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Experimental investigation of heat transfer for pulsating flow of GOPs-water nanofluid in a microchannel
International Communications in Heat and Mass Transfer 110 (2020) 104403
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Experimental investigation of heat transfer for pulsating flow of GOPs-water nanofluid in a microchannel
T
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Chong Xu, Shanglong Xu , Shiteng Wei, Pengyan Chen School of mechanical and Electrical engineering, University of Electronic Science and Technology of China, Chengdu, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Graphene oxide Nanofluid Pulsating flow Microchannel Heat transfer
The effects of mass fraction (φ) of graphene oxide particles (GOPs) and pulsating frequency (f) on heat transfer and pressure drop in a microchannel with arrayed pin-fins were experimentally investigated. Five different mass fractions of graphene oxide nanofluids were prepared and used as working fluids. Experiments were performed under the condition that the pulsating frequency was from 1 to 5 Hz, the mass fractions was from 0.02% to 0.2% and the average Reynolds number was 272, 407 and 544. The results show that the heat transfer is enhanced significantly when the frequency is in the range of 2 to 5 Hz. For the frequency of 1 Hz, the pulsating flow has a negative effect on temperature uniformity. With the increase of mass fraction, the heat transfer performance is improved while no significant change is found in pressure drop. The pulsating flow leads to a significant enhancement of pressure drop for frequency at 2 Hz. The combination of pulsating and nanofluid can obtain higher heat transfer efficiency under limited size of microchannel heat sink and low inlet Reynolds numbers. This study has a certain guiding significance for the development of microchannel liquid cooling technology.
1. Introduction With the rapid development of the electronic devices, the traditional thermal management and cooling technology is facing the huge challenge. Liquid cooling technology attracts more and more researchers [1]. The concept of ‘nanofluid’ was proposed by Choi [2] in 1995. It was found that the thermal conductivity of the nanofluids significantly increased when compared to the base fluids. More and more attentions have been paid to the method of enhancing the heat transfer performance by adding particles to base fluid [3]. The available particles mainly include metal or metal oxide [4,5], carbon nanotubes or graphene oxide [6,7]. These particles usually have higher thermal conductivity than the base fluid. Compared the base fluid, the thermal conductivity of suspensions was improved by adding these particles [8]. By using the Al2O3-H2O nanofluids with volume fractions of 0.15% and 0.26% as the working fluid, Xinyu Wu et al. [9] investigated the influence of Reynolds number, Prandtl number and nanoparticle concentration on the pressure drop and convective heat transfer. The experimental results showed that the Nusselt number increased with the increase in nanoparticle concentration, Reynolds number and Prandtl number. Peng tie et al.'s [10] study showed that the suspended nanoparticles would improve heat transfer characteristic while the dispersant added into nanofluids reduced the heat transfer coefficient.
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Corresponding author. E-mail address: [email protected] (S. Xu).
https://doi.org/10.1016/j.icheatmasstransfer.2019.104403
0735-1933/ © 2019 Elsevier Ltd. All rights reserved.
Kumar and Sonawane [11] proved that there was a significant enhancement in thermal conductivity and heat transfer as the concentration of nanoparticles increased. They also found an improvement in thermal conductivity as the temperature increases. Mehrizi et al. numerically [12] investigated the effect of nanoparticles on natural convection heat transfer in two-dimensional horizontal annulus by lattice Boltzmann method. The results showed that the Nusselt number and the maximum stream functions increased with the increased concentration of nanoparticle. Because of the excellent hydrophilic and thermal performance, the graphene oxide is gradually used for liquid-cooling of electronic systems. Compared to the other nanofluids with spherical nanoparticles, the nanofluids containing graphene oxide are expected to have better heat transfer performance. By using diesel oil as the base fluid, Naddaf et al. [13] experimentally studied the heat transfer and pressure drop performance of GNP and MWCNT nanofluids. The results showed that the increasing of concentration and velocity could improve the heat transfer performance. And compared with pure diesel oil, the increase in pressure drop caused by adding of nanoparticles was non-significant. Ponangi et al. [14] added the GOPs nanofluid into an automobile radiator to enhance the heat transfer coefficient. They found that the maximum enhancement of heat transfer coefficient can reach 56.45% at 40 °C. Ranjbarzadeh et al. [15] found that the average Nusselt number
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and friction factor were enhanced up to 51.4% and 21% compared to pure water when the volume concentration was 0.2%. Esfahani et al.'s [16] study showed that the thermal conductivity of graphene oxide nanofluids depended on both particle-size distribution and viscosity of nanofluids. The forced convective heat transfer of GOPs-water-ethylene glycol in laminar flow regime was numerically studied by Sajjad et al. [17]. The results indicated that the enhancement coefficient was lower when the heat transfer was in laminar flow regime. The heat transfer efficiency can be further increased by applying pulsating flow in the flow channel. Many present studies demonstrated that the strong mixing of coolant was the main cause of heat transfer enhancement by using pulsating flow. Jin et al. [18] experimentally investigated the heat transfer enhancement by pulsating flow in a triangular grooved channel. By introducing the pulsating flow, a maximum of 350% of heat transfer enhancement was obtained at Re = 270, St = 0.34, and η = 0.5. The strong mixing was caused by the repeated sequence of vortex in the groove. The fluid mixing enhancement was maximized when the pulsation period was matched with the time of growing period of vortex. Akdag et al. [19] numerically studied the combined effect of pulsating flow and nanofluid on heat transfer performance in a wavy channel. The strong vorticity was produced in the flow field because of the wavy channel structure and pulsating effect. The vortex growth was completed to satisfaction and the vortex expansion was enough for good mixing for pulsating flow in the low frequency range. Thus, the heat transfer was enhanced significantly at low frequency. The strong vorticity also delayed in nanoparticles sedimentation process. Jafari et al. [20] investigated the effects of pulsating flow on convection heat transfer of SWCNT-nanofluid in a wavy channel using the LBM. The results showed that the pulsating flow played a more important role in heat transfer enhancement than SWCNT nanofluid. Compared with the parallel microchannels, a microchannel network with special-shaped structure usually have better hydrodynamic characteristic and heat exchange performance [21]. The pin-fins are widely employed in microchannel heat sinks for their greater heat exchange area. On the other hand, the channels are formed by Pin-fins have the similar fluctuation structure to wave channel. The combination of wave channel and pulsating flow can significantly enhance mixing of coolant which leads to better heat transfer performance [19]. The heat transfer performance of pin-fins with circular, square, rhombus, rectangular, and elliptical were compared in Abdel-Rehim's [22] study. It was shown that the heat transfer performance of elliptical pin-fins configuration was better than other configurations. And the staggered alignment is the better option than in-line alignment. In Kosar and Peles's study [23], the heat transfer and pressure drop of five heat sinks with micro pin-fins of different spacing, arrangements, and shapes using forced flow of deionized water investigated. It was indicated that the pin-fins have streamlined shape and sharp pointed regions showed better thermalhydraulic performances at moderate Reynolds numbers. Based on the above mentioned studies, a microchannel heat sink with fish-shaped pin-fins was designed in the study. GOPs-water nanofluids with various mass fraction were prepared by ultrasonic method, and its stability was verified. The effects of nanofluid concentration, pulsating frequency, average Reynolds number on the heat transfer efficiency in a microchannel with pin-fins array were experimentally investigated. The average Nusselt number, equivalent thermal resistance and pressure drop were presented for different cases.
Table 1 Parameters of the nanoparticles. Average thickness
Average diameter
Specific heat
Heat conductivity
3–6 nm
10–20 μm
1400 J/kg·°C
3000 W·mK−1
Fig. 1. SEM image of GOPs.
of GOPs (Pheno Prc, Phenom World BV, Netherlands). The GOPs-water nanofluids with 5 different mass fraction (0.02%, 0.05%, 0.1%, 0.15%, 0.2%) were prepared by ultrasonic method for 90 min, and the power was provided by ultrasonic washing machine (PL-S08, Dongguan kangshijie ultrasonic technology co. LTD, Dongguan, China), as shown in Fig. 2. The GOPs will aggregate and deposit after a long time, which brings a bad influence on the heat transfer performance of nanofluids. So the stability of nanofluids is crucial to assure the accuracy of experimental datas. 2.2. Stability analysis For evaluating the stability of the GOPs-water nanofluids, the Zeta potential and light absorbance were measured by a zeta potential analyzer [25,26] (90PlusPALS, Brookhaven, USA) and an UV–vis spectrophotometr [13] (UV765PC, Doryang precision instrument co. LTD, Shanghai, China). Based on recent reports in the literature, the maximum absorption peak of the GO (graphene oxide) nanofluid appears at the incident wavelength equal 227 nm [16,27]. According to the Beer-Lambert law, there is a linear relationship between light absorbance and concentration of the nanofluid, which can be expressed in Eq. (1).
I A = lg ⎛ 0 ⎞ = Kbε ⎝I⎠
(1)
where A is the light absorbance, I0 and I is the intensity of the incident and transmitted light, respectively; K is the molar absorptivity, b is the
2. Material and methods 2.1. Preparation of nanofluids The two-step method [24] was used for preparing nanofluids. And the GOPs was provided by Hangzhou hangdan photoelectric technology co. LTD. The shape of the nanoparticles is thin slice, and the parameters of the nanoparticles are shown in Table 1. Fig. 1 shows the SEM images
Fig. 2. Photograph of prepared GOPs-water nanofluid with different concentration. 2
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Fig. 3. Absorbance of GOPs-water nanofluids with PVP (1% of mass fraction). Fig. 5. Schematic of experimental apparatus.
optical distance, ε is solute molarity. PVP [28] with 1% wt used as the dispersant is added in the GOPswater nanofluids. Fig. 3 show the measured absorbance of nanofluids with dispersant. It is observed that nanofluids with dispersant shows good stability for 4 h. The absorbance of nanofluid with 0.2% mass fraction has droped about 3.9% after 4 h. The decreased value of low concentration is more less than that of 0.2% mass fraction. So the stability of the nanofluids can satisfy the experiments requirement. The Zeta potential of nanofluids for 4 h after preparation is shown in Fig. 4. The Zeta potential values of nanofluids with different concentration are below −30 mV. It can be concluded that the nanofluids have good stability [26].
structure parameters of microchannel are shown in Fig. 9. Its total length and width are 56 mm and 40 mm. The detailed sizes of microchannel are shown in Fig. 9(a). The lf and Af are the arc length and the cross sectional area of pin-fin. The micro pump drives the cold nanofluid from the liquid storage tank to the microchannel for absorbing heat. The flowmeter is connected between the micro pump and inlet of test module to measure the real-time flowrate. The warm nanofluid is cooled by a radiator. Then the cold nanofluid go back into the liquid storage tank. The tank is equipped with a temperature sensor connected to the fan controller which controls the fan speed according to the signal that from temperature senor. This keeps the temperature of nanofluid at a certain value. A flowmeter monitors the peak rate of pulsating flow. As shown in Fig. 6, a ceramic heater is used as the heat source. By adjusting the impulse voltage to change the heating power. Two flexible pipes were connected on the pipe joints at the inlet and outlet. Two thermocouples (Pt1000) are inserted into the thermometer holes which with 1 mm diameter were perforated on the two flexible pipes at the distance of 2 mm from the pipe joints. Cotton with about 20 mm thick was used as insulating material to surround the pipe joints and the thermometer section to thermal insulation. A differential pressure gauge (SW-512, SNDWAY, Dongguan, China) is used to measure the pressure drop between inlet and outlet. The temperature distribution and maximum temperature of test module can be obtained by the infrared thermal imager (Ti9, FLUKE, Washington, America). Table 2 shows the parameters of main experiment instruments.
2.3. Experimental system The experimental system consists of a flow loop, a pulse power system, a test section and measuring instruments (Fig. 5). The flow loop includes a micro pump (ZC-A40, Lin an zhongchuang electronic appliances co. LTD, Hangzhou, China), a flowmeter (FC-W, Anhui zongzhe instrument technology co. LTD, Hefei, China), a microchannel heat sink, a radiator, a liquid storage tank and pipes. The schematic of pulse power system is shown in Fig. 7. It includes a pulse signal generator, a signal amplifier and a DC power. The pulse signal generator produces the square waveforms with different frequencies and duty cycles. Then it is amplified by the signal amplifier. The voltage amplitude is controlled by the DC power. The system provides impulse voltage for the pump to produce pulsating flow. The microchannel heat sink is made of aluminum alloy and fabricated using 3D printing technology that based on selective laser melting (SLM) process. The microchannel structure is shown in Fig. 8. Its dimension error is within 1.5%. The designed model as well as the
2.4. Experimental parameters Five mass fractions of 0.2%, 0.15%, 0.1%, 0.05% and 0.02% are
Fig. 4. Zeta potential of nanofluids for 4 h after preparation.
Fig. 6. Schematic of test module. 3
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Table 2 The parameters of main experiment instruments. Instrument
Model
Range
Precision
UV–vis spectrophotometer Micro pump Elliptical gear flowmeter Thermocouple Differential pressure gauge Infrared thermal imager
UV765PC ZC-A40 FC-W Pt1000 SW-512 Ti9
190–1100 nm 0–720 L/h 1–200 mL/s −50–150 °C ± 13.79 kPa −20–250 °C
± 0.3% / ± 1% ± 0.1 °C ± 0.3%FS ± 5%
Fig. 7. Schematic of pulse power system.
Fig. 8. Microchannel heat sink, (a) Microchannel structure by SLM, (b) Cover plate, (c) Assembly.
Fig. 9. Dimensional drawing of (a) designed structure and (b) Cover plate. The lf and Af are the arc length and the cross sectional area of pin-fin. Fig. 11. Nu vs φ for different pulsating frequency and Reynolds numbers.
Fig. 10. Impulse voltage and generated pulsating flow. 4
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Fig. 13. Variation of heat transfer enhancement factor with pulsating frequency under different average Reynolds number. Fig. 12. Variation of maximum thermal resistance with pulsating frequency for different average Reynolds numbers.
Favg = 0.7 × Fam
prepared for GONs-water nanofluids in the experiments. The cold nanofluid temperature is set as 15 °C. The duty cycle of 5 different frequencies (1, 2, 3, 4 and 5) voltage amplitude is a constant value of 70%(Fig. 10a). As the experimental parameter for comparison, the flow rate of steady flow is equal the time average value of pulsating flow. It is calculated by the Eq. (2). In Fig. 7b, the time-frequency of the flow rate has the similar pulse shape with pulse signal.
(2)
3. Data reduction and uncertainties analysis 3.1. Data processing and equations The specific heat capacity and density of nanofluid, ρnf and cnf are determined by the Eq. (3) [29] and Eq. (4) [30]:
ρnf = ρn φ V + ρ b (1 − φ V ) 5
(3)
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Reavg=272
1.45
Δpf /Δps
1.4 1.35 1.3 1.25 1.2 0
1
2
3
4
5
f(Hz) φ=0.2%
φ=0.15%
φ=0.1%
φ=0.05%
φ=0.02%
a
Reavg=407
1.3
Δpf /Δps
1.25
1.2
1.15
1.1 0
1
2
3
4
5
f(Hz) φ=0.2%
φ=0.15%
φ=0.1%
φ=0.05%
φ=0.02%
b
Reavg=272
1.25
Δpf /Δps
1.2 1.15 1.1 1.05 1 0
1
2
3
4
5
f(Hz) φ=0.2%
φ=0.15%
φ=0.1%
φ=0.05%
φ=0.02%
c Fig. 14. Variation of heat transfer enhancement factor with mass fraction under different average Reynolds number.
cnf =
Fig. 15. Effect of pulsating frequency and mass fraction on relative pressure drop.
cbf (1 − φ V ) ρbf + cn φ V ρn ρnf
(4)
φV =
where cnf is the specific heat at constant pressure of GOPs-water nanofluid, cb is the specific heat at constant pressure of water, cn is the specific heat of GOPs, φV is the volume fractions of GOPs. And φV can be expressed by Eq. (5):
Vn = Vnf
φ ρn 1 ρnf
=
φρnf ρn
(5)
The thermal conductivity of nanofluid could be calculated based on the Eq. (6) which was proposed by Davis [30].
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knf kb
( − 1) =1+ ( + 2) − φ ( kn kb
3
kn kb
kn kb
Table 4 The uncertainties of calculated parameters.
⎡φ + f ⎛ kn ⎞ φ 7 + O (φ 3) ⎤ V V ⎥ ⎢ V ⎝ kb ⎠ −1 ⎣ ⎦ ⎜
)
⎟
(6)
where the knf is the thermal conductivity of nanofluid, kb is the thermal conductivity of water, kn is the thermal conductivity of GOPs, φv is the volume fraction of GOPs. The value of f(k) is 0.5 in this case. The absorbed heat by the nanofluids per unit time flowing through the microchannel is calculated from the flowing Eq. (7):
̇ nf (Tout − Tin ) = Favg ρnf cnf (Tout − Tin ) Qnf = mc
Reavg = ρnf vavg Lc / μnf
Tmax − Tin Qnf
1
(10)
where Tmin is the minimum wall temperature of the heat sink.
havg Lc (11)
Where As is area of convective heat transfer surfaces in the microchannel.
As = 2 × (WL − NAf ) + 4Nlf H
(12)
3.2. Uncertainty analysis The uncertainties in the measurement instruments are presented in Table 3. The uncertainties of the heat flux, heat transfer coefficient and average nusselt number are calculated as follows:
ΔQnf Qnf
2
Δhavg havg
⎜
⎟
(13)
2
2
⎛ ΔQnf ⎞ + ⎛ Δ(Tw − (Tout + Tin )/2) ⎞ ⎜ ⎟ ⎝ Tw − (Tout + Tin )/2 ⎠ ⎝ Qnf ⎠
=
ΔNuavg Nuavg
2
⎛ ΔFavg ⎞ + ⎛ Δ(Tout − Tin ) ⎞ ⎜ ⎟ ⎝ Tout − Tin ⎠ ⎝ Favg ⎠
=
⎜
2
=
⎟
(14)
η=
2
⎛ Δhavg ⎞ + ⎛ ΔE ⎞ ⎜ ⎟ ⎝ E ⎠ ⎝ havg ⎠
(15)
Instruments
Accuracy
Tout and Tin Tmax and Tw Favg E
Thermometer Infrared thermal imager Flowmeter Manufacture error
± 0.1 °C ± 5% ± 1% ± 0.02 mm
(16)
Nup Nus
(17)
where Nup is the average Nusslt number under pulsating flow and Nus is the Nusslt number for the steady flow. The relationship between the heat transfer enhancement factor and pulsating frequency for different mass fraction at Reavg = 272, 407 and 544 are shown in Fig. 13a, b and c. The pulsating flow in the microchannel caused good mixing between the warm fluid near the wall and cold fluid in the main flow. The pulsating flow for pulsating frequency at f = 1 Hz has a slightly effect on the heat transfer enhancement compared to the steady flow. There is a definite increase of heat transfer enhancement factor when the pulsating frequency is increased from
Table 3 The uncertainties for test results. Parameters
⎟
The effects of pulsating frequency (f), mass fraction of nanoparticle (φ), and time average inlet Reynolds number (Reavg) on heat transfer is investigated. It is altered periodically due to the time periodic flow field occurs in the microchannel. The average Nusselt number (Nuavg) is an important parameter to characterize the heat transfer capability. The Nuavg with mass fraction of nanoparticle (φ) and pulsating frequency (f) for Reavg = 272, 407, 544 are shown in Fig. 11a, b, c. It is indicated that the heat transfer performance is improved with the increase of φ due to the adding of nanoparticles that enhances the heat conductivity (knf) of fluid. The Nuavg is from 4.5 to 10.3 when Reavg increases from 272 to 544 for different φ and f. In addition, the average Nusselt number for pulsating flow (f = 1–5 Hz) is higher than for steady flow (f = 0 Hz). It may be due to the strength of mixing and disturbance of nanofluids in the microchannel. Fig. 12 shows the maximum thermal resistance for different pulsating frequencies and mass fractions under various average Reynolds numbers. The maximum thermal resistance under pulsating flow for frequency at 1 Hz is higher than that of steady flow. When the frequency exceeds to 1 Hz (f = 2, 3, 4, 5), the values of maximum thermal resistance under pulsating flow are lower than under steady flow. The variation of maximum thermal resistance is gentle as the frequency increases from 3 Hz to 5 Hz. The change trends of maximum thermal resistance with frequency are generally similar under different average Reynolds numbers. As predicted, the increasing of average Reynolds number and mass fraction leads to a decrease of the maximum thermal resistance under both steady and pulsating flows. The heat transfer enhancement factor (η) is a dimensionless parameter which is defined as the ratio of Nup to Nus (expressed by the Eq. (15)), which is used to evaluate the effect of pulsating flow on heat transfer enhancement. If the value of η is > 1.0, the pulsating flow plays a positive role in the heat transfer enhancement.
Qnf
knf
2
⎜
4.1. Heat transfer performance
(9)
As ⎡ 2 (Tmax + Tmin )‐ 2 (Tout + Tin ) ⎤ ⎣ ⎦
2
⎛ ΔQnf ⎞ + ⎛ Δ(Tmax ‐Tin ) ⎞ ⎟ ⎝ Tmax ‐Tin ⎠ ⎝ Qnf ⎠
⎜
4. Results and discussion
where Tmax is the maximum temperature on the bottom surface of ceramic heater.
Nuavg =
1% 1% 5.4% 5.9% 6% 0.5% 5.4%
And the calculation results are reported in Table 4.
(8)
1
Characteristic length (Lc) Flow rate (Favg) Heat transfer (Qnf) Average heat transfer coefficient (havg) Average Nusselt number (Nuavg) Cooling performance(Tmax) Maximum thermal resistance (Rmax)
ΔRmax = Rmax
where vavg is the integral average flow velocity, Lc is the characteristic length and μnf is the viscosity. The total thermal resistance Rtot, average convective heat transfer coefficient havg and average nusselt number Nuavg are determined from the following Eq. (9) [31], Eqs. (10) and (11):
havg =
Uncertaintiy
(7)
where ṁ is the mass flow rate of nanofluid, Tout is the outlet temperature and Tin is the inlet temperature. The time average inlet Reynolds's number is defined as Eq. (8):
Rtot =
Parameters
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pulsating flow has a significant effect on the increasing of relative pressure drop. It reaches a maximum value when the pulsating frequency is 2 Hz. The enhancement becomes more weakly with the increasing of average Reynolds number.
1 Hz to 3 Hz. But it changes slightly when f is in the range of 3–5 Hz. The peak value of η is the optimal value for heat transfer enhancement. The cold and warm nanofluids are efficiently mixed in the microchannel at the optimal pulsating frequency. But in different cases, the maximum value of η is not fixed. The optimal pulsating frequency is 4 Hz for the Reavg = 272 while it is 3 Hz for the Reavg = 544. For Reavg = 407, the value of η occurs at 3 Hz or 4 Hz for different φ. The maximum heat transfer enhancement occurs at lower pulsating frequency with the increasing of Reynolds number. The average Reynolds number affects not only the value of optimal pulsating frequency, but also the strength of heat transfer enhancement effect. As shown in the Fig. 14a, b, c, the maximum heat transfer enhancement factor is η = 1.33 (Reavg = 272, f = 4, φ = 0.1%), η = 1.29 (Reavg = 407, f = 4, φ = 0.15%), η = 1.22 (Reavg = 544, f = 3, φ = 0.15%). It is indicated that the pulsating flow plays a stronger role in enhancing heat transfer at lower average Reynolds number.
Nomenclature c f GOPs h k Lc Nu Q R Re T Δp
4.2. Relative pressure drop
specific heat (J kg−1 K−1) pulsating frequency (Hz) graphene oxide particles convective heat transfer coefficient (W/m2°C) thermal conductivity (W/m°C) characteristic length (mm) Nusselt number amount of heat transferred per time (W) thermal resistance(°C/W) Reynolds number temperature (°C) pressure drop (Pa)
Greek characters
A dimensionless pressure drop ratio (ΔPp/ΔPs) is defined as relative pressure drop. ΔPp, ΔPs are the pressure drop in pulsating and steady flow condition, respectively. In the Fig. 15a, b, c, the role of pulsating frequency (f), mass fraction (φ) and average Reynolds number (Reavg) on relative pressure drop in the microchannel is observed. The mass fraction effect is not obvious. The relative pressure drop has a slight increase with the increasing of mass fraction. The results show that the pulsating flow contributes a significant increase to it. The relative pressure drop reaches the maximum value at f = 2 Hz. It slowly decreases while the pulsating frequency increases from 3 Hz to 5 Hz, close to the value of steady flow. In addition, it is indicated that the effect of pulsating flow on relative pressure drop is weakened as the average Reynolds numbers increases.
ρ μ φ φV η
density (kg m-3) viscosity (mPa s) mass fraction volume fraction enhancement factor
Subscripts avg am p s nf b n in out max w
5. Conclusion In this study, the effect of various concentrations of GOPs-water nanofluids in a pin-fin microchannel on heat transfer under pulsating inlet velocity is investigated experimentally. The effect of pulsating frequency (f = 0, 1, 2, 3, 4, 5), mass fraction (φ = 0.02%, 0.05%, 0.1%, 0.15%, 0.2%) and time average Reynolds number (Reavg = 272, 407, 544) on heat transfer enhancement is discussed. The main conclusions are as follows: The heat transfer performance of GOPs-water nanofluids is improved with the mass fraction of GOPs increases for the nanofluid at the concentration of 0.02%–0.2%. The increasing of average Reynolds number can enhance the heat transfer performance of nanofluids under the low Reynolds number (272–544). The low frequency (f < 2 Hz) pulsating flow has no significant effect on heat transfer enhancement of nanofluids compared to the steady flow. When the pulsating frequency is in the range of 3–5 Hz, the heat transfer of nanofluids is enhanced obviously. And the heat transfer enhancement factor reaches the maximum value at the optimal pulsating (f = 3 or 4 Hz). The average Reynolds number affects the value of optimal pulsating frequency as well as heat transfer rate.The optimal pulsating frequency is equal 3 Hz corresponding to the average Reynolds number is 544, and 4 Hz corresponding to average Reynolds number is 277. The pulsating flow has more enhancement effect on heat transfer at low average Reynolds number. The heat transfer enhancement factor reaches 1.33 for average Reynolds number is 277. The heat sink shows a worse thermal performance when the pulsating frequency is 1 Hz in this experiment. The changing of mass fraction of nanofluids in a small range (0.02%–0.2%) has slightly influence on the relative pressure drop. The
average amplitude puslating flow steady flow nanofluid base fluid nanoparticle inlet outlet maximum wall
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was supported by Sichuan Science and Technology Project of China (No. 2019YFG0360). References [1] W.T. Ji, A.M. Jacobi, Y.L. He, W.Q. Tao, Summary and evaluation on single-phase heat transfer enhancement techniques of liquid laminar and turbulent pipe flow, Int. J. Heat Mass Transf. 88 (2015) 735–754. [2] U.S. Choi, J.A. Eastman, Enhancing Thermal Conductivity of Fluids with Nanoparticles, 231 ASME Publ.Fed, 1995, pp. 99–106. [3] M.N. Golubovic, H.D. Madhawa Hettiarachchi, W.M. Worek, W.J. Minkowycz, Nanofluids and critical heat flux, experimental and analytical study, Appl. Therm. Eng. 29 (7) (2009) 1281–1288. [4] I. Behroyan, P. Ganesan, S. He, S. Sivasankaran, Turbulent forced convection of Cu–water nanofluid: CFD model comparison, Int. Commun. Heat Mass Transf. 67 (2015) 163–172. [5] N. Tran, Y.-J. Chang, C.-C. Wang, Optimization of thermal performance of multinozzle trapezoidal microchannel heat sinks by using nanofluids of Al2O3 and TiO2, Int. J. Heat Mass Transf. 117 (2018) 787–798.
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[6] A. Naddaf, S. Zeinali Heris, Experimental study on thermal conductivity and electrical conductivity of diesel oil-based nanofluids of graphene nanoplatelets and carbon nanotubes, Int. Commun. Heat Mass Transf. 95 (2018) 116–122. [7] E.M. Cárdenas Contreras, G.A. Oliveira, E.P. Bandarra Filho, Experimental analysis of the thermohydraulic performance of graphene and silver nanofluids in automotive cooling systems, Int. J. Heat Mass Transf. 132 (2019) 375–387. [8] M.H. Mirbagheri, M. Akbari, B. Mehmandoust, Proposing a new experimental correlation for thermal conductivity of nanofluids containing of functionalized multiwalled carbon nanotubes suspended in a binary base fluid, Int. Commun. Heat Mass Transf. 98 (2018) 216–222. [9] X.Y. Wu, H.Y. Wu, P. Cheng, Pressure drop and heat transfer of Al2O3-H2O nanofluids through silicon microchannels, J. Micromech. Microeng. 19 (10) (2009) 105020. [10] P. Tie, Q. Li, Y. Xuan, Heat transfer performance of Cu–water nanofluids in the jet arrays impingement cooling system, Int. J. Therm. Sci. 77 (2014) 199–205. [11] N. Kumar, S.S. Sonawane, Experimental study of thermal conductivity and convective heat transfer enhancement using CuO and TiO 2 nanoparticles, Int. Commun. Heat Mass Transf. 76 (2016) 98–107. [12] A.A. Mehrizi, M. Farhadi, S. Shayamehr, Natural convection flow of Cu–Water nanofluid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method, Int. Commun. Heat Mass Transf. 44 (44) (2013) 147–156. [13] A. Naddaf, S. Zeinali Heris, B. Pouladi, An experimental study on heat transfer performance and pressure drop of nanofluids using graphene and multi-walled carbon nanotubes based on diesel oil, Powder Technol. 352 (2019) 369–380. [14] B.R. Ponangi, S. Sumanth, V. Krishna, T.R. Seetharam, K.N. Seetharamu, Heat transfer analysis of radiator using graphene oxide nanofluids, IOP Conf. Ser-Mater. Sci. 346 (2018). [15] R. Ranjbarzadeh, A.H.M. Isfahani, M. Afrand, A. Karimipour, M. Hojaji, An experimental study on heat transfer and pressure drop of water/graphene oxide nanofluid in a copper tube under air cross-flow: applicable as a heat exchanger, Appl. Therm. Eng. 125 (2017) 69–79. [16] M.R. Esfahani, E.M. Languri, M.R. Nunna, Effect of particle size and viscosity on thermal conductivity enhancement of graphene oxide nanofluid, Int. Commun. Heat Mass Transf. 76 (2016) 308–315. [17] M. Sajjad, M.S. Kamran, R. Shaukat, M.I.M. Zeinelabdeen, Numerical investigation of laminar convective heat transfer of graphene oxide/ethylene glycol-water nanofluids in a horizontal tube, Eng. Sci. Technol. Int. J. 21 (4) (2018) 727–735. [18] D.X. Jin, Y.P. Lee, D.Y. Lee, Effects of the pulsating flow agitation on the heat
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Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Experimental investigation of heat transfer for pulsating flow of GOPs-water nanofluid in a microchannel
T
⁎
Chong Xu, Shanglong Xu , Shiteng Wei, Pengyan Chen School of mechanical and Electrical engineering, University of Electronic Science and Technology of China, Chengdu, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Graphene oxide Nanofluid Pulsating flow Microchannel Heat transfer
The effects of mass fraction (φ) of graphene oxide particles (GOPs) and pulsating frequency (f) on heat transfer and pressure drop in a microchannel with arrayed pin-fins were experimentally investigated. Five different mass fractions of graphene oxide nanofluids were prepared and used as working fluids. Experiments were performed under the condition that the pulsating frequency was from 1 to 5 Hz, the mass fractions was from 0.02% to 0.2% and the average Reynolds number was 272, 407 and 544. The results show that the heat transfer is enhanced significantly when the frequency is in the range of 2 to 5 Hz. For the frequency of 1 Hz, the pulsating flow has a negative effect on temperature uniformity. With the increase of mass fraction, the heat transfer performance is improved while no significant change is found in pressure drop. The pulsating flow leads to a significant enhancement of pressure drop for frequency at 2 Hz. The combination of pulsating and nanofluid can obtain higher heat transfer efficiency under limited size of microchannel heat sink and low inlet Reynolds numbers. This study has a certain guiding significance for the development of microchannel liquid cooling technology.
1. Introduction With the rapid development of the electronic devices, the traditional thermal management and cooling technology is facing the huge challenge. Liquid cooling technology attracts more and more researchers [1]. The concept of ‘nanofluid’ was proposed by Choi [2] in 1995. It was found that the thermal conductivity of the nanofluids significantly increased when compared to the base fluids. More and more attentions have been paid to the method of enhancing the heat transfer performance by adding particles to base fluid [3]. The available particles mainly include metal or metal oxide [4,5], carbon nanotubes or graphene oxide [6,7]. These particles usually have higher thermal conductivity than the base fluid. Compared the base fluid, the thermal conductivity of suspensions was improved by adding these particles [8]. By using the Al2O3-H2O nanofluids with volume fractions of 0.15% and 0.26% as the working fluid, Xinyu Wu et al. [9] investigated the influence of Reynolds number, Prandtl number and nanoparticle concentration on the pressure drop and convective heat transfer. The experimental results showed that the Nusselt number increased with the increase in nanoparticle concentration, Reynolds number and Prandtl number. Peng tie et al.'s [10] study showed that the suspended nanoparticles would improve heat transfer characteristic while the dispersant added into nanofluids reduced the heat transfer coefficient.
⁎
Corresponding author. E-mail address: [email protected] (S. Xu).
https://doi.org/10.1016/j.icheatmasstransfer.2019.104403
0735-1933/ © 2019 Elsevier Ltd. All rights reserved.
Kumar and Sonawane [11] proved that there was a significant enhancement in thermal conductivity and heat transfer as the concentration of nanoparticles increased. They also found an improvement in thermal conductivity as the temperature increases. Mehrizi et al. numerically [12] investigated the effect of nanoparticles on natural convection heat transfer in two-dimensional horizontal annulus by lattice Boltzmann method. The results showed that the Nusselt number and the maximum stream functions increased with the increased concentration of nanoparticle. Because of the excellent hydrophilic and thermal performance, the graphene oxide is gradually used for liquid-cooling of electronic systems. Compared to the other nanofluids with spherical nanoparticles, the nanofluids containing graphene oxide are expected to have better heat transfer performance. By using diesel oil as the base fluid, Naddaf et al. [13] experimentally studied the heat transfer and pressure drop performance of GNP and MWCNT nanofluids. The results showed that the increasing of concentration and velocity could improve the heat transfer performance. And compared with pure diesel oil, the increase in pressure drop caused by adding of nanoparticles was non-significant. Ponangi et al. [14] added the GOPs nanofluid into an automobile radiator to enhance the heat transfer coefficient. They found that the maximum enhancement of heat transfer coefficient can reach 56.45% at 40 °C. Ranjbarzadeh et al. [15] found that the average Nusselt number
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and friction factor were enhanced up to 51.4% and 21% compared to pure water when the volume concentration was 0.2%. Esfahani et al.'s [16] study showed that the thermal conductivity of graphene oxide nanofluids depended on both particle-size distribution and viscosity of nanofluids. The forced convective heat transfer of GOPs-water-ethylene glycol in laminar flow regime was numerically studied by Sajjad et al. [17]. The results indicated that the enhancement coefficient was lower when the heat transfer was in laminar flow regime. The heat transfer efficiency can be further increased by applying pulsating flow in the flow channel. Many present studies demonstrated that the strong mixing of coolant was the main cause of heat transfer enhancement by using pulsating flow. Jin et al. [18] experimentally investigated the heat transfer enhancement by pulsating flow in a triangular grooved channel. By introducing the pulsating flow, a maximum of 350% of heat transfer enhancement was obtained at Re = 270, St = 0.34, and η = 0.5. The strong mixing was caused by the repeated sequence of vortex in the groove. The fluid mixing enhancement was maximized when the pulsation period was matched with the time of growing period of vortex. Akdag et al. [19] numerically studied the combined effect of pulsating flow and nanofluid on heat transfer performance in a wavy channel. The strong vorticity was produced in the flow field because of the wavy channel structure and pulsating effect. The vortex growth was completed to satisfaction and the vortex expansion was enough for good mixing for pulsating flow in the low frequency range. Thus, the heat transfer was enhanced significantly at low frequency. The strong vorticity also delayed in nanoparticles sedimentation process. Jafari et al. [20] investigated the effects of pulsating flow on convection heat transfer of SWCNT-nanofluid in a wavy channel using the LBM. The results showed that the pulsating flow played a more important role in heat transfer enhancement than SWCNT nanofluid. Compared with the parallel microchannels, a microchannel network with special-shaped structure usually have better hydrodynamic characteristic and heat exchange performance [21]. The pin-fins are widely employed in microchannel heat sinks for their greater heat exchange area. On the other hand, the channels are formed by Pin-fins have the similar fluctuation structure to wave channel. The combination of wave channel and pulsating flow can significantly enhance mixing of coolant which leads to better heat transfer performance [19]. The heat transfer performance of pin-fins with circular, square, rhombus, rectangular, and elliptical were compared in Abdel-Rehim's [22] study. It was shown that the heat transfer performance of elliptical pin-fins configuration was better than other configurations. And the staggered alignment is the better option than in-line alignment. In Kosar and Peles's study [23], the heat transfer and pressure drop of five heat sinks with micro pin-fins of different spacing, arrangements, and shapes using forced flow of deionized water investigated. It was indicated that the pin-fins have streamlined shape and sharp pointed regions showed better thermalhydraulic performances at moderate Reynolds numbers. Based on the above mentioned studies, a microchannel heat sink with fish-shaped pin-fins was designed in the study. GOPs-water nanofluids with various mass fraction were prepared by ultrasonic method, and its stability was verified. The effects of nanofluid concentration, pulsating frequency, average Reynolds number on the heat transfer efficiency in a microchannel with pin-fins array were experimentally investigated. The average Nusselt number, equivalent thermal resistance and pressure drop were presented for different cases.
Table 1 Parameters of the nanoparticles. Average thickness
Average diameter
Specific heat
Heat conductivity
3–6 nm
10–20 μm
1400 J/kg·°C
3000 W·mK−1
Fig. 1. SEM image of GOPs.
of GOPs (Pheno Prc, Phenom World BV, Netherlands). The GOPs-water nanofluids with 5 different mass fraction (0.02%, 0.05%, 0.1%, 0.15%, 0.2%) were prepared by ultrasonic method for 90 min, and the power was provided by ultrasonic washing machine (PL-S08, Dongguan kangshijie ultrasonic technology co. LTD, Dongguan, China), as shown in Fig. 2. The GOPs will aggregate and deposit after a long time, which brings a bad influence on the heat transfer performance of nanofluids. So the stability of nanofluids is crucial to assure the accuracy of experimental datas. 2.2. Stability analysis For evaluating the stability of the GOPs-water nanofluids, the Zeta potential and light absorbance were measured by a zeta potential analyzer [25,26] (90PlusPALS, Brookhaven, USA) and an UV–vis spectrophotometr [13] (UV765PC, Doryang precision instrument co. LTD, Shanghai, China). Based on recent reports in the literature, the maximum absorption peak of the GO (graphene oxide) nanofluid appears at the incident wavelength equal 227 nm [16,27]. According to the Beer-Lambert law, there is a linear relationship between light absorbance and concentration of the nanofluid, which can be expressed in Eq. (1).
I A = lg ⎛ 0 ⎞ = Kbε ⎝I⎠
(1)
where A is the light absorbance, I0 and I is the intensity of the incident and transmitted light, respectively; K is the molar absorptivity, b is the
2. Material and methods 2.1. Preparation of nanofluids The two-step method [24] was used for preparing nanofluids. And the GOPs was provided by Hangzhou hangdan photoelectric technology co. LTD. The shape of the nanoparticles is thin slice, and the parameters of the nanoparticles are shown in Table 1. Fig. 1 shows the SEM images
Fig. 2. Photograph of prepared GOPs-water nanofluid with different concentration. 2
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Fig. 3. Absorbance of GOPs-water nanofluids with PVP (1% of mass fraction). Fig. 5. Schematic of experimental apparatus.
optical distance, ε is solute molarity. PVP [28] with 1% wt used as the dispersant is added in the GOPswater nanofluids. Fig. 3 show the measured absorbance of nanofluids with dispersant. It is observed that nanofluids with dispersant shows good stability for 4 h. The absorbance of nanofluid with 0.2% mass fraction has droped about 3.9% after 4 h. The decreased value of low concentration is more less than that of 0.2% mass fraction. So the stability of the nanofluids can satisfy the experiments requirement. The Zeta potential of nanofluids for 4 h after preparation is shown in Fig. 4. The Zeta potential values of nanofluids with different concentration are below −30 mV. It can be concluded that the nanofluids have good stability [26].
structure parameters of microchannel are shown in Fig. 9. Its total length and width are 56 mm and 40 mm. The detailed sizes of microchannel are shown in Fig. 9(a). The lf and Af are the arc length and the cross sectional area of pin-fin. The micro pump drives the cold nanofluid from the liquid storage tank to the microchannel for absorbing heat. The flowmeter is connected between the micro pump and inlet of test module to measure the real-time flowrate. The warm nanofluid is cooled by a radiator. Then the cold nanofluid go back into the liquid storage tank. The tank is equipped with a temperature sensor connected to the fan controller which controls the fan speed according to the signal that from temperature senor. This keeps the temperature of nanofluid at a certain value. A flowmeter monitors the peak rate of pulsating flow. As shown in Fig. 6, a ceramic heater is used as the heat source. By adjusting the impulse voltage to change the heating power. Two flexible pipes were connected on the pipe joints at the inlet and outlet. Two thermocouples (Pt1000) are inserted into the thermometer holes which with 1 mm diameter were perforated on the two flexible pipes at the distance of 2 mm from the pipe joints. Cotton with about 20 mm thick was used as insulating material to surround the pipe joints and the thermometer section to thermal insulation. A differential pressure gauge (SW-512, SNDWAY, Dongguan, China) is used to measure the pressure drop between inlet and outlet. The temperature distribution and maximum temperature of test module can be obtained by the infrared thermal imager (Ti9, FLUKE, Washington, America). Table 2 shows the parameters of main experiment instruments.
2.3. Experimental system The experimental system consists of a flow loop, a pulse power system, a test section and measuring instruments (Fig. 5). The flow loop includes a micro pump (ZC-A40, Lin an zhongchuang electronic appliances co. LTD, Hangzhou, China), a flowmeter (FC-W, Anhui zongzhe instrument technology co. LTD, Hefei, China), a microchannel heat sink, a radiator, a liquid storage tank and pipes. The schematic of pulse power system is shown in Fig. 7. It includes a pulse signal generator, a signal amplifier and a DC power. The pulse signal generator produces the square waveforms with different frequencies and duty cycles. Then it is amplified by the signal amplifier. The voltage amplitude is controlled by the DC power. The system provides impulse voltage for the pump to produce pulsating flow. The microchannel heat sink is made of aluminum alloy and fabricated using 3D printing technology that based on selective laser melting (SLM) process. The microchannel structure is shown in Fig. 8. Its dimension error is within 1.5%. The designed model as well as the
2.4. Experimental parameters Five mass fractions of 0.2%, 0.15%, 0.1%, 0.05% and 0.02% are
Fig. 4. Zeta potential of nanofluids for 4 h after preparation.
Fig. 6. Schematic of test module. 3
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Table 2 The parameters of main experiment instruments. Instrument
Model
Range
Precision
UV–vis spectrophotometer Micro pump Elliptical gear flowmeter Thermocouple Differential pressure gauge Infrared thermal imager
UV765PC ZC-A40 FC-W Pt1000 SW-512 Ti9
190–1100 nm 0–720 L/h 1–200 mL/s −50–150 °C ± 13.79 kPa −20–250 °C
± 0.3% / ± 1% ± 0.1 °C ± 0.3%FS ± 5%
Fig. 7. Schematic of pulse power system.
Fig. 8. Microchannel heat sink, (a) Microchannel structure by SLM, (b) Cover plate, (c) Assembly.
Fig. 9. Dimensional drawing of (a) designed structure and (b) Cover plate. The lf and Af are the arc length and the cross sectional area of pin-fin. Fig. 11. Nu vs φ for different pulsating frequency and Reynolds numbers.
Fig. 10. Impulse voltage and generated pulsating flow. 4
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Fig. 13. Variation of heat transfer enhancement factor with pulsating frequency under different average Reynolds number. Fig. 12. Variation of maximum thermal resistance with pulsating frequency for different average Reynolds numbers.
Favg = 0.7 × Fam
prepared for GONs-water nanofluids in the experiments. The cold nanofluid temperature is set as 15 °C. The duty cycle of 5 different frequencies (1, 2, 3, 4 and 5) voltage amplitude is a constant value of 70%(Fig. 10a). As the experimental parameter for comparison, the flow rate of steady flow is equal the time average value of pulsating flow. It is calculated by the Eq. (2). In Fig. 7b, the time-frequency of the flow rate has the similar pulse shape with pulse signal.
(2)
3. Data reduction and uncertainties analysis 3.1. Data processing and equations The specific heat capacity and density of nanofluid, ρnf and cnf are determined by the Eq. (3) [29] and Eq. (4) [30]:
ρnf = ρn φ V + ρ b (1 − φ V ) 5
(3)
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Reavg=272
1.45
Δpf /Δps
1.4 1.35 1.3 1.25 1.2 0
1
2
3
4
5
f(Hz) φ=0.2%
φ=0.15%
φ=0.1%
φ=0.05%
φ=0.02%
a
Reavg=407
1.3
Δpf /Δps
1.25
1.2
1.15
1.1 0
1
2
3
4
5
f(Hz) φ=0.2%
φ=0.15%
φ=0.1%
φ=0.05%
φ=0.02%
b
Reavg=272
1.25
Δpf /Δps
1.2 1.15 1.1 1.05 1 0
1
2
3
4
5
f(Hz) φ=0.2%
φ=0.15%
φ=0.1%
φ=0.05%
φ=0.02%
c Fig. 14. Variation of heat transfer enhancement factor with mass fraction under different average Reynolds number.
cnf =
Fig. 15. Effect of pulsating frequency and mass fraction on relative pressure drop.
cbf (1 − φ V ) ρbf + cn φ V ρn ρnf
(4)
φV =
where cnf is the specific heat at constant pressure of GOPs-water nanofluid, cb is the specific heat at constant pressure of water, cn is the specific heat of GOPs, φV is the volume fractions of GOPs. And φV can be expressed by Eq. (5):
Vn = Vnf
φ ρn 1 ρnf
=
φρnf ρn
(5)
The thermal conductivity of nanofluid could be calculated based on the Eq. (6) which was proposed by Davis [30].
6
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knf kb
( − 1) =1+ ( + 2) − φ ( kn kb
3
kn kb
kn kb
Table 4 The uncertainties of calculated parameters.
⎡φ + f ⎛ kn ⎞ φ 7 + O (φ 3) ⎤ V V ⎥ ⎢ V ⎝ kb ⎠ −1 ⎣ ⎦ ⎜
)
⎟
(6)
where the knf is the thermal conductivity of nanofluid, kb is the thermal conductivity of water, kn is the thermal conductivity of GOPs, φv is the volume fraction of GOPs. The value of f(k) is 0.5 in this case. The absorbed heat by the nanofluids per unit time flowing through the microchannel is calculated from the flowing Eq. (7):
̇ nf (Tout − Tin ) = Favg ρnf cnf (Tout − Tin ) Qnf = mc
Reavg = ρnf vavg Lc / μnf
Tmax − Tin Qnf
1
(10)
where Tmin is the minimum wall temperature of the heat sink.
havg Lc (11)
Where As is area of convective heat transfer surfaces in the microchannel.
As = 2 × (WL − NAf ) + 4Nlf H
(12)
3.2. Uncertainty analysis The uncertainties in the measurement instruments are presented in Table 3. The uncertainties of the heat flux, heat transfer coefficient and average nusselt number are calculated as follows:
ΔQnf Qnf
2
Δhavg havg
⎜
⎟
(13)
2
2
⎛ ΔQnf ⎞ + ⎛ Δ(Tw − (Tout + Tin )/2) ⎞ ⎜ ⎟ ⎝ Tw − (Tout + Tin )/2 ⎠ ⎝ Qnf ⎠
=
ΔNuavg Nuavg
2
⎛ ΔFavg ⎞ + ⎛ Δ(Tout − Tin ) ⎞ ⎜ ⎟ ⎝ Tout − Tin ⎠ ⎝ Favg ⎠
=
⎜
2
=
⎟
(14)
η=
2
⎛ Δhavg ⎞ + ⎛ ΔE ⎞ ⎜ ⎟ ⎝ E ⎠ ⎝ havg ⎠
(15)
Instruments
Accuracy
Tout and Tin Tmax and Tw Favg E
Thermometer Infrared thermal imager Flowmeter Manufacture error
± 0.1 °C ± 5% ± 1% ± 0.02 mm
(16)
Nup Nus
(17)
where Nup is the average Nusslt number under pulsating flow and Nus is the Nusslt number for the steady flow. The relationship between the heat transfer enhancement factor and pulsating frequency for different mass fraction at Reavg = 272, 407 and 544 are shown in Fig. 13a, b and c. The pulsating flow in the microchannel caused good mixing between the warm fluid near the wall and cold fluid in the main flow. The pulsating flow for pulsating frequency at f = 1 Hz has a slightly effect on the heat transfer enhancement compared to the steady flow. There is a definite increase of heat transfer enhancement factor when the pulsating frequency is increased from
Table 3 The uncertainties for test results. Parameters
⎟
The effects of pulsating frequency (f), mass fraction of nanoparticle (φ), and time average inlet Reynolds number (Reavg) on heat transfer is investigated. It is altered periodically due to the time periodic flow field occurs in the microchannel. The average Nusselt number (Nuavg) is an important parameter to characterize the heat transfer capability. The Nuavg with mass fraction of nanoparticle (φ) and pulsating frequency (f) for Reavg = 272, 407, 544 are shown in Fig. 11a, b, c. It is indicated that the heat transfer performance is improved with the increase of φ due to the adding of nanoparticles that enhances the heat conductivity (knf) of fluid. The Nuavg is from 4.5 to 10.3 when Reavg increases from 272 to 544 for different φ and f. In addition, the average Nusselt number for pulsating flow (f = 1–5 Hz) is higher than for steady flow (f = 0 Hz). It may be due to the strength of mixing and disturbance of nanofluids in the microchannel. Fig. 12 shows the maximum thermal resistance for different pulsating frequencies and mass fractions under various average Reynolds numbers. The maximum thermal resistance under pulsating flow for frequency at 1 Hz is higher than that of steady flow. When the frequency exceeds to 1 Hz (f = 2, 3, 4, 5), the values of maximum thermal resistance under pulsating flow are lower than under steady flow. The variation of maximum thermal resistance is gentle as the frequency increases from 3 Hz to 5 Hz. The change trends of maximum thermal resistance with frequency are generally similar under different average Reynolds numbers. As predicted, the increasing of average Reynolds number and mass fraction leads to a decrease of the maximum thermal resistance under both steady and pulsating flows. The heat transfer enhancement factor (η) is a dimensionless parameter which is defined as the ratio of Nup to Nus (expressed by the Eq. (15)), which is used to evaluate the effect of pulsating flow on heat transfer enhancement. If the value of η is > 1.0, the pulsating flow plays a positive role in the heat transfer enhancement.
Qnf
knf
2
⎜
4.1. Heat transfer performance
(9)
As ⎡ 2 (Tmax + Tmin )‐ 2 (Tout + Tin ) ⎤ ⎣ ⎦
2
⎛ ΔQnf ⎞ + ⎛ Δ(Tmax ‐Tin ) ⎞ ⎟ ⎝ Tmax ‐Tin ⎠ ⎝ Qnf ⎠
⎜
4. Results and discussion
where Tmax is the maximum temperature on the bottom surface of ceramic heater.
Nuavg =
1% 1% 5.4% 5.9% 6% 0.5% 5.4%
And the calculation results are reported in Table 4.
(8)
1
Characteristic length (Lc) Flow rate (Favg) Heat transfer (Qnf) Average heat transfer coefficient (havg) Average Nusselt number (Nuavg) Cooling performance(Tmax) Maximum thermal resistance (Rmax)
ΔRmax = Rmax
where vavg is the integral average flow velocity, Lc is the characteristic length and μnf is the viscosity. The total thermal resistance Rtot, average convective heat transfer coefficient havg and average nusselt number Nuavg are determined from the following Eq. (9) [31], Eqs. (10) and (11):
havg =
Uncertaintiy
(7)
where ṁ is the mass flow rate of nanofluid, Tout is the outlet temperature and Tin is the inlet temperature. The time average inlet Reynolds's number is defined as Eq. (8):
Rtot =
Parameters
7
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pulsating flow has a significant effect on the increasing of relative pressure drop. It reaches a maximum value when the pulsating frequency is 2 Hz. The enhancement becomes more weakly with the increasing of average Reynolds number.
1 Hz to 3 Hz. But it changes slightly when f is in the range of 3–5 Hz. The peak value of η is the optimal value for heat transfer enhancement. The cold and warm nanofluids are efficiently mixed in the microchannel at the optimal pulsating frequency. But in different cases, the maximum value of η is not fixed. The optimal pulsating frequency is 4 Hz for the Reavg = 272 while it is 3 Hz for the Reavg = 544. For Reavg = 407, the value of η occurs at 3 Hz or 4 Hz for different φ. The maximum heat transfer enhancement occurs at lower pulsating frequency with the increasing of Reynolds number. The average Reynolds number affects not only the value of optimal pulsating frequency, but also the strength of heat transfer enhancement effect. As shown in the Fig. 14a, b, c, the maximum heat transfer enhancement factor is η = 1.33 (Reavg = 272, f = 4, φ = 0.1%), η = 1.29 (Reavg = 407, f = 4, φ = 0.15%), η = 1.22 (Reavg = 544, f = 3, φ = 0.15%). It is indicated that the pulsating flow plays a stronger role in enhancing heat transfer at lower average Reynolds number.
Nomenclature c f GOPs h k Lc Nu Q R Re T Δp
4.2. Relative pressure drop
specific heat (J kg−1 K−1) pulsating frequency (Hz) graphene oxide particles convective heat transfer coefficient (W/m2°C) thermal conductivity (W/m°C) characteristic length (mm) Nusselt number amount of heat transferred per time (W) thermal resistance(°C/W) Reynolds number temperature (°C) pressure drop (Pa)
Greek characters
A dimensionless pressure drop ratio (ΔPp/ΔPs) is defined as relative pressure drop. ΔPp, ΔPs are the pressure drop in pulsating and steady flow condition, respectively. In the Fig. 15a, b, c, the role of pulsating frequency (f), mass fraction (φ) and average Reynolds number (Reavg) on relative pressure drop in the microchannel is observed. The mass fraction effect is not obvious. The relative pressure drop has a slight increase with the increasing of mass fraction. The results show that the pulsating flow contributes a significant increase to it. The relative pressure drop reaches the maximum value at f = 2 Hz. It slowly decreases while the pulsating frequency increases from 3 Hz to 5 Hz, close to the value of steady flow. In addition, it is indicated that the effect of pulsating flow on relative pressure drop is weakened as the average Reynolds numbers increases.
ρ μ φ φV η
density (kg m-3) viscosity (mPa s) mass fraction volume fraction enhancement factor
Subscripts avg am p s nf b n in out max w
5. Conclusion In this study, the effect of various concentrations of GOPs-water nanofluids in a pin-fin microchannel on heat transfer under pulsating inlet velocity is investigated experimentally. The effect of pulsating frequency (f = 0, 1, 2, 3, 4, 5), mass fraction (φ = 0.02%, 0.05%, 0.1%, 0.15%, 0.2%) and time average Reynolds number (Reavg = 272, 407, 544) on heat transfer enhancement is discussed. The main conclusions are as follows: The heat transfer performance of GOPs-water nanofluids is improved with the mass fraction of GOPs increases for the nanofluid at the concentration of 0.02%–0.2%. The increasing of average Reynolds number can enhance the heat transfer performance of nanofluids under the low Reynolds number (272–544). The low frequency (f < 2 Hz) pulsating flow has no significant effect on heat transfer enhancement of nanofluids compared to the steady flow. When the pulsating frequency is in the range of 3–5 Hz, the heat transfer of nanofluids is enhanced obviously. And the heat transfer enhancement factor reaches the maximum value at the optimal pulsating (f = 3 or 4 Hz). The average Reynolds number affects the value of optimal pulsating frequency as well as heat transfer rate.The optimal pulsating frequency is equal 3 Hz corresponding to the average Reynolds number is 544, and 4 Hz corresponding to average Reynolds number is 277. The pulsating flow has more enhancement effect on heat transfer at low average Reynolds number. The heat transfer enhancement factor reaches 1.33 for average Reynolds number is 277. The heat sink shows a worse thermal performance when the pulsating frequency is 1 Hz in this experiment. The changing of mass fraction of nanofluids in a small range (0.02%–0.2%) has slightly influence on the relative pressure drop. The
average amplitude puslating flow steady flow nanofluid base fluid nanoparticle inlet outlet maximum wall
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