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Powder Technology 305 (2017) 206–216
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Experimental investigation of MWCNT–water nanofluids flow and convective heat transfer characteristics in multiport minichannels with smooth/micro-fin surface Y.H. Diao ⁎, C.Z. Li, J. Zhang, Y.H. Zhao, Y.M. Kang The Department of Building Environment and Facility Engineering, The College of Architecture and Civil Engineering, Beijing University of Technology, No.100 Pingleyuan, Chaoyang District, Beijing 100124, China
a r t i c l e
i n f o
Article history: Received 2 July 2016 Received in revised form 28 September 2016 Accepted 3 October 2016 Available online 05 October 2016 Keywords: Nanofluids Micro-fin Heat transfer Friction factor Performance evaluation Criterion
a b s t r a c t This paper reports on the results of an experimental study on the heat transfer and flow performance of multiwalled carbon nanotubes (MWCNT) in aqueous suspensions flowing in multiport minichannel flat tubes with smooth/micro-fin surface under a constant heat flux condition. The MWCNT–water nanofluids volume concentrations are 0.001%, 0.005%, 0.01%, and 0.1%. Results indicate that the friction factor and the Nusselt number of the nanofluids are higher than those of water. The Nusselt number does not increase with volume concentration. The heat transfer of nanofluids in the micro-fin tubes is higher than that of nanofluids in the smooth tube. However, the heat transfer enhancement of nanofluids in the micro-fin tubes is lower than that of nanofluids in the smooth tube. The effect of micro-fin spacing is more evident in nanofluids than in water. Nanofluids with a concentration of 0.01% flowing in the tube with closely spaced micro-fin tube exhibit the optimal thermal performance in accordance with the performance evaluation criterion. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Advancements in thermal loads for an extensive range of industrial applications, including microelectronics, power generation, aerospace and automotive engineering, require the exploitation of micro/miniscale heat exchangers, which provide a high heat transfer coefficient. The thermal conductivity of heat transfer fluids also plays a crucial role in the development of high thermal performance systems. Nanofluids, which were first proposed by Choi in 1995 [1], are prepared by dispersing metal, metallic oxide, carbon nanotubes (CNTs), or other nanoparticles into water, ethylene glycol, engine oil, or another base fluid. In the past decade, considerable increases in the thermal conductivities of nanofluids have been reported. Furthermore, numerous attempts have been made to investigate heat transfer and flow performances of all kinds of nanofluids. Pak and Cho [2] conducted experiments to investigate the heat transfer and pressure drop of Al2O3 and TiO2 aqueous nanofluids in turbulent flow in a stainless steel tube. They reported that 1.34 vol.% Al2O3– water nanofluid exhibited 45% heat transfer enhancement compared with the base fluid and 2.78 vol.% TiO2–water nanofluids exhibited 75% heat transfer enhancement. However, the increase in Darcy friction factors of both nanofluids was insignificant compared with that of the base fluid. Ding et al. [3] examined the heat transfer characteristic of ⁎ Corresponding author. E-mail address: [email protected] (Y.H. Diao).
http://dx.doi.org/10.1016/j.powtec.2016.10.011 0032-5910/© 2016 Elsevier B.V. All rights reserved.
multiwalled carbon nanotubes (CNT) in the laminar flow region in a horizontal tube. Their experimental results showed that the maximum heat transfer enhancement was approximately 350% for 0.5 wt.% CNT nanofluid at a Reynolds number of 800. Garg et al. [4] experimentally investigated the convective heat transfer performance of MWCNT aqueous nanofluids in laminar flow. They observed that the maximum enhancement in convective heat transfer was 32% at Re = 600. Liao and Liu [5] presented an experimental study on the heat transfer and flow drag characteristics of MWCNT–water nanofluids in both the laminar and turbulent flow regions in a small horizontal tube. They concluded that heat transfer was sharply enhanced in high mass concentrations, whereas flow characteristic was nearly the same as that of water. Duangthongsuk and Wongwises [6] conducted an experimental study on the turbulent flow and heat transfer of TiO2–water nanofluids in a horizontal double tube. The heat transfer enhancement for 1.0 vol.% nanofluids was found to be approximately 26% higher than that of water, but heat transfer decreased by 14% at the highest concentration (2.0 vol.%). Meanwhile, pressure drop slightly increased with nanofluids concentration. Amrollahi et al. [7] measured the convective heat transfer coefficients of functionalized MWCNT–water nanofluids in laminar and turbulent flow in a uniformly heated horizontal tube at the entrance region. Their experimental results showed that the heat transfer coefficient increased by up to 33%–40% for a 0.25 wt.% nanofluids in laminar and turbulent flows. Yu et al. [8] investigated the heat transfer characteristics of Al2O3 nanofluids which is based on the mixture of ethylene glycol and water in a circular copper tube with
Y.H. Diao et al. / Powder Technology 305 (2017) 206–216
Nomenclature a channel width, m A total cross section area, m2 b channel height, m specific heat capacity, J/kg K cp d diameter, m hydraulic diameter, m Dh f friction factor G mass flow rate, kg/s h heat transfer coefficient, W/m2 K k thermal conductivity, W/m K L tube length, m Nu Nusselt number Pe perimeter, m PEC performance evaluation criterion Pr Prandtl number ΔP total pressure differential, Pa frictional pressure loss, Pa ΔPf singular pressure loss, Pa ΔPm q heat flux, W/m2 Q heat transfer rate gained by fluid, W Re Reynolds number T temperature, °C Greek symbols α aspect ratio, b/a (0 b α b 1) β ratio of the nanolayer thickness to the original particle φ volume concentration μ dynamic viscosity, Pa · s ρ mass density, kg/m3 χ axial distance, m Subscripts bf base fluid f fluid nf nanofluid p particle in inlet out outlet w wall
207
studied heat transfer and flow characteristics in micro-fin tubes. They argued that heat transfer of a micro-fin tube was 190% higher than that of a smooth tube in turbulent flow. Despite an increase in pressure drop, the heat transfer results for a micro-fin tube were still 80% higher than that in a smooth tube. Han and Lee [12] studied heat transfer and flow characteristics in micro-fin tubes at a Re range of 1000–8000 and Pr range of 4–7. They reported that the high relative roughness of micro-fin tubes is the main factor to the enhancement of efficiency index. Wei et al. [13] measured flow friction and heat transfer in a micro-fin tube at Re ranging from 2500 to 90,000 and Pr varying from 3.2 to 220. Their results showed that a critical Re for heat transfer enhancement existed for the micro-fin tube. The friction factor of the micro-fin tube was 40%–50% higher than that of the smooth tube at Re N 10,000. Celen et al. [14] experimentally analyzed flow characteristics in smooth and micro-fin tubes at a mass flow rate range of 0.023–0.100 kg/s. They found that pressure drop in the micro-fin tube was higher than that in the smooth tube because the micro-fins produced swirl flow and flow recirculation. Derakhshan et al. [15] experimentally investigated mixed convection heat transfer characteristics and performance evaluation of MWCNT–oil nanofluids flowing in smooth and micro-fin tubes. It is found that the heat transfer of nanofluids is enhanced compared with that of the base fluid inside smooth and micro-fin tubes. Their performance evaluation also showed that using nanofluids instead of the base fluid is a better way to enhance convection heat transfer performance compared with applying the micro-fin tube instead of the smooth tube. From the literature survey, it is clear that most of the existing studies have investigated the heat transfer and flow characteristics of nanofluids in smooth tubes or pure fluids in micro-fin tubes. Experimental data on the heat transfer and flow characteristics of nanofluids in micro-fin tubes remain limited. Accordingly, the pressure drop and heat transfer characteristics of MWCNT–water nanofluids flowing within multiport minichannel flat tubes with smooth/micro-fin surface were examined in the present study. The effect of surfactant on the heat transfer and flow characteristics in the tubes was also investigated.
2. Preparation and thermophysical properties of nanofluids 2.1. Preparation of nanofluids
the internal diameter of 2.7 mm with a constant temperature. It was found that heat transfer increased with an increase in nanofluids concentration and the maximum enhancement is 106% at Re = 2000 with the 2 vol.% nanofluids, which attributes to both the increase of thermal conductivity and the interaction of particle–particle, particle–liquid and the micro convection in nanofluids. Zhang et al. [9] performed an experiment to investigate the heat transfer and flow characteristics of TiO2–water nanofluids in a multiport minichannel flat tube with a 1.65 mm hydraulic diameter. They found that 0.01 vol.% was the optimal nanofluids volume concentration and its enhancement of heat transfer being 61% at the Re ≈ 6100. And 0.01 vol.% nanofluids also exhibited optimal thermal performance. Bahremand et al. [10] studied experimentally and numerically the heat transfer and flow characteristics of water–silver nanofluid with turbulent convection flow region in helically coiled tubes under constant wall heat flux. They found that the heat transfer characteristics of nanofluids increase with the volume concentration of nanofluids. And they also observed that the increase of nanoparticle diameter deteriorates the heat transfer of nanofluids. Moreover, a higher surface-area-to-volume ratio is another method to guide the design of heat transfer devices. As enhanced tubes, microfin tubes are widely adopted because of their capability to extend the heat transfer surface and generate turbulence in fluid flow to offer the potential for improving heat transfer performance. Copetti et al. [11]
Preparing nanofluids is a vital step in experimental studies on nanofluids. The nanofluids are prepared via a two-step method that is widely accepted by scholars studying the flow and heat transfer of nanofluids [16]. The carbon nanotubes with COOH functional groups are purchased from Chengdu Organic Chemicals Co. Ltd. These CNTs have a density of approximately 2.1 g cm−3, an outer diameter of 20– 30 nm, and a length 0.5–2 μm. Dry nanotube powder was dispersed into water. Given that nanoparticles are always prone to aggregate in deionized water (DI), two methods may be used to obtain a stable liquid suspension. And the two methods are sequentially applied to stabilize nanofluids. The first method is to use the surfactant gum arabic (GA) for MWCNT nanofluids. The second method is to oscillate the mixture in an ultrasonic water bath for approximately 4 h. The volume concentrations φ of nanofluids adopted in this study are 0.001 vol.%, 0.005 vol.%, 0.01 vol.%, and 0.1 vol.%. The scanning electron microscope (SEM) images of the MWCNT nanofluids are shown in Fig.1. Both nanofluids are kept stable for approximately a week. In order to investigate the effects of surfactant on the flow and heat transfer characteristics, the GA aqueous solution is also used as a working fluid. The weight of GA added to aqueous solution is equal to that added to the corresponding MWCNT–water nanofluids (i.e., 0.001 wt.% to 0.001 vol.%, 0.005 wt.% to 0.005 vol.%, 0.01 wt.% to 0.05 vol.%, and 0.1 wt.% to 0.1 vol.%).
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Thermal conductivity ( W/m K)
0.75
0.01% MWCNT-Water nanofluids Water Yu and Choi model 0.70
0.65
0.60
(a)
20
25
30
35
40
Fig. 2. Effective thermal conductivities of nanofluid with 0.01% volume concentration at three different temperatures (error bar ±5%).
The thermal conductivity and viscosity of the nanofluids are significant properties for the convective heat transfer performance. Thermal conductivity is measured using the transient hot-wire method. The measuring apparatus used is Hot Disk 2500S thermal property meter. The Hot Disk 2500S is initially calibrated using distilled water before measuring the other fluids. Measurements are taken thrice to ensure that measurement accuracy is within ±5%. The thermal conductivity of the prepared nanofluids and the Yu and Choi [17] correlation model are shown in Fig. 2. The Yu and Choi model is defined as.
(b)
knf kp þ 2kbf þ 2 kp −kbf ð1 þ βÞ3 φ ¼ ; kbf kp þ 2kbf − kp −kbf ð1 þ βÞ3 φ
ð3Þ
where β is the ratio of nanolayer thickness to the original particle. In calculating the thermal conductivities of nanofluids, β is generally set as 0.1. The thermal conductivities of the 0.01 vol.% MWCNT nanofluids at different temperatures are 9%, 9.3%, and 9.5% higher than that of distilled water. Viscosity is measured at 20 °C using a rotating viscometer. The relative viscosity (μnf/μbf) between the nanofluids and DI water, as well as the Batchelor correlation [18], is presented in Fig. 3. The well-known
(c)
1.16
Fig. 1. SEM images of the MWCNT nanofluids: (a) 0.001% volume concentration, (b) 0.01% volume concentration, and (c) 0.1% volume concentration.
The density of the nanofluids is provided by the Pak and Cho [2] correlation: ρnf ðT Þ ¼ ð1−φÞρbf ðT Þ þ φρp ðT Þ:
cp;nf ¼
ρnf ðT Þ
1.08
1.04
ð1Þ 1.00
The specific heat of the nanofluids is calculated using the Pak and Cho [2] correlation: φ ρcp p ðT Þ þ ð1−φÞ ρcp bf ðT Þ
µ nf / µ bf
2.2. Thermophysical properties of nanofluids
1.12
MWCNT-water nanofluids Batchelor correlation
:
ð2Þ
0.96
1E-3
0.01
0.1
Volume Fraction(%) Fig. 3. Relative viscosities of nanofluids at various volume concentrations (error bar ±5%).
Y.H. Diao et al. / Powder Technology 305 (2017) 206–216
209
Fig. 4. Schematic of the experimental apparatus.
Batchelor correlation is expressed as follows: μ nf ¼ μ bf
1 þ 2:5φ þ 6:25φ2 :
ð4Þ
As shown in Fig. 3, relative viscosity increases with an increase in nanofluids concentration. 3. Experimental apparatus The schematic of the experimental apparatus is illustrated in Fig. 4. The experimental apparatus consists of a flow loop, a heating unit, a cooling loop, and a data acquisition system. The flow loop contains a water bath, a liquid pump, an exhaust valve, a Coriolis mass flow meter, a test section, and a double-pipe heat exchanger. The cooling loop, which includes the double-pipe heat exchanger and a water chilling unit, is used to keep the temperature of the nanofluids constant. The water bath is also used to keep the fluids temperature precisely invariable. The mass flow rate in the flow loop is measured using the Coriolis mass flow meter. The fluid, which is firstly pumped from the water bath, flows through the Coriolis mass flow meter, the test section, the doublepipe heat exchanger and finally returns to the water bath. The test section, which is shown in Fig. 5, is an aluminum multiport minichannel flat tube with a length of 450 mm. The cross section of the flat tube is shown in Fig. 6. Fig. 6(c–d) shows that the minichannel has a fin. Smooth tube (1) has 9 parallel minichannels and the others have 11
parallel minichannels. The geometric dimensions are listed in Table 1. To obtain better connection with the experimental system, two manifolds are designed to avoid the non-uniform flow distribution effect and welded onto both ends of the aluminum multiport minichannel flat tube. The inlet and outlet temperatures of the fluid are measured by two T-type thermocouples inserting both manifolds. To measure the wall temperatures at the axial locations of the tube, ten K-type thermocouples are evenly mounted on the upper and lower external surface of the flat tube. The test section is thermally insulated with thick thermal insulation materials to maintain a constant heat flux condition along the axial direction of the flat tube. The inlet and outlet press drops of the fluids are measured with a pressure difference transducer and the joints are mounted at the bottom of the two manifolds. 4. Data reduction 4.1. Pressure drop The hydraulic diameter and aspect ratio of the minichannels with and without micro-fins are respectively calculated from Dh ¼
4A and α ¼ a=b 0bαb1: Pe
ð5Þ
Thermocouple
Manifold
Pressure transducer
Fig. 5. Schematic of the test section.
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(c)
(d)
S1
S2
b
a
S1
Hfin Wfin (e) Fig. 6. Cross section of the multiport minichannel flat tube.
The total pressure difference with the test section is expressed as ΔP ¼ ΔP f þ ΔP m
ð6Þ
where the frictional pressure difference ΔPf is
ΔP f ¼ f
L G ; D h ρ f A2
ð7Þ
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Table 1 Geometric dimensions of the multiport minichannel flat tube. No.
a (mm)
b (mm)
α (b/a)
Dh (mm)
Hfin (mm)
Wfin (mm)
S2 (mm)
Smooth (1) Smooth (2) Micro-fin (1) Micro-fin (2)
2.36 1.99 2.03 2.0
2.03 2.08 2.1 2.1
0.86 0.96 0.97 0.95
2.18 2.03 1.71 1.69
– – 0.25 0.25
– – 0.28 0.27
– – 0.27 0.95
and the singular pressure difference ΔPm is determined by the method presented in Ref. [19]. The Reynolds number and the Darcy frictional factor f are respectively defined as G Dh ; Re ¼ A μf f ¼ ΔP f
Re ¼
Ren and Nu ¼
10 X
ð16Þ
Nun
k¼1
4.3. Uncertainty analysis
2 Dh ρ f A : 2 L G
ð9Þ The temperature measurement precision is ±0.1 °C. The uncertainty in mass flow rate measurement is 0.2%. The uncertainty in pressure measurement is 0.25%. Indirect parameters, such as Re, f, and Nu, are calculated using.
The heat transfer rate obtained by the fluid flowing through the test section can be calculated from.
10 X k¼1
ð8Þ
4.2. Heat transfer
Q ¼ G cp T f ;out −T f ;in :
ð10Þ
The wall heat flux can be defined as the heat transfer rate gained by the fluids, i.e., q¼
Finally, the averaged Reynolds number and Nusselt number can be calculated by.
Q : L Pe
ð11Þ
z ¼ f ðy1 ; y2 yn Þ; " 2 2 2 #12 ∂z ∂z ∂z δz ¼ δy þ δy þþ δy : ∂y1 1 ∂y2 2 ∂yn n
ð17Þ
The uncertainties of the relevant parameters used in this study are listed in Table 2. 5. Results and discussion 5.1. Experiments with water
On the basis of energy balance, the mean temperature of the fluids at the longitudinal position χ in a tube can be given by T f ðχ Þ ¼ T f ;in þ
Q χ: G cp; f ðχ Þ L
ð12Þ
The local heat transfer coefficient is defined as hðχ Þ ¼
q : T w ðχ Þ−T f ðχ Þ
ð13Þ
The local Nusselt number can be calculated from Nuðχ Þ ¼
hðχ Þ Dh : k f ðχ Þ
The experiments are first conducted with the base fluid (water) in smooth tube (1) to verify the integrity and reliability of the experimental facility. 5.1.1. Heat transfer The average Nusselt number as a function of the Reynolds number is shown in Fig. 7 with the smooth tube (1). As indicated by the friction factor, the transition from laminar to turbulent flow occurs at Re ≈ 1800. Several established heat transfer correlations, which are listed in Table 3, are also plotted in Fig. 7. In the laminar region, the measured data are slightly lower than the predicted data from the Stephan
ð14Þ
Water Shah and London equation [20] Garimella equation [21] Hausen equation [22] Stephan and Preuß er equation [23]
The local Reynolds number is determined from G Dh : A μ f ðχ Þ
ð15Þ
Nu
Re ¼
10
Table 2 Uncertainties of the experimental parameters. Parameter
Value
Uncertainty (%)
Dh (mm) Q (W) Re f Nu
2.03–2.18 125–230 130–5600 0.029–0.66 20–36
3.30–3.49 2.0–6.37 3.23–3.48 9.77–10.89 7.84–11.9
100
1000
10000
Re Fig. 7. Average Nusselt number versus Reynolds number (water) for smooth tube (1).
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Table 3 Conventional correlations from the literature for comparing the experimental data. Reference
Correlation
Condition
Range of validity
Shah and London [20]
Nu ¼ 8:235ð1−2:0421α þ 3:0854α 2 −2:4765α 3 þ 1:0578α 4 −0:1861α 5
Fully developed
Laminar
Garimella et al. [21]
Nu ¼ ðNulam 10 þ f ;exp½ð360−ReÞ=925 þ Nu 1 2 g Nu 2
118 b Re b 10,671
6.48 b Pr b 11.2
Thermally developing turbulent
2200 b Re b 104
Simultaneously developing (constant wall heat flux)
0.7 b Pr b 7
−5 0:1
lam
Hausen [22]
Þ
turb
0:14
μ
Nu ¼ 0:116ðRe2=3 −125ÞPr1=3 ½1 þ ðD=LÞ2=3 ðμ f Þ w
Stephan and Preuβer [23]
Nu ¼ 4:364 þ
1:33
0:086ðRePrD=LÞ 1þ0:1 ;PrðReD=LÞ0:83
and Preuβer equation. However, the measured data and the predicted data display the same trend. In the turbulent region, the trend of the measured data is more approximate to that of the predicted data from the Garimella equation. As shown in Fig. 8, the average Nusselt number are plotted against the Reynolds number of water for the smooth tube (2), micro-fin tubes (1) and (2). As expected, the heat transfer rate in the micro-fin tubes is higher than that in the smooth tube. This result can be explained as follows. Compared with a smooth surface, micro-fins could promote disturbance as well as increase the heat transfer area; thus, the heat transfer rate in the micro-fin tubes is enhanced. The Nusselt number of micro-fin tube (1) is slightly higher than that of micro-fin tube (2). The effect of micro-fin spacing S2 on heat transfer is inconspicuous. 5.1.2. Pressure drop Fig. 9 shows the experimental data for the friction factor as a function of Re compared with the conventional theory correlations for smooth tube (1). The Shah and London equation [20] and the Blasius equation [24] are used to compare with the data for water in smooth tube. The Shah and London equation, f . Re = 96(1 − 1.3553 ⋅ α + 1.9467 ⋅ α2 − 1.7012 ⋅ α3 + 0.9564 ⋅ α4 − 0.2537⋅ α5), (18)is applied to a fully developed laminar flow in rectangular channels. The Blasius equation, f ¼ 0:316 Re−0:25 ;
ð19Þ
is valid within the range of Re b 2 × 104 for a fully developed turbulent flow regime. Fig. 9 shows that the experimental data agree well with the Shah and London equation in the laminar flow regime. In the turbulent flow regime, the friction factor obtained from the experiments is lower than
that calculated from Eq. (19). Furthermore, the transition from laminar flow to turbulent flow occurs at Re ≈ 1800, and the fully developed turbulent flow begins to establish at Re ≈ 2300. As is shown in Fig. 10, friction factors are plotted against the Reynolds number of water for the smooth tube (2), micro-fin tubes (1) and (2). As expected, the friction factors in the micro-fin tubes are higher than that of the smooth tube. The presence of micro-fins contributes to friction. The micro-fin spacing S2 has a little effect on the friction factor in the laminar flow region and nearly no effect on that in the turbulent flow region. For the micro-fin tubes, there exists a slightly earlier laminar–turbulent transition at Re = 1650 compared with the smooth tube. This behavior may be attributed to the micro-fins causing a stronger disturbance to the flow, which results in a slightly earlier laminar–turbulent transition.
5.2. Experiments with surfactant As is shown in Fig. 11, the corresponding friction factors of the surfactant solution at low concentrations are approximately the same as that of DI water. However, the friction factor of 0.1 wt.% surfactant solution is slightly higher than that of water because the viscosity of this solution is higher than that of water. In the laminar flow regime, the heat transfer of the solution is slightly lower than that of water. In the turbulent flow regime, the friction factor and heat transfer of the solution are nearly uniform with those of DI water. The results show that the effect of the surfactant on the heat transfer rate is more evident at 0.1 wt.% concentration in the laminar flow regime. The thickness of the thermal boundary layer plays a dominant role in heat transfer in laminar flow. An increase in viscosity leads to an increase in thermal boundary layer thickness, which, in turn, results in a decrease in the heat transfer coefficient. Thus, the effect of viscosity on turbulent heat transfer can be ignored.
1
Water Shah and London equation [20] Blasius equation [24]
10
f
Nu
Smooth tube (2) Micro-fin tube (1) Micro-fin tube (2)
0.1
100
1000
10000
Re Fig. 8. Average Nusselt number versus Reynolds number (water) for different tubes.
100
1000
10000
Nu Fig. 9. Friction factor versus Reynolds number (water) for the smooth tube (1).
Y.H. Diao et al. / Powder Technology 305 (2017) 206–216
213
1
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
f
Nu
Smooth tube (2) Micro-fin tube (1) Micro-fin tube (2)
0.1
100
1000
10
100
10000
1000
Re Fig. 10. Friction factor versus Reynolds number (water) for the different tubes.
5.3. Experiments with MWCNT nanofluids 5.3.1. Heat transfer The Nu of nanofluids at different concentrations and that of DI water are shown in Figs. 12–14. In the smooth and micro-fin tubes, the Nu
Nu
Water 0.001wt.% GA 0.005wt.% GA 0.01wt.% GA 0.1wt.% GA
10
100
1000
10000
Re
(a) Average Nusselt number versus Reynolds number
10000
Re Fig. 12. Average Nusselt number versus Reynolds number (MWCNT nanofluids) for the smooth tube (2).
values of the nanofluids are higher than those of the base fluid and increase with increasing Re. At φ ≤ 0.01 vol.%, the Nu values of the nanofluids increase with volume concentration. At φ ≥ 0.01 vol.%, the Nu values decrease with an increase in volume concentration. Thus, an optimum volume concentration exists for enhancing heat transfer. This is due to the fact that as the nanofluids concentrations increase, the thermal conductivity and viscosity of nanofluids become higher than those of the base fluid. The increase in thermal conductivity leads to heat transfer enhancement. An increase in viscosity results in a decrease in heat transfer due to increase in boundary layer thickness because of viscosity. Another factor that enhances heat transfer is the chaotic movement of nanotubes. Such movement reduces the thickness of the thermal boundary layer and accelerates the energy exchange process. However, as volume concentration increases and particles easily agglomerate, particle movements are hindered. Consequently, at φ ≤ 0.01 vol.%, the factors intensified by the heat transfer outweigh the effect of the reduced factors. At φ ≥ 0.01 vol.%, the opposite case occurs. Similar results can be found in [6,25]. In view of the uniform optimum concentration for the three flat tubes, the ratios of Nu between the 0.01 vol.% nanofluids and the base fluid for the smooth tube (2), micro-fin tubes (1) and (2) are plotted against the Re in Fig. 15. As shown in Fig. 15, the enhancement ratio of the Nu for the smooth tube is higher than that for the micro-fin tubes at the same Re, which indicates that the effect of nanoparticles on heat transfer enhancement in the smooth tube is greater than that in the
1
Water 0.001wt.% GA 0.005wt.% GA 0.01wt.% GA 0.1wt.% GA
f
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
100
Nu
0.1
1000
10
10000
Re
(b) Friction factor versus Reynolds number Fig. 11. Comparison of the friction factor and Nu obtained from water and surfactant solution at different concentrations.
100
1000
10000
Re Fig. 13. Average Nusselt number versus Reynolds number (MWCNT nanofluids) for the micro-fin tube (1).
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Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
10
100
f
Nu
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.% 0.1
1000
10000
100
Re Fig. 14. Average Nusselt number versus Reynolds number (MWCNT nanofluids) for the micro-fin tube (2).
micro-fin tubes. This result can be attributed to the micro-fins disturbing the random motions of the nanoparticles and their movements when the nanoparticles interact with the micro-fins. The presence of micro-fins can affect the chaotic movement of nanoparticles; consequently, heat transfer enhancement for micro-fin tubes reduces compared with for in the smooth tube. However, the Nu of the microfin tubes is higher than that of the smooth tube in each volume concentrations. Similar findings are reported in [15,26]. This result can be mainly attributed to the increase in the heat transfer area as well as disturbance for micro-fin tubes compared with the smooth tube. Meanwhile, in the Ref. [26], their results show that about 5% increase in the value of Nusselt number ratio in smooth tube can be obtained compared with that of the micro-fin tube at the Richardson number = 0.1 which happens at the maximum mass fraction of 0.2 wt.%. However, in the current experiment, only 2% increase in the of Nusselt number ratio in smooth tube can be observed compared with that of the micro-fin tube (1) at the Reynolds number ≈ 1000 which happens at the optimal concentration of 0.01 vol.%. The difference results mainly from a number of factors, such as the different kinds of base fluids, the large difference in concentrations of nanofluids, etc., which are supposed to be the important reasons for the discrepancy of enhancement ratio. Moreover, the ratio of the Nu of nanofluids flowing in micro-fin tube (1) is higher than that in micro-fin tube (2). Furthermore, given that the results of the heat transfer of water show that the effect of micro-fin spacing S2 is unremarkable, the combined
10000
Re Fig. 16. Friction factor versus Reynolds number (MWCNT nanofluids) for the smooth tube (2).
effect of the micro-fins and the random motions of the nanoparticles can explain the phenomenon that the thermal conductivity of nanofluids in micro-fin tube (1) is higher than that of nanofluids in micro-fin tube (2). 5.3.2. Pressure drop Pressure drop measurement is essential to the design of heat exchangers for industrial units. The friction factors with respect to the Re of the nanofluids at various volume concentrations in the smooth tube (2), micro-fin tubes (1) and (2) are plotted in Figs. 16–18. The results show that the friction factors of nanofluids slightly increase with an increase in nanofluids concentration. The average increase values in such friction factors with respect to water are listed in Table 4. The viscosity of nanofluids highly depends on the concentration of the dispersed nanotubes. Thus, with increasing of nanotubes concentration, the viscosity of nanofluids is enhanced, which results in an increase in the friction factor. However, compared with friction factor of water, the ratios of the increase values of the friction factors of nanofluids in the three tubes are not obviously different. 5.4. Performance evaluation analysis To evaluate the overall thermal performance of MWCNT–water nanofluids and micro-fin tubes, a performance evaluation criterion 1
Smooth tube (2) Micro-fin tube (1) Micro-fin tube (2)
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
f
Nunf/Nubf
1000
0.1
1
100
1000
Re Fig. 15. Ratio of Nu versus Reynolds number between 0.01 vol.% nanofluids and the base fluid in different flat tubes.
100
1000
10000
Re Fig. 17. Friction factor versus Reynolds number (MWCNT nanofluids) for the micro-fin tube (1).
Y.H. Diao et al. / Powder Technology 305 (2017) 206–216 1
215
1.6
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
f
PEC
1.4
0.1
0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
1.2
1.0
100
1000
10000
100
1000
Re
Re
(a)
Fig. 18. Friction factor versus Reynolds number (MWCNT nanofluids) for the micro-fin tube (2). 1.4
(PEC), which considers both pressure drop and heat transfer enhancement, should be defined. PEC is expressed as follows [27]: 13 PEC ¼ Nunf =Nubf = f nf = f bf
0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
PEC ¼ ðNufin;nf =Nusmooth;bf Þ= f fin;nf =f smooth;bf
1.2
1.0
100
1000
Re
(b)
1.4
PEC
If PEC b 1, then the nanofluids are worse as heat transfer fluid than the base fluid; by contrast, if PEC N 1, then the nanofluids are better heat transfer fluid than the base fluid. In similar studies, the parameter has been found to evaluate device enhancement or nanofluids applicability [28–30]. Fig. 19 presents the PEC values of MWCNT–water nanofluids at different concentrations as functions of the Re based on the base fluid for the different flat tubes. PEC is almost increasing with increasing Re, and the effect of nanofluids concentration on PEC is unremarkable in the laminar flow region. However, PEC clearly increases with nanofluids concentration in the turbulent flow region. For 0.01 vol.% nanofluids, the nanofluids in the three tubes exhibit better heat transfer performances than that for the base fluid. Furthermore, the nanofluids in all the tubes demonstrate better heat transfer performances in the turbulent flow regime. Thus, using nanofluids significantly affects the turbulent flow region. The maximum PEC values of the MWCNT–water nanofluids at 0.01 vol.% for smooth tubes (2), microfin (1) and (2) are 1.42, 1.37, and 1.32 at Re ≈ 5200, 5300, and 5300, respectively. Moreover, another PEC can be calculated from the following equation:
PEC
ð20Þ
0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
1.2
ð21Þ 1.0
Through the preceding equation, the PEC of the 0.01 vol.% nanofluids flowing in the micro-fin tubes can be obtained using the base fluid flowing in the smooth tube as basis. Fig. 20 presents the PEC of 0.01 vol.% nanofluids flowing in the micro-fin tubes as functions of Re based on the base fluid flowing in the smooth tube. Fig. 20 clearly shows that the overall thermal performance of micro-fin tube (1) is
Smooth (2) Micro-fin (1) Micro-fin (2)
1000
Re
(c) Fig. 19. PEC versus Reynolds number (MWCNT nanofluids) for (a) smooth tube (2), (b) micro-fin tube (1), and (c) micro-fin tube (2).
Table 4 Average increase in f of the nanofluids with respect to the base fluid. Flat tube number
100
Nanofluids concentrations 0.001
0.005
0.01
0.1
5.67% 4.01% 5.13%
7.74% 6.45% 8.12%
9.70% 9.03% 10.52%
11.97% 11.60% 12.87%
superior to that of micro-fin tube (2), especially in the turbulent flow region. In general, the maximum thermal performance value is 1.59, which is obtained at a nanofluid concentration of 0.01 vol.% and Re ≈ 5300 for the micro-fin tube (1).
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Y.H. Diao et al. / Powder Technology 305 (2017) 206–216 1.8
References Micro-fin tube (1) Micro-fin tube (2)
1.6
PEC
1.4
1.2
1.0 100
1000
Re Fig. 20. PEC versus Reynolds number (0.01 vol.% MWCNT nanofluids).
6. Conclusion This study presents the effects of micro-fin tubes and different concentrations of MWCNT–water nanofluids on flow characteristics, convective heat transfer, and overall thermal performance at Reynolds number ranging from 130 to 5300 under a constant heat flux condition. The following conclusions can be drawn from the study. (1) At a concentration of ≤0.01 vol.%, heat transfer is enhanced with an increase in concentration. At a concentration of ≥ 0.01 vol.%, heat transfer enhancement deteriorates with an increase in concentration. Given the increase in the viscosity of nanofluids, the friction factor slightly increases with increasing volume concentration. (2) The water in the micro-fin tubes can enhance heat transfer and the friction factor compared with that in the smooth tube. A slightly earlier laminar–turbulent transition occurs for the water in the micro-fin tubes. The enhancement of the friction factor of nanofluids in the micro-fin tubes is nearly the same as that of nanofluids in the smooth tube. The heat transfer enhancement of nanofluids in the micro-fin tubes is lower than that of nanofluids in the smooth tube. However, the heat transfer of equally concentrated nanofluids in the micro-fin tube is higher than that of nanofluids in the smooth tube. The effect of microfin spacing on the heat transfer of nanofluids is more evident than that of the heat transfer of water. (3) Compared with the base fluid (water), nanofluids in the smooth and micro-fin tubes exhibit enhanced thermal performance at most Re values, particularly in turbulent flow. For nanofluids with an optimum concentration (i.e., 0.01 vol.%), the overall thermal performance of micro-fin tube (1) is higher than that of micro-fin tube (2), especially in turbulent flow. (4) The surfactant solutions with low concentrations have no effect on the heat transfer and flow characteristics of the flat tubes. By contrast, the surfactant solutions with high concentrations slightly decrease heat transfer and enhance the friction factor.
Acknowledgements The project was financially supported by the Scientific Research Project of Beijing Educational Committee (Grant No. KM201510005022). The authors are grateful for the support of sponsor.
[1] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. Singer, H.P. Wang (Eds.), Development and Applications of Non-Newtonian Flows, FED-vol. 231/MD-vol. 66, ASME, New York 1995, pp. 99–106. [2] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer 11 (2) (1998) 151–170. [3] Y. Ding, H. Alias, D. Wen, R.A. Williams, Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids), Int. J. Heat Mass Transf. 49 (1–2) (2006) 240–250. [4] P. Garg, J.L. Alvarado, C. Marsh, T.A. Carlson, D.A. Kessler, K. Annamalai, An experimental study on the effect of ultrasonication on viscosiy and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids, Int. J. Heat Mass Transf. 52 (29) (2009) 5090–5101. [5] L. Liang, Z.-h. Liu, Forced convective flow drag and heat transfer characteristics of carbon nanotube suspensions in a horizontal small tube, Heat Mass Transf. 45 (2009) 1129–1136. [6] W. Duangthongsuk, S. Wongwises, An experimental study on the heat transfer performance and pressure drop of TiO2-water nanofluids flowing under a turbulent flow regime, Int. J. Heat Mass Transf. 53 (1–3) (2010) 334–344. [7] A. Amrollahi, A.M. Rashidi, R. Lotfi, M. Emami Meibodi, K. Kashefi, Convection heat transfer of functionalized MWNT in aqueous fluids in laminar and turbulent flow at the entrance region, Int. Commun. Heat Mass Transf. 37 (2010) 717–723. [8] W. Yu, H. Xie, Y. Li, L. Chen, Q. Wang, Experimental investigation on the heat transfer properties of Al2O3 nanofluids using the mixture of ethylene glycol and water as base fluid, Powder Technol. 230 (2012) 14–19. [9] J. Zhang, Y. Diao, Y. Zhao, Y. Zhang, Experimental study of TiO2-water nanofluid flow and heat transfer characteristics in a multiport minichannel flat tube, Int. J. Heat Mass Transf. 79 (2014) 628–638. [10] H. Bahremand, A. Abbassi, M. Saffar-Avval, Experimental and numerical investigation of turbulent nanofluid flow in helically coiled tubes under constant wall heat flux using Eulerian–Lagrangian approach, Powder Technol. 269 (2015) 93–100. [11] J.B. Copetti, M.H. Macagnan, D. de Souza, D. de Souza, Experiments with micro-fin tube in single phase, Int. J. Refrig. 27 (8) (2014) 876–883. [12] D.H. Han, K.J. Lee, Single-phase heat transfer and flow characteristics of micro-fin tubes, Appl. Therm. Eng. 25 (2005) 1657–1669. [13] L. Xiao-Wei, M. Ji-An, L. Zhi-Xin, Experimental study of single phase pressure drop and heat transfer in a micro-fin tube, Exp. Thermal Fluid Sci. 32 (2007) 641–648. [14] A. Celen, A.S. Dalkilic, S. Wongwises, Experimental analysis of the single phase pressure drop characteristics of smooth and microfin tubes, Int. Commun. Heat Mass Transf. 46 (2013) 58–66. [15] M.M. Derakhshan, M.A. Akhavan-Behabadi, S.G. Mohseni, Experiments on mixed convection heat transfer and performance evaluation of MWCNT–oil nanofluid flow in horizontal and vertical microfin tubes, Exp. Thermal Fluid Sci. 61 (2015) 241–248. [16] K.H. Solangi, S.N. Kazi, M.R. Luhur, A. Badarudin, A. Amiri, R. Sadri, M.N.M. Zubir, S. Gharehkhana, K.H. Teng, A comprehensive review of thermo-physical properties and convective heat transfer to nanofluids, Energy 89 (2015) 1065–1086. [17] W. Yu, C. SUS, The role of interfacial layers in the enhanced thermal conductivity of nanofluids: a renovated Maxwell model, J. Nanopart. Res. 5 (1–2) (2003) 167–171. [18] G.K. Batchelor, The effect of Brownian motion on the bulk stress in a suspension of spherical particles, J. Fluid Mech. 83 (1977) 97–117. [19] B. Agostini, A. Bontemps, B. Thonon, Effects of geometrical and thermophysical parameters on heat transfer measurements in small-diameter channels, Heat Transf. Eng. 27 (2006) 14–24. [20] R. Shah, A. London, Laminar Flow Forced Convection in Ducts, Academic Press, London, 1978. [21] S. Garimella, W.J. Dowling, M. van der Veen, J.D. Killion, The effect of simultaneously developing flow on heat transfer in rectangular tubes, Heat Transf. Eng. 22 (6) (2001) 12–25. [22] H. Hausen, Neue Gleichungen fur die Wameiibertragung bei Freier oder Erzwungerner Stromung, Allg. Warmetchn. 9 (1959) 75–79. [23] K. Stephan, P. Preuβer, Warmeubergang und Maximale Warmestromdichte Beim Behaltersieden Binarer und Ternarer Flussigkeitsgemische, Chemie Ingenieur Technik 51 (1) (1979) 37. [24] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, Wiley, New York, 1996. [25] B. Sahin, G.G. Gültekin, E. Manay, S. Karagoz, Experimental investigation of heat transfer and pressure drop characteristics of Al2O3–water nanofluid, Exp. Therm. Fluid Sci. 50 (2013) 21–28. [26] M.M. Derakhshan, M.A. Akhavan-Behabadi, Mixed convection of MWCNT-heat transfer oil nanofluid inside inclined plain and microfin tubes under laminar assisted flow, Int. J. Therm. Sci. 99 (2016) 1–8. [27] V.D. Zimparov, N.L. Vulchanov, Performance evaluation criteria for enhanced heat transfer surfaces, Int. J. Heat Mass Transf. 37 (12) (1994) 1807–1816. [28] M.H. Esfe, S. Saedodin, OmidMahiab, S. Wongwises, Thermophysical properties, heat transfer and pressure drop of COOH-functionalized multi walled carbon nanotubes/ water nanofluids, Int. Commun. Heat Mass Transf. 58 (2014) 176–183. [29] A.A. Abbasian Arani, J. Amani, Experimental investigation of diameter effect on heat transfer performance and pressure drop of TiO2-water nanofluid, Exp. Thermal Fluid Sci. 44 (2013) 520–533. [30] K. Wongchareea, S. 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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Experimental investigation of MWCNT–water nanofluids flow and convective heat transfer characteristics in multiport minichannels with smooth/micro-fin surface Y.H. Diao ⁎, C.Z. Li, J. Zhang, Y.H. Zhao, Y.M. Kang The Department of Building Environment and Facility Engineering, The College of Architecture and Civil Engineering, Beijing University of Technology, No.100 Pingleyuan, Chaoyang District, Beijing 100124, China
a r t i c l e
i n f o
Article history: Received 2 July 2016 Received in revised form 28 September 2016 Accepted 3 October 2016 Available online 05 October 2016 Keywords: Nanofluids Micro-fin Heat transfer Friction factor Performance evaluation Criterion
a b s t r a c t This paper reports on the results of an experimental study on the heat transfer and flow performance of multiwalled carbon nanotubes (MWCNT) in aqueous suspensions flowing in multiport minichannel flat tubes with smooth/micro-fin surface under a constant heat flux condition. The MWCNT–water nanofluids volume concentrations are 0.001%, 0.005%, 0.01%, and 0.1%. Results indicate that the friction factor and the Nusselt number of the nanofluids are higher than those of water. The Nusselt number does not increase with volume concentration. The heat transfer of nanofluids in the micro-fin tubes is higher than that of nanofluids in the smooth tube. However, the heat transfer enhancement of nanofluids in the micro-fin tubes is lower than that of nanofluids in the smooth tube. The effect of micro-fin spacing is more evident in nanofluids than in water. Nanofluids with a concentration of 0.01% flowing in the tube with closely spaced micro-fin tube exhibit the optimal thermal performance in accordance with the performance evaluation criterion. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Advancements in thermal loads for an extensive range of industrial applications, including microelectronics, power generation, aerospace and automotive engineering, require the exploitation of micro/miniscale heat exchangers, which provide a high heat transfer coefficient. The thermal conductivity of heat transfer fluids also plays a crucial role in the development of high thermal performance systems. Nanofluids, which were first proposed by Choi in 1995 [1], are prepared by dispersing metal, metallic oxide, carbon nanotubes (CNTs), or other nanoparticles into water, ethylene glycol, engine oil, or another base fluid. In the past decade, considerable increases in the thermal conductivities of nanofluids have been reported. Furthermore, numerous attempts have been made to investigate heat transfer and flow performances of all kinds of nanofluids. Pak and Cho [2] conducted experiments to investigate the heat transfer and pressure drop of Al2O3 and TiO2 aqueous nanofluids in turbulent flow in a stainless steel tube. They reported that 1.34 vol.% Al2O3– water nanofluid exhibited 45% heat transfer enhancement compared with the base fluid and 2.78 vol.% TiO2–water nanofluids exhibited 75% heat transfer enhancement. However, the increase in Darcy friction factors of both nanofluids was insignificant compared with that of the base fluid. Ding et al. [3] examined the heat transfer characteristic of ⁎ Corresponding author. E-mail address: [email protected] (Y.H. Diao).
http://dx.doi.org/10.1016/j.powtec.2016.10.011 0032-5910/© 2016 Elsevier B.V. All rights reserved.
multiwalled carbon nanotubes (CNT) in the laminar flow region in a horizontal tube. Their experimental results showed that the maximum heat transfer enhancement was approximately 350% for 0.5 wt.% CNT nanofluid at a Reynolds number of 800. Garg et al. [4] experimentally investigated the convective heat transfer performance of MWCNT aqueous nanofluids in laminar flow. They observed that the maximum enhancement in convective heat transfer was 32% at Re = 600. Liao and Liu [5] presented an experimental study on the heat transfer and flow drag characteristics of MWCNT–water nanofluids in both the laminar and turbulent flow regions in a small horizontal tube. They concluded that heat transfer was sharply enhanced in high mass concentrations, whereas flow characteristic was nearly the same as that of water. Duangthongsuk and Wongwises [6] conducted an experimental study on the turbulent flow and heat transfer of TiO2–water nanofluids in a horizontal double tube. The heat transfer enhancement for 1.0 vol.% nanofluids was found to be approximately 26% higher than that of water, but heat transfer decreased by 14% at the highest concentration (2.0 vol.%). Meanwhile, pressure drop slightly increased with nanofluids concentration. Amrollahi et al. [7] measured the convective heat transfer coefficients of functionalized MWCNT–water nanofluids in laminar and turbulent flow in a uniformly heated horizontal tube at the entrance region. Their experimental results showed that the heat transfer coefficient increased by up to 33%–40% for a 0.25 wt.% nanofluids in laminar and turbulent flows. Yu et al. [8] investigated the heat transfer characteristics of Al2O3 nanofluids which is based on the mixture of ethylene glycol and water in a circular copper tube with
Y.H. Diao et al. / Powder Technology 305 (2017) 206–216
Nomenclature a channel width, m A total cross section area, m2 b channel height, m specific heat capacity, J/kg K cp d diameter, m hydraulic diameter, m Dh f friction factor G mass flow rate, kg/s h heat transfer coefficient, W/m2 K k thermal conductivity, W/m K L tube length, m Nu Nusselt number Pe perimeter, m PEC performance evaluation criterion Pr Prandtl number ΔP total pressure differential, Pa frictional pressure loss, Pa ΔPf singular pressure loss, Pa ΔPm q heat flux, W/m2 Q heat transfer rate gained by fluid, W Re Reynolds number T temperature, °C Greek symbols α aspect ratio, b/a (0 b α b 1) β ratio of the nanolayer thickness to the original particle φ volume concentration μ dynamic viscosity, Pa · s ρ mass density, kg/m3 χ axial distance, m Subscripts bf base fluid f fluid nf nanofluid p particle in inlet out outlet w wall
207
studied heat transfer and flow characteristics in micro-fin tubes. They argued that heat transfer of a micro-fin tube was 190% higher than that of a smooth tube in turbulent flow. Despite an increase in pressure drop, the heat transfer results for a micro-fin tube were still 80% higher than that in a smooth tube. Han and Lee [12] studied heat transfer and flow characteristics in micro-fin tubes at a Re range of 1000–8000 and Pr range of 4–7. They reported that the high relative roughness of micro-fin tubes is the main factor to the enhancement of efficiency index. Wei et al. [13] measured flow friction and heat transfer in a micro-fin tube at Re ranging from 2500 to 90,000 and Pr varying from 3.2 to 220. Their results showed that a critical Re for heat transfer enhancement existed for the micro-fin tube. The friction factor of the micro-fin tube was 40%–50% higher than that of the smooth tube at Re N 10,000. Celen et al. [14] experimentally analyzed flow characteristics in smooth and micro-fin tubes at a mass flow rate range of 0.023–0.100 kg/s. They found that pressure drop in the micro-fin tube was higher than that in the smooth tube because the micro-fins produced swirl flow and flow recirculation. Derakhshan et al. [15] experimentally investigated mixed convection heat transfer characteristics and performance evaluation of MWCNT–oil nanofluids flowing in smooth and micro-fin tubes. It is found that the heat transfer of nanofluids is enhanced compared with that of the base fluid inside smooth and micro-fin tubes. Their performance evaluation also showed that using nanofluids instead of the base fluid is a better way to enhance convection heat transfer performance compared with applying the micro-fin tube instead of the smooth tube. From the literature survey, it is clear that most of the existing studies have investigated the heat transfer and flow characteristics of nanofluids in smooth tubes or pure fluids in micro-fin tubes. Experimental data on the heat transfer and flow characteristics of nanofluids in micro-fin tubes remain limited. Accordingly, the pressure drop and heat transfer characteristics of MWCNT–water nanofluids flowing within multiport minichannel flat tubes with smooth/micro-fin surface were examined in the present study. The effect of surfactant on the heat transfer and flow characteristics in the tubes was also investigated.
2. Preparation and thermophysical properties of nanofluids 2.1. Preparation of nanofluids
the internal diameter of 2.7 mm with a constant temperature. It was found that heat transfer increased with an increase in nanofluids concentration and the maximum enhancement is 106% at Re = 2000 with the 2 vol.% nanofluids, which attributes to both the increase of thermal conductivity and the interaction of particle–particle, particle–liquid and the micro convection in nanofluids. Zhang et al. [9] performed an experiment to investigate the heat transfer and flow characteristics of TiO2–water nanofluids in a multiport minichannel flat tube with a 1.65 mm hydraulic diameter. They found that 0.01 vol.% was the optimal nanofluids volume concentration and its enhancement of heat transfer being 61% at the Re ≈ 6100. And 0.01 vol.% nanofluids also exhibited optimal thermal performance. Bahremand et al. [10] studied experimentally and numerically the heat transfer and flow characteristics of water–silver nanofluid with turbulent convection flow region in helically coiled tubes under constant wall heat flux. They found that the heat transfer characteristics of nanofluids increase with the volume concentration of nanofluids. And they also observed that the increase of nanoparticle diameter deteriorates the heat transfer of nanofluids. Moreover, a higher surface-area-to-volume ratio is another method to guide the design of heat transfer devices. As enhanced tubes, microfin tubes are widely adopted because of their capability to extend the heat transfer surface and generate turbulence in fluid flow to offer the potential for improving heat transfer performance. Copetti et al. [11]
Preparing nanofluids is a vital step in experimental studies on nanofluids. The nanofluids are prepared via a two-step method that is widely accepted by scholars studying the flow and heat transfer of nanofluids [16]. The carbon nanotubes with COOH functional groups are purchased from Chengdu Organic Chemicals Co. Ltd. These CNTs have a density of approximately 2.1 g cm−3, an outer diameter of 20– 30 nm, and a length 0.5–2 μm. Dry nanotube powder was dispersed into water. Given that nanoparticles are always prone to aggregate in deionized water (DI), two methods may be used to obtain a stable liquid suspension. And the two methods are sequentially applied to stabilize nanofluids. The first method is to use the surfactant gum arabic (GA) for MWCNT nanofluids. The second method is to oscillate the mixture in an ultrasonic water bath for approximately 4 h. The volume concentrations φ of nanofluids adopted in this study are 0.001 vol.%, 0.005 vol.%, 0.01 vol.%, and 0.1 vol.%. The scanning electron microscope (SEM) images of the MWCNT nanofluids are shown in Fig.1. Both nanofluids are kept stable for approximately a week. In order to investigate the effects of surfactant on the flow and heat transfer characteristics, the GA aqueous solution is also used as a working fluid. The weight of GA added to aqueous solution is equal to that added to the corresponding MWCNT–water nanofluids (i.e., 0.001 wt.% to 0.001 vol.%, 0.005 wt.% to 0.005 vol.%, 0.01 wt.% to 0.05 vol.%, and 0.1 wt.% to 0.1 vol.%).
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Thermal conductivity ( W/m K)
0.75
0.01% MWCNT-Water nanofluids Water Yu and Choi model 0.70
0.65
0.60
(a)
20
25
30
35
40
Fig. 2. Effective thermal conductivities of nanofluid with 0.01% volume concentration at three different temperatures (error bar ±5%).
The thermal conductivity and viscosity of the nanofluids are significant properties for the convective heat transfer performance. Thermal conductivity is measured using the transient hot-wire method. The measuring apparatus used is Hot Disk 2500S thermal property meter. The Hot Disk 2500S is initially calibrated using distilled water before measuring the other fluids. Measurements are taken thrice to ensure that measurement accuracy is within ±5%. The thermal conductivity of the prepared nanofluids and the Yu and Choi [17] correlation model are shown in Fig. 2. The Yu and Choi model is defined as.
(b)
knf kp þ 2kbf þ 2 kp −kbf ð1 þ βÞ3 φ ¼ ; kbf kp þ 2kbf − kp −kbf ð1 þ βÞ3 φ
ð3Þ
where β is the ratio of nanolayer thickness to the original particle. In calculating the thermal conductivities of nanofluids, β is generally set as 0.1. The thermal conductivities of the 0.01 vol.% MWCNT nanofluids at different temperatures are 9%, 9.3%, and 9.5% higher than that of distilled water. Viscosity is measured at 20 °C using a rotating viscometer. The relative viscosity (μnf/μbf) between the nanofluids and DI water, as well as the Batchelor correlation [18], is presented in Fig. 3. The well-known
(c)
1.16
Fig. 1. SEM images of the MWCNT nanofluids: (a) 0.001% volume concentration, (b) 0.01% volume concentration, and (c) 0.1% volume concentration.
The density of the nanofluids is provided by the Pak and Cho [2] correlation: ρnf ðT Þ ¼ ð1−φÞρbf ðT Þ þ φρp ðT Þ:
cp;nf ¼
ρnf ðT Þ
1.08
1.04
ð1Þ 1.00
The specific heat of the nanofluids is calculated using the Pak and Cho [2] correlation: φ ρcp p ðT Þ þ ð1−φÞ ρcp bf ðT Þ
µ nf / µ bf
2.2. Thermophysical properties of nanofluids
1.12
MWCNT-water nanofluids Batchelor correlation
:
ð2Þ
0.96
1E-3
0.01
0.1
Volume Fraction(%) Fig. 3. Relative viscosities of nanofluids at various volume concentrations (error bar ±5%).
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209
Fig. 4. Schematic of the experimental apparatus.
Batchelor correlation is expressed as follows: μ nf ¼ μ bf
1 þ 2:5φ þ 6:25φ2 :
ð4Þ
As shown in Fig. 3, relative viscosity increases with an increase in nanofluids concentration. 3. Experimental apparatus The schematic of the experimental apparatus is illustrated in Fig. 4. The experimental apparatus consists of a flow loop, a heating unit, a cooling loop, and a data acquisition system. The flow loop contains a water bath, a liquid pump, an exhaust valve, a Coriolis mass flow meter, a test section, and a double-pipe heat exchanger. The cooling loop, which includes the double-pipe heat exchanger and a water chilling unit, is used to keep the temperature of the nanofluids constant. The water bath is also used to keep the fluids temperature precisely invariable. The mass flow rate in the flow loop is measured using the Coriolis mass flow meter. The fluid, which is firstly pumped from the water bath, flows through the Coriolis mass flow meter, the test section, the doublepipe heat exchanger and finally returns to the water bath. The test section, which is shown in Fig. 5, is an aluminum multiport minichannel flat tube with a length of 450 mm. The cross section of the flat tube is shown in Fig. 6. Fig. 6(c–d) shows that the minichannel has a fin. Smooth tube (1) has 9 parallel minichannels and the others have 11
parallel minichannels. The geometric dimensions are listed in Table 1. To obtain better connection with the experimental system, two manifolds are designed to avoid the non-uniform flow distribution effect and welded onto both ends of the aluminum multiport minichannel flat tube. The inlet and outlet temperatures of the fluid are measured by two T-type thermocouples inserting both manifolds. To measure the wall temperatures at the axial locations of the tube, ten K-type thermocouples are evenly mounted on the upper and lower external surface of the flat tube. The test section is thermally insulated with thick thermal insulation materials to maintain a constant heat flux condition along the axial direction of the flat tube. The inlet and outlet press drops of the fluids are measured with a pressure difference transducer and the joints are mounted at the bottom of the two manifolds. 4. Data reduction 4.1. Pressure drop The hydraulic diameter and aspect ratio of the minichannels with and without micro-fins are respectively calculated from Dh ¼
4A and α ¼ a=b 0bαb1: Pe
ð5Þ
Thermocouple
Manifold
Pressure transducer
Fig. 5. Schematic of the test section.
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(c)
(d)
S1
S2
b
a
S1
Hfin Wfin (e) Fig. 6. Cross section of the multiport minichannel flat tube.
The total pressure difference with the test section is expressed as ΔP ¼ ΔP f þ ΔP m
ð6Þ
where the frictional pressure difference ΔPf is
ΔP f ¼ f
L G ; D h ρ f A2
ð7Þ
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211
Table 1 Geometric dimensions of the multiport minichannel flat tube. No.
a (mm)
b (mm)
α (b/a)
Dh (mm)
Hfin (mm)
Wfin (mm)
S2 (mm)
Smooth (1) Smooth (2) Micro-fin (1) Micro-fin (2)
2.36 1.99 2.03 2.0
2.03 2.08 2.1 2.1
0.86 0.96 0.97 0.95
2.18 2.03 1.71 1.69
– – 0.25 0.25
– – 0.28 0.27
– – 0.27 0.95
and the singular pressure difference ΔPm is determined by the method presented in Ref. [19]. The Reynolds number and the Darcy frictional factor f are respectively defined as G Dh ; Re ¼ A μf f ¼ ΔP f
Re ¼
Ren and Nu ¼
10 X
ð16Þ
Nun
k¼1
4.3. Uncertainty analysis
2 Dh ρ f A : 2 L G
ð9Þ The temperature measurement precision is ±0.1 °C. The uncertainty in mass flow rate measurement is 0.2%. The uncertainty in pressure measurement is 0.25%. Indirect parameters, such as Re, f, and Nu, are calculated using.
The heat transfer rate obtained by the fluid flowing through the test section can be calculated from.
10 X k¼1
ð8Þ
4.2. Heat transfer
Q ¼ G cp T f ;out −T f ;in :
ð10Þ
The wall heat flux can be defined as the heat transfer rate gained by the fluids, i.e., q¼
Finally, the averaged Reynolds number and Nusselt number can be calculated by.
Q : L Pe
ð11Þ
z ¼ f ðy1 ; y2 yn Þ; " 2 2 2 #12 ∂z ∂z ∂z δz ¼ δy þ δy þþ δy : ∂y1 1 ∂y2 2 ∂yn n
ð17Þ
The uncertainties of the relevant parameters used in this study are listed in Table 2. 5. Results and discussion 5.1. Experiments with water
On the basis of energy balance, the mean temperature of the fluids at the longitudinal position χ in a tube can be given by T f ðχ Þ ¼ T f ;in þ
Q χ: G cp; f ðχ Þ L
ð12Þ
The local heat transfer coefficient is defined as hðχ Þ ¼
q : T w ðχ Þ−T f ðχ Þ
ð13Þ
The local Nusselt number can be calculated from Nuðχ Þ ¼
hðχ Þ Dh : k f ðχ Þ
The experiments are first conducted with the base fluid (water) in smooth tube (1) to verify the integrity and reliability of the experimental facility. 5.1.1. Heat transfer The average Nusselt number as a function of the Reynolds number is shown in Fig. 7 with the smooth tube (1). As indicated by the friction factor, the transition from laminar to turbulent flow occurs at Re ≈ 1800. Several established heat transfer correlations, which are listed in Table 3, are also plotted in Fig. 7. In the laminar region, the measured data are slightly lower than the predicted data from the Stephan
ð14Þ
Water Shah and London equation [20] Garimella equation [21] Hausen equation [22] Stephan and Preuß er equation [23]
The local Reynolds number is determined from G Dh : A μ f ðχ Þ
ð15Þ
Nu
Re ¼
10
Table 2 Uncertainties of the experimental parameters. Parameter
Value
Uncertainty (%)
Dh (mm) Q (W) Re f Nu
2.03–2.18 125–230 130–5600 0.029–0.66 20–36
3.30–3.49 2.0–6.37 3.23–3.48 9.77–10.89 7.84–11.9
100
1000
10000
Re Fig. 7. Average Nusselt number versus Reynolds number (water) for smooth tube (1).
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Table 3 Conventional correlations from the literature for comparing the experimental data. Reference
Correlation
Condition
Range of validity
Shah and London [20]
Nu ¼ 8:235ð1−2:0421α þ 3:0854α 2 −2:4765α 3 þ 1:0578α 4 −0:1861α 5
Fully developed
Laminar
Garimella et al. [21]
Nu ¼ ðNulam 10 þ f ;exp½ð360−ReÞ=925 þ Nu 1 2 g Nu 2
118 b Re b 10,671
6.48 b Pr b 11.2
Thermally developing turbulent
2200 b Re b 104
Simultaneously developing (constant wall heat flux)
0.7 b Pr b 7
−5 0:1
lam
Hausen [22]
Þ
turb
0:14
μ
Nu ¼ 0:116ðRe2=3 −125ÞPr1=3 ½1 þ ðD=LÞ2=3 ðμ f Þ w
Stephan and Preuβer [23]
Nu ¼ 4:364 þ
1:33
0:086ðRePrD=LÞ 1þ0:1 ;PrðReD=LÞ0:83
and Preuβer equation. However, the measured data and the predicted data display the same trend. In the turbulent region, the trend of the measured data is more approximate to that of the predicted data from the Garimella equation. As shown in Fig. 8, the average Nusselt number are plotted against the Reynolds number of water for the smooth tube (2), micro-fin tubes (1) and (2). As expected, the heat transfer rate in the micro-fin tubes is higher than that in the smooth tube. This result can be explained as follows. Compared with a smooth surface, micro-fins could promote disturbance as well as increase the heat transfer area; thus, the heat transfer rate in the micro-fin tubes is enhanced. The Nusselt number of micro-fin tube (1) is slightly higher than that of micro-fin tube (2). The effect of micro-fin spacing S2 on heat transfer is inconspicuous. 5.1.2. Pressure drop Fig. 9 shows the experimental data for the friction factor as a function of Re compared with the conventional theory correlations for smooth tube (1). The Shah and London equation [20] and the Blasius equation [24] are used to compare with the data for water in smooth tube. The Shah and London equation, f . Re = 96(1 − 1.3553 ⋅ α + 1.9467 ⋅ α2 − 1.7012 ⋅ α3 + 0.9564 ⋅ α4 − 0.2537⋅ α5), (18)is applied to a fully developed laminar flow in rectangular channels. The Blasius equation, f ¼ 0:316 Re−0:25 ;
ð19Þ
is valid within the range of Re b 2 × 104 for a fully developed turbulent flow regime. Fig. 9 shows that the experimental data agree well with the Shah and London equation in the laminar flow regime. In the turbulent flow regime, the friction factor obtained from the experiments is lower than
that calculated from Eq. (19). Furthermore, the transition from laminar flow to turbulent flow occurs at Re ≈ 1800, and the fully developed turbulent flow begins to establish at Re ≈ 2300. As is shown in Fig. 10, friction factors are plotted against the Reynolds number of water for the smooth tube (2), micro-fin tubes (1) and (2). As expected, the friction factors in the micro-fin tubes are higher than that of the smooth tube. The presence of micro-fins contributes to friction. The micro-fin spacing S2 has a little effect on the friction factor in the laminar flow region and nearly no effect on that in the turbulent flow region. For the micro-fin tubes, there exists a slightly earlier laminar–turbulent transition at Re = 1650 compared with the smooth tube. This behavior may be attributed to the micro-fins causing a stronger disturbance to the flow, which results in a slightly earlier laminar–turbulent transition.
5.2. Experiments with surfactant As is shown in Fig. 11, the corresponding friction factors of the surfactant solution at low concentrations are approximately the same as that of DI water. However, the friction factor of 0.1 wt.% surfactant solution is slightly higher than that of water because the viscosity of this solution is higher than that of water. In the laminar flow regime, the heat transfer of the solution is slightly lower than that of water. In the turbulent flow regime, the friction factor and heat transfer of the solution are nearly uniform with those of DI water. The results show that the effect of the surfactant on the heat transfer rate is more evident at 0.1 wt.% concentration in the laminar flow regime. The thickness of the thermal boundary layer plays a dominant role in heat transfer in laminar flow. An increase in viscosity leads to an increase in thermal boundary layer thickness, which, in turn, results in a decrease in the heat transfer coefficient. Thus, the effect of viscosity on turbulent heat transfer can be ignored.
1
Water Shah and London equation [20] Blasius equation [24]
10
f
Nu
Smooth tube (2) Micro-fin tube (1) Micro-fin tube (2)
0.1
100
1000
10000
Re Fig. 8. Average Nusselt number versus Reynolds number (water) for different tubes.
100
1000
10000
Nu Fig. 9. Friction factor versus Reynolds number (water) for the smooth tube (1).
Y.H. Diao et al. / Powder Technology 305 (2017) 206–216
213
1
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
f
Nu
Smooth tube (2) Micro-fin tube (1) Micro-fin tube (2)
0.1
100
1000
10
100
10000
1000
Re Fig. 10. Friction factor versus Reynolds number (water) for the different tubes.
5.3. Experiments with MWCNT nanofluids 5.3.1. Heat transfer The Nu of nanofluids at different concentrations and that of DI water are shown in Figs. 12–14. In the smooth and micro-fin tubes, the Nu
Nu
Water 0.001wt.% GA 0.005wt.% GA 0.01wt.% GA 0.1wt.% GA
10
100
1000
10000
Re
(a) Average Nusselt number versus Reynolds number
10000
Re Fig. 12. Average Nusselt number versus Reynolds number (MWCNT nanofluids) for the smooth tube (2).
values of the nanofluids are higher than those of the base fluid and increase with increasing Re. At φ ≤ 0.01 vol.%, the Nu values of the nanofluids increase with volume concentration. At φ ≥ 0.01 vol.%, the Nu values decrease with an increase in volume concentration. Thus, an optimum volume concentration exists for enhancing heat transfer. This is due to the fact that as the nanofluids concentrations increase, the thermal conductivity and viscosity of nanofluids become higher than those of the base fluid. The increase in thermal conductivity leads to heat transfer enhancement. An increase in viscosity results in a decrease in heat transfer due to increase in boundary layer thickness because of viscosity. Another factor that enhances heat transfer is the chaotic movement of nanotubes. Such movement reduces the thickness of the thermal boundary layer and accelerates the energy exchange process. However, as volume concentration increases and particles easily agglomerate, particle movements are hindered. Consequently, at φ ≤ 0.01 vol.%, the factors intensified by the heat transfer outweigh the effect of the reduced factors. At φ ≥ 0.01 vol.%, the opposite case occurs. Similar results can be found in [6,25]. In view of the uniform optimum concentration for the three flat tubes, the ratios of Nu between the 0.01 vol.% nanofluids and the base fluid for the smooth tube (2), micro-fin tubes (1) and (2) are plotted against the Re in Fig. 15. As shown in Fig. 15, the enhancement ratio of the Nu for the smooth tube is higher than that for the micro-fin tubes at the same Re, which indicates that the effect of nanoparticles on heat transfer enhancement in the smooth tube is greater than that in the
1
Water 0.001wt.% GA 0.005wt.% GA 0.01wt.% GA 0.1wt.% GA
f
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
100
Nu
0.1
1000
10
10000
Re
(b) Friction factor versus Reynolds number Fig. 11. Comparison of the friction factor and Nu obtained from water and surfactant solution at different concentrations.
100
1000
10000
Re Fig. 13. Average Nusselt number versus Reynolds number (MWCNT nanofluids) for the micro-fin tube (1).
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Y.H. Diao et al. / Powder Technology 305 (2017) 206–216 1
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
10
100
f
Nu
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.% 0.1
1000
10000
100
Re Fig. 14. Average Nusselt number versus Reynolds number (MWCNT nanofluids) for the micro-fin tube (2).
micro-fin tubes. This result can be attributed to the micro-fins disturbing the random motions of the nanoparticles and their movements when the nanoparticles interact with the micro-fins. The presence of micro-fins can affect the chaotic movement of nanoparticles; consequently, heat transfer enhancement for micro-fin tubes reduces compared with for in the smooth tube. However, the Nu of the microfin tubes is higher than that of the smooth tube in each volume concentrations. Similar findings are reported in [15,26]. This result can be mainly attributed to the increase in the heat transfer area as well as disturbance for micro-fin tubes compared with the smooth tube. Meanwhile, in the Ref. [26], their results show that about 5% increase in the value of Nusselt number ratio in smooth tube can be obtained compared with that of the micro-fin tube at the Richardson number = 0.1 which happens at the maximum mass fraction of 0.2 wt.%. However, in the current experiment, only 2% increase in the of Nusselt number ratio in smooth tube can be observed compared with that of the micro-fin tube (1) at the Reynolds number ≈ 1000 which happens at the optimal concentration of 0.01 vol.%. The difference results mainly from a number of factors, such as the different kinds of base fluids, the large difference in concentrations of nanofluids, etc., which are supposed to be the important reasons for the discrepancy of enhancement ratio. Moreover, the ratio of the Nu of nanofluids flowing in micro-fin tube (1) is higher than that in micro-fin tube (2). Furthermore, given that the results of the heat transfer of water show that the effect of micro-fin spacing S2 is unremarkable, the combined
10000
Re Fig. 16. Friction factor versus Reynolds number (MWCNT nanofluids) for the smooth tube (2).
effect of the micro-fins and the random motions of the nanoparticles can explain the phenomenon that the thermal conductivity of nanofluids in micro-fin tube (1) is higher than that of nanofluids in micro-fin tube (2). 5.3.2. Pressure drop Pressure drop measurement is essential to the design of heat exchangers for industrial units. The friction factors with respect to the Re of the nanofluids at various volume concentrations in the smooth tube (2), micro-fin tubes (1) and (2) are plotted in Figs. 16–18. The results show that the friction factors of nanofluids slightly increase with an increase in nanofluids concentration. The average increase values in such friction factors with respect to water are listed in Table 4. The viscosity of nanofluids highly depends on the concentration of the dispersed nanotubes. Thus, with increasing of nanotubes concentration, the viscosity of nanofluids is enhanced, which results in an increase in the friction factor. However, compared with friction factor of water, the ratios of the increase values of the friction factors of nanofluids in the three tubes are not obviously different. 5.4. Performance evaluation analysis To evaluate the overall thermal performance of MWCNT–water nanofluids and micro-fin tubes, a performance evaluation criterion 1
Smooth tube (2) Micro-fin tube (1) Micro-fin tube (2)
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
f
Nunf/Nubf
1000
0.1
1
100
1000
Re Fig. 15. Ratio of Nu versus Reynolds number between 0.01 vol.% nanofluids and the base fluid in different flat tubes.
100
1000
10000
Re Fig. 17. Friction factor versus Reynolds number (MWCNT nanofluids) for the micro-fin tube (1).
Y.H. Diao et al. / Powder Technology 305 (2017) 206–216 1
215
1.6
Water 0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
f
PEC
1.4
0.1
0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
1.2
1.0
100
1000
10000
100
1000
Re
Re
(a)
Fig. 18. Friction factor versus Reynolds number (MWCNT nanofluids) for the micro-fin tube (2). 1.4
(PEC), which considers both pressure drop and heat transfer enhancement, should be defined. PEC is expressed as follows [27]: 13 PEC ¼ Nunf =Nubf = f nf = f bf
0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
PEC ¼ ðNufin;nf =Nusmooth;bf Þ= f fin;nf =f smooth;bf
1.2
1.0
100
1000
Re
(b)
1.4
PEC
If PEC b 1, then the nanofluids are worse as heat transfer fluid than the base fluid; by contrast, if PEC N 1, then the nanofluids are better heat transfer fluid than the base fluid. In similar studies, the parameter has been found to evaluate device enhancement or nanofluids applicability [28–30]. Fig. 19 presents the PEC values of MWCNT–water nanofluids at different concentrations as functions of the Re based on the base fluid for the different flat tubes. PEC is almost increasing with increasing Re, and the effect of nanofluids concentration on PEC is unremarkable in the laminar flow region. However, PEC clearly increases with nanofluids concentration in the turbulent flow region. For 0.01 vol.% nanofluids, the nanofluids in the three tubes exhibit better heat transfer performances than that for the base fluid. Furthermore, the nanofluids in all the tubes demonstrate better heat transfer performances in the turbulent flow regime. Thus, using nanofluids significantly affects the turbulent flow region. The maximum PEC values of the MWCNT–water nanofluids at 0.01 vol.% for smooth tubes (2), microfin (1) and (2) are 1.42, 1.37, and 1.32 at Re ≈ 5200, 5300, and 5300, respectively. Moreover, another PEC can be calculated from the following equation:
PEC
ð20Þ
0.001vol.% 0.005vol.% 0.01vol.% 0.1vol.%
1.2
ð21Þ 1.0
Through the preceding equation, the PEC of the 0.01 vol.% nanofluids flowing in the micro-fin tubes can be obtained using the base fluid flowing in the smooth tube as basis. Fig. 20 presents the PEC of 0.01 vol.% nanofluids flowing in the micro-fin tubes as functions of Re based on the base fluid flowing in the smooth tube. Fig. 20 clearly shows that the overall thermal performance of micro-fin tube (1) is
Smooth (2) Micro-fin (1) Micro-fin (2)
1000
Re
(c) Fig. 19. PEC versus Reynolds number (MWCNT nanofluids) for (a) smooth tube (2), (b) micro-fin tube (1), and (c) micro-fin tube (2).
Table 4 Average increase in f of the nanofluids with respect to the base fluid. Flat tube number
100
Nanofluids concentrations 0.001
0.005
0.01
0.1
5.67% 4.01% 5.13%
7.74% 6.45% 8.12%
9.70% 9.03% 10.52%
11.97% 11.60% 12.87%
superior to that of micro-fin tube (2), especially in the turbulent flow region. In general, the maximum thermal performance value is 1.59, which is obtained at a nanofluid concentration of 0.01 vol.% and Re ≈ 5300 for the micro-fin tube (1).
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Y.H. Diao et al. / Powder Technology 305 (2017) 206–216 1.8
References Micro-fin tube (1) Micro-fin tube (2)
1.6
PEC
1.4
1.2
1.0 100
1000
Re Fig. 20. PEC versus Reynolds number (0.01 vol.% MWCNT nanofluids).
6. Conclusion This study presents the effects of micro-fin tubes and different concentrations of MWCNT–water nanofluids on flow characteristics, convective heat transfer, and overall thermal performance at Reynolds number ranging from 130 to 5300 under a constant heat flux condition. The following conclusions can be drawn from the study. (1) At a concentration of ≤0.01 vol.%, heat transfer is enhanced with an increase in concentration. At a concentration of ≥ 0.01 vol.%, heat transfer enhancement deteriorates with an increase in concentration. Given the increase in the viscosity of nanofluids, the friction factor slightly increases with increasing volume concentration. (2) The water in the micro-fin tubes can enhance heat transfer and the friction factor compared with that in the smooth tube. A slightly earlier laminar–turbulent transition occurs for the water in the micro-fin tubes. The enhancement of the friction factor of nanofluids in the micro-fin tubes is nearly the same as that of nanofluids in the smooth tube. The heat transfer enhancement of nanofluids in the micro-fin tubes is lower than that of nanofluids in the smooth tube. However, the heat transfer of equally concentrated nanofluids in the micro-fin tube is higher than that of nanofluids in the smooth tube. The effect of microfin spacing on the heat transfer of nanofluids is more evident than that of the heat transfer of water. (3) Compared with the base fluid (water), nanofluids in the smooth and micro-fin tubes exhibit enhanced thermal performance at most Re values, particularly in turbulent flow. For nanofluids with an optimum concentration (i.e., 0.01 vol.%), the overall thermal performance of micro-fin tube (1) is higher than that of micro-fin tube (2), especially in turbulent flow. (4) The surfactant solutions with low concentrations have no effect on the heat transfer and flow characteristics of the flat tubes. By contrast, the surfactant solutions with high concentrations slightly decrease heat transfer and enhance the friction factor.
Acknowledgements The project was financially supported by the Scientific Research Project of Beijing Educational Committee (Grant No. KM201510005022). The authors are grateful for the support of sponsor.
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