure and mass flow rate. Nariai et al. [36] who investigated the thermal hydraulic behaviour in a once-through steam generator, where the helically coiled tube was heated with liquid sodium, also concluded that the effect of the curvature of the helical coils on the heat transfer coefficient was not significant. Their correlation is based on the correlation presented by Schrock and Grossman’s [37] for vertical straight tubes, thus including the Lockhart–Martinelli parameter, which is a strong function of the steam quality. Nariai et al. also reported that for system pressures in excess of 3.5 MPa, their results did not agree with the correlation by Schrock and Grossman. This was attributed to the fact that the latter correlation was derived with experimental data within the pressure range of 0.5–3.5 MPa. Through their investigation of the flow boiling heat transfer characteristics and dryout at low mass fluxes Hwang et al. [23] also reported a good agreement of their experimental results with the Steiner and Taborek [38] correlation for straight tubes. In a similar investigation under a range of system pressure conditions, Chung et al. [12] also reported a good agreement with the latter correlation. Both authors attributed this good fit to the fact that the secondary flow did not result in a significant influence on the flow boiling heat transfer characteristics. The two studies by Hwang et al. and Chung et al. are amongst the few studies to have investigated the flow boiling heat transfer in helically coiled tubes at a system pressure in excess of 3.5 MPa and with regions of steam quality lower than 0.1. Hwang et al. reported that over all the regions of steam quality under investigation, the nucleate boiling element had the dominant effect when compared to convective boiling. Therefore, the flow boiling heat transfer coefficient was reported to be quasi-independent of the mass flux and steam

quality (Fig. 3). This finding was attributed to their experimental conditions whereby the mass and heat fluxes were in a lower and higher range respectively when compared to the experimental work done by other researchers [11,34,36]. The latter conclusions contrast to the findings reported by Owhadi et al. [34] who concluded that at a higher mass flux and lower heat flux, the nucleate boiling element was only more significant at the lower end of the steam quality range. At the upper end of the mass and heat flux ranges, Chung et al. [12] also reported an increase in the boiling heat transfer coefficient with the system pressure. However, this parameter is not directly represented in the correlation by Steiner and Taborek. As illustrated in Table 1, the correlations for straight tubes by Chen [35] and Schrock and Grossman [37] can reasonably predict the flow boiling heat transfer coefficient for large diameter (inner diameter > 12 mm) helically coiled tubes at system pressures lower than 3.5 MPa whilst the Steiner and Taborek correlation [38] for straight vertical tubes can predict the heat transfer coefficient for large diameter helically coiled tubes at system pressures lower than 7 MPa. Furthermore, the use of these correlations does not appear to be a function of the helical coil curvature ratios and orientation. Correlations for a wide range of steam quality regions were reported by Kozeki et al. [24] Campolunghi et al. [39] and Guo et al. [25]. Through the investigation of the heat transfer characteristics in helically coiled tubes heated by high temperature water, Kozeki et al. [24] identified the two-phase forced convective component as the principal mode of heat transfer. They attributed this result to the effect of the centrifugal force and the associated secondary flow. Their experimental data is useful due to the wide range of steam quality regions investigated. As illustrated in Table 1, Kozeki et al. correlated their results for the heat transfer coefficient as a function of the Lockhart–Martinelli parameter (Eq. (3)) with reasonable accuracy. The latter is a strong function of the steam quality.

htp ¼ C1 hst



1

vtt

C 2

ð3Þ

where htp and hst are the convective heat transfer coefficients for two-phase and single-phase flow in a helical tube with a tube diameter of 21.7 mm. C1 and C2 are empirical constants, 2.5 and 0.75 respectively, for experimental conditions with: steam quality in the range of 0–1, system pressure in the range of 0.5–2.1 MPa, mass flux in the range of 161–486 kg/m2 s and heat flux in the range of 151–348 kW/m2. Campolunghi et al. [39] investigated the heat transfer characteristics in a coiled once-through steam generating tube at high system pressures, these being in the range of 8–17 MPa. Their experimental work is useful due to the high system pressures investigated. They proposed a correlation for the flow boiling heat transfer coefficients based on a dimensional formula which is a function of the operational pressure and heat flux. However, unlike other correlations reviewed in the present study, this correlation is not a function of the steam quality. Guo et al. [25] investigated the two-phase boiling heat transfer characteristics in helical tubes at varying axial angles. They defined the convective boiling heat transfer regime through three regions, namely, the nucleate boiling, forced convection and the post-dryout regions. In agreement with the conclusions made by Kubair [40], Guo et al. reported that for conditions below the dryout region, the heat transfer coefficient is a strong function of the system pressure. They reported that well known correlations such as those presented by Kozeki et al. [24] and Crain and Bell [41] did not adequately reflect the effect of the system pressure. Therefore, the latter parameter was included in their correlations for the convective heat transfer coefficient for the nucleate boiling and forced convection regimes. The latter

557

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565 Table 2 Review of experimental studies on the flow boiling/condensing heat transfer characteristics of R-134a in helically coiled tubes. Authors

Heat exchanger type/Flow regime

Vertical orientation and smooth tubes Kang et al. [45] Tube-in-tube 12.7 mm IDit 21.2 mm IDot D = 177.8 mm Laminar and turbulent Vertical Wongwises and Polsongkram Tube-in-tube [46] 7.2 mm IDit 9.52 mm ODit 21.2 mm IDot 23.2 mm ODot D = 305 mm Vertical Aria et al. [49]

Tube-in-tube 8.9 mm IDit 9.52 mm ODit 29 mm IDot D = 305 mm Vertical

Vertical orientation and micro-finned tube Cui et al. [51] Micro-finned 11.2 mm ID 12.7 mm OD D = 185 mm Vertical

Principal experimental parameters

Quality

Proposed correlation and mean error

dit = 0.075 100 < G < 400 T = 33 °C 1500 < Re < 9000

0
Nutp Pr0:4 

dit = 0.025 5 < q < 10 400 < G < 800 10 < T < 20

0
¼ 2:3ðRe Þ

0:94

Re ¼

mx2r qffiffiffiffi ql qg

ll

(
37.3% to 35.7%)
0:0238 Nutp ¼ 6895:98De0:432 Pr l
5:055 ðBoE4Þ0:132 vtt eq 
l 
0:5   q r 0:5 Deeq ¼ Rel þ Reg lg q l R l

g

Rel ¼ Gð1
xÞ2r l l

Reg ¼ Gx2r lg (±10%) dit = 0.031 112 < G < 152

0.1 < x < 0.8


5:055 ðBoE4Þ0:125 v
0:036 Nutp ¼ 7850De0:43 eq Pr l tt 
l 
0:5   ql g r 0:5 Deeq ¼ Rel þ Reg l q R l

g

Rel ¼ Gð1
xÞ2r l l

Reg ¼ Gx2r lg (±15%) d = 0.061 0.5 < P < 0.58 MPa 2.0 < q < 21.8 65 < G < 320

0.05 < x < 0.92


0:2 1=6 qg 0:6 Nutp ¼ 8:76Rem Prl K 0:09 De0:1 N
0:414 cb ql
i
h qg 1=3 ql yG N cb ¼ q 1 þ x q
1 ð q Þ h
g i l ql Rem ¼ G2r l 1þx q
1 l

g

(±13.8%) Various orientations and smooth tubes Yu et al. [50] Tube-in-tube 9.4 mm IDit 12.7 mm ODit 21.2 mm IDot D = 177.8 mm Laminar and turbulent Horizontal/inclined (45°)/ vertical Horizontal orientation and smooth tubes Li et al. [52] Tube-in-tube 9.4 mm IDit 12.7 mm ODit 21.2 mm IDot D = 177.8 mm Horizontal Chen et al. [53] 7.6 mm ID 10 mm OD D = 300 mm Horizontal

Elsayed et al. [54]

1.1 < ID < 2.8 mm 1.47 < OD < 4 mm 30 < D < 60 mm Horizontal

dit = 0.057 100 < G < 400 1500 < Re < 10,000

N/A

None

dit = 0.057 2.0 < q < 21.8 100 < G < 400 35 < Tsat < 45

0.1 < x < 0.8

None

d = 0.025 0.2 < P < 0.75 MPa 0.115 < Q < 2.1 50 < G < 260

0.18 < x < 0.40

0.037 < d < 0.047 0.35 < P < 0.6 MPa 2.5 < q < 12 100 < G < 450

0.2 < x < 0.9


0:27
¼ 2:84 v1 þ 46162Bo1:15
0:88 tt

  0:9 qg 0:5 ll 0:1 vtt ¼ 1
x x ql lg  0:1 Nu ¼ 0:023Re0:85 Pr0:4 Rr (±15%) hTP ¼ F e hlf Shcooper where; S¼1
x htp hst

Fe ¼

ðhTP
SÞhcooper h

kl hlfReReCrit ¼ 41 Re Prl R 2r !

1þ

0:061

Del ðRr Þ

2

1=6

(±16%)

correlations predicted their experimental data with a relatively good accuracy of ±15%. Crain and Bell [41] presented correlations for the average heat transfer coefficient which is also a function of the Lockhart–Martinelli parameter. However, unlike similar correlations presented by Kozeki et al. [24] and Nariai et al. [36] their correlation is based on the ratio of the two-phase heat transfer coefficient to the vapour heat transfer coefficient. Crain and Bell [41] attributed this to the high quality steam regions used in their investigation.

The sole study which investigated the effects of pulsation on the transient heat transfer characteristics under pressure drop type oscillations was reported by Guo et al. [42]. They reported that the time-averaged heat transfer coefficient under pressure drop oscillations was lower than that observed for stable conditions. Therefore, two correlations were proposed for the calculation of the time-averaged heat transfer coefficient under the first and second pressure drops. Their correlation is a function of a number of system and design parameters, including the coil curvature ratio.

558

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

Fig. 4. Variation of the local heat transfer coefficient with vapour quality, mass and heat flux (Cui et al. [51], Fig. 2).

 d of their However, the authors failed to define the variable N correlation. For helically coiled tubes with small tube diameters (inner diameter < 12 mm) and at regions of steam quality in excess of 0.1, Bai and Guo [43] and Zhao et al. [11] proposed a correlation for the flow boiling heat transfer coefficient that is similar to those presented by Nariai et al. [36] and Guo et al. [25], thus based on Eq. (3). However, in contrast to the conclusions made by the latter authors, Zhao et al. [11] reported that in small diameter tubes, the nucleation and convection mechanisms of heat transfer have an equal influence on the heat transfer coefficient. The correlation presented by Zhao et al. [11] predicted their experimental results with a relatively good accuracy of ±12%. However, this is only valid for a narrow range of regions of steam quality and Reynolds numbers. Small diameter coiled pipes were also used by Yi et al. [44] to investigate the heat transfer characteristics and flow patterns in the evaporator section in a looped heat pipe. In contrast to the findings reported for larger diameter tubes [36,40], Yi et al. concluded that in the single-phase and bubbly regions, the disturbance induced by the pulsation and secondary flow resulted in a higher heat transfer coefficients when compared to similar studies for straight pipes. Therefore, Yi et al. proposed two correlations to predict the heat transfer before and after the critical heat flux point which predicted their experimental results with reasonable accuracy. 2.2. R-134a Table 2 summarises the experimental studies and relevant correlations presented for the flow boiling and condensation of R-134a in helically coiled tube heat exchangers. A number of researchers reported that the heat transfer coefficient is a strong function of the coil orientation. Therefore, the studies reported in this section are summarised according to the coil orientation and surface finish. This contrasts to the results presented in the previous section, a difference that can be attributed to the specific volume of steam and R-134a as a function of the system pressure. A pioneering investigation of the condensing heat transfer and pressure drop characteristics of R-134a in helical coils was done by Kang et al. [45] who reported an overall increase in the heat transfer coefficient with the refrigerant mass flux and cooling water Reynolds number. An increase of 30% in the heat transfer coefficient was also reported with a drop in the wall temperature (22–12 °C). Kang et al. presented a correlation (Table 2) for the calculation of the heat transfer coefficient that is a function of a modified Reynolds number. The latter captures the influence of

the mean vapour quality and mass flux. Wongwises and Polsongkram [46] investigated the boiling heat transfer coefficient and the pressure drop of R-134a in helically coiled concentric tubein-tube heat exchangers. They reported heat transfer coefficients that were 30–37% higher than those measured with horizontal straight tubes and an enhanced mean heat transfer coefficient with an increase in the mean vapour quality, heat and mass flux and saturation temperature. To calculate the heat transfer coefficient, Wongwises and Polsongkram presented a correlation based on the model presented by Cavallini and Zecchin [47] and Jung et al. [48] for the flow condensation heat transfer coefficient of refrigerants in straight tubes. This correlation was later modified by Aria et al. [49] to predict the flow boiling heat transfer coefficient in vertical helically coiled tube heat exchangers. Yu et al. [50] investigated the condensation heat transfer of the refrigerant R-134a flowing inside a helically coiled pipe cooled by counter-flow water through the annulus. They reported that the heat transfer coefficient was a strong function of the coil orientation with the highest refrigerant side heat transfer coefficient recorded at an inclined position. In fact, the latter was measured as 6–7 times more than the heat transfer coefficient in the vertical orientation. However, their findings are limited in scope as the key experimental conditions were not reported. The sole study that investigated the flow boiling in helically coiled tubes with micro-fins was reported by Cui et al. [51]. As illustrated in Fig. 4, they also reported an increase in the heat transfer coefficient with quality and mass and heat flux. Cui et al. attributed the slight decrease in the heat transfer coefficient with quality and heat flux to the partial dryout occurring at the upper part of the tube. Furthermore, they reported that at low vapour qualities, the heat transfer coefficient was a strong function of the heat flux whereas at higher qualities, the mass flux was more significant. A correlation for the calculation of the heat transfer coefficient was presented which is a function of the Reynolds (mixture), Prandtl, Dean and Convective Boiling numbers, relative heat conductivity and density of the liquid and vapour. The condensation heat transfer coefficient of R-134a in straight and helically coiled horizontal heat exchangers was investigated by Li et al. [52] who also reported an increase in the heat transfer coefficient with mass flux and vapour quality. The mean heat transfer coefficient for the helically coiled heat exchanger was reported to be 4–13.8% higher than that for straight tubes. Through the investigation of the flow boiling heat transfer characteristics and the wall temperature distribution at low mass flux and pressure conditions, Chen et al. [53] reported that whilst the heat transfer coefficient increased with increasing mass and heat flux

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

559

Table 3 Review of experimental studies of the heat transfer characteristics of nanofluids in helically coiled tubes. Authors

Heat exchanger type/ flow regime

Nanofluid

Copper and copper oxide nanoparticles and water Akbaridoust et al. Laminar Cu/H2O [28] 200 < Re < 1000 CuO/H2O Suresh et al. [60] Horizontal with smooth and dimpled surface Turbulent 4.85 mm ID 6.3 mm OD 2500 < Re < 6000 CuO/H2O Kannadasan et al. Horizontal and [56] vertical Turbulent 9 mm ID 10.5 mm OD D = 124 mm 1600 < De < 4000 Copper oxide nanoparticles and oil Horizontal laminar Hashemi and 14.37 mm ID AkhavanD = 324 mm Behabadi [61] Re < 125 700 < Pr < 2050 Multi-walled carbon AkhavanBehabadi et al. [58] Fakoor Pakdaman et al. [59]

CuO/oil

nanotubes nanoparticles and oil Multi-walled Vertical carbon Laminar nanotubes/oil 15.6 mm ID 220 < D < 320 mm Multi-walled Vertical carbon Laminar nanotubes/oil 15.6 mm ID 220 < D < 320 mm 100 < Re < 1800

Aluminium oxide and titanium dioxide nanoparticles and water Al2O3/H2O Kahani et al. [57] Horizontal Laminar and turbulent TiO2/H2O 500 < Re < 4500 5.89 < Pr < 8.95 115.3 < He < 1311.4 Al2O3 /H2O Mukesh Kumar Laminar et al. [3] 5100 < Re < 8700 9 mm ID 10.5 mm OD D = 93 mm Al2O3/H2O Wu et al. [55] Double pipe Laminar and turbulent 13.28 mm IDit 26 mm IDot D = 254 mm 800 < Re < 10,000

Heat transfer coefficient enhancement over single-phase water flow

Volume or weight conc.

Proposed correlation and mean error

Enhancement 25% at Re = 800

0.1–0.2% (VF) 0.1–0.3% (VF)

None Nu ¼ 0:00105Re0:984 Pr0:4 ð1 þ £Þ
80:78 ð1 þ pdr Þ (±15%)

0.1–0.2% (VC)

Nu ¼ 1:5De0:827 d0:0008 u1:1697 (Horizontal: ±10.2%)

Enhancement 19–39% Increasing with concentration of CuO

Enhancement 49% in Nusselt number at vertical orientation

2:089

Nu ¼ 3:67De0:67 d0:009 u1:004 (Vertical: ±10%)

Enhancement 82% at Re = 82.2

0.5–2% (WC)

Nu ¼ 41:73Re0:346 Pr
0:286 ½1 þ £0:18 (
15% to +18%)

Enhancement 60% in Nusselt number

0.1–0.4% (WC)

None

Enhancement 6.4 PI

0.1–0.4% (WC)

None

Enhancement 45% Al2O3 27% TiO2

0.25–1.0% (VC)

Nu ¼ 0:5He0:522 Pr 0:613 u0:0815 (TiO2/H2O) (±15%) Nu ¼ 0:7068He0:514 Pr 0:563 u0:112 (Al2O3/H2O) (
25% to +18%)

Enhancement 25–28%

0.1–0.8% (VC)

None

Insignificant

0.78–7.04% (WC)

Nu ¼ 0:089De0:775 Pr 0:4 (±5%) 800 < Re < 2500 100 < De < 1300 4 < Pr < 7 U < 2%

and vapour quality, the effect of pressure was found to be indeterminate. This contrasts to the results reported by Kubair [40] and Guo et al. [25] for steam/water flow boiling heat transfer where the heat transfer coefficient was reported to be a strong function of the system pressure, with an increase in the heat transfer coefficient with pressure. These findings could be attributed to the difference in the specific volume of steam and R-134a as a function of the system pressure. In fact, the specific volume of steam is much higher at lower system pressures [40]. Chen et al. developed a correlation for the calculation of the heat transfer coefficient based on the Lockhart–Martinelli parameter type correlations as originally presented by Kozeki et al. [24] and Bai and Guo [43]. Elsayed et al. [54] reported a unique study that investigated the effects of the tube and coil diameters on the flow boiling heat transfer characteristics in horizontal coils with tube diameters less than 2 mm. They reported an enhancement of 63% and 150% in the heat transfer coefficient with a decrease in the tube and coil

diameters respectively. Elsayed et al. also reported that the increase in the mass flow rate resulted in a stronger effect on the flow boiling heat transfer coefficient. This was attributed to the increase in the secondary flow. A correlation was presented for the calculation of the boiling heat transfer coefficient that is a function of the boiling suppression factor, the liquid film heat transfer coefficient and the enhancement factor.

3. Nanofluids 3.1. Experimental studies Very few studies have investigated the heat transfer characteristics of nanofluids in curved or helically coiled tube heat exchangers. The paucity of research in the application of nanofluids in curved or helically coiled tube heat exchangers has resulted in

560

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

some controversy due to the significant differences in the reported results. Table 3 summarises the experimental studies done according to the nanoparticles and the base fluids investigated. The nanoparticles which have been frequently reported by researchers are the oxides of copper and aluminium whilst water and oil are the sole base fluids investigated. Recent work reported by Wu et al. [55] investigated the application of nanofluids in helically coiled tube heat exchangers. Their research investigated the pressure drop and convective heat transfer performance of Al2O3/water nanofluids under laminar and turbulent flow conditions. They reported that the effect of nanoparticles on the Reynolds number, pressure drop and heat transfer performance is negligible. These findings were mainly attributed to the mitigation of the secondary flow as a result of the higher viscosity and density of the nanofluid. In fact, the highest heat transfer improvement with nanofluids over pure water was measured at 3%. As a result of their conclusion that no multiphase phenomena characterised the system, they presented a correlation for the Nusselt number that is similar to singlephase correlations, thus being a function of the dimensionless Prandtl and Dean numbers. Wu et al. also eliminated the possibility of Brownian motion due to the nanoparticles. Other studies have reported significantly different results. Mukesh Kumar et al. [3] reported that a volumetric concentration of 0.8% Al2O3 nanoparticles with water at turbulent flow conditions, resulted in a 28% increase in the convective heat transfer coefficient. In contrast to the conclusions made by Wu et al. [55], Mukesh Kumar et al. [3] attributed the improved heat transfer coefficient to the enhancement of the intensity of the secondary flow and the induced fluid mixing due to Brownian motion as a result of the nanoparticles suspended in water. These conflicting results could be attributed to the smaller curvature ratios used by Wu et al., thus reducing the centrifugal force acting on the two-phases. Kannadasan et al. [56] also reported an increase in the heat transfer performance and the friction factor with CuO nanoparticles under turbulent flow conditions. As illustrated in Fig. 5, they reported enhanced heat transfer rates with vertically orientated coils which they attributed to the rapidly developing secondary flows. Correlations were also presented for the calculation of the Nusselt number and the friction factor, both of which are a function of the Dean number, the ratio of the internal tube radius to the mean coil radius and the volume concentration. Similarly, Kahani et al. [57] reported a significant enhancement to the heat transfer rate through the use of Al2O3 and TiO2 nanoparticles at 1% volume concentration under laminar and turbulent flow conditions whilst Akhavan-Behabadi et al. [58] reported a 60% increase in the Nusselt number with the application of multi-walled carbon nanotubes nanoparticles to the oil base fluid in helical coils. Kahani et al.

[57] presented correlations for the calculation of the Nusselt number as a function of the helical coil number, Prandtl number and the volume concentration. Fakoor-Pakdaman et al. [59] also reported an enhancement in the heat transfer coefficient with the addition of 0.4% multi-walled carbon nanotubes nanoparticles to oil as a base fluid. They reported their results in terms of the performance index (PI) given in Eq. (4) which captures the simultaneous effects of heat transfer and pressure drop with the use of nanofluids and helical tubes on the overall performance of the heat exchanger. When the performance index is greater than unity, the PI implies that the benefits gained through enhanced heat transfer coefficients outweigh the effects of larger pressure drops through the heat exchanger as a result of nanoparticles and helical tubes. h

g ¼ DhPst

ð4Þ

DP st

where h* is the mean heat transfer coefficient after the application of enhancement techniques, hst is the mean heat transfer coefficient in a straight tube with the base fluid only, DP* is the mean pressure drop after the application of enhancement techniques and DPst is the mean pressure drop inside a straight tube with the base fluid only. Akhavan-Behabadi et al. [58] and Akbaridoust et al. [28] also reported that the geometrical variables such as the reduction of the coil-to-tube diameter ratio and the increase of the pitch totube-diameter ratio, resulted in enhanced heat transfer rates for both the base fluid and nanofluids. However, Kahani et al. [57] suggested that the latter had a weaker effect on the heat transfer rate when compared to the coil-to-tube diameter ratio. AkhavanBehabadi et al. [58] also reported that the Reynolds number increment resulted in the strongest impact on the heat transfer rate at the highest concentration of nanoparticles, this being 0.4% by weight. They attributed this result to the higher viscosity of the base fluid (oil) at lower Reynolds numbers thus limiting the freedom of movement of the nanoparticles. Suresh et al. [60] investigated the use of CuO nanofluids with water in horizontally placed smooth tubes as well as with tubes equipped with dimple protrusions of 0.6 mm added as a passive enhancement to the performance of the heat exchangers. They reported that at higher Reynolds numbers, the dimples, combined with 0.3% CuO nanoparticles resulted in an increase of up to 39% in the measured Nusselt number. However, such geometrical features resulted in an increase in the tube friction factor in the range of 2– 10%. Suresh et al. [60] also presented empirical correlations for the calculation of the Nusselt number and friction factor as a function of the dimple characteristics, nanoparticles concentration and the dimensionless Reynolds and Prandtl numbers. Their results are in

Fig. 5. Variation of the Nusselt number with the Dean number in turbulent flow horizontal (left) and vertical orientations (Kannadasan et al. [56], Figs. 4 and 5).

561

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

agreement with those of Kannadsan et al. [56] for similar experimental parameters. However, the latter did not use dimple protrusions and hence, these results may require further investigation. From a wider perspective, the open literature presents further controversy with respect to the actual mechanism of heat transfer in tubes with nanofluid systems. Williams et al. [62] reported that existing single-phase heat transfer correlations accurately predicted the nanofluid turbulent convective heat transfer coefficient in straight horizontal tubes through the use of the measured temperature and loading-dependent thermal conductivities and viscosities. However, Timofeeva et al. [63] reported that due to the significant area of nanoparticles, the solid/liquid boundary layer between nanoparticles and the base liquid contributes to the fluid properties, thus resulting in a three-phase system in traditional fluid/solid two-phase nanofluids.

kBrownian

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jT ¼ 5E4bVF qbf C p;bf f ðT; VFÞ 2qnp rdnp

where the Boltzmann constant, j = 1.3807E-23 J/K. Modelling function for CuO, 1% 6 VF 6 6%, b:

b ¼ 9:881ð100VFÞ
0:9446 Modelling function for Al2O3, 1% 6 VF 6 10%, b:

b ¼ 8:4407ð100VFÞ
1:07304

ð5Þ

Momentum

q

dV þ r:sij
rP þ qFB ¼ 0 dT

ð6Þ

Energy

q

De @Q þ qðr:V Þ ¼
r:Q þ / dT @T

ð7Þ

where V is the fluid velocity, FB are the body forces, Q is the heat transfer by conduction and / is the energy dissipation term. The numerical analysis studies reviewed in this section assumed that the nanofluid flow through the tubes is incompressible, singlephase and fully developed, both thermally and hydrodynamically. The SIMPLEC algorithm was used by a number of studies to solve the flow field [13,64], whilst for turbulent flow modelling, the standard turbulence k–e model as proposed by Launder and Spalding, was used [26]. The thermophysical properties of the nanofluids were obtained using the equations given in Eqs. (8)–(19) [13,64,66]. Density

qnf ¼ ð1
VF Þqbf þ VF qnp

ð8Þ

Heat capacity

    ðqC p Þnf ¼ ð1
VF Þ qC p bf þ VF qC p np

ð9Þ

Effective thermal conductivity:

keff ¼ kstatic þ kBrownian

ð10Þ

Static thermal conductivity:

kstatic

"   # knp þ 2kbf
2 kbf
knp VF   ¼ kbf knp þ 2kbf þ kbf
knp VF

Brownian thermal conductivity:

ð14Þ

Modelling function for ZnO, 1% 6 VF 6 7%, b:

b ¼ 8:4407ð100VFÞ
1:07304

ð15Þ

Modelling function for SiO2, 1% 6 VF 6 10%, b:

Modelling function, f(T, VF): The earliest numerical study for the heat transfer characteristics with nanofluid flow in helical tubes was reported in 2011, thus suggesting that there is scope for further research in this field of study. In fact, no numerical studies have investigated the heat transfer characteristics of oil based nanofluids. The majority of studies summarised in this section were developed through the use of commercially available software packages based on the finite volume method, these being the ANSYS CFX [27] and FLUENT [64,65] programmes. Therefore, the governing equations for flow and heat transfer, given in Eqs. (5)–(7), were solved to obtain the temperature distribution and pressure drop along the tubes. Continuity

@q þ r:ðqV Þ ¼ 0 @T

ð13Þ

b ¼ 1:9526ð100VFÞ
1:4594

3.2. Numerical studies

ð11Þ

ð12Þ

f ðT; VF Þ ¼ ð2:8217E
2ÞVF þ ð3:917E
3Þ

ð16Þ

T To

þ ðVF ð
3:0699E
2Þ
ð3:91123E
3ÞÞ

ð17Þ

Dynamic viscosity:

leff 1 ¼ lbf 1
34:87
dinp 
0:3 VF 1:03 dibf

ð18Þ

where the equivalent diameter of the base fluid molecule is:

dibf ¼

6M Npqbf

!

ð19Þ

The numerical studies for the heat transfer coefficient with nanofluids in helically coiled tubes are summarised in Table 4. Jamshidi et al. [31] developed CFD simulations for Al2O3 nanofluids in helical coils under laminar flow conditions. In contrast to the experimental work highlighted in the previous section, they used volume concentrations of nanoparticles in excess of 1% with a highest concentration of 3%. They validated their study through the use of the single-phase correlations such as that published by Xin and Ebadian [29], and reported an enhancement of circa 52% in the heat transfer rate with the addition of nanoparticles. In agreement with literature, their study suggested that a volume concentration in excess of 1% (Fig. 6) does not result in a significant impact on the resultant heat transfer coefficient. Similar conclusions were also made by Huminic and Huminic [27] through a numerical investigation of the heat transfer characteristics of CuO and TiO2 nanofluids in a double tube helical heat exchanger and by Khairul et al. [66] through their numerical study of CuO, Al2O3 and ZnO nanoparticles with water. Narrien and Mohammed [64] also reported a reduction in the convective heat transfer coefficient with volumetric concentrations of CuO nanoparticles in water in excess of 2% while Sasmito et al. [65] reported that volumetric concentrations in excess of 1% are not recommended for coiled tubes due to a significantly lower impact on the heat transfer coefficient. Both authors attributed these findings to the resultant increase in the pressure drop with higher concentrations of nanoparticles. Sasmito et al. also concluded that Al2O3 nanoparticles produced marginally better results when compared to CuO nanoparticles, whilst Khairul et al. reported marginally better results with Al2O3 nanoparticles at laminar flow conditions. The latter conclusions contrast to the findings reported by Rabienataj Darzi et al. [26] who reported an increase in the heat transfer coefficient from 21% to 58% with the addition of 2% and 4% Al2O3 nanoparticles to water. Rabienataj Darzi et al. [26] also reported that the combination of 4% nanoparticles and the use of corrugated

562

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

Table 4 Review of numerical studies of the heat transfer characteristics of nanofluids in helically coiled tubes. Authors

Heat exchanger type/flow regime

Nanofluid

Heat transfer coefficient enhancement over single-phase water flow

Volume or weight concentration

Proposed correlation and mean error

Huminic and Huminic [27]

Double tube Laminar 5 < De < 22.5 Square tubes Laminar

CuO/H2O TiO2/H2O

Enhancement with the concentration of nanofluid and Dean number (14%)

0.5–3 (VC)

None

Al2O3/ H2O CuO/H2O Al2O3/ H2O CuO/H2O

Enhancement 50% in the near inlet region with Al2O3

0–1% (VC)

None

Enhancement 52%

1–3% (VC)

None

Enhancement (up to 46%) with: (i) Reduction in the helix angle (ii) Increase in the tube inner diameter (iii) Reduction in the annulus diameter Enhancement 7.14% CuO

4% (VC)

None

1–4% (VC)

None

Enhancement for 1–2% VC CuO Reduction for 2–4% VC CuO

1–4% (VC)

None

Enhancement 21–58%

2–4% (VC)

Sasmito et al. [65]

Jamshidi et al. [31] Mohammed and Narrein [13]

Laminar 1700 < Re < 2500 Laminar _ < 0.06 0.01 < m

Khairul et al. [66]

Laminar 3–6 L/min

Narrein and Mohammed [64]

Laminar _ < 0.06 0.01 < m

Rabienataj Darzi et al. [26]

Corrugated tubes Turbulent 10,000 < Re < 40,000

SiO2/H2O CuO/H2O Al2O3/ H2O ZnO/H2O CuO/H2O Al2O3/ H2O ZnO/H2O Al2O3/ H2O

h i 
0:8  0:4 0:77 Nu ¼ 0:052 pd 1
£ de ½1
£0:28 ½Re
1500½1
£ ½Pr 0:44 h i 1 þ 2:5ð1
£Þ
5:8 (±14%)

the combination of a 4% CuO nanofluid through the use of numerical methods. They concluded that the heat transfer coefficient can be enhanced through the reduction of the helix radius and annulus diameter and an increase in the tube diameter. These results further complement the results reported by Akhavan-Behabadi et al. [58] and Akbaridoust et al. [28] for the influence of the heat exchanger geometrical parameters on the heat transfer coefficient. 4. Scope for further research

Fig. 6. CFD simulation of the enhancement to the Nusselt number with Al2O3 nanoparticles to water (Jamshidi et al. [31], Fig. 3a).

tubes to increase the surface roughness enhanced the heat transfer coefficient by a factor of 3.31. In view of this, they provided a correlation for the calculation of the Nusselt number which incorporated the geometrical characteristics of the corrugated tubes. Akbaridoust et al. [28] compared their experimental results for CuO/H2O nanofluids in helical coils with varying curvature ratios with a numerical model developed using the FORTRAN programming language to solve the three dimensional governing equations. They reported similar trends between the two methods with the heat transfer coefficient increasing with the Reynolds number, radius of curvature and nanofluid concentration. However, they also reported a significant difference between the numerical and experimental results which was subsequently mitigated through the use of a modified dispersion method. Mohammed and Narrein [13] investigated the effects of the geometrical parameters with

Apart from the controversies highlighted in Section 3 and the inherent scope for clarification, there is significant scope for further studies in the field of the applications of nanofluids in helically coiled heat exchangers at three-phase flow conditions. The latter could be the result of dissolved gases or flow boiling. Such studies are notoriously complex and should be undertaken by research groups with significant experience in the research of multiphase flow. In fact, related studies in nanofluid pool boiling have also presented some conflict over whether nanoparticles can enhance or degrade boiling heat transfer [67]. Tu et al. [68] and Wen and Ding [69] reported an enhancement of up to 60% with nanofluid pool boiling using Al2O3 and c-Al2O3 respectively whilst Das et al. [70,71] and Jackson and Bryan [72] reported a deterioration in the range of 10–40% with Al2O3 and Au nanoparticles respectively. Further studies are also required to confirm the optimal concentration of the various types of nanofluids as well as the most appropriate nanofluid for different system parameters. As a case in point, for laminar flow conditions at similar volumetric concentrations, Sasmito et al. [65] reported marginally better results with Al2O3 nanoparticles while Khairul et al. [66] reported that the optimal results were achieved with CuO nanoparticles. The significant heat transfer coefficient enhancement of 330% reported by Rabienataj Darzi et al. [26] through the use of corrugated tubes in combination with Al2O3/H2O nanofluids should also be investigated further through experimental methods. This enhancement is significantly different from that reported by the empirical and numerical

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

studies reviewed in the current report and hence should suggest a significant potential for further research. Further studies should also be undertaken in the numerical analysis of nanofluids flow through helically coiled tubes at turbulent flow regimes. In fact, the sole numerical study which investigated such conditions was reported by Rabienataj Darzi et al. [26]. Furthermore, Naphon [7] argued that in spite of the fact that a number of authors investigated the heat transfer characteristics in single-phase flow in helically coiled heat exchangers, there are some doubts on whether the current methodology used yields a reliable prediction for the heat transfer characteristics. Recent experimental results by Fsadni et al. [15] and Ge et al. [73], have demonstrated that the two-phase flow phenomenon present in sealed wet heating systems finds its origins in the dissolved air present in water circulating in the sealed system. The result is a bubbly flow, with the bubble size, nucleation rate and dissolution rate being a strong function of the bulk fluid Reynolds number, dissolved gas concentration and bulk fluid temperature. This phenomenon creates a further scope for research on the resultant two-phase convective heat transfer mechanism in helically coiled tube heat exchangers. Furthermore, a comprehensive understanding of the resultant two-phase flow characteristics, such as the relevant frictional pressure drop, phase distribution and their ramifications on the heat transfer characteristics is required. There are very few studies in the open literature which have investigated the phase distribution for bubbly flow in helical coils. This can be attributed to the general difficulty in developing reliable multiphase flow visualisation methods with curved tube heat exchangers. Mandal and Das [74] and Murai et al. [75] reported that the phase with the lower density is subjected to a smaller centrifugal force which forces the gas bubbles to move towards the inner side of the coil’s wall. However, Saffari et al. [76] reported that due to the enhanced fluid mixing induced by the secondary flow, bubbly flow, characterised with small bubble diameters, could result in a quasi-homogenous distribution of the secondary phase. This draws an analogy to similar experimental investigations with nanofluids where no significant phase separation was reported [55]. A recent development in the field of two-phase flow has resulted in the injection of air microbubbles in the flow to achieve a reduction in the system frictional pressure drop. However, most of this research has focused on the injection of bubbles over flat plates and in straight tubes with minimal consideration for the investigation of the pressure drop reduction in coiled tubes. Furthermore, no such studies were undertaken for heat exchangers. Jacob et al. [77] and Kato et al. [78] investigated the drag reduction by microbubbles on flat plates whilst Mazzitelli et al. [79], Bao-Guo and Nan-sheng [80] and Nouri et al. [81] investigated the drag reduction inside a channel. The latter authors reported that bubble injection can be used to decrease the flow transfer costs. In fact, they reported a 35% reduction in the pressure drop in turbulent upward pipe flow with the maximum experimental void fraction of 9%. This is attributed to the congregation of the larger bubbles at the pipe wall. To the best of the authors’ knowledge, the sole investigation with coiled tubes was done by Saffari et al. [76] who reported an increase in the magnitude of drag reduction with increasing volumetric void fraction and decreasing Reynolds and Dean numbers at adiabatic conditions. Furthermore, there are no parallel studies using numerical methods. Therefore, this presents significant opportunities for research through the investigation of the resultant two-phase pressure drop, phase distribution and heat transfer characteristics with bubbly flow in curved tubes. 5. Conclusions This paper has provided a review of all the studies available in the open literature on the two-phase flow heat transfer

563

characteristics in helically coiled heat exchangers. When compared to single-phase flow, this field of study is characterised by a scarcity of studies. Most relevant studies have been discussed and analysed and the correlations to calculate the heat transfer coefficient as well as the principal experimental parameters have been tabulated for steam/water boiling, R-134a boiling and condensation, and nanofluid flow. The principal conclusions in this paper can be summarised through the following points:  For steam and water boiling heat transfer, literature suggests that the curvature effects of the helical coils on the heat transfer coefficient are not significant. In fact, for large diameter tubes (inner diameter > 12 mm) and at system pressures lower than 7 MPa some leading authors have adopted widely used correlations for the flow boiling heat transfer coefficient in straight tubes. For large diameter tubes, literature suggests that at higher steam qualities (x > 0.1), the principal mode of heat transfer is through convection whereas at lower qualities (x < 0.1) the nucleate boiling component is also present. In contrast, for small diameter tubes (inner diameter < 12 mm), the nucleation and convection mechanisms of heat transfer have the same importance over the full range of steam quality. The heat transfer coefficient was also found to be a strong function of the system pressure and heat flux. Literature presents numerous correlations for the prediction of the two-phase boiling heat transfer coefficient, with the majority being a function of the Lockhart–Martinelli parameter.  Literature suggests that the condensing and boiling heat transfer coefficient of R-134a in helically coiled tubes is significantly higher than that for straight tubes. The majority of authors reported the R-134a heat transfer coefficient as a function of the heat and mass flux, quality, saturation temperature, coil orientation and geometry. However, the effect of pressure was found to be indeterminate.  The applications of nanofluids in helically coiled heat exchangers is in conflict on whether nanoparticles can improve or degrade the heat transfer coefficient. Whilst the majority of authors reported a significant increase in the measured heat transfer coefficient with nanofluids over single-phase water, a contemporary study by a leading research group at the University of Lund has reported a negligible enhancement to the heat transfer performance. This is attributed to the mitigation of the secondary flow due to the higher density and viscosity of the nanofluids. A number of authors have also reported significantly different results with the concentration of nanofluids. In fact, some authors reported a degradation of performance with volumetric concentrations in excess of 1% while other authors reported a significant enhancement to the heat transfer performance. In addition to the scope for further research to address the controversies surrounding the application of nanofluids, this paper has identified key fields which require further investigation, namely; the non-boiling gas and water two-phase flow and the nanofluid and gas three-phase flow heat transfer characteristics in helically coiled tubes. The latter conditions are of particular interest to research and development engineers working in the field of space heating.

Acknowledgments The author of this study would like to thank the University of Central Lancashire, UK for facilitating the completion of this study as well as the various authors who have been contacted during the course of this study.

564

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

References [1] D.J. Goering, J.A.C. Humphrey, R. Greif, The dual influence of curvature and buoyancy in fully developed tube flows, Int. J. Heat Mass Transfer 40 (1997) 2187–2199. [2] D.G. Pabhanjan, G.S.V. Raghavan, T.J. Rennie, Comparison of heat transfer rates between a straight tube heat exchanger and a helically coiled heat exchanger, Int. Commun. Heat Mass Transfer 29 (2) (2002) 185–191. [3] P.C. Mukesh Kumar, J. Kumar, S. Suresh, Experimental investigation on convective heat transfer and friction factor in a helically coiled tube with Al2O3/water nanofluid, J. Mech. Sci. Technol. 27 (1) (2013) 239–245. [4] S.S. Pawar, K. Sunnapwar, Experimental studies on heat transfer to Newtonian and non-Newtonian fluids in helical coils with laminar and turbulent flow, Exp. Therm. Fluid Sci. 44 (2013) 792–804. [5] D.S. Austen, H.M. Soliman, Laminar flow and heat transfer in helically coiled tubes with substantial pitch, Exp. Therm. Fluid Sci. 1 (1988) 183–194. [6] C. Yildiz, Y. Bicer, D. Pehlivan, Influence of fluid rotation on the heat transfer and pressure drop in double-pipe heat exchangers, Appl. Energy 54 (1) (1996) 49–56. [7] P. Naphon, Thermal performance and pressure drop of the helical-coil heat exchangers with and without helically crimped fins, Int. Commun. Heat Mass Transfer 34 (2007) 321–330. [8] C. Yildiz, Y. Bicer, D. Pehlivan, Heat transfer and pressure drop in a heat exchanger with a helical pipe containing inside springs, Energy Conserv. Manage. 38 (6) (1997) 619–624. [9] L. Guo, X. Chen, Z. Feng, B. Bai, Transient convective heat transfer in a helical coiled tube with pulsatile fully developed turbulent flow, Int. J. Heat Mass Transfer 41 (1998) 2867–2875. [10] C. Yildiz, Y. Bicer, D. Pehlivan, Heat transfers and pressure drops in rotating helical pipes, Appl. Energy 50 (1995) 85–94. [11] L. Zhao, L. Guo, B. Bai, Y. Hou, X. Zhang, Convective boiling heat transfer and two-phase flow characteristics inside a small horizontal helically coiled tubing once-through steam generator, Int. J. Heat Mass Transfer 46 (2003) 4779– 4788. [12] Y. Chung, K. Bae, K.K. Kim, W. Lee, Boiling heat transfer and dryout in helically coiled tubes under different pressure conditions, Ann. Nucl. Energy 71 (2014) 298–303. [13] H.A. Mohammed, K. Narrein, Thermal and hydraulic characteristics of nanofluid flow in a helically coiled tube heat exchanger, Int. Commun. Heat Mass Transfer 39 (2012) 1375–1383. [14] G. Huminic, A. Huminic, Application of nanofluids in heat exchangers: a review, Renew. Sustainable Energy Rev. 16 (2012) 5625–5638. [15] A.M. Fsadni, Y.T. Ge, A.G. Lamers, Measurement of bubble detachment diameters from the surface of the boiler heat exchanger in a domestic central heating system, Appl. Therm. Eng. 31 (14–15) (2011) 2808–2818. [16] S.A. Berger, L. Talbot, L.S. Yao, Flow in curved pipes, Annu. Rev. Fluid Mech. 15 (1983) 461–512. [17] R.K. Shah, S.D. Joshi, Convective heat transfer in curved ducts, in: S. Kakac, R.K. Shah, W. Aung (Eds.), Handbook of Single Phase Convective Heat Transfer, Wiley Interscience, New York, 1987, pp. 5.1–5.46. [18] P. Naphon, S. Wongwises, A review of flow and heat transfer characteristics in curved tubes, Renew. Sustainable Energy Rev. 10 (5) (2006) 463–490. [19] S.S. Pawar, K. Sunnapwar, B.A. Mujawar, A critical review of heat transfer through helical coils of circular cross section, J. Sci. Ind. Res. 70 (2011) 835– 843. [20] K. Akagawa, S. Tadashi, U. Minoru, Study on a gas–liquid two-phase flow in helically coiled tubes, Bull. JSME 14 (72) (1971) 564–571. [21] A. Awwad, R.C. Xin, Z.F. Dong, M.A. Ebadian, H.M. Soliman, Measurement and correlation of the pressure drop in air–water two-phase flow in horizontal helicoidal pipes, Int. J. Multiphase Flow 21 (4) (1995) 607–619. [22] M. Fakoor-Pakdaman, M.A. Akhavan-Behabadi, P. Razi, An empirical study on the pressure drop characteristics of nanofluid flow inside helically coiled tubes, Int. J. Therm. Sci. 65 (2013) 206–213. [23] K.W. Hwang, D.E. Kim, K.H. Yang, J.M. Kim, M.H. Kim, H.S. Park, Experimental study of flow boiling heat transfer and dryout characteristics at low mass flux in helically-coiled tubes, Nucl. Eng. Des. 273 (2014) 529–541. [24] M. Kozeki, H. Nariai, T. Furukawa, K. Kurosu, A study of helically coiled tube once-through steam generator, Bull. JSME 13 (66) (1970) 1485–1494. [25] L.J. Guo, X.J. Chen, C. Xu, C. Guo, K. Lai, Forced convection boiling heat transfer and dryout characteristics in helical coiled tubes with various axial angles, in: Proceedings of the 11th Conference IHTC, vol. 2, Kyongju, Korea, 1998b, pp. 261–266. [26] A.A. Rabienataj Darzi, M. Farhadi, K. Sedighi, S. Aallahyari, Aghajani. Delavar, Turbulent heat transfer of Al2O3–water nanofluid inside helically corrugated tubes: numerical study, Int. Commun. Heat Mass Transfer 41 (2013) 68–75. [27] G. Huminic, A. Huminic, Heat transfer characteristics in double tube helical heat exchangers using nanofluids, Renew. Sustainable Energy Rev. 54 (2011) 4280–4287. [28] F. Akbaridoust, M. Raksha, A. Abbassi, M. Saffar-Avval, Experimental and numerical investigation of nanofluid heat transfer in helically coiled tubes at constant wall temperature using dispersion model, Int. J. Heat Mass Transfer 58 (2013) 480–491. [29] R.C. Xin, M.A. Ebadian, The effects of Prandtl numbers on local and average convective heat transfer characteristics in helical pipe, ASME J. Heat Transfer 119 (1997). 497–473.

[30] R.A. Seban, E.F. Mclaughlin, Heat transfer in tube coils with laminar and turbulent flow, Int. J. Heat Mass Transfer 6 (1963) 387–395. [31] N. Jamshidi, M. Farhadi, K. Sedighi, G. Domeiry, Optimisation of design parameters for nanofluids flowing inside helical coils, Int. Commun. Heat Mass Transfer 39 (2012) 311–317. [32] Salimpour, Heat transfer coefficients of shell and coiled tube heat exchangers, Exp. Therm. Fluid Sci. 33 (2009) 203–207. [33] A.N. Dravid, K.A. Smith, E.W. Merrill, P.L.T. Brain, Effect of secondary fluid on laminar flow heat transfer in helically coiled tubes, Am. Inst. Chem. Eng. J. 17 (5) (1971) 1114–1122. [34] A. Owhadi, K.J. Bell, B. Crain Jr., Forced convection boiling inside helically coiled tubes, Int. J. Heat Mass Transfer 11 (1968) 1179–1793. [35] J.C. Chen, A correlation for boiling heat transfer to saturated fluids in convective flow, I&EC Process Des. Dev. 5 (3) (1966) 322–329. [36] H. Nariai, M. Kobayashi, T. Matsuoka, Friction pressure drop and heat transfer coefficient of two-phase flow in helically coiled tube once-through steam generator for integrated type marine water reactor, J. Nucl. Sci. Technol. 19 (11) (1982) 936–947. [37] V.E. Schrock, L.M. Grossman, Forced convection boiling in tubes, Nucl. Sci. Eng. 12 (4) (1962) 474–481. [38] D. Steiner, J. Taborek, Flow boiling heat transfer in vertical tubes correlated by an asymptotic model, Heat Transfer Eng. 13 (2) (1992) 43–69. [39] F. Campolumghi, M. Cumo, G. Ferrari, G. Palazzi, Full scale tests and thermal design for coiled once-through heat exchangers, Am. Inst. Chem. Eng. Symp. Ser. 73 (1977) 215–222. [40] V.G. Kubair, Heat transfer to multiphase flow in coiled pipes, heat transfer, in: C.L. Tien, et al. (Eds.), Proceedings of the 8th International Heat Transfer Conference, vol. 5, San Francisco, USA, 1986, pp. 2355–2360. [41] B. Crain, K.J. Bell, Forced convection heat transfer to a two-phase mixture of water and steam in a helical coil, Am. Inst. Chem. Eng. Symp. Ser. 69 (1973) 30–36. [42] L. Guo, Z. Feng, X. Chen, Transient convective heat transfer of steam–water two-phase flow in a helical tube under pressure drop type oscillations, Int. J. Heat Mass Transfer 45 (2002) 533–542. [43] B.F. Bai, L.J. Guo, Study on convective boiling heat transfer in horizontal helically coiled tubes, Chin. J. Nucl. Sci. Eng. 17 (1997) 302–308. [44] J. Yi, Z.-H. Liu, J. Wang, Heat transfer characteristics of the evaporator section using helical coiled pipes in a looped heat pipe, Appl. Therm. Eng. 23 (2003) 89–99. [45] H.J. Kang, C.X. Lin, M.A. Ebadian, Condensation of R134a flowing inside helicoidal pipe, Int. J. Heat Mass Transfer 43 (2000) 2553–2564. [46] S. Wongwises, M. Polsongkram, Evaporation heat transfer and pressure drop of HFC-134a in a helically coiled concentric tube-in-tube heat exchanger, Int. J. Heat Mass Transfer 49 (2006) 658–670. [47] A. Cavallini, R. Zecchin, A dimensionless correlation for heat transfer coefficient in forced convection condensation, in: Proceedings of the Sixth International Heat Transfer Conference, Tokyo, 1974, pp. 309–313. [48] D. Jung, K.H. Song, Y. Cho, S. Kim, Flow condensation heat transfer coefficients of pure refrigerants, Int. J. Refrig. 26 (2003) 4–11. [49] H. Aria, M.A. Akhavan-Behabadi, F.M. Shemirani, Experimental investigation of flow boiling heat transfer and pressure drop of HFC-134a inside a vertical helically coiled tube, Heat Transfer Eng. 33 (2) (2012) 79–86. [50] B. Yu, J.T. Han, C.X. Kang, A. Awwad, M.A. Ebadian, Condensation heat transfer of R-134A flow inside helical pipes at different orientations, Int. Commun. Heat Mass Transfer 30 (6) (2003) 745–754. [51] W. Cui, L. Li, M. Xin, T.C. Jen, Q. Chen, Q. Liao, A heat transfer correlation of flow boiling in micro-finned helically coiled tube, Int. J. Heat Mass Transfer 49 (2006) 2851–2858. [52] S. Li, H. Jitian, S. Guoping, P. Jihong, Condensation heat transfer of R-134a in a horizontal straight and helically coiled tube-in-tube heat exchangers, J. Hydrodyn. 19 (6) (2007) 677–682. [53] C.N. Chen, J.T. Han, T.C. Jen, L. Shao, Thermo-chemical characteristics of R134a flow boiling in helically coiled tubes at low mass flux and low pressure, Thermochim. Acta 512 (2011) 163–169. [54] A.M. Elsayed, R.K. Al-Dadah, S. Mahmoud, A. Rezk, Investigation of flow boiling heat transfer inside small diameter helically coiled tubes, Int. J. Refrig. 35 (2012) 2179–2187. [55] Z. Wu, L. Wang, B. Sunden, Pressure drop and convective heat transfer of water and nanofluids in a double-pipe helical heat exchanger, Appl. Therm. Eng. 60 (2013) 266–274. [56] N. Kannadasan, K. Ramanathan, S. Suresh, Comparison of heat transfer and pressure drop in horizontal and vertical helically coiled heat exchanger with Cu/water based nanofluids, Exp. Therm. Fluid Sci. 42 (2012) 64–70. [57] M. Kahani, S.Z. Heris, S.M. Mousavi, Comparative study between metal oxide nanopowders on thermal characteristics of nanofluid flow through helical coils, Powder Technol. 246 (2013) 82–92. [58] M.A. Akhavan-Behabadi, Pakdaman M. Fakoor, M. Ghazvini, Experimental investigation on the convective heat transfer of nanofluid flow inside vertical helically coiled tubes under uniform wall temperature condition, Int. Commun. Heat Mass Transfer 39 (2012) 556–564. [59] M. Fakoor-Pakdaman, M.A. Akhavan-Behabadi, P. Razi, An experimental investigation on thermo-physical properties and overall performance of MWCNT/heat transfer oil nanofluid flow inside vertical helically coiled tubes, Int. J. Therm. Sci. 40 (2012) 103–111. [60] S. Suresh, M. Chandrasekar, Sekhar S. Chandra, Experimental studies on heat transfer and friction factor characteristics of CuO/water nanofluid under

A.M. Fsadni, J.P.M. Whitty / International Journal of Heat and Mass Transfer 95 (2016) 551–565

[61]

[62]

[63] [64] [65]

[66]

[67]

[68]

[69]

turbulent flow in a helically dimpled tube, Exp. Therm. Fluid Sci. 35 (2011) 542–549. S.M. Hashemi, M.A. Akhavan-Behabadi, An empirical study on heat transfer and pressure drop characteristics of CuO-base oil nanofluid flow in a horizontal helically coiled tube under constant heat flux, Int. Commun. Heat Mass Transfer 39 (2012) 144–151. W. Williams, J. Buongiorno, L.W. Hu, Experimental investigation of turbulent convective heat transfer and pressure loss of alumina/water and zirconia/ water nanoparticle colloids (nanofluids) in horizontal tubes, ASME J. Heat Transfer 130 (2008) 042412. E.V. Timofeeva, W. Yu, D.M. France, D. Singh, S.J.L. Routbort, Nanofluids for heat transfer: an engineering approach, Nanoscale Res. Lett. 6 (2011) 182. K. Narrien, H.A. Mohammed, Influence of nanofluids and rotation on helically coiled tube heat exchanger performance, Techmochim. Acta 564 (2013) 13–23. P.A. Sasmito, J.C. Kurnia, A.S. Mujumdar, Numerical evaluation of laminar heat transfer enhancement in nanofluid flow in coiled square tubes, Nanoscale Res. Lett. 6 (2011) 376. M.A. Khairul, R. Saidur, M.M. Rahman, M.A. Alim, A. Hossain, Z. Abdin, Heat transfer and thermodynamic analyses of a helically coiled heat exchanger using different types of nanofluids, Int. J. Heat Mass Transfer 67 (2013) 398– 403. R.A. Taylor, P.E. Phelan, Pool boiling of nanofluids: comprehensive review of existing data and limited new data, Int. J. Heat Mass Transfer 52 (2009) 5339– 5347. J.P. Tu, N. Dinh, T. Theofanous, An experimental study of nanofluid boiling heat transfer, in: Proceedings of the 6th International Symposium on Heat Transfer, Beijing, China, 2004. D. Wen, Y. Ding, Experimental investigation into the pool boiling heat transfer of aqueous based gamma alumina nanofluids, J. Nanopart. Res. 7 (2) (2005) 265–274.

565

[70] S.K. Das, N. Putra, P. Thiesen, W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids, ASME Trans. J. Heat Transfer 125 (2003) 567–574. [71] S.K. Das, N. Putra, W. Roetzel, Pool boiling characteristics of nanofluids, Int. J. Heat Mass Transfer 46 (2003) 851–862. [72] J. Jackson, J. Bryan, Investigation into the pool boiling characteristics of gold nanofluids (Master’s Thesis), University of Missouri, Columbia, 2007. [73] Y.T. Ge, A.M. Fsadni, H.S. Wang, Bubble dissolution in horizontal turbulent flow in a domestic central heating system, Int. J. Appl. Energy 108 (2013) 477–485. [74] S.N. Mandal, S.K. Das, Gas–liquid flow through coils, Korean J. Chem. Eng. 204 (4) (2003) 624–630. [75] Y. Murai, S. Yoshikawa, S. Toda, M. Ishikawa, F. Yamamoto, Structure of air–water two-phase flow in helically coiled tubes, Nucl. Eng. Des. 236 (2006) 94–106. [76] H. Saffari, R. Moosavi, E. Gholami, N.M. Nouri, The effect of bubble in the pressure drop reduction in helical coil, Exp. Therm. Fluid Sci. 51 (2013) 251– 256. [77] B. Jacob, A. Olivieri, M. Miozzi, E.F. Campana, R. Piva, Drag reduction by microbubbles in a turbulent boundary layer, Phys. Fluids 22 (11) (2010) 115104. [78] H. Kato, T. Iwashina, M. Miyanaga, H. Yamaguchi, Effect of microbubbles on the structure of turbulence in a turbulent boundary layer, J. Mar. Sci. Technol. 4 (1999) 155–162. [79] I. Mazzitelli, D. Lohse, F. Toschi, The effect of micro bubbles on developed turbulence, Phys. Fluids 15 (1) (2003) L5. [80] C. Bao-Guo, L. Nan-Sheng, Direct numerical simulations of turbulent channel flows with consideration of the buoyancy effect of the bubble phase, J. Hydrodyn. 23 (3) (2011) 282–288. [81] N.M. Nouri, S.Y. Motlagh, M. Navidbakhsh, M. Dalilhaghi, A.A. Moltani, Bubble effect on pressure drop reduction in upward pipe flow, Exp. Therm. Fluid Sci. 44 (2013) 592–598.