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An experimental study on the proper criterion to judge the thermal performance of the nanofluids
International Communications in Heat and Mass Transfer 82 (2017) 20–28
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
An experimental study on the proper criterion to judge the thermal performance of the nanofluids R. Sajedi a,⁎, M. Jafari a, Sh. Nasirivatan b, B. Osanloo a a b
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
a r t i c l e
i n f o
Available online 5 February 2017 Keywords: Experimental Nanofluid Heat exchanger Pumping power Reynolds number
a b s t r a c t This work is dedicated to finding a suitable measure to judge thermal performance of nanofluids. The importance of this issue arises from misleading claim of excess heat transfer of nanofluids compared to the base fluid, neglecting the hydraulic effects such as increase in pressure drop. To clarify the issue, the experimental setup with capability to create constant Reynolds number and constant pumping power is constructed. Thermal behavior of nanofluids of silicon oxide/water and aluminum oxide/water and distilled water in developing region of laminar flow regime is investigated. In this regard, the convective heat transfer coefficient within the finned tube heat exchanger is evaluated. According to the results, the concentration of nanoparticle in the base fluid will have a significant impact on the amount of deflection of these two criteria, so that by increasing the nanoparticle's concentration the difference between these two measures becomes greater. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Since the need for cooling in the industry has been one of the major concerns of engineers, and development of industries increases the amount of heat generation per unit area, investigators are trying to use different methods to reach the maximum possible cooling in the minimum space. In this context, the use of nanofluids is of great interest for researchers. Li and Xuan [1,2] performed an experimental study to investigate the rate of heat transfer and properties of copper/water nanofluid flowing in a pipe in the laminar and turbulent regimes with constant heat flux boundaries. Research results showed that the nanoparticles significantly improve the rate of heat transfer, while the friction coefficient of the nanofluids has not been changed much compared to the base fluid. Thermal behavior of the graphite nanofluids under the laminar regime in the circular pipe is experimentally investigated by Yang [3]. Results showed that the nanoparticles increase the rate of heat transfer in the laminar regime. But the increase was much less than expected values based on the static measurement of thermal conductivity. In an experimental study, the convective heat transfer coefficient of the base fluid of water and nanofluid of alumina/water were investigated under conditions of constant wall temperature in a pipe by Zeinali Heris et al. [4]. Six volume concentrations in the range of 0.2%–2.5% and different Reynolds number in the range of 700 to 2050 have been ⁎ Corresponding author at: Faculty of Mechanical Engineering, University of Tabriz, 5166616471, Iran. E-mail address: [email protected] (R. Sajedi).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2017.02.002 0735-1933/© 2017 Elsevier Ltd. All rights reserved.
tested for the alumina nanofluids. Results indicated that the common relationships for anticipation of convective heat transfer coefficient in a pipe with constant temperature boundaries fails to use in the nanofluid. It is also necessary to mention that all the results in this paper are provided for the same Peclet Number of base fluid and nanofluid. Anoop et al. [5] presented an experimental study to investigate the effects of nanoparticle's size on the convective heat transfer coefficient of nanofluid of alumina/water in the laminar and developing regions. In this work, alumina nanoparticles in two sizes of 45 and 150 nm are used. Based on the results, the use of smaller nanoparticles has greater increase in convective heat transfer coefficient of nanofluid relative to the base fluid. They also concluded that addition of nanoparticles in the developing zone further increases the convective heat transfer coefficient, compared to the developed zone. Another interesting result of this study was the ability of single-phase relations to predict the convective heat transfer coefficient in the nanofluid. Also in this article all results have been reported for the constant Reynolds number. Hwang et al. [6] measured the pressure drop and heat transfer coefficient of the nanofluid of alumina oxide/water in a circular heat pipe in the laminar regime and fully developed zone. The experimental results showed that the friction coefficient of nanofluid can be computed using analytical equation of Darcy for single-phase flows. On the other hand, the convective heat transfer coefficient for nanofluid in the volume concentration of 0.3% showed an increase of 8% compared to the base fluid which could be estimated by equation of Shah. Recently Esmailzadeh et al. [7] experimentally studied heat transfer properties of aluminum oxide nanoparticles in the water. They applied the constant heat flux along a meter pipe to compute the convective
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Nomenclature Latin symbols P Pressure [pa] V Velocity [m/s] Re Reynolds number [−] Pr Prandtl number [−] T Temperature [°C] v_ Flow rate [L/S] K Thermal conductivity [W/m K] Cp Specific heat [J/kg∗K] hHeat transfer coefficient [W/ m2 ∗k] Q Heat transfer rate [Watt] Nu Nusselt number [−] mW Mili Watt Greek symbols μ fluid dynamic viscosity [Pa.s] ρ fluid density [kg/ m3] φ volume concentrations Subscript nf bf p f tub in out b w
nano fluid base fluid nanoparticle fluid tube inlet outlet bulk wall
heat transfer coefficient at different Reynolds numbers in the laminar regime. They also studied the pressure drop in the presence of different nanoparticle. They found that by increasing the percentage of nanoparticles heat transfer coefficient increases and the increase of heat transfer at the entrance of the pipe is much more intuitive. Also they examined the heat transfer and friction factor characteristics of γ-Al2O3/water through circular tube with twisted tape [8]. Ferrouillat et al. [9] studied the impact of shape factor in the silicon oxide and zinc oxide nanoparticles in the water-based fluid. They worked at temperatures of 20 and 50 °C and at Reynolds numbers ranging from 200 to 15,000. Results indicated a slight increase in Nusselt number of nanofluid compared to the based fluid of water. An energy performance evaluation criterion was defined based on the increase of the rate of heat transfer and pumping power. It was observed that the zinc oxide nanoparticles with a larger shape factor of 3 have reached to a high level of energy performance the same as water. Azmi et al. [10] presented an experimental study on the forced heat transfer and frictional losses in the turbulent flow regime in the presence of oxide silicon nanoparticles. Their results were reported in the Reynolds number between 5000 and 27,000 and bulk temperature of 30 °C. According to the results, it was seen that in the presence of nanoparticles with a volume fraction of 3% the increase in the heat transfer coefficient and frictional losses increase 32.7% and 17.1%, respectively. Darzi et al. [11] experimentally worked on the heat transfer and fluid properties of nano silica in the turbulent flow regime in the pipe with a spiral strip. They used 30 nm silica nanoparticles. They implemented tests for a simple pipe and five pipes with different peach and height values. The results showed that the use of spiral pipes with low angles of helix and high altitude has significant impact on the increase of heat transfer compared to negligible frictional losses. Javadi et al. [12] studied the thermo-physical and heat transfer properties of nanofluids in a plane heat exchanger. They compared the thermo-
21
physical and heat-transfer properties of nanofluids containing nanoparticles of silicon oxide, titanium oxide and aluminum oxide in a plate heat exchanger with water-based fluid. According to the results, aluminum oxide and titanium oxide enhance the rate of heat transfer more than silicon oxide. Ebrahimi et al. [13] presented an experimental study on the forced heat transfer characteristics of silicon oxide nanoparticles in the automobile radiators. They investigated the effects of inlet temperature; flow rate and volume concentrations of different nanoparticles. Results showed that by increasing the inlet temperature, Reynolds number and volume concentration of the nanoparticles, the Nusselt number will grow. Researchers at Argonne national laboratory [14] examined the issue of the proper criterion of comparison between the base fluid and nanofluids. In this paper three criteria are studied to measure the effectiveness of nanofluids instead of base fluid for increasing the heat transfer. According to the results, using the criteria of the constant Reynolds number between the base fluid and nanofluid to judge the increase of heat transfer is incorrect. But, the use of constant velocity could be picked up as an acceptable criterion. Also, they introduced the use same pumping power between nanofluids and base fluid as a proper criterion of comparison. Haghighi et al. [15] investigated the effectiveness of nanofluids in increasing the heat transfer using four criteria of the constant Reynolds number, constant velocity, constant mass flow rate and the constant pumping power. In this study, three nanofluids of alumina/ water, titanium oxide/water and selenium oxide/water were tested in the mass concentration of 9%. According to the results, the equation of Shah which predicts the Nusselt number of the laminar flow under constant heat flux boundaries, could successfully anticipate the convective heat transfer coefficient for all three nanofluids. The same conclusion is valid for Darcy equation to predict the coefficient of friction for the nanofluids. Also this paper rejects the criterion of the constant Reynolds number to measure the heat transfer coefficient of nanofluid and base fluid and states that the criterion of the constant pumping power would be the best comparable measure. This work, tries to obtain and highlight a proper comparative measure, using results of constant pumping power and constant Reynolds number. Silicon oxide and aluminum oxide nanoparticles in the water based fluid in the developing region of laminar flow regime are tested. Experimental results for nanofluids of alumina oxide/water and silicon oxide/water in four concentrations are compared with base fluid of distilled water in four different temperatures. 2. Experimental apparatus Testing equipment to measure the convective heat transfer coefficient is shown in Fig. 1. Equipment used in the experiment consists of a pump, a finned tube exchanger, risers, a reservoir tank, heater, dimmer and a main tank. A vertical external extended finned heat exchanger is an aluminum finned with height of H = 500 mm, inner radius of ri = 3.5 and outer radius of ro = 22.5 mm. Owing to symmetry, cross sectional view of half part of the heat exchanger is shown schematically in Fig. 2. As depicted in this figure fin's thickness t is 2 mm and length is l = 12.5 mm. Also this heat exchanger has 20 fins with S = 1.14 mm distance in the roots. A 2.5-l plastic tank is used as a principal reservoir. Fluid pumped from the main tank into the system. Pump has maximum flow rate of 5200 l per hour and head of 3.5 m. In order to control the flow rate, a return line with a valve at the outlet of the pump is installed. A 2000 W heater is installed in the upper tank and adjusting is done with a dimmer. Upper tank is connected to the heat exchanger with a copper pipe. As it is shown in Fig. 3, ten temperature sensors of SMT160 with confidence limits of ± 0.5 °C are installed in the longitudinal direction to achieve wall temperature of the heat exchanger. Inlet and outlet temperatures are measured by the thermocouples
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Fig. 1. a) The experimental setup and details. b) Schematic view.
Fig. 2. Cross sectional view of half part of the heat exchanger.
which are located before and after the heat exchanger. Also a sample of thermocouples was calibrated in an ice\water mixture before their locating on the test sections, and each experiment was repeated for four times. All data are stored once every 20 s using a computer data recording system. There is also a cooling fan discharges air (500 m3 per hour) into a conduit made of Plexiglas with a cross-section of 13.5 × 13.5 (cm) which is mounted on the longitudinal direction of the heat exchanger. To measure the mass flow rate, the required time for specified amount of water in the beaker is recorded. Also for yielding the constant inlet temperature, a heater with dimmer controlled power was placed in top reservoir to reach the steady state condition. Four sets of experiments corresponding for four different inlet temperatures of 40, 50, 60 and 70 were done. To ensure the existence of steady state conditions, thermocouple's data was exactly probed and after about 15 min the point where the recorded temperature differences reach to thermocouple's accuracy range identified as a steady state condition.
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Fig. 3. Thermocouple's locations on the heat exchanger.
IEP. Consequently experiments conducted solely on the homogeneous mixtures of SiO2 nanoparticles in distilled water.
Table 1 Nanoparticles thermo-physical properties [33]. Nanoparticle
W Thermal conductivity ðmk Þ
Kg Density ðm 3Þ
Specific heat ðKgJ kÞ
Al2O3 SiO2
36 1.4
3880 2220
773 745
4. Results and discussion 4.1. Thermo-physical properties of nanofluids Thermo-physical properties of nanofluids have been obtained using the following relationship:
3. Preparation of nanofluid Proper preparation of nanofluids has prominent role in the accuracy of laboratory results in the study of nanofluids. Also the stability of the suspension and thermo-physical properties strongly depends on the particle size, particle shape, particle type and physical properties of nanoparticles. In this study, nanoparticles of SiO2 with average particle size of 25 nm and γ-Al2O3 nanoparticles with an average size of 20 nm are purchased from US. Research Nanomaterial's Company and physical specifications given in Table 1, are used. Fig. 4 shows TEM image of nanoparticles of SiO2 and Al2O3. As it is shown the SiO2 and Al2O3nanoparticles are in the range of 20 to 30 nm. Also, XRD diagram of Fig. 5 indicates that the SiO2 nanoparticles are in amorphous type and Al2O3 crystalline. The stability of nanofluids is guaranteed using a 240 w and 50 Hz FUNGILAB ultrasonic cleaner. Also nanofluid is first mixed for half an hour using a magnetic stirrer and then is placed for 3 h at ultrasonic waves. Furthermore, no surfactant substance has been used in the preparing of the nanofluids and PH level of the suspension will not be changed. The used of PH-meter of Metrohm (Swiss, 827-PH lab) showed that the PH changes for the concentration of 0.5% to 2.5% are in the range of (9.35 to 8.23) and (5.96 to 4.94) for SiO2/water and Al2O3/water, respectively. On the other hand, it was shown [16] that the value of IEP for nano-silica and gamma alumina in water-based fluid is in the range of (3.5 to 1.7) and (7 to 8) respectively, which guarantees that the PH values for the current samples are enough far from
a) TEM image of SiO2 nanoparticles.
ðρÞnf ¼ ð1−ϕÞρbf þ ϕρp ;
ð1Þ
ðρcP Þnf ¼ ð1−ϕÞ ρcp bf þ ϕ ρcp p ;
ð2Þ
μr ¼
−0:061 μ nf T nf −0:038 φ 11:3 dp ¼ 1þ 1þ 1þ 100 μw 70 170
knf ¼
kp þ 2k f þ 2ϕp kp −k f kf : kp þ 2k f þ ϕp kp −k f
ð3Þ
ð4Þ
Eqs. (1) and (2) are obtained using the classical equations for the liquidsolid mixtures and are considered as the key relationships to calculate the density and specific heat of nanofluids [17–19]. But the calculation of effective thermal conductivity and effective viscosity of nanofluids are fewer consensuses among researchers. Here the equation of Sharma et al. [20] is used for evaluating the effective viscosity, and Maxwell equation is used for calculation of effective conductivity [21]. Necessary conditions for the use of Eq. (3) includes: operation temperature lower than 70 °C, volumetric concentration less than 4% and nanoparticles diameter less than 170 nm, which are all imposed in the current work. Timofeeva et al. [22] and Haghighi et al. [15] performed an experimental study and have shown that the
b) TEM image of Al2O3 nanoparticles.
Fig. 4. TEM image of nanoparticles of SiO2 and Al2O3.
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a) XRD diagram of Al2O3 nanoparticles.
Lin (Counts)
400
300
200
100
0 2
10
20
30
40
50
60
70
2-Theta - Scale
b) XRD diagram of SiO2 nanoparticles. Fig. 5. XRD diagram of nanoparticles.
effective thermal conductivity of the nanofluids with temperature change is still well predicted with Maxwell equation. 4.2. Validation of experimental results The Sider-Tate equation [23] to predict the average convective heat transfer coefficient inside a circular duct in the laminar and developing regions with fixed wall temperature is presented as follows: D 1=3 μ b 0:14 Nu ¼ 1:86 RePr h ; L μw
ð5Þ
Table 2 Uncertainty values of parameters.
Fig. 6. Convective heat transfer coefficient for distilled water at temperatures of 60 °C; experimental and Sider-Tate equation.
Parameter
Uncertainty values (%)
Q V Re h
1.22 0.312 0.342 4.77
h
4.773
R. Sajedi et al. / International Communications in Heat and Mass Transfer 82 (2017) 20–28
Re ¼
ρVDh ; μb
ð6Þ
Pr ¼
μ b Cp ; k
ð7Þ
25
T in þ T out ; 2
ð10Þ
Q ¼ m C p ðT in −T out Þ;
ð11Þ
Tb ¼
hdtube ; k
Where μb and μ w are viscosity of the fluid at the bulk and wall temperatures, ρ is fluid density, V is the velocity, Cp expresses the specific heat of the fluid, k stands for thermal conductivity of the fluid and D h and L, are hydraulic diameter and tube length, respectively. Keys and Crawford [24] have pointed out that in a heat exchanger _ is much more than other, a similar where heat capacity of one fluid mc situation of the constant wall temperature will occur. Therefore, in this study due to the relatively large difference between the heat capacity of cooling air and hot water this equation can be used with a good approximation. In order to obtain the convective heat transfer coefficient of the fluid h, as well as corresponding Nusselt number Nu inside the heat exchanger, the following relationships are used:
Where Tb is the average temperature of the fluid; Tw is the average _ is the mass flow rate of fluid through temperatures of the sensors, and m the pipe. In addition, all thermo-physical properties are found in the average temperature of the fluid. In order to validate the experimental results, the obtained results of convective heat transfer coefficient are compared with the values of Sider-Tate equation, and are presented in Fig. 6. An acceptable agreement between the experimental results and equation of Sider-Tate is seen, so that almost all experimental data are with an error of less than 20%.
Q ¼ hAΔT ¼ hAðT b −T w Þ;
4.3. Analysis of uncertainty
Tw ¼
ð8Þ
T 1 þ T 2 þ T 3 þ T 4 þ T 5 þ T 6 þ T 7 þ T 8 þ T 9 þ T 10 ; 10
ð9Þ
Nuexp ¼
ð12Þ
Uncertainty analysis of the measured parameters can be divided into two groups: independent parameters and dependent parameters. To calculate the uncertainty of dependent parameters such as R that is
T=40 °C
T=50 °C
T=60 °C
T=70 °C
Fig. 7. The values of h for water, silicon oxide/water and alumina/water (0.5% to 2.5%) in constant Reynolds number criterion.
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R. Sajedi et al. / International Communications in Heat and Mass Transfer 82 (2017) 20–28
ð13Þ
in Fig. 7 at four operating temperatures of 40, 50, 60 and 70 °C. Results of Fig. 7 express that the use of nanofluilds of silicon oxide/water and alumina/water is justified just in high concentrations. As another point, increasing the operating temperature, reduces the values of HTC, which is consistent with results of Eq. (5) in which, the reduction of Prandtl Number decreases the HTC.
It should be also noted that the uncertainty related to the physical properties is estimated using Beckwith method [26]. Computed uncertainty values of parameters are provided in Table 2.
4.4.2. Constant pumping power Heat transfer coefficients of alumina/water and silicon oxide/water are represented in Fig. 8 for constant pumping power between base fluid and nanofluids. In order to calculate the fluid pumping power following equation is used:
the function of several parameters such as Xi the following equation is used [25]: " 2 2 2 #12 X 1 ∂R X 2 ∂R X n ∂R uX 1 þ uX 2 þ…þ uX n R ∂X 1 R ∂X 2 R ∂X n
uR ¼ ∓
4.4. Heat transfer of nanofluid and base fluid
_ Pumping::power ¼ ∀ΔP;
4.4.1. Constant Reynolds number In general four comparison criteria can be found between nanofluid and base fluid in the literature: constant Reynolds number, constant velocity, constant mass flow rate and the constant pumping power. Among these four criteria, the results base on the constant Reynolds number, have been much more reported than other measures. The comparison between water and silicon oxide/water at four concentrations of 0.5% to 2.5% and alumina/water at the same concentrations are shown
_ stands for volumetric flow rate of the fluid. According to the Where ∀ results, which are presented in Fig. 8, a significant difference in the amount of heat transfer coefficient of nanofluid and base fluid does not exist even in high concentrations based on the criterion of constant pumping power. Even the slight reduction in the amount of heat transfer coefficient of silicon oxide/water is recognizable. This is due to overcome of effects of an increase in viscosity to increase of thermal
T=40 °C
T=50 °C
T=60 °C
T=70 °C
Fig. 8. The values of h for water, silicon oxide/water and alumina/water (0.5% to 2.5%) in constant Pumping Power criterion.
ð16Þ
R. Sajedi et al. / International Communications in Heat and Mass Transfer 82 (2017) 20–28
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Table 3 NP comparison between nanofluid and base water. T = 40 ° C
T = 70 ° C
Re
Silicon oxide/water (0.5%)
Alumina/water (0.5%)
Silicon oxide/water (2.5%)
Alumina/water (2.5%)
611.1 944.4 1167 1278 1500
1.24% 1.4% 1.43% 1.38% 1.39%
2.33% 2.32% 2.11% 2.125% 2.2%
10.65% 10.7% 10.95% 10.82% 11.01%
12.93% 13.05% 13.31% 13.25% 13.5%
T = 40 ° C
T = 70 ° C
Pumping power [mW]
Silicon oxide/water (0.5%)
Alumina/water (0.5%)
Silicon oxide/water (2.5%)
Alumina/water (2.5%)
29.65 35.02 46.16 60.11
−0.22% −0.39% −0.21% −0.27%
0.45% 0.34% 0.44% 0.34%
−1.16% −1.12% −1.23% −1.24%
1.56% 1.68% 1.5% 1.23%
conductivity. For the sake of quantitative comparisons, the parameter of Nano-performance is defined as: hnf −hbf ; NP ¼ hbf
ð17Þ
And its results are presented in Table 3 for two operating temperatures of 40 °C and 70 °C, and concentrations of 0.5% and 2.5%. Comparing the results between two criteria of constant pumping power and constant Reynolds number, indicates that behalf of significant increase of NP for constant Reynolds number, not any considerable NP increment observed for constant pumping power. For instance, in the case of Re = 1500, T = 40 °C and concentration of 0.5% NP numbers for SiO2/water and Al2O3/water are 1.39% and 2.2%, respectively, which are meaningfully more than those of constant pumping power in the same condition. This discrepancy is more considerable in the high concentrations, where for the case of Re = 1500, T = 70 °C and concentration of 2.5% NP varies from 11.01% and 13.5%, for SiO2/water and Al2O3/ water, respectively, in which the NP equals with −1.24% and 1.23% for SiO2/water and Al2O3/water in the case of constant pumping power. Hence, the use of constant pumping power leads to the different results of constant Reynolds number. Also, by comparing Figs. 7 and 8, it can be realized that by increasing the concentration of nanofluids, this difference is even greater. In other words, with increasing the concentration of nanofluids, the constant Reynolds number criterion leads to more misleading result. The authors [27] studied the effect of using different criteria to compare the change of heat transfer between nanofluid of silicon oxide/water and based fluid of water in turbulent flow regime. The work has shown that the use of silicon oxide nanofluid of 2.5% leads to 15% difference between results of constant pumping power and constant Reynolds. Also this work recommends the use of constant pumping power as a measure of comparison. 5. Conclusion This work compares the results of two criteria of constant Reynolds number and constant pumping power in convective heat transfer coefficient, between nanofluids and based fluid in developing laminar region. According to the results, a significant difference between these two criteria was found. Result of this work, points out to the concentration effect on the deflection of these two criteria. As the concentration increases the difference between these two measures becomes greater. For example, in the same condition and concentration of 0.5%, maximum deflection between these two criteria is about 2%, but in concentration of 2.5% this discrepancy yields up to 12.5%. Based on this fact, the use of constant Reynolds number is introduced as a misleading measure.
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Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
An experimental study on the proper criterion to judge the thermal performance of the nanofluids R. Sajedi a,⁎, M. Jafari a, Sh. Nasirivatan b, B. Osanloo a a b
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
a r t i c l e
i n f o
Available online 5 February 2017 Keywords: Experimental Nanofluid Heat exchanger Pumping power Reynolds number
a b s t r a c t This work is dedicated to finding a suitable measure to judge thermal performance of nanofluids. The importance of this issue arises from misleading claim of excess heat transfer of nanofluids compared to the base fluid, neglecting the hydraulic effects such as increase in pressure drop. To clarify the issue, the experimental setup with capability to create constant Reynolds number and constant pumping power is constructed. Thermal behavior of nanofluids of silicon oxide/water and aluminum oxide/water and distilled water in developing region of laminar flow regime is investigated. In this regard, the convective heat transfer coefficient within the finned tube heat exchanger is evaluated. According to the results, the concentration of nanoparticle in the base fluid will have a significant impact on the amount of deflection of these two criteria, so that by increasing the nanoparticle's concentration the difference between these two measures becomes greater. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Since the need for cooling in the industry has been one of the major concerns of engineers, and development of industries increases the amount of heat generation per unit area, investigators are trying to use different methods to reach the maximum possible cooling in the minimum space. In this context, the use of nanofluids is of great interest for researchers. Li and Xuan [1,2] performed an experimental study to investigate the rate of heat transfer and properties of copper/water nanofluid flowing in a pipe in the laminar and turbulent regimes with constant heat flux boundaries. Research results showed that the nanoparticles significantly improve the rate of heat transfer, while the friction coefficient of the nanofluids has not been changed much compared to the base fluid. Thermal behavior of the graphite nanofluids under the laminar regime in the circular pipe is experimentally investigated by Yang [3]. Results showed that the nanoparticles increase the rate of heat transfer in the laminar regime. But the increase was much less than expected values based on the static measurement of thermal conductivity. In an experimental study, the convective heat transfer coefficient of the base fluid of water and nanofluid of alumina/water were investigated under conditions of constant wall temperature in a pipe by Zeinali Heris et al. [4]. Six volume concentrations in the range of 0.2%–2.5% and different Reynolds number in the range of 700 to 2050 have been ⁎ Corresponding author at: Faculty of Mechanical Engineering, University of Tabriz, 5166616471, Iran. E-mail address: [email protected] (R. Sajedi).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2017.02.002 0735-1933/© 2017 Elsevier Ltd. All rights reserved.
tested for the alumina nanofluids. Results indicated that the common relationships for anticipation of convective heat transfer coefficient in a pipe with constant temperature boundaries fails to use in the nanofluid. It is also necessary to mention that all the results in this paper are provided for the same Peclet Number of base fluid and nanofluid. Anoop et al. [5] presented an experimental study to investigate the effects of nanoparticle's size on the convective heat transfer coefficient of nanofluid of alumina/water in the laminar and developing regions. In this work, alumina nanoparticles in two sizes of 45 and 150 nm are used. Based on the results, the use of smaller nanoparticles has greater increase in convective heat transfer coefficient of nanofluid relative to the base fluid. They also concluded that addition of nanoparticles in the developing zone further increases the convective heat transfer coefficient, compared to the developed zone. Another interesting result of this study was the ability of single-phase relations to predict the convective heat transfer coefficient in the nanofluid. Also in this article all results have been reported for the constant Reynolds number. Hwang et al. [6] measured the pressure drop and heat transfer coefficient of the nanofluid of alumina oxide/water in a circular heat pipe in the laminar regime and fully developed zone. The experimental results showed that the friction coefficient of nanofluid can be computed using analytical equation of Darcy for single-phase flows. On the other hand, the convective heat transfer coefficient for nanofluid in the volume concentration of 0.3% showed an increase of 8% compared to the base fluid which could be estimated by equation of Shah. Recently Esmailzadeh et al. [7] experimentally studied heat transfer properties of aluminum oxide nanoparticles in the water. They applied the constant heat flux along a meter pipe to compute the convective
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Nomenclature Latin symbols P Pressure [pa] V Velocity [m/s] Re Reynolds number [−] Pr Prandtl number [−] T Temperature [°C] v_ Flow rate [L/S] K Thermal conductivity [W/m K] Cp Specific heat [J/kg∗K] hHeat transfer coefficient [W/ m2 ∗k] Q Heat transfer rate [Watt] Nu Nusselt number [−] mW Mili Watt Greek symbols μ fluid dynamic viscosity [Pa.s] ρ fluid density [kg/ m3] φ volume concentrations Subscript nf bf p f tub in out b w
nano fluid base fluid nanoparticle fluid tube inlet outlet bulk wall
heat transfer coefficient at different Reynolds numbers in the laminar regime. They also studied the pressure drop in the presence of different nanoparticle. They found that by increasing the percentage of nanoparticles heat transfer coefficient increases and the increase of heat transfer at the entrance of the pipe is much more intuitive. Also they examined the heat transfer and friction factor characteristics of γ-Al2O3/water through circular tube with twisted tape [8]. Ferrouillat et al. [9] studied the impact of shape factor in the silicon oxide and zinc oxide nanoparticles in the water-based fluid. They worked at temperatures of 20 and 50 °C and at Reynolds numbers ranging from 200 to 15,000. Results indicated a slight increase in Nusselt number of nanofluid compared to the based fluid of water. An energy performance evaluation criterion was defined based on the increase of the rate of heat transfer and pumping power. It was observed that the zinc oxide nanoparticles with a larger shape factor of 3 have reached to a high level of energy performance the same as water. Azmi et al. [10] presented an experimental study on the forced heat transfer and frictional losses in the turbulent flow regime in the presence of oxide silicon nanoparticles. Their results were reported in the Reynolds number between 5000 and 27,000 and bulk temperature of 30 °C. According to the results, it was seen that in the presence of nanoparticles with a volume fraction of 3% the increase in the heat transfer coefficient and frictional losses increase 32.7% and 17.1%, respectively. Darzi et al. [11] experimentally worked on the heat transfer and fluid properties of nano silica in the turbulent flow regime in the pipe with a spiral strip. They used 30 nm silica nanoparticles. They implemented tests for a simple pipe and five pipes with different peach and height values. The results showed that the use of spiral pipes with low angles of helix and high altitude has significant impact on the increase of heat transfer compared to negligible frictional losses. Javadi et al. [12] studied the thermo-physical and heat transfer properties of nanofluids in a plane heat exchanger. They compared the thermo-
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physical and heat-transfer properties of nanofluids containing nanoparticles of silicon oxide, titanium oxide and aluminum oxide in a plate heat exchanger with water-based fluid. According to the results, aluminum oxide and titanium oxide enhance the rate of heat transfer more than silicon oxide. Ebrahimi et al. [13] presented an experimental study on the forced heat transfer characteristics of silicon oxide nanoparticles in the automobile radiators. They investigated the effects of inlet temperature; flow rate and volume concentrations of different nanoparticles. Results showed that by increasing the inlet temperature, Reynolds number and volume concentration of the nanoparticles, the Nusselt number will grow. Researchers at Argonne national laboratory [14] examined the issue of the proper criterion of comparison between the base fluid and nanofluids. In this paper three criteria are studied to measure the effectiveness of nanofluids instead of base fluid for increasing the heat transfer. According to the results, using the criteria of the constant Reynolds number between the base fluid and nanofluid to judge the increase of heat transfer is incorrect. But, the use of constant velocity could be picked up as an acceptable criterion. Also, they introduced the use same pumping power between nanofluids and base fluid as a proper criterion of comparison. Haghighi et al. [15] investigated the effectiveness of nanofluids in increasing the heat transfer using four criteria of the constant Reynolds number, constant velocity, constant mass flow rate and the constant pumping power. In this study, three nanofluids of alumina/ water, titanium oxide/water and selenium oxide/water were tested in the mass concentration of 9%. According to the results, the equation of Shah which predicts the Nusselt number of the laminar flow under constant heat flux boundaries, could successfully anticipate the convective heat transfer coefficient for all three nanofluids. The same conclusion is valid for Darcy equation to predict the coefficient of friction for the nanofluids. Also this paper rejects the criterion of the constant Reynolds number to measure the heat transfer coefficient of nanofluid and base fluid and states that the criterion of the constant pumping power would be the best comparable measure. This work, tries to obtain and highlight a proper comparative measure, using results of constant pumping power and constant Reynolds number. Silicon oxide and aluminum oxide nanoparticles in the water based fluid in the developing region of laminar flow regime are tested. Experimental results for nanofluids of alumina oxide/water and silicon oxide/water in four concentrations are compared with base fluid of distilled water in four different temperatures. 2. Experimental apparatus Testing equipment to measure the convective heat transfer coefficient is shown in Fig. 1. Equipment used in the experiment consists of a pump, a finned tube exchanger, risers, a reservoir tank, heater, dimmer and a main tank. A vertical external extended finned heat exchanger is an aluminum finned with height of H = 500 mm, inner radius of ri = 3.5 and outer radius of ro = 22.5 mm. Owing to symmetry, cross sectional view of half part of the heat exchanger is shown schematically in Fig. 2. As depicted in this figure fin's thickness t is 2 mm and length is l = 12.5 mm. Also this heat exchanger has 20 fins with S = 1.14 mm distance in the roots. A 2.5-l plastic tank is used as a principal reservoir. Fluid pumped from the main tank into the system. Pump has maximum flow rate of 5200 l per hour and head of 3.5 m. In order to control the flow rate, a return line with a valve at the outlet of the pump is installed. A 2000 W heater is installed in the upper tank and adjusting is done with a dimmer. Upper tank is connected to the heat exchanger with a copper pipe. As it is shown in Fig. 3, ten temperature sensors of SMT160 with confidence limits of ± 0.5 °C are installed in the longitudinal direction to achieve wall temperature of the heat exchanger. Inlet and outlet temperatures are measured by the thermocouples
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Fig. 1. a) The experimental setup and details. b) Schematic view.
Fig. 2. Cross sectional view of half part of the heat exchanger.
which are located before and after the heat exchanger. Also a sample of thermocouples was calibrated in an ice\water mixture before their locating on the test sections, and each experiment was repeated for four times. All data are stored once every 20 s using a computer data recording system. There is also a cooling fan discharges air (500 m3 per hour) into a conduit made of Plexiglas with a cross-section of 13.5 × 13.5 (cm) which is mounted on the longitudinal direction of the heat exchanger. To measure the mass flow rate, the required time for specified amount of water in the beaker is recorded. Also for yielding the constant inlet temperature, a heater with dimmer controlled power was placed in top reservoir to reach the steady state condition. Four sets of experiments corresponding for four different inlet temperatures of 40, 50, 60 and 70 were done. To ensure the existence of steady state conditions, thermocouple's data was exactly probed and after about 15 min the point where the recorded temperature differences reach to thermocouple's accuracy range identified as a steady state condition.
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Fig. 3. Thermocouple's locations on the heat exchanger.
IEP. Consequently experiments conducted solely on the homogeneous mixtures of SiO2 nanoparticles in distilled water.
Table 1 Nanoparticles thermo-physical properties [33]. Nanoparticle
W Thermal conductivity ðmk Þ
Kg Density ðm 3Þ
Specific heat ðKgJ kÞ
Al2O3 SiO2
36 1.4
3880 2220
773 745
4. Results and discussion 4.1. Thermo-physical properties of nanofluids Thermo-physical properties of nanofluids have been obtained using the following relationship:
3. Preparation of nanofluid Proper preparation of nanofluids has prominent role in the accuracy of laboratory results in the study of nanofluids. Also the stability of the suspension and thermo-physical properties strongly depends on the particle size, particle shape, particle type and physical properties of nanoparticles. In this study, nanoparticles of SiO2 with average particle size of 25 nm and γ-Al2O3 nanoparticles with an average size of 20 nm are purchased from US. Research Nanomaterial's Company and physical specifications given in Table 1, are used. Fig. 4 shows TEM image of nanoparticles of SiO2 and Al2O3. As it is shown the SiO2 and Al2O3nanoparticles are in the range of 20 to 30 nm. Also, XRD diagram of Fig. 5 indicates that the SiO2 nanoparticles are in amorphous type and Al2O3 crystalline. The stability of nanofluids is guaranteed using a 240 w and 50 Hz FUNGILAB ultrasonic cleaner. Also nanofluid is first mixed for half an hour using a magnetic stirrer and then is placed for 3 h at ultrasonic waves. Furthermore, no surfactant substance has been used in the preparing of the nanofluids and PH level of the suspension will not be changed. The used of PH-meter of Metrohm (Swiss, 827-PH lab) showed that the PH changes for the concentration of 0.5% to 2.5% are in the range of (9.35 to 8.23) and (5.96 to 4.94) for SiO2/water and Al2O3/water, respectively. On the other hand, it was shown [16] that the value of IEP for nano-silica and gamma alumina in water-based fluid is in the range of (3.5 to 1.7) and (7 to 8) respectively, which guarantees that the PH values for the current samples are enough far from
a) TEM image of SiO2 nanoparticles.
ðρÞnf ¼ ð1−ϕÞρbf þ ϕρp ;
ð1Þ
ðρcP Þnf ¼ ð1−ϕÞ ρcp bf þ ϕ ρcp p ;
ð2Þ
μr ¼
−0:061 μ nf T nf −0:038 φ 11:3 dp ¼ 1þ 1þ 1þ 100 μw 70 170
knf ¼
kp þ 2k f þ 2ϕp kp −k f kf : kp þ 2k f þ ϕp kp −k f
ð3Þ
ð4Þ
Eqs. (1) and (2) are obtained using the classical equations for the liquidsolid mixtures and are considered as the key relationships to calculate the density and specific heat of nanofluids [17–19]. But the calculation of effective thermal conductivity and effective viscosity of nanofluids are fewer consensuses among researchers. Here the equation of Sharma et al. [20] is used for evaluating the effective viscosity, and Maxwell equation is used for calculation of effective conductivity [21]. Necessary conditions for the use of Eq. (3) includes: operation temperature lower than 70 °C, volumetric concentration less than 4% and nanoparticles diameter less than 170 nm, which are all imposed in the current work. Timofeeva et al. [22] and Haghighi et al. [15] performed an experimental study and have shown that the
b) TEM image of Al2O3 nanoparticles.
Fig. 4. TEM image of nanoparticles of SiO2 and Al2O3.
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a) XRD diagram of Al2O3 nanoparticles.
Lin (Counts)
400
300
200
100
0 2
10
20
30
40
50
60
70
2-Theta - Scale
b) XRD diagram of SiO2 nanoparticles. Fig. 5. XRD diagram of nanoparticles.
effective thermal conductivity of the nanofluids with temperature change is still well predicted with Maxwell equation. 4.2. Validation of experimental results The Sider-Tate equation [23] to predict the average convective heat transfer coefficient inside a circular duct in the laminar and developing regions with fixed wall temperature is presented as follows: D 1=3 μ b 0:14 Nu ¼ 1:86 RePr h ; L μw
ð5Þ
Table 2 Uncertainty values of parameters.
Fig. 6. Convective heat transfer coefficient for distilled water at temperatures of 60 °C; experimental and Sider-Tate equation.
Parameter
Uncertainty values (%)
Q V Re h
1.22 0.312 0.342 4.77
h
4.773
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Re ¼
ρVDh ; μb
ð6Þ
Pr ¼
μ b Cp ; k
ð7Þ
25
T in þ T out ; 2
ð10Þ
Q ¼ m C p ðT in −T out Þ;
ð11Þ
Tb ¼
hdtube ; k
Where μb and μ w are viscosity of the fluid at the bulk and wall temperatures, ρ is fluid density, V is the velocity, Cp expresses the specific heat of the fluid, k stands for thermal conductivity of the fluid and D h and L, are hydraulic diameter and tube length, respectively. Keys and Crawford [24] have pointed out that in a heat exchanger _ is much more than other, a similar where heat capacity of one fluid mc situation of the constant wall temperature will occur. Therefore, in this study due to the relatively large difference between the heat capacity of cooling air and hot water this equation can be used with a good approximation. In order to obtain the convective heat transfer coefficient of the fluid h, as well as corresponding Nusselt number Nu inside the heat exchanger, the following relationships are used:
Where Tb is the average temperature of the fluid; Tw is the average _ is the mass flow rate of fluid through temperatures of the sensors, and m the pipe. In addition, all thermo-physical properties are found in the average temperature of the fluid. In order to validate the experimental results, the obtained results of convective heat transfer coefficient are compared with the values of Sider-Tate equation, and are presented in Fig. 6. An acceptable agreement between the experimental results and equation of Sider-Tate is seen, so that almost all experimental data are with an error of less than 20%.
Q ¼ hAΔT ¼ hAðT b −T w Þ;
4.3. Analysis of uncertainty
Tw ¼
ð8Þ
T 1 þ T 2 þ T 3 þ T 4 þ T 5 þ T 6 þ T 7 þ T 8 þ T 9 þ T 10 ; 10
ð9Þ
Nuexp ¼
ð12Þ
Uncertainty analysis of the measured parameters can be divided into two groups: independent parameters and dependent parameters. To calculate the uncertainty of dependent parameters such as R that is
T=40 °C
T=50 °C
T=60 °C
T=70 °C
Fig. 7. The values of h for water, silicon oxide/water and alumina/water (0.5% to 2.5%) in constant Reynolds number criterion.
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ð13Þ
in Fig. 7 at four operating temperatures of 40, 50, 60 and 70 °C. Results of Fig. 7 express that the use of nanofluilds of silicon oxide/water and alumina/water is justified just in high concentrations. As another point, increasing the operating temperature, reduces the values of HTC, which is consistent with results of Eq. (5) in which, the reduction of Prandtl Number decreases the HTC.
It should be also noted that the uncertainty related to the physical properties is estimated using Beckwith method [26]. Computed uncertainty values of parameters are provided in Table 2.
4.4.2. Constant pumping power Heat transfer coefficients of alumina/water and silicon oxide/water are represented in Fig. 8 for constant pumping power between base fluid and nanofluids. In order to calculate the fluid pumping power following equation is used:
the function of several parameters such as Xi the following equation is used [25]: " 2 2 2 #12 X 1 ∂R X 2 ∂R X n ∂R uX 1 þ uX 2 þ…þ uX n R ∂X 1 R ∂X 2 R ∂X n
uR ¼ ∓
4.4. Heat transfer of nanofluid and base fluid
_ Pumping::power ¼ ∀ΔP;
4.4.1. Constant Reynolds number In general four comparison criteria can be found between nanofluid and base fluid in the literature: constant Reynolds number, constant velocity, constant mass flow rate and the constant pumping power. Among these four criteria, the results base on the constant Reynolds number, have been much more reported than other measures. The comparison between water and silicon oxide/water at four concentrations of 0.5% to 2.5% and alumina/water at the same concentrations are shown
_ stands for volumetric flow rate of the fluid. According to the Where ∀ results, which are presented in Fig. 8, a significant difference in the amount of heat transfer coefficient of nanofluid and base fluid does not exist even in high concentrations based on the criterion of constant pumping power. Even the slight reduction in the amount of heat transfer coefficient of silicon oxide/water is recognizable. This is due to overcome of effects of an increase in viscosity to increase of thermal
T=40 °C
T=50 °C
T=60 °C
T=70 °C
Fig. 8. The values of h for water, silicon oxide/water and alumina/water (0.5% to 2.5%) in constant Pumping Power criterion.
ð16Þ
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Table 3 NP comparison between nanofluid and base water. T = 40 ° C
T = 70 ° C
Re
Silicon oxide/water (0.5%)
Alumina/water (0.5%)
Silicon oxide/water (2.5%)
Alumina/water (2.5%)
611.1 944.4 1167 1278 1500
1.24% 1.4% 1.43% 1.38% 1.39%
2.33% 2.32% 2.11% 2.125% 2.2%
10.65% 10.7% 10.95% 10.82% 11.01%
12.93% 13.05% 13.31% 13.25% 13.5%
T = 40 ° C
T = 70 ° C
Pumping power [mW]
Silicon oxide/water (0.5%)
Alumina/water (0.5%)
Silicon oxide/water (2.5%)
Alumina/water (2.5%)
29.65 35.02 46.16 60.11
−0.22% −0.39% −0.21% −0.27%
0.45% 0.34% 0.44% 0.34%
−1.16% −1.12% −1.23% −1.24%
1.56% 1.68% 1.5% 1.23%
conductivity. For the sake of quantitative comparisons, the parameter of Nano-performance is defined as: hnf −hbf ; NP ¼ hbf
ð17Þ
And its results are presented in Table 3 for two operating temperatures of 40 °C and 70 °C, and concentrations of 0.5% and 2.5%. Comparing the results between two criteria of constant pumping power and constant Reynolds number, indicates that behalf of significant increase of NP for constant Reynolds number, not any considerable NP increment observed for constant pumping power. For instance, in the case of Re = 1500, T = 40 °C and concentration of 0.5% NP numbers for SiO2/water and Al2O3/water are 1.39% and 2.2%, respectively, which are meaningfully more than those of constant pumping power in the same condition. This discrepancy is more considerable in the high concentrations, where for the case of Re = 1500, T = 70 °C and concentration of 2.5% NP varies from 11.01% and 13.5%, for SiO2/water and Al2O3/ water, respectively, in which the NP equals with −1.24% and 1.23% for SiO2/water and Al2O3/water in the case of constant pumping power. Hence, the use of constant pumping power leads to the different results of constant Reynolds number. Also, by comparing Figs. 7 and 8, it can be realized that by increasing the concentration of nanofluids, this difference is even greater. In other words, with increasing the concentration of nanofluids, the constant Reynolds number criterion leads to more misleading result. The authors [27] studied the effect of using different criteria to compare the change of heat transfer between nanofluid of silicon oxide/water and based fluid of water in turbulent flow regime. The work has shown that the use of silicon oxide nanofluid of 2.5% leads to 15% difference between results of constant pumping power and constant Reynolds. Also this work recommends the use of constant pumping power as a measure of comparison. 5. Conclusion This work compares the results of two criteria of constant Reynolds number and constant pumping power in convective heat transfer coefficient, between nanofluids and based fluid in developing laminar region. According to the results, a significant difference between these two criteria was found. Result of this work, points out to the concentration effect on the deflection of these two criteria. As the concentration increases the difference between these two measures becomes greater. For example, in the same condition and concentration of 0.5%, maximum deflection between these two criteria is about 2%, but in concentration of 2.5% this discrepancy yields up to 12.5%. Based on this fact, the use of constant Reynolds number is introduced as a misleading measure.
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