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Investigation into Au nanofluids for solar photothermal conversion
International Journal of Heat and Mass Transfer 108 (2017) 1894–1900
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Investigation into Au nanofluids for solar photothermal conversion Meijie Chen a, Yurong He a,⇑, Jian Huang a, Jiaqi Zhu b a b
School of Energy Science & Engineering, Harbin Institute of Technology, Harbin 150001, China School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
a r t i c l e
i n f o
Article history: Received 11 September 2016 Received in revised form 29 December 2016 Accepted 4 January 2017
Keywords: Au nanofluid Solar energy Photothermal conversion Absorption efficiency
a b s t r a c t We herein investigate the solar photothermal conversion performances of Au nanofluids both experimentally and theoretically. In the experiments, the Au nanofluids are loaded into a beaker and are exposed to solar radiation. The solar photothermal conversion efficiency performances of the Au nanofluids using different nanoparticle (NP) volume fractions and solar intensities are discussed. Experimental results show that the equilibrium temperature increases as the NP volume fraction and solar intensity increase, although the extent of variation in the photothermal conversion efficiency declines under these conditions. Furthermore, a theoretical analysis based on the Rayleigh scattering approximation and the Beer-Lambert Law to predict the solar absorption efficiency is discussed. A good agreement between the calculated absorption efficiency and the experimental solar photothermal conversion efficiency is reported. The absorption efficiency increases exponentially with increasing collector height and NP volume fraction. Moreover, the optimization of NP selection and collector design for direct absorption solar collectors without consideration of the temperature field is of particular scientific importance. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Solar energy is one of the most renewable and clean energy resources, and as such it has attracted significant research interest [1–4]. Indeed, efforts to achieve the efficient utilization of solar energy have been reported using a number of different approaches [5–7], with some of the most common approaches including photovoltaic conversion, photochemical conversion, and photothermal conversion. Photovoltaic conversion is a process that directly converts solar irradiation to electricity [8], while photochemical conversion converts solar energy to chemical energy [9], with examples including photocatalysis [10] and water-splitting to produce hydrogen [11]. However, despite being popular approaches, these two technologies exhibit low energy conversion efficiencies [1,5]. In contrast, photothermal conversion is a more traditional, simple, and effective approach that converts solar irradiation to heat as thermal energy, and has attracted renewed research interest in the past decade, especially in the application of nanofluid-based direct solar absorption collectors (DASCs) [12–14]. When compared with a base fluid alone, nanoparticles (NPs) dispersed in a base fluid can enhance the photothermal conversion performance of a system through the enhanced absorption and scattering of nanofluids ⇑ Corresponding author. E-mail address: [email protected] (Y. He). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.005 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
[15]. Otanicar et al. [16] investigated DASCs based on carbon nanotubes, graphite, and silver nanofluids. They observed an improvement in efficiency 65% upon the use of nanofluids as the absorption medium. In addition, a study by Taylor et al. [17] compared the spectroscopic measurement of extinction coefficients over wavelengths important for solar energy with model predictions. Other recent studies [16,18–21] have also indicated the importance of selecting suitable nanofluids to improve the efficiency of DASCs. A number of noble metal NPs have attracted significant interest because of their unique properties, including large optical field enhancements, which result in the strong scattering and absorption of photons. The enhancement in the optical and photothermal properties of noble metal NPs arises from the resonant oscillation of their free electrons in the presence of photons, also known as localized surface plasmon resonance (LSPR) [22,23]. Plasmon resonances can be damped radiatively by photon scattering, or nonradiatively through conversion of photons to heat energy. The combination of these two mechanisms has greatly enhanced the solar absorption and photothermal conversion performances of nanofluids. In addition, the plasmonic band of plasmonic nanostructures can be easily altered by tailoring the nanostructure shape, thus enabling them to interact with photons in different spectral ranges, and ultimately resulting in the efficient utilization of solar light [24]. Zhang et al. [25] studied plasmonic Au NPs with the aim of improving solar thermal conversion efficiencies, and
M. Chen et al. / International Journal of Heat and Mass Transfer 108 (2017) 1894–1900
found that Au NPs exhibited improved photothermal conversion capabilities compared to other reported materials (carbon nanotubes and graphite). Moreover, Duan and Xuan et al. [26,27] investigated the solar absorption of core-shell NPs both experimentally and theoretically. They found that the optical absorption of core-shell plasmonic nanofluids was enhanced through the LSPR effect on the Ag surface. In addition to the NP material employed, other factors that influenced the photothermal conversion efficiency for plasmonic nanofluids included the collector height, the NP volume faction, and the solar intensity [28], and as such should be further investigated to obtain optimal conditions for plasmonic nanofluids employed in DASCs. It was also reported that the calculated values of solar photothermal conversion efficiencies of working fluids varied with different experimental devices due to different heat dissipations during the solar photothermal conversion processes [15,16,25,27]. Thus, we herein report the calculation of the solar photothermal conversion efficiencies of plasmonic Au nanofluids based on energy balance with a full consideration of heat dissipation. Firstly, the solar photothermal conversion performances of Au nanofluids are investigated experimentally. Au NPs are prepared via a citrate reduction method. In addition, the solar photothermal conversion efficiency performances of Au nanofluids with different NP volume fractions and solar intensities are discussed. Furthermore, a theoretical model based on the Rayleigh scattering approximation and the Beer-Lambert Law is also developed to predict the solar absorption efficiency. Finally, the experimental and theoretical results are compared to optimize the DASC parameters without consideration of the temperature field. 2. Materials and methods 2.1. Au nanoparticle synthesis Au NPs were synthesized via a previously reported citrate reduction method [29]. A 2.5 mL of 10 mM HAuCl4 (Au P48%, Aladdin Co. Ltd.) aqueous solution was added to a 100 mL of 5 mM sodium citrate (99%, Aladdin Co. Ltd.) aqueous solution with vigorous stirring. The resulting solution was heated at 100 °C for 30 min to give an Au nanofluid NP volume fraction of 2.5 ppm assuming a complete reaction. Au nanofluids containing different NP volume fractions were obtained by dilution of this solution and were used in subsequent photothermal conversion experiments. Scanning electron microscopy (SEM) was performed using a Zeiss Supra 55 Sapphire electron microscope at a bias voltage of 30 kV. The average NP sizes were determined from SEM images by averaging the diameters of at least 100 NPs using the Nano Measurer 1.2 program. Optical absorbance spectra were measured at 25 °C using a UV–Vis spectrophotometer (Pgeneral TU1901) in a 4 mm quartz cuvette with water as the reference. 2.2. Photothermal conversion experiments A schematic representation of the photothermal conversion device is shown in Fig. 1. A sample of the working fluid (10 mL) was stirred inside a PMMA beaker (300 rpm) to reduce fluid temperature gradients. The beaker was held using a clamp stand to avoid direct thermal conduction through contact with the surfaces. Therefore, ignoring radiation effects due to the low fluid temperature (<100 °C), only thermal convection through the air took place approximately. The beaker was covered using quartz glass to prevent water loss. To monitor the fluid temperature, four T-type thermocouples were installed at different heights (H = 4, 8, 12, and 16 mm). The working fluid was irradiated with a solar simulator (3, 5 and 10 suns, Beijing Education Au-light Co., Ltd., CEL-
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HXF300 type). Temperatures were recorded every 2 min for 60 min until a thermal equilibrium state had been reached. The solar simulator was then turned off, and the fluid was allowed to cool to room temperature 25 °C. The solar photothermal conversion efficiency was calculated based on the energy balance during the process, i.e., energy absorbed and converted by the working fluid from the solar radiation is equal to the sum of the heat dissipated to the surroundings and the energy increasing the temperature of fluid and beaker. As outlined in Eq. (1) [30,31]:
ðM f cp;f þ M b cp;b Þ
dDT þ BDT ¼ I0 Ai gpt dt
ð1Þ
where Mf is the fluid mass, cp;f is the constant-pressure solution heat capacity, which is treated as a constant with such low NP volume fractions (0.5, 1.0, 1.5 and 2.5 ppm) in this work, Mb is the beaker mass, cp;b is the constant-pressure beaker heat capacity, DT is the temperature difference between time t and the starting time, B is the heat dissipation coefficient since heat loss occurs mainly by heat convection, I0 is the solar radiation intensity, Ai is the irradiated area, and gpt is the photothermal conversion efficiency of the working fluid. Relevant parameter values are shown in Table 1. The heat dissipation coefficient B can be determined by switching off the solar simulator as indicated in Eq. (2):
ðM f cp;f þ M b cp;b Þ
dDT þ BDT ¼ 0 dt
ð2Þ
The solution of Eq. (2) can be written as Eq. (3), and coefficients B and C can be determined by fitting the experimental data of the fluid temperature after the solar simulator has been switched off:
lnðDTÞ ¼
Bt þC M f cp;f þ M b cp;b
ð3Þ
Finally, the photothermal conversion efficiency gpt can be obtained by considering the equilibrium state of the nanofluid in Eq. (4) when water is the base fluid and the heating process reaches its equilibrium state:
BDT ¼ I0 Ai gpt
ð4Þ
3. Theoretical model To better understand the solar absorption ability of the Au nanofluid, a theoretical model was developed to predict its absorption of solar radiation. Solar radiation intensities between 200 and 3000 nm were obtained using the black body relationship based on Planck’s law. Atmospheric absorption was neglected in this calculation [16,35]. Hence, the incident solar intensity can describe the amount of electromagnetic energy within a certain wavelength radiated by a black body at the thermal equilibrium state given by:
hc0 2 1 Ibk ðk; T s Þ ¼ 2hc0 = k5 exp kkB T s
ð5Þ
where Ibk is the spectral intensity of the black body, h is Planck’s constant, kB is the Boltzmann constant, c0 is the speed of light in a vacuum, k is the wavelength, and T s is the solar temperature. The incident solar heat flux I0 is equal to C 0 Ibk after the modification of the spectral intensity of the black body, where C 0 is the modification factor. The air mass is 1.5 (i.e., AM = 1.5), which represents the solar spectrum at the mid-latitudes, and the solar intensity is 1000 W/m2 according to the ASTM G-173 standard. The value of C 0 is taken as 0.74 to match the solar intensity at AM = 1.5. Regarding the optical properties of nanofluids, a complex relationship between absorption and scattering must be considered due to the presence of small NPs. For the present experimental study, the Au NP size d was 10 nm, as shown in Fig. 2A. An
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Solar Simulator
Quartz glass Fluid
PMMA box (10 mL)
Clamp
Thermocouple
Stirrer Data acquisition
Magnetic stirrer
Computer
Fig. 1. Schematic representation of the photothermal conversion device.
The maximum particle volume fraction for independent scattering
Table 1 Relevant parameter values at the ambient temperature. Parameter
Value
Constant-pressure solution heat capacity cp;f (J kg1 °C1) Constant-pressure beaker heat capacity cp;b (J kg1 °C1) Fluid mass M f (g) Beaker mass M b (g) Irradiated area Ai (m2)
4183 1464 10.0 5.6
f v ;max ¼ ½1:81a=ðp þ 2aÞ3 , which depends the size parameter a and the particle volume fraction f v . Therefore, the absorption and scattering coefficients can be calculated based on the Rayleigh scattering approximation and independent scattering expressed as [16,35]:
2 104
ka;np
ð6Þ
approximation of the Rayleigh scattering can be applied to simplify the calculation. This approximation is valid when the size parameter a 1, which is defined as a ¼ pd=k. When the Mie scattering formula is expanded into a power series with a as a variable, its second and later items can be neglected compared with the first term in this case. Therefore, the solution of Rayleigh scattering can be obtained. In physical terms, Rayleigh scattering can be understood as the regime in which the particle size is much smaller than the wavelength of the incident radiation. Moreover, NPs with relatively low volume fractions were applied to the experiments, and the absorption and scattering of the NPs could be considered independent scattering in the scattering regime map [32].
(A)
ks;np ¼
ð7Þ
ke;np ¼ ka;np þ ks;np
ð8Þ
where ka;np ; ks;np , and ke;np are the NP absorption, scattering, and extinction coefficients respectively. In addition, f v is the NP volume fraction, and m is the normalized refractive index of the NP, defined by:
0.5
0.40
0.4
Au/H 2O-2.5ppm Au/H 2O-1.5ppm
0.3
Au/H 2O-1.0ppm Au/H 2O-0.5ppm
(D) Peak absorbance (a.u.)
Absorbance (a.u.)
2 3 8p4 d f v m2 1 m2 þ 2 k4
(B)
(C)
0.2 0.1 0.0 300
( " #) 12pf v m2 1 p2 d2 m2 1 m4 þ 27m2 þ 38 ¼ Im 1þ m2 þ 2 2m2 þ 3 k 15k2 m2 þ 2
400
500
600
Wavelength / nm
700
800
0.32
Exp. data Linear fit of Exp. data
0.24 0.16 0.08 0.00 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Volume fraction / ppm
Fig. 2. Characterization of the Au nanoparticles. (A) SEM image of the Au nanoparticles (scale bar: 20 nm). (B) Photograph of the Au nanofluids containing different nanoparticle volume fractions. (C) Absorbance spectra of the four different Au nanofluids. (D) Relationship between the peak absorbance and the NP volume fraction.
M. Chen et al. / International Journal of Heat and Mass Transfer 108 (2017) 1894–1900
m¼
mnp nbf
ð9Þ
where mnp and nbf are the complex reflective index of the NP and the base fluid relative to the ambient environment, respectively. According to the Beer-Lambert Law [33], the spectral radiation intensity decreases exponentially along its transfer direction. Based on this, an efficiency known as the absorption efficiency gabs was introduced to evaluate the theoretical maximum solar photothermal conversion efficiency:
R 3lm
gabs ¼
I ðkÞ 1 ekðk;f v Þh 0:2lm 0 R 3lm I ðkÞdk 0:2lm 0
dk
ð10Þ
4. Results and discussion The SEM image of the Au NPs is shown in Fig. 2 along with the absorbance spectra of the Au nanofluids. The average size of Au NPs were determined from SEM images by averaging diameters of at least 100 particles through a software application (Nano Measurer 1.2). The average Au NP diameter was calculated as 10 nm. In addition, Fig. 2B shows a photograph of the Au nanofluids prepared using four different NP volume fractions (i.e., 0.5, 1.0, 1.5, and 2.5 ppm), where the color1 became less intense as the NP volume fraction decreased. Furthermore, the uniform color of the solutions indicated that the Au NPs were well dispersed in the base fluid. The peak absorbance wavelength of all Au nanofluids was 524 nm, as shown in Fig. 2C, and the linear relationship between the peak absorbance and the NP volume fraction can be seen clearly in Fig. 2D. The temperature profiles of the Au nanofluids containing four different NP volume fractions were recorded under solar intensities of 10, 5, and 3 suns. The increase in temperature of the different fluids with irradiation time is depicted in Fig. 3A and C. As shown, the temperatures of the Au nanofluids increased logarithmically upon simulated solar irradiation, reaching a plateau or equilibrium due to equal heat dissipation and heat yield. This equilibrium temperature increased with an increase in both NP volume fraction fv and solar intensity I0, as shown in Fig. 3B and D. Furthermore, a linear relationship between the equilibrium temperature and the solar intensity could be clearly seen. Indeed, such a relationship was previously reported in the work of Jiang et al. [34], indicating that the photothermal conversion efficiency represents an intrinsic property of the Au nanofluids. Prior to calculating the photothermal conversion efficiency, Eqs. (2) and (3) must be employed to determine the heat dissipation coefficient B. As shown in Fig. 3E, the water temperatures at the four different heights examined were similar during the cooling process, indicating uniform temperature distribution and heat dissipation in the fluid under stirring. Therefore, the arithmetic average value of the four temperatures at different heights was used as the fluid temperature in the photothermal conversion efficiency calculations. To further confirm that the heat dissipation coefficient B was a constant, the temperature profiles of the Au nanofluids were measured after reaching the equilibrium temperature. As shown in Fig. 3F, the presence of Au NPs in the water had no significant effect on the heat dissipation coefficient over a constant fluid volume (i.e., 10 mL). Therefore, the average heat dissipation coefficient B was calculated as 2.15 ± 0.05 J K1 min1 based on the slopes of the best fitting lines shown in Fig. 3E and F. The solar photothermal conversion efficiencies gpt were obtained from the heat dissipation coefficients B. As indicated by Eq. (4), under equal solar intensities with different NP volume frac1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.
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tions, the solar photothermal conversion efficiency and the fluid temperature were directly proportional (see Fig. 3B). According to the Beer-Lambert Law [33], the photothermal conversion efficiency increased with an increase in the NP volume fraction due to enhanced absorption at high NP volume fractions. Moreover, the extent of variation in the photothermal conversion efficiency declined as the NP volume fraction increased, indicating that the solar absorption reached saturation at a certain NP volume fraction. This was also suggested by other published simulation results [16,28,35]. In contrast, at the same NP volume fraction but at different solar intensities, the solar photothermal conversion efficiency and the fluid equilibrium temperature were inversely proportional, as shown in Fig. 3D. In this case, the decline in the solar photothermal conversion efficiency upon increasing the solar intensity could be attributed to the limited absorption ability of the nanofluid under high solar intensities, despite a high equilibrium temperature being obtained. Due to the large calculated wavelength range of the solar radiation (i.e., 200–3000 nm), it was difficult to obtain the extinction coefficient of the nanofluid via experimental measurements. Thus, the absorption and scattering coefficients were calculated based on the Rayleigh scattering approximation and independent scattering as indicated in Eqs. (6)–(8). In addition, the complex refractive index of the Au NP was obtained from Ref. [36] as outlined in Fig. 4A. Furthermore, the theoretical and experimental results for the absorbance of the Au NP with an NP volume fraction of 2.5 ppm were compared between 300 and 800 nm. The results shown in Fig. 4B indicate an agreement between the experimental and theoretical results (i.e., deviation 613.2% at the maximum absorbance). The half width of the absorbance spectra obtained experimentally was larger than that obtained theoretically due to the presence of larger NPs in the fluids, which caused a red shift in the experimental absorbance spectra. Using Eq. (10), the absorption efficiency gabs was obtained to evaluate the theoretical maximum solar photothermal conversion efficiency gpt of the fluid. As indicated in Fig. 4C the absorption efficiency gabs and the solar photothermal conversion efficiency gpt were in good agreement. In the theoretical calculation of the photothermal conversion efficiency, the heat dissipation was considered using Eqs. (1)–(4). Indeed, the absorption efficiency gabs was comparable to the solar photothermal conversion efficiency gpt , indicating that the absorption efficiency gabs can be used as a parameter for NP optimization and collector design without considering the temperature field. The absorption efficiency gabs is shown in Fig. 5A as a function of the collector height H and the NP volume fraction fv, and was found to increase exponentially with increasing collector height and NP volume fraction due to H and fv being in the exponential terms in Eq. (10). Indeed, relatively low collector heights and NP volume fractions yielded optimal absorption efficiencies, with only small increases being observed at high values of H and fv. Fig. 5A therefore provides a simple and efficient mean to select the NP volume fraction and collector height. For example, to obtain a solar absorption efficiency of 89.38%, the parameters can be selected according to the black line shown in Fig. 5A. At this point, the NP volume fraction ranged from 6 to 20 ppm, while the collection height ranged from 43 to 100 mm. However, the optimized NP volume fraction and collector height could also be obtained based on the costs of NP and collector preparation. When the cost of the Au nanofluid per NP volume fraction was five-fold the cost of the DASC per unit of height, the total cost U cost of the DASC on varying the NP volume fraction can be determined from Fig. 5B using a solar absorption efficiency of 89.38%. Thus, to obtain a solar absorption efficiency of 89.38%, the optimized NP volume fraction and collector height must be 10 ppm and 70 mm, respectively, when considering the minimum total cost of the DASC.
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70
Au/H 2O-0.5ppm-10suns Au/H 2O-1.5ppm-10suns H2O-10suns
(A)
(B)
T ηpt I0=10 suns
o
60
60 o
T/ C
50 40
50 50 40
30 20
0
10
20
30
40
50
40 0.0
60
0.5
1.0
1.5
70
65
Au/H 2O-2.5ppm-10suns Au/H 2O-2.5ppm-5suns
(C) 60
2.0
2.5
30
3.0
fv / ppm
Time t / min
60
Au/H 2O-2.5ppm-3suns
95
T ηpt
(D)
90
fv=2.5 ppm
o
Temperature T / C
ηpt / %
Temperature T / C
60
70
70
Au/H2O-1.0ppm-10suns Au/H2O-2.5ppm-10suns
o
T/ C
55
40
80 50 75
30 20
45
0
10
20
30
40
50
40
60
70
2
4
6
3.5
10
65 12
5
(E)
1.4 0.7
H2O-10suns
Linear Fit of Au/H 2 O: Slope = -0.0044, R2 = 0.9985
4
In (T-To )
2.1
Au/H 2 O-1.5ppm-10suns
(F)
H= 4mm H= 8mm H=12mm H=16mm H 2O
2.8
0.0
8
I0 / sun
Time t / min
In (T-To )
ηpt / %
85 50
Linear Fit of H 2 O: Slope = -0.0042, R2 = 0.9997
3 2 1
0
10
20
30
40
50
60
Time t / min
0
0
10
20
30
40
50
60
Time t / min
Fig. 3. Solar photothermal conversion processes of the four different fluids. (A) and (C) Increase in temperature of the different fluids. (B) and (D) Equilibrium temperatures and photothermal conversion efficiencies of the different fluids. (E) and (F) Experimental (discrete points) and fitted (solid line) temperature decay processes of the different fluids after switching off the solar simulator.
5. Conclusions We herein investigated the solar photothermal conversion performances of Au nanofluids and calculated the solar photothermal conversion efficiency, taking into account the heat dissipation of the system. Based on the calculations and measurements, the following conclusions could be made: Experimental results showed that the equilibrium temperature increased upon increasing both the NP volume fraction and the solar intensity. A linear relationship was clearly observed between the equilibrium temperature and the solar intensity. The photothermal conversion efficiency of the fluid increased as the NP volume fraction increased, due to the enhanced absorption at high NP volume fractions. However, the extent of variation in the photothermal conversion efficiency decreased with an increase of the NP volume fraction. A theoretical model based on the Rayleigh scattering approximation and the Beer-Lambert Law was employed to predict the
solar radiation absorption efficiency. Indeed, a good agreement between the solar absorption efficiency and the solar photothermal conversion efficiency was obtained. Furthermore, the absorption efficiency increased exponentially upon increasing the collector height and the NP volume fraction. Examination of the solar absorption efficiency allowed an optimization of the NP volume fraction and direct solar absorption collector design without considering the temperature field. Acknowledgements This work was financially supported by the National Natural Science Foundation of China (Grant No. 51322601), the Natural Science Funds of Heilongjiang Province for Distinguished Young Scholars (Grant No. JC2016009), the Science Creative Foundation for Distinguished Young Scholars in Harbin (Grant No. 2014RFYXJ004), and the Fundamental Research Funds for the Central Universities (Grant No. HIT. BRETIV. 201315).
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21
Imaginary part k Real part n
(B)
1.2
9
0.8
Real part n
15 12
Mod. data Exp. data
0.4
1.6
Absorbance (a.u.)
18
Imaginary part k
0.5
2.0
(A)
6
0.3 0.2 0.1
0.4 3 0
0
500
1000
1500
2000
2500
0.0 300
0.0 3000
400
500
600
700
800
Wavelength / nm
Wavelength / nm 90
(C) Efficency / %
72 54 36 ηpt ηabs
18 0 0.0
0.7
1.4
2.1
2.8
Volume fraction / ppm Fig. 4. Simulation of Au NP properties. (A) Real and imaginary complex refractive indices for the Au nanoparticles. (B) Comparison of the calculated and measured absorbance values. (C) Comparison of the experimental photothermal conversion efficiency gpt and the predicated absorption efficiency gabs.
(A)
h / mm
80
60
40
20
0 0
4
8
ηabs / % 97.50 The Optimize Ponit 89.38 81.25 73.13 65.00 56.88 89.38 48.75 40.63 32.50 24.38 16.25 8.125 0.000 12 16 20
fv / ppm
145
(B)
ηabs = 89.38 %
140 135
Ucost / unit
100
fv = 10 ppm
130
h= 70 mm
125 120 115 4
8
12
16
20
fv / ppm
Fig. 5. Optimal DASC design. (A) Absorption efficiencies as a function of collector height h and Au NP volume fraction fv. (B) The total DASC cost with reference to the NP volume fraction at a solar absorption efficiency of 89.38%.
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[24] Y. Xiong, R. Long, D. Liu, X. Zhong, C. Wang, Z.Y. Li, Y. Xie, Solar energy conversion with tunable plasmonic nanostructures for thermoelectric devices, Nanoscale 4 (15) (2012) 4416–4420. [25] H. Zhang, H.J. Chen, X. Du, D. Wen, Photothermal conversion characteristics of gold nanoparticle dispersions, Sol. Energy 100 (2014) 141–147. [26] Y. Xuan, H. Duan, Q. Li, Enhancement of solar energy absorption using a plasmonic nanofluid based on TiO2/Ag composite nanoparticles, RSC Adv. 4 (31) (2014) 16206–16213. [27] H. Duan, Y. Xuan, Synthesis and optical absorption of Ag/CdS core/shell plasmonic nanostructure, Sol. Energy Mater. Sol. Cells 121 (2014) 8–13. [28] A. Lenert, E.N. Wang, Optimization of nanofluid volumetric receivers for solar thermal energy conversion, Sol. Energy 86 (1) (2012) 253–265. [29] Y. Yang, S. Matsubara, M. Nogami, One-dimensional self-assembly of gold nanoparticles for tunable surface plasmon resonance properties, Nanotechnology 17 (2006) 2821. [30] J.R. Cole, N.A. Mirin, M.W. Knight, G.P. Goodrich, N.J. Halas, Photothermal efficiencies of nanoshells and nanorods for clinical therapeutic applications, J. Phys. Chem. C 113 (2009) 12090–12094. [31] H. Chen, L. Shao, T. Ming, Z. Sun, C. Zhao, B. Yang, J. Wang, Understanding the photothermal conversion efficiency of gold nanocrystals, Small 6 (2010) 2272– 2280. [32] C.L. Tien, Thermal radiation in packed and fluidized beds, J. Heat Transf. – Trans. ASME 110 (1988) 1230–1242. [33] D.F. Swinehart, The Beer-Lambert law, J. Chem. Educ. 39 (7) (1962) 333. [34] K. Jiang, D.A. Smith, A. Pinchuk, Size-dependent Photothermal conversion efficiencies of plasmonically heated gold nanoparticles, J. Phys. Chem. C 117 (51) (2013) 27073–27080. [35] H. Tyagi, P. Phelan, R. Prasher, Predicted efficiency of a low-temperature nanofluid-based direct absorption solar collector, J. Sol.Energy Eng. 131 (4) (2009) 041004. [36] A. Sadao, Handbook of Optical Constants of Metals, World Scientific, Singapore, 2012, pp. 68–77.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Investigation into Au nanofluids for solar photothermal conversion Meijie Chen a, Yurong He a,⇑, Jian Huang a, Jiaqi Zhu b a b
School of Energy Science & Engineering, Harbin Institute of Technology, Harbin 150001, China School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
a r t i c l e
i n f o
Article history: Received 11 September 2016 Received in revised form 29 December 2016 Accepted 4 January 2017
Keywords: Au nanofluid Solar energy Photothermal conversion Absorption efficiency
a b s t r a c t We herein investigate the solar photothermal conversion performances of Au nanofluids both experimentally and theoretically. In the experiments, the Au nanofluids are loaded into a beaker and are exposed to solar radiation. The solar photothermal conversion efficiency performances of the Au nanofluids using different nanoparticle (NP) volume fractions and solar intensities are discussed. Experimental results show that the equilibrium temperature increases as the NP volume fraction and solar intensity increase, although the extent of variation in the photothermal conversion efficiency declines under these conditions. Furthermore, a theoretical analysis based on the Rayleigh scattering approximation and the Beer-Lambert Law to predict the solar absorption efficiency is discussed. A good agreement between the calculated absorption efficiency and the experimental solar photothermal conversion efficiency is reported. The absorption efficiency increases exponentially with increasing collector height and NP volume fraction. Moreover, the optimization of NP selection and collector design for direct absorption solar collectors without consideration of the temperature field is of particular scientific importance. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Solar energy is one of the most renewable and clean energy resources, and as such it has attracted significant research interest [1–4]. Indeed, efforts to achieve the efficient utilization of solar energy have been reported using a number of different approaches [5–7], with some of the most common approaches including photovoltaic conversion, photochemical conversion, and photothermal conversion. Photovoltaic conversion is a process that directly converts solar irradiation to electricity [8], while photochemical conversion converts solar energy to chemical energy [9], with examples including photocatalysis [10] and water-splitting to produce hydrogen [11]. However, despite being popular approaches, these two technologies exhibit low energy conversion efficiencies [1,5]. In contrast, photothermal conversion is a more traditional, simple, and effective approach that converts solar irradiation to heat as thermal energy, and has attracted renewed research interest in the past decade, especially in the application of nanofluid-based direct solar absorption collectors (DASCs) [12–14]. When compared with a base fluid alone, nanoparticles (NPs) dispersed in a base fluid can enhance the photothermal conversion performance of a system through the enhanced absorption and scattering of nanofluids ⇑ Corresponding author. E-mail address: [email protected] (Y. He). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.005 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
[15]. Otanicar et al. [16] investigated DASCs based on carbon nanotubes, graphite, and silver nanofluids. They observed an improvement in efficiency 65% upon the use of nanofluids as the absorption medium. In addition, a study by Taylor et al. [17] compared the spectroscopic measurement of extinction coefficients over wavelengths important for solar energy with model predictions. Other recent studies [16,18–21] have also indicated the importance of selecting suitable nanofluids to improve the efficiency of DASCs. A number of noble metal NPs have attracted significant interest because of their unique properties, including large optical field enhancements, which result in the strong scattering and absorption of photons. The enhancement in the optical and photothermal properties of noble metal NPs arises from the resonant oscillation of their free electrons in the presence of photons, also known as localized surface plasmon resonance (LSPR) [22,23]. Plasmon resonances can be damped radiatively by photon scattering, or nonradiatively through conversion of photons to heat energy. The combination of these two mechanisms has greatly enhanced the solar absorption and photothermal conversion performances of nanofluids. In addition, the plasmonic band of plasmonic nanostructures can be easily altered by tailoring the nanostructure shape, thus enabling them to interact with photons in different spectral ranges, and ultimately resulting in the efficient utilization of solar light [24]. Zhang et al. [25] studied plasmonic Au NPs with the aim of improving solar thermal conversion efficiencies, and
M. Chen et al. / International Journal of Heat and Mass Transfer 108 (2017) 1894–1900
found that Au NPs exhibited improved photothermal conversion capabilities compared to other reported materials (carbon nanotubes and graphite). Moreover, Duan and Xuan et al. [26,27] investigated the solar absorption of core-shell NPs both experimentally and theoretically. They found that the optical absorption of core-shell plasmonic nanofluids was enhanced through the LSPR effect on the Ag surface. In addition to the NP material employed, other factors that influenced the photothermal conversion efficiency for plasmonic nanofluids included the collector height, the NP volume faction, and the solar intensity [28], and as such should be further investigated to obtain optimal conditions for plasmonic nanofluids employed in DASCs. It was also reported that the calculated values of solar photothermal conversion efficiencies of working fluids varied with different experimental devices due to different heat dissipations during the solar photothermal conversion processes [15,16,25,27]. Thus, we herein report the calculation of the solar photothermal conversion efficiencies of plasmonic Au nanofluids based on energy balance with a full consideration of heat dissipation. Firstly, the solar photothermal conversion performances of Au nanofluids are investigated experimentally. Au NPs are prepared via a citrate reduction method. In addition, the solar photothermal conversion efficiency performances of Au nanofluids with different NP volume fractions and solar intensities are discussed. Furthermore, a theoretical model based on the Rayleigh scattering approximation and the Beer-Lambert Law is also developed to predict the solar absorption efficiency. Finally, the experimental and theoretical results are compared to optimize the DASC parameters without consideration of the temperature field. 2. Materials and methods 2.1. Au nanoparticle synthesis Au NPs were synthesized via a previously reported citrate reduction method [29]. A 2.5 mL of 10 mM HAuCl4 (Au P48%, Aladdin Co. Ltd.) aqueous solution was added to a 100 mL of 5 mM sodium citrate (99%, Aladdin Co. Ltd.) aqueous solution with vigorous stirring. The resulting solution was heated at 100 °C for 30 min to give an Au nanofluid NP volume fraction of 2.5 ppm assuming a complete reaction. Au nanofluids containing different NP volume fractions were obtained by dilution of this solution and were used in subsequent photothermal conversion experiments. Scanning electron microscopy (SEM) was performed using a Zeiss Supra 55 Sapphire electron microscope at a bias voltage of 30 kV. The average NP sizes were determined from SEM images by averaging the diameters of at least 100 NPs using the Nano Measurer 1.2 program. Optical absorbance spectra were measured at 25 °C using a UV–Vis spectrophotometer (Pgeneral TU1901) in a 4 mm quartz cuvette with water as the reference. 2.2. Photothermal conversion experiments A schematic representation of the photothermal conversion device is shown in Fig. 1. A sample of the working fluid (10 mL) was stirred inside a PMMA beaker (300 rpm) to reduce fluid temperature gradients. The beaker was held using a clamp stand to avoid direct thermal conduction through contact with the surfaces. Therefore, ignoring radiation effects due to the low fluid temperature (<100 °C), only thermal convection through the air took place approximately. The beaker was covered using quartz glass to prevent water loss. To monitor the fluid temperature, four T-type thermocouples were installed at different heights (H = 4, 8, 12, and 16 mm). The working fluid was irradiated with a solar simulator (3, 5 and 10 suns, Beijing Education Au-light Co., Ltd., CEL-
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HXF300 type). Temperatures were recorded every 2 min for 60 min until a thermal equilibrium state had been reached. The solar simulator was then turned off, and the fluid was allowed to cool to room temperature 25 °C. The solar photothermal conversion efficiency was calculated based on the energy balance during the process, i.e., energy absorbed and converted by the working fluid from the solar radiation is equal to the sum of the heat dissipated to the surroundings and the energy increasing the temperature of fluid and beaker. As outlined in Eq. (1) [30,31]:
ðM f cp;f þ M b cp;b Þ
dDT þ BDT ¼ I0 Ai gpt dt
ð1Þ
where Mf is the fluid mass, cp;f is the constant-pressure solution heat capacity, which is treated as a constant with such low NP volume fractions (0.5, 1.0, 1.5 and 2.5 ppm) in this work, Mb is the beaker mass, cp;b is the constant-pressure beaker heat capacity, DT is the temperature difference between time t and the starting time, B is the heat dissipation coefficient since heat loss occurs mainly by heat convection, I0 is the solar radiation intensity, Ai is the irradiated area, and gpt is the photothermal conversion efficiency of the working fluid. Relevant parameter values are shown in Table 1. The heat dissipation coefficient B can be determined by switching off the solar simulator as indicated in Eq. (2):
ðM f cp;f þ M b cp;b Þ
dDT þ BDT ¼ 0 dt
ð2Þ
The solution of Eq. (2) can be written as Eq. (3), and coefficients B and C can be determined by fitting the experimental data of the fluid temperature after the solar simulator has been switched off:
lnðDTÞ ¼
Bt þC M f cp;f þ M b cp;b
ð3Þ
Finally, the photothermal conversion efficiency gpt can be obtained by considering the equilibrium state of the nanofluid in Eq. (4) when water is the base fluid and the heating process reaches its equilibrium state:
BDT ¼ I0 Ai gpt
ð4Þ
3. Theoretical model To better understand the solar absorption ability of the Au nanofluid, a theoretical model was developed to predict its absorption of solar radiation. Solar radiation intensities between 200 and 3000 nm were obtained using the black body relationship based on Planck’s law. Atmospheric absorption was neglected in this calculation [16,35]. Hence, the incident solar intensity can describe the amount of electromagnetic energy within a certain wavelength radiated by a black body at the thermal equilibrium state given by:
hc0 2 1 Ibk ðk; T s Þ ¼ 2hc0 = k5 exp kkB T s
ð5Þ
where Ibk is the spectral intensity of the black body, h is Planck’s constant, kB is the Boltzmann constant, c0 is the speed of light in a vacuum, k is the wavelength, and T s is the solar temperature. The incident solar heat flux I0 is equal to C 0 Ibk after the modification of the spectral intensity of the black body, where C 0 is the modification factor. The air mass is 1.5 (i.e., AM = 1.5), which represents the solar spectrum at the mid-latitudes, and the solar intensity is 1000 W/m2 according to the ASTM G-173 standard. The value of C 0 is taken as 0.74 to match the solar intensity at AM = 1.5. Regarding the optical properties of nanofluids, a complex relationship between absorption and scattering must be considered due to the presence of small NPs. For the present experimental study, the Au NP size d was 10 nm, as shown in Fig. 2A. An
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Solar Simulator
Quartz glass Fluid
PMMA box (10 mL)
Clamp
Thermocouple
Stirrer Data acquisition
Magnetic stirrer
Computer
Fig. 1. Schematic representation of the photothermal conversion device.
The maximum particle volume fraction for independent scattering
Table 1 Relevant parameter values at the ambient temperature. Parameter
Value
Constant-pressure solution heat capacity cp;f (J kg1 °C1) Constant-pressure beaker heat capacity cp;b (J kg1 °C1) Fluid mass M f (g) Beaker mass M b (g) Irradiated area Ai (m2)
4183 1464 10.0 5.6
f v ;max ¼ ½1:81a=ðp þ 2aÞ3 , which depends the size parameter a and the particle volume fraction f v . Therefore, the absorption and scattering coefficients can be calculated based on the Rayleigh scattering approximation and independent scattering expressed as [16,35]:
2 104
ka;np
ð6Þ
approximation of the Rayleigh scattering can be applied to simplify the calculation. This approximation is valid when the size parameter a 1, which is defined as a ¼ pd=k. When the Mie scattering formula is expanded into a power series with a as a variable, its second and later items can be neglected compared with the first term in this case. Therefore, the solution of Rayleigh scattering can be obtained. In physical terms, Rayleigh scattering can be understood as the regime in which the particle size is much smaller than the wavelength of the incident radiation. Moreover, NPs with relatively low volume fractions were applied to the experiments, and the absorption and scattering of the NPs could be considered independent scattering in the scattering regime map [32].
(A)
ks;np ¼
ð7Þ
ke;np ¼ ka;np þ ks;np
ð8Þ
where ka;np ; ks;np , and ke;np are the NP absorption, scattering, and extinction coefficients respectively. In addition, f v is the NP volume fraction, and m is the normalized refractive index of the NP, defined by:
0.5
0.40
0.4
Au/H 2O-2.5ppm Au/H 2O-1.5ppm
0.3
Au/H 2O-1.0ppm Au/H 2O-0.5ppm
(D) Peak absorbance (a.u.)
Absorbance (a.u.)
2 3 8p4 d f v m2 1 m2 þ 2 k4
(B)
(C)
0.2 0.1 0.0 300
( " #) 12pf v m2 1 p2 d2 m2 1 m4 þ 27m2 þ 38 ¼ Im 1þ m2 þ 2 2m2 þ 3 k 15k2 m2 þ 2
400
500
600
Wavelength / nm
700
800
0.32
Exp. data Linear fit of Exp. data
0.24 0.16 0.08 0.00 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Volume fraction / ppm
Fig. 2. Characterization of the Au nanoparticles. (A) SEM image of the Au nanoparticles (scale bar: 20 nm). (B) Photograph of the Au nanofluids containing different nanoparticle volume fractions. (C) Absorbance spectra of the four different Au nanofluids. (D) Relationship between the peak absorbance and the NP volume fraction.
M. Chen et al. / International Journal of Heat and Mass Transfer 108 (2017) 1894–1900
m¼
mnp nbf
ð9Þ
where mnp and nbf are the complex reflective index of the NP and the base fluid relative to the ambient environment, respectively. According to the Beer-Lambert Law [33], the spectral radiation intensity decreases exponentially along its transfer direction. Based on this, an efficiency known as the absorption efficiency gabs was introduced to evaluate the theoretical maximum solar photothermal conversion efficiency:
R 3lm
gabs ¼
I ðkÞ 1 ekðk;f v Þh 0:2lm 0 R 3lm I ðkÞdk 0:2lm 0
dk
ð10Þ
4. Results and discussion The SEM image of the Au NPs is shown in Fig. 2 along with the absorbance spectra of the Au nanofluids. The average size of Au NPs were determined from SEM images by averaging diameters of at least 100 particles through a software application (Nano Measurer 1.2). The average Au NP diameter was calculated as 10 nm. In addition, Fig. 2B shows a photograph of the Au nanofluids prepared using four different NP volume fractions (i.e., 0.5, 1.0, 1.5, and 2.5 ppm), where the color1 became less intense as the NP volume fraction decreased. Furthermore, the uniform color of the solutions indicated that the Au NPs were well dispersed in the base fluid. The peak absorbance wavelength of all Au nanofluids was 524 nm, as shown in Fig. 2C, and the linear relationship between the peak absorbance and the NP volume fraction can be seen clearly in Fig. 2D. The temperature profiles of the Au nanofluids containing four different NP volume fractions were recorded under solar intensities of 10, 5, and 3 suns. The increase in temperature of the different fluids with irradiation time is depicted in Fig. 3A and C. As shown, the temperatures of the Au nanofluids increased logarithmically upon simulated solar irradiation, reaching a plateau or equilibrium due to equal heat dissipation and heat yield. This equilibrium temperature increased with an increase in both NP volume fraction fv and solar intensity I0, as shown in Fig. 3B and D. Furthermore, a linear relationship between the equilibrium temperature and the solar intensity could be clearly seen. Indeed, such a relationship was previously reported in the work of Jiang et al. [34], indicating that the photothermal conversion efficiency represents an intrinsic property of the Au nanofluids. Prior to calculating the photothermal conversion efficiency, Eqs. (2) and (3) must be employed to determine the heat dissipation coefficient B. As shown in Fig. 3E, the water temperatures at the four different heights examined were similar during the cooling process, indicating uniform temperature distribution and heat dissipation in the fluid under stirring. Therefore, the arithmetic average value of the four temperatures at different heights was used as the fluid temperature in the photothermal conversion efficiency calculations. To further confirm that the heat dissipation coefficient B was a constant, the temperature profiles of the Au nanofluids were measured after reaching the equilibrium temperature. As shown in Fig. 3F, the presence of Au NPs in the water had no significant effect on the heat dissipation coefficient over a constant fluid volume (i.e., 10 mL). Therefore, the average heat dissipation coefficient B was calculated as 2.15 ± 0.05 J K1 min1 based on the slopes of the best fitting lines shown in Fig. 3E and F. The solar photothermal conversion efficiencies gpt were obtained from the heat dissipation coefficients B. As indicated by Eq. (4), under equal solar intensities with different NP volume frac1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.
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tions, the solar photothermal conversion efficiency and the fluid temperature were directly proportional (see Fig. 3B). According to the Beer-Lambert Law [33], the photothermal conversion efficiency increased with an increase in the NP volume fraction due to enhanced absorption at high NP volume fractions. Moreover, the extent of variation in the photothermal conversion efficiency declined as the NP volume fraction increased, indicating that the solar absorption reached saturation at a certain NP volume fraction. This was also suggested by other published simulation results [16,28,35]. In contrast, at the same NP volume fraction but at different solar intensities, the solar photothermal conversion efficiency and the fluid equilibrium temperature were inversely proportional, as shown in Fig. 3D. In this case, the decline in the solar photothermal conversion efficiency upon increasing the solar intensity could be attributed to the limited absorption ability of the nanofluid under high solar intensities, despite a high equilibrium temperature being obtained. Due to the large calculated wavelength range of the solar radiation (i.e., 200–3000 nm), it was difficult to obtain the extinction coefficient of the nanofluid via experimental measurements. Thus, the absorption and scattering coefficients were calculated based on the Rayleigh scattering approximation and independent scattering as indicated in Eqs. (6)–(8). In addition, the complex refractive index of the Au NP was obtained from Ref. [36] as outlined in Fig. 4A. Furthermore, the theoretical and experimental results for the absorbance of the Au NP with an NP volume fraction of 2.5 ppm were compared between 300 and 800 nm. The results shown in Fig. 4B indicate an agreement between the experimental and theoretical results (i.e., deviation 613.2% at the maximum absorbance). The half width of the absorbance spectra obtained experimentally was larger than that obtained theoretically due to the presence of larger NPs in the fluids, which caused a red shift in the experimental absorbance spectra. Using Eq. (10), the absorption efficiency gabs was obtained to evaluate the theoretical maximum solar photothermal conversion efficiency gpt of the fluid. As indicated in Fig. 4C the absorption efficiency gabs and the solar photothermal conversion efficiency gpt were in good agreement. In the theoretical calculation of the photothermal conversion efficiency, the heat dissipation was considered using Eqs. (1)–(4). Indeed, the absorption efficiency gabs was comparable to the solar photothermal conversion efficiency gpt , indicating that the absorption efficiency gabs can be used as a parameter for NP optimization and collector design without considering the temperature field. The absorption efficiency gabs is shown in Fig. 5A as a function of the collector height H and the NP volume fraction fv, and was found to increase exponentially with increasing collector height and NP volume fraction due to H and fv being in the exponential terms in Eq. (10). Indeed, relatively low collector heights and NP volume fractions yielded optimal absorption efficiencies, with only small increases being observed at high values of H and fv. Fig. 5A therefore provides a simple and efficient mean to select the NP volume fraction and collector height. For example, to obtain a solar absorption efficiency of 89.38%, the parameters can be selected according to the black line shown in Fig. 5A. At this point, the NP volume fraction ranged from 6 to 20 ppm, while the collection height ranged from 43 to 100 mm. However, the optimized NP volume fraction and collector height could also be obtained based on the costs of NP and collector preparation. When the cost of the Au nanofluid per NP volume fraction was five-fold the cost of the DASC per unit of height, the total cost U cost of the DASC on varying the NP volume fraction can be determined from Fig. 5B using a solar absorption efficiency of 89.38%. Thus, to obtain a solar absorption efficiency of 89.38%, the optimized NP volume fraction and collector height must be 10 ppm and 70 mm, respectively, when considering the minimum total cost of the DASC.
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70
Au/H 2O-0.5ppm-10suns Au/H 2O-1.5ppm-10suns H2O-10suns
(A)
(B)
T ηpt I0=10 suns
o
60
60 o
T/ C
50 40
50 50 40
30 20
0
10
20
30
40
50
40 0.0
60
0.5
1.0
1.5
70
65
Au/H 2O-2.5ppm-10suns Au/H 2O-2.5ppm-5suns
(C) 60
2.0
2.5
30
3.0
fv / ppm
Time t / min
60
Au/H 2O-2.5ppm-3suns
95
T ηpt
(D)
90
fv=2.5 ppm
o
Temperature T / C
ηpt / %
Temperature T / C
60
70
70
Au/H2O-1.0ppm-10suns Au/H2O-2.5ppm-10suns
o
T/ C
55
40
80 50 75
30 20
45
0
10
20
30
40
50
40
60
70
2
4
6
3.5
10
65 12
5
(E)
1.4 0.7
H2O-10suns
Linear Fit of Au/H 2 O: Slope = -0.0044, R2 = 0.9985
4
In (T-To )
2.1
Au/H 2 O-1.5ppm-10suns
(F)
H= 4mm H= 8mm H=12mm H=16mm H 2O
2.8
0.0
8
I0 / sun
Time t / min
In (T-To )
ηpt / %
85 50
Linear Fit of H 2 O: Slope = -0.0042, R2 = 0.9997
3 2 1
0
10
20
30
40
50
60
Time t / min
0
0
10
20
30
40
50
60
Time t / min
Fig. 3. Solar photothermal conversion processes of the four different fluids. (A) and (C) Increase in temperature of the different fluids. (B) and (D) Equilibrium temperatures and photothermal conversion efficiencies of the different fluids. (E) and (F) Experimental (discrete points) and fitted (solid line) temperature decay processes of the different fluids after switching off the solar simulator.
5. Conclusions We herein investigated the solar photothermal conversion performances of Au nanofluids and calculated the solar photothermal conversion efficiency, taking into account the heat dissipation of the system. Based on the calculations and measurements, the following conclusions could be made: Experimental results showed that the equilibrium temperature increased upon increasing both the NP volume fraction and the solar intensity. A linear relationship was clearly observed between the equilibrium temperature and the solar intensity. The photothermal conversion efficiency of the fluid increased as the NP volume fraction increased, due to the enhanced absorption at high NP volume fractions. However, the extent of variation in the photothermal conversion efficiency decreased with an increase of the NP volume fraction. A theoretical model based on the Rayleigh scattering approximation and the Beer-Lambert Law was employed to predict the
solar radiation absorption efficiency. Indeed, a good agreement between the solar absorption efficiency and the solar photothermal conversion efficiency was obtained. Furthermore, the absorption efficiency increased exponentially upon increasing the collector height and the NP volume fraction. Examination of the solar absorption efficiency allowed an optimization of the NP volume fraction and direct solar absorption collector design without considering the temperature field. Acknowledgements This work was financially supported by the National Natural Science Foundation of China (Grant No. 51322601), the Natural Science Funds of Heilongjiang Province for Distinguished Young Scholars (Grant No. JC2016009), the Science Creative Foundation for Distinguished Young Scholars in Harbin (Grant No. 2014RFYXJ004), and the Fundamental Research Funds for the Central Universities (Grant No. HIT. BRETIV. 201315).
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21
Imaginary part k Real part n
(B)
1.2
9
0.8
Real part n
15 12
Mod. data Exp. data
0.4
1.6
Absorbance (a.u.)
18
Imaginary part k
0.5
2.0
(A)
6
0.3 0.2 0.1
0.4 3 0
0
500
1000
1500
2000
2500
0.0 300
0.0 3000
400
500
600
700
800
Wavelength / nm
Wavelength / nm 90
(C) Efficency / %
72 54 36 ηpt ηabs
18 0 0.0
0.7
1.4
2.1
2.8
Volume fraction / ppm Fig. 4. Simulation of Au NP properties. (A) Real and imaginary complex refractive indices for the Au nanoparticles. (B) Comparison of the calculated and measured absorbance values. (C) Comparison of the experimental photothermal conversion efficiency gpt and the predicated absorption efficiency gabs.
(A)
h / mm
80
60
40
20
0 0
4
8
ηabs / % 97.50 The Optimize Ponit 89.38 81.25 73.13 65.00 56.88 89.38 48.75 40.63 32.50 24.38 16.25 8.125 0.000 12 16 20
fv / ppm
145
(B)
ηabs = 89.38 %
140 135
Ucost / unit
100
fv = 10 ppm
130
h= 70 mm
125 120 115 4
8
12
16
20
fv / ppm
Fig. 5. Optimal DASC design. (A) Absorption efficiencies as a function of collector height h and Au NP volume fraction fv. (B) The total DASC cost with reference to the NP volume fraction at a solar absorption efficiency of 89.38%.
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