1
Yearly performance of a hybrid PV operating with nanofluid
2
Evangelos Bellos, Christos Tzivanidis
3 4 5 6
Thermal Department, School of Mechanical Engineering, National Technical University of Athens, Zografou, Heroon Polytechniou 9, 15780 Athens, Greece. Corresponding author: Evangelos Bellos (
[email protected] , +30 210 772 2340)
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Abstract The objective of this study is to estimate the yearly thermal and electrical enhancement of a hybrid PV operating with nanofluids. The examined nanofluid is Cu/water and it is compared with water as working fluid for various operating conditions. An integrated solar thermal system with a hybrid PV and a storage tank is examined for twelve typical days in order its yearly performance to be determined. Different storage tank volumes are investigated because the storage capacity influence on the thermal and the exergetic performance of the system. According to the final results, the storage tank of 150 L is found to be the most suitable solution for the hybrid PV of 2 m2 collecting area, using exergetic criteria. For this case, the yearly thermal performance enhancement is about 4.35%, while the electrical and exergetic enhancements are 1.49% and 3.19% respectively. Moreover it is found that the yearly enhancement is higher in the cases with greater storage tanks. The study is performed with a developed thermal model in EES (Engineering Equation Solver) which is validated with experimental literature results. The climate data has been taken from literature for Athens, Greece.
23 24
Keywords Hybrid PV, Thermal model, Yearly performance, Daily performance, Nanofluids
25 26 27 28 29 30 31 32 33 34 35 36 37
1. Introduction Renewable energy sources utilization is one of the most promising ways for achieving the energy sustainability in our society [1-3]. Solar energy is able to be converted ether to useful heat ether to electricity, fact that makes it a flexible energy source [45]. Solar collectors are the devices which able the suitable conversion of solar energy to useful outputs. They are separated mainly to solar thermal collectors and to photovoltaic panels [6]. The solar thermal collectors are devices like heat exchangers which capture the incident solar energy and they convert it into useful heat. On the other hand, the photovoltaic panels capture the incident solar energy and they convert it on electricity. The last years, the hybrid photovoltaics (PV) gain more and more attention because these devices are simultaneously thermal collectors and photovoltaics [7-8]. More specifically, these devices captures the incident solar energy and the convert it both to useful heat and to electricity.
38 39 40
The hybrid PV or thermal PV (PVT) are ideal devices for utilization in the building sector because the produced useful heat is usually in low temperature levels (~50 oC) and it can be used for domestic hot water or for space heating proposes [9-10]. 1
41 42 43 44 45
Moreover, the buildings have great electrical needs and the produced electricity can be utilized directly in them. Many techniques have been applied the last years in order to increase the performance of the hybrid PV. The most usual are the use of concentrators (CPC –PVT) [11-14] and the use of nanofluids as working fluids in them [15-18].
46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
The use of nanofluids is one technique which increases the thermal output of the collector with simultaneous effective cooling of the PV cells. Khanjari et al. [19] examined the use of Ag (φ=10%) nanoparticle in water and finally proved 3.9% electrical enhancement and 12.43% thermal enhancement. On the other hand, lower enhancement was found with Al2O3 (φ=10%) in the same study with 1.83% electrical and 4.54% thermal enhancement. Ghadiri et al. [20] examined the use of Fe3O4 (φ=3%) in water and finally they found 4.93% electrical improvement and 46.29% thermal improvement. Xu and Kleinstreuer [21] investigated the use of Al2 O3 nanoparticle in water (φ=5%) and they proved 9.72% electrical enhancement and no thermal enhancement. The same authors [22] proved that lower concentration (φ=4%) of Al2 O3 leads only to 1.45% electrical enhancement without thermal enhancement. Al-Shamani et al. [23] examined three different nanoparticles with 1% concentration. They proved that SiC leads to 42.97% electrical enhancement and 13.16% thermal enhancement, while SiO2 and TiO2 to lower improvements. Rejeb et al. [24] performed an interesting study about the utilization of Al2O3 and Cu (φ=0.4%) in hybrid PV. They finally proved that Cu leads to higher electrical and thermal improvements (0.77% and 79.97% respectively) compared to Al2O3 with 0.15% and 8.88% respectively. Moreover, it is essentially to state that Ag and Cu have been proved to be the most effective nanoparticles compared to the other usual, according the studies [25-26]. Another interesting study proved that higher amounts of nanoparticles lead to greater thermal and exergetic enhancements [27]. Khanjari et al. [28] proved that the use of Al2 O3 nanoparticles inside water leads always to higher thermal performance in a hybrid PV. More specifically, they examined various solar irradiation levels and fluid inlet temperature levels in order to perform a multilateral study.
71 72 73 74 75 76 77 78 79 80 81 82
As it is obvious from the previous literature studies, the use of nanofluids enhances both the electrical and the thermal performance of hybrid PV. The majority of the literature studies are focused on determining the performance of the system with nanofluids and not the daily yield of an integrated hybrid PV with a storage tank operating with nanofluid. This study aims to estimate the yearly performance enhancement by the utilization of nanoparticles inside the base fluid (water). Cu is the examined nanoparticle and this selection is based on the above literature review which indicate it as one of the most suitable nanoparticles. A typical hybrid PV is examined for the weather conditions of Athens (Greece) for twelve different typical days, one for every month. A thermal model is developed in EES (Engineering Equation Solver) and it is validated with an experimental literature study. Moreover, it is essential to state that the methodology of ISO 9459-2 [29] is followed for the definition of the 2
83 84 85
daily thermal performance of the integrated system. Furthermore, it is essential to state that different storage tank volumes are examined in order to determine the most suitable choice for the examined system.
86 87 88 89 90
2. Materials and methods This section is devoted for the description of the followed methodology. The examined model is described with many details and the basic mathematical modeling is given. Moreover, the properties of the working fluids and the weather data are also given with details.
91 92 93 94 95 96 97 98
2.1 The examined system The examined collector is a hybrid PV collector which is depicted in figure 1. More specifically, one intermediate strip of this collector is given in this figure. There is glass cover, PV cell, absorber plate, working fluid tube and insulation. Liquid working fluids are investigated in this study and there are totally 10 risers in the collector (N=10). Table 1 summarizes all the data about the collector dimensions and the other useful parameters [30-31]. The hybrid PV is examined also with a storage tank and figure 2 depicts this configuration.
99
Table 1. Basic parameters of the examined hybrid PV [30-31] Parameter Value Collector aperture (Ac) 2 m2 Collector length (L) 1.916 m Number of water tubes (N) 10 tubes Inner tube diameter (din) 7.72 ∙ 10-3 m Outer tube diameter (dout) 9.52 ∙ 10-3 m Cover transmittance (τ) 0.83 Plate absorbance (α) 0.95 Cover emittance (εc) 0.88 Plate emittance (εp) 0.93 Reference efficiency of PV (ηref) 0.173 Packing factor (PF) 0.804 Reference temperature (Tref) 298 K Temperature coefficient (b) 0.00405 K-1 Insulation layer thickness (Lins) 0.03 m Plate – Cover distance (δpc) 0.03 m Collector slope (βcol) 45o Insulation thermal conductivity (kins) 0.034 W/mK Density of Cu (ρnp) 8933 kg/m3 Specific heat capacity of Cu (cpnp) 396 J/kg/K Thermal conductivity of Cu (knp) 332 W/mK
100
3
101 102
Figure 1. The examined strip of the hybrid PV
103 104
Figure 2. The examined system with storage tank
105 106 107
2.2 Mathematical modeling 2.2.1 Basic equation for the collector performance definition The available solar irradiation in the collector level is calculated as:
108
Qs Ac GT ,
109
The useful heat production is calculated by the energy balance on the fluid volume:
110
Qu mc c p Tout Tin ,
(1)
(2) 4
111 112
The thermal efficiency of the collector is the ratio of the useful heat to the available solar irradiation on the collector level:
113
th
114
The electricity production can be calculated as [28]:
115
Pel Ac PF PV ,
116 117
The electrical efficiency of the PV cell is a function of the cell temperature as it is presented below [28,30]:
118
PV ref 1 b Tcell Tref ,
119
The electrical efficiency of the collector is calculated as:
120
el
121 122
The total efficiency of the collector includes the useful heat output and the electricity production, as equation 7 shows [28,30]:
123
tot
124 125
The exergetic output of the solar collector includes the electricity production and the exergy flow of the useful heat [32]:
126
T Ex u Qu mc c p Tam ln out Pel , Tin
127 128
The exergy flow of the solar irradiation is estimated according to the Petela model [33]:
129
4 T 1 T 4 Ex s Qs 1 am am , 3 Tsun 3 Tsun
130 131
The exergetic efficiency of the solar collector is the ratio of the useful exergy production to the exergy flow of the solar irradiation [34]:
132
ex
Qu , Qs
Pel , Qs
Qu Pel , Qs
Exu , Ex s
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
133 134 5
135 136 137 138
2.2.2 The developed thermal model The basic equation in the present model is the energy balance on the absorber. Equation 11 shows that the absorbed solar irradiation is converted to useful heat, to electricity and to thermal losses [32].
139
Qs
140 141 142 143
The total useful heat is calculated also using the heat transfer from the tube to the working fluid. It is essential to state that the tube and the plate, as well as the cell are assumed to have the same temperature level. Moreover, equation 12 includes the symbol “N” in order to take into account all the risers of the collector.
144
Qu N Din L h f Tp T fm ,
145 146
The mean working fluid temperature is assumed to be the mean value of the inlet and the outlet temperature [35]:
147
T fm
148
The collector thermal losses are separated to top and back losses.
149
Qloss Qtop Qback ,
150 151 152 153 154
The top losses can be calculated according to equations 15 and 16. Equation 15 describes the heat transfer between plate and cover, while equation 16 between cover and ambient. In steady state conditions, as in the present study, these thermal losses are assumed to be the same and so the temperature levels of the plate and of the cover can be calculated.
155
Qloss
Qu Pel Qloss ,
(11)
(12)
Tin Tout , 2
(13)
(14)
Ac T p4 Tc4 , Ac hin T p Tc 1 1 1
p
(15)
c
156
4 Qloss Ac hout Tc Tam Ac c Tc4 Tsky ,
157
The sky temperature is estimated according to the following usual formula [36]:
158
1. 5 Tsky 0.0552 Tam ,
159 160
The back losses are given as, taking into account the thermal resistance of the insulation layer and the heat convection with the ambient:
161
Qback
Ac T p Tam , Lins 1 hout k ins
(16)
(17)
(18)
6
162 163 164 165 166
2.2.3 Calculation of the heat transfer coefficients In this subsection, the calculations of the various heat transfer coefficients are presented. Firstly, the heat transfer coefficient between plate and cover (hin) is presented. The number Rayleigh is used in this calculation because the heat transfer is performed with natural convection [37]: 3 g T p Tc pc
167
Ra air
168
Nu air
169
1708 a1 max 0, 1 , Ra cos air
(20b)
170
1 Ra air cos 3 a 2 max 0, 1 , 5830
(20c)
171 172 173
It is essential to state that the properties of the air are calculated in the mean temperature between cover and plate temperatures [37]. Moreover β is calculated as 1/(Tp+Tc).
174 175
The heat transfer coefficient between cover and ambient is given by the following formula [38]:
176
hout 5.7 3.8 Vw ,
177 178 179
The calculation of the heat transfer between tube and working fluid is performed by the utilization of Nusselt number for flow inside the tubes. The Reynolds number is calculated as:
180
mc N , Re f Din f
181 182 183
All the examined cases in this work are characterized as laminar cases because the Reynolds number is lower than the limit of 2300. Thus the following formula for laminar flow has been utilized for the water case [39]:
2 air
hin pc kair
Prair ,
(19)
1708 sin 1.8 1.6 1 1.44 1 1 2 , Raair cos
(20a)
(21)
4
184
Nu f
h f Din kf
D 0.0668 in Re f Pr f L , 3.66 2 Din 3 1 0.04 Re f Pr f L
(22)
(23)
7
185 186 187 188 189
2.2.4 Nanofluid modeling The utilization of Cu nanoparticles inside the water makes the fluid thermal properties to be different than water. Using the equations 24 to 27, the main thermal properties of the nanofluids are estimated. As base fluid (bs) is assumed the water, as nanoparticle (np) the Cu and their mixture is the nanofluid (nf).
190
Density [40]:
191
nf bf 1 np ,
192
Specific thermal capacity [41]:
193
c p ,nf
194
Thermal conductivity (Maxwell equation) [42-43]:
195
knf
196
Dynamic viscosity [44]:
197
nf bf 1 2.5 6.5 2 ,
198 199
The Nusselt number for Water-Cu mixture is estimated according to equation 28 which is suitable for laminar flow, as in the examined cases [45]:
200
Nu f 0.4328 (1 11.285 0.754 Re Pr
201 202 203 204 205 206 207 208 209
The examined concentration of nanoparticles inside the water (φ) is studied up to 4%. Table 2 includes the main thermal properties for the various working fluids and for four characteristic temperature levels which are associated with the operating temperature levels in the PVT. It is obvious that the specific capacity is lower in nanofluid, while the other thermal properties are higher. The higher thermal conductivity of the nanofluid is the main reason for the higher heat transfer coefficients in the examined cases. Especially in laminar flow, as in this work, the higher thermal conductivity is an important factor which is able to establish the utilization of nanofluids.
(24)
bf 1 c p ,bf np c p ,np , nf nf
(25)
knp 2 kbf 2 kbf knp , knp kbf knp 2 kbf kbf
(26)
(27)
0.218
) Re 0.333 Pr 0.4 ,
(28)
210 211 212 213 8
214
Table 2. Thermal properties of the nanofluids (Water + Cu) and of the water Τ (Κ) φ (%) ρ (kg/m3) cp (J/kgK) k (W/mK) μ∙10-3 (Pa s) 300 0 997 4183 0.598 0.854 300 1 1076 3869 0.604 0.876 300 2 1155 3597 0.609 0.899 300 3 1235 3361 0.614 0.923 300 4 1314 3153 0.620 0.949 320 0 989 4182 0.627 0.577 320 1 1069 3865 0.633 0.592 320 2 1148 3593 0.638 0.608 320 3 1228 3355 0.644 0.624 320 4 1307 3147 0.650 0.641 340 0 980 4185 0.647 0.422 340 1 1059 3866 0.653 0.433 340 2 1139 3591 0.659 0.444 340 3 1218 3352 0.665 0.456 340 4 1298 3142 0.671 0.469 360 0 967 4201 0.660 0.326 360 1 1047 3876 0.666 0.335 360 2 1127 3598 0.672 0.343 360 3 1206 3356 0.678 0.353 360 4 1286 3144 0.684 0.362
215 216 217 218 219 220 221 222
2.2.5 Storage tank modeling The storage tank modeling is based on the thermal zones modeling which is usually utilized in solar thermal applications [37, 46]. According to this model, the storage tank is separated into horizontal zones which usually have the same height. The fluid temperature inside every zone is assumed to be uniform. Mass and heat is exchanged between the neighbor zones and so there is temperature stratification inside the tank; the hotter fluid with the lower density is located in the upper part of the tank while the colder water with higher density is stored in the lower part of the tank.
223 224 225 226 227
The general energy balance on the storage tank is given by equation 29. The stored energy is the difference between the useful thermal output from the collector minus the thermal losses to the environment. In the present study, there is no load extraction during the daily operation and the load is assumed to be extracted in the end of the day.
228
Qst Qu Qloss ,
229 230 231
Equations 30 to 32 are the energy balances in the three utilized mixing zones. These energy balance equations are similar with equation 29 but they are more analytical and adjusted for every zone separately.
232
f VT 3
cp
dTs1 mc c p Tout Ts1 U T AT 1 Ts1 Tam , dt
(29)
(30)
9
233
234
f VT 3
f VT 3
cp
dTs 2 mc c p Ts1 Ts 2 U T AT 2 Ts 2 Tam , dt
(31)
cp
dTs 3 mc c p Ts 2 Ts 3 U T AT 3 Ts 3 Tam , dt
(32)
235 236
It is essential to state that the inlet temperature in the collector is assumed to be equal to the temperature level in the lower part of the storage tank:
237
Tin Ts 3 ,
238 239 240
The mean storage tank temperature is approximately the mean value of the three temperature levels inside the tank. This assumption is reasonable because all the zones include the same amount of fluid.
241
Ts
242
Equations 35 to 37 give the outer storage tank surface for the three mixing zones:
243
AT 1
244
AT 2
(33)
Ts1 Ts 2 Ts 3 , 3
DT2 4
DT LT 3
DT LT 3
DT2
(34)
,
,
(35)
(36)
DT LT
245
AT 3
246
The storage tank is assumed to be cylindrical and its volume is calculated as:
247
VT
248 249 250
Finally, it is important to state that the tank diameter has selected to be equal to its total height [46]; an assumption without significant influence on the results, as it is proved after a simple sensitivity analysis.
251 252
2.2.6 Daily performance indexes The daily incident solar irradiation per m2 on the collector level is given as:
253
H T GT 10 3 dth ,
254
The daily solar energy on the collector aperture is calculated as:
255
Es Ac H T ,
4
DT2 4
3
,
LT ,
ND
(37)
(38)
(39)
(40)
10
256 257 258 259
The daily stored energy is calculated according to the following equation. This equation takes into account the fluid temperature in the start and in the end of the day. The stored energy inside the tank is assumed to be the useful thermal production in daily basis, according to ISO 9459-2.
260
Est
261
The daily electrical energy production is calculated as:
262
Eel Pel 10 3 dt h ,
263
The daily exergetic output of the system is estimated as:
264
T Z u Eel E st 1 am Ts ,end
265 266
The total exergy of the daily solar irradiation is calculated according to equation 44, using the Petela model:
267
4 T 1 T 4 Z s Ac H T 1 am am , 3 Tsun 3 Tsun
268
The daily thermal efficiency of the system (collector and storage tank) is given as:
269
th, sys
270
The daily electrical efficiency of the system is given as:
271
el , sys
272
The daily total efficiency (thermal and electrical) of the system is given as:
273
tot, sys
274
The daily exergetic efficiency is calculated as:
275
ex,sys
276 277 278
2.2.7 Weather data modeling
f VT c p Ts ,end Ts ,start 10 3 3600
,
(41)
(42)
ND
,
Est , Es
Eel , Es
Est Eel , Es
Zu , Zs
(43)
(44)
(45)
(46)
(47)
(48)
11
279 280 281 282 283 284
The weather data in this work regard the climate conditions of Athens, Greece (37o59’N, 23o44’E). The 21th day of every month is selected as the most appropriate day for examination, according to the ASHRAE standards. For these days, some useful parameters are calculated. The solar declination angle is given according to equation 49 [37]. The parameter “Day” is the day number in the year (for example Day=1 for the 1st of January).
285
23 .45 sin 2
286
The day duration is calculated as [37]:
287
ND
288 289 290
The solar irradiation for every moment is calculated according to the following formula [47]. This formula assumes that the incident solar irradiation on the collector level is a sine function which is a realistic assumption.
291
GT
292 293
The ambient temperature during the day is assumed to be given according to the following equation [48]:
294
295 296 297 298 299 300 301 302 303 304 305
284 Day , 365
2 arccos tan0 tan , 15
10 3 2 ND
t h , sin ND
(49)
(50)
(51)
N th D 2 DR 2 , Tam Tam, m cos 2 (52) 2 24 Equation 52 indicates that the maximum ambient temperature is observed at 14:00, a realistic assumption. It would be useful to state that the time parameter (th) takes values from 0 to ND in equations 51 and 52. Table 3 includes all the important data about the solar potential and the ambient temperature level for all the examined months [49-50]. Also the solar declination angle and the day duration are given for the twelve examined days. Figures 3 and 4 illustrate the incident solar irradiation and the ambient temperature level during the twelves examined days respectively. It is important to state that these weather data correspond to the literature data for Athens climate and they represent typical days for all the months. Thus, it is possible to determine the monthly performance of the collector by examining only one day every month.
306 307 308
Table 3. Weather data for the 21th day of each month [49-50] 12
Month January February March April May June July August September October November December
HT (kWh/m2) 3.308 4.236 5.161 5.829 6.202 6.466 6.649 6.533 5.842 4.697 3.525 2.988
GT,max (W/m2) 531.3 615.6 675.5 692.1 685.1 693.8 732.4 774.5 766.0 686.3 568.5 501.4
Day (-) 21 52 81 111 141 172 202 233 264 294 325 355
δ (ο ) -20.14 -11.23 0.00 11.58 20.14 23.45 20.44 11.75 -0.20 -11.75 -20.44 -23.45
ND (h) 9.78 10.81 12.00 13.23 14.22 14.64 14.26 13.25 11.98 10.75 9.74 9.36
Tam,m (K) 281.61 282.41 285.25 289.58 294.18 297.97 299.71 299.03 296.02 291.69 286.94 283.33
DR (K) 7.67 8.21 9.17 10.36 11.45 12.17 12.29 11.78 10.77 9.57 8.45 7.77
309 800
21ᵗʰ January 21ᵗʰ February
700
GT (W/m2)
21ᵗʰ March
600
21ᵗʰApril
500
21ᵗʰ May 21ᵗʰ June
400
21ᵗʰ July
300
21ᵗʰ August 21ᵗʰ September
200
21ᵗʰ October
100
21ᵗʰ November 21ᵗʰ December
0 0 310 311
3
6
9
12
15
18
21
24
Hours Figure 3. Daily incident solar irradiation for all the examined months
13
21ᵗʰ January 21ᵗʰ May 21ᵗʰ September
21ᵗʰ February 21ᵗʰ June 21ᵗʰ October
21ᵗʰ March 21ᵗʰ July 21ᵗʰ November
21ᵗʰApril 21ᵗʰ August 21ᵗʰ December
310
305
Tam (K)
300 295 290 285
280 275 0
3
6
9
12
15
18
21
24
Hours
312 313
Figure 4. Daily ambient temperature for all the examined months
314 315 316 317 318 319 320 321 322 323 324
2.3 Followed methodology In this subsection, the main information about the followed methodology is given. The equations of the subsection 2.2 are utilized in the developed thermal model which is written EES (Engineering Equation Solver) [51]. The water properties have been taken by the EES libraries [52], while the nanofluid properties have been calculated using the equations 24-27 and all the properties are included in table 2. The nanofluid concentration is examined up to 4%, a reasonable range which is usually selected in similar studies. Important simulation parameters are included in table 4. The volumetric flow rate is selected to be 3 L/min for the majority of the examined cases and equation 53 shows the way that this parameter is connected with the mass flow rate in the developed modeling:
325
Vc L / min
326 327 328 329 330 331 332 333 334
At this point, it is important to indicate the range of the parameters that have been examined parametrically. The working fluid inlet temperature is examined from the ambient temperature in every case up to 360 K. The storage tank volume is examined from 50 L up to 300 L with step equal to 50 L. The volumetric flow rate is examined from 0.5 L/min up to 4 L/min with step equal to 0.5 L/min. These parameters have been examined in the parametric analysis of subsection 3.1. It is important to state that in the comparison between water and nanofluids, the volumetric flow rate has been kept constant and not the mass flow rate, in order the variation in the fluid density to be taken into account.
mc
f
1000 L / m3 60 s / min , `
(53)
14
335 336 337 338 339 340 341 342
In the simulation of the time dependent problem, the integrated system (collector and storage tank) are examined during the day hours, with the parameter t h to vary from 0 to ND. During the day, there is no thermal load and all the useful heat production is stored in the tank. In the end of the day, all the stored useful energy is evaluated, as ISO 9459-2 indicates. More specifically, equation 41 is used for the useful thermal output determination. In the simulation of the daily performance, the differential equations which are associated with the storage tank stratification are solved by using a usual discretizing method, as equation 54 shows:
343
T T NEW T OLD , t t
344 345 346
In this study, the time step (Δt) of solution procedure is selected to be 30 s, after a simple sensitivity analysis. In the start of the day, the fluid inside the storage tank is assumed to have temperature equal to the ambient.
347
Table 4. Reference values of various parameters Parameter Value Storage tank thermal loss coefficient (UT) 0.5 W/m2K Sun temperature (Tsun) 5770 K Athens latitude (φ0) 37.97ο Incident solar irradiation (GT) 800 W/m2 Flow rate (Vc) 3 L/min Wind speed (Vw) 1.3 m/s Ambient temperature (Tam) 300 K
(54)
348 349 350 351 352 353 354 355 356 357 358 359 360
2.4 Validation of the developed model The developed thermal model is validated with the literature study in Ref. [30]. In this study, the authors examined experimentally and numerically a hybrid PV, with the same characteristics as in table 1. In this subsection, the comparison between the experimental results of Ref [40] and the results of developed thermal model of this study is given. Figures 5, 6 and 7 show the comparison between this study and Ref [40] for various water inlet temperatures. It is obvious that the results for the thermal efficiency (figure 4), the electrical efficiency (figure 5) and the total efficiency (figure 6) validate the accuracy of the developed thermal model. More specifically, the mean deviation of thermal efficiency is about 2.3%, of the electrical efficiency 1.3% and of the total efficiency 1.8%; low values which clearly indicate the adoption of the developed thermal model as reliable.
15
0,6 0,5
ηth
0,4 0,3
This study
0,2
Literature
0,1 0,0 0
0,01
0,02
0,04
0,05
0,06
0,07
0,08
(Tin-Tam)/GT
361 362
0,03
Figure 5. Thermal efficiency comparison between this study and the literature 0,14 0,13
This study Literature
ηel
0,12 0,11 0,10
0,09 0
0,01
0,02
0,04
0,05
0,06
0,07
0,08
(Tin-Tam)/GT
363 364
0,03
Figure 6. Electrical efficiency comparison between this study and the literature 0,8 0,7
0,6
ηtot
0,5 0,4
This study
0,3
Literature
0,2 0,1 0,0 0
365 366
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
(Tin-Tam)/GT Figure 7. Total efficiency comparison between this study and the literature 16
367 368 369 370 371 372 373 374 375 376
3. Results 3.1 Parametric analysis of the solar collector In this subsection, the hybrid PV collector is examined parametrically in order to determine its performance under various operating cases. The preliminary results for operation with water as working fluid were presented in subsection 2.4. The first investigated parameter in subsection 3.1 is the Cu concentration (φ) on the collector performance. Figures 8 to 11 are devoted for this investigation by giving the thermal, the electrical, the total and the exergetic performance of the collector for various inlet temperatures and nanoparticle concentrations. The flow rate is equal to 3 L/min for all the cases of figure 8 to 11.
377 378 379 380 381 382 383 384 385
Figure 8 illustrates the thermal efficiency of the solar collector for inlet temperatures from 300 K to 360 K and for concentration rations of Cu from 0% to 4%. It is obvious that higher concentration increases the thermal performance of the collector. However, after 2% concentration, the enhancement is very low. The same results can be extracted by figure 9 for the electrical efficiency, by figure 10 for the total efficiency and by figure 11 for the exergetic performance. Thus, the concentration of 2% can be selected as the most suitable. It is useful to be said that higher concentration leads to higher operational cost and thus the lowest concentration of Cu which leads to high performance have to be selected.
386
0,7
Tin = 300 K
Tin = 310 K
Tin = 320 K
Tin = 340 K
Tin = 350 K
Tin = 360 K
Tin = 330 K
0,6
ηth
0,5 0,4 0,3 0,2 0,1 0,0 0
387 388 389
0,01
0,02
0,03
0,04
φ Figure 8. Collector thermal efficiency with the nanoparticle concentrations for various inlet temperatures
17
0,140
Tin = 300 K
Tin = 310 K
Tin = 320 K
Tin = 340 K
Tin = 350 K
Tin = 360 K
Tin = 330 K
0,135 0,130
ηel
0,125 0,120 0,115 0,110 0,105 0,100 0
0,01
0,03
0,04
φ
390 391 392
0,02
Figure 9. Collector electrical efficiency with the nanoparticle concentrations for various inlet temperatures
393
0,8
Tin = 300 K
Tin = 310 K
Tin = 320 K
Tin = 340 K
Tin = 350 K
Tin = 360 K
Tin = 330 K
0,7 0,6
ηtot
0,5 0,4 0,3 0,2 0,1 0,0 0
394 395 396
0,01
0,02
0,03
0,04
φ Figure 10. Collector total efficiency with the nanoparticle concentrations for various inlet temperatures
397
18
0,18
Tin = 300 K
Tin = 310 K
Tin = 320 K
Tin = 340 K
Tin = 350 K
Tin = 360 K
Tin = 330 K
ηex
0,17
0,16
0,15
0,14 0
0,01
0,02
0,03
0,04
φ
398 399 400
Figure 11. Collector exergetic efficiency with the nanoparticle concentrations for various inlet temperatures
401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416
Figure 12 depicts the efficiency comparison between and nanofluid (2%). This nanofluid [water + Cu (φ=2%)] will be used in the following analysis and will be called simply nanofluid. The flow rate is equal to 3 L/min for all the examined cases in figure 12. It is obvious that thermal (Figure 12a), electrical (Figure 12b) and total (Figure 12c) efficiencies are getting lower for higher inlet temperatures. Nanofluid leads always to higher performance with the higher enhancement to be observed in lower temperatures. Moreover, figure 12d proves that nanofluid leads to higher exergetic performance for all the examined inlet temperatures. It is interesting to state that the optimum inlet temperature exergetically for both water and nanofluid is about 320 K. This result indicates the use of the present hybrid PV in applications which demand useful heat close to this temperature level. This means that hybrid PV is ideal solution for applications as space heating and domestic hot water production for example. Equations 55 to 58 give the thermal and electrical efficiency for the two examined working fluids. More specifically, these equations have been created by approximating the curves of figures 12a and 12b with polynomials. The R2 in these approximations is close to 1; fact that proves the suitable fitting.
417
th water 0.5626 5.8285
(55)
418
2 Tin Tam Tin Tam 0.01610 , th nanofluid 0.5982 6.1289 GT GT
(56)
419
el water 0.1339 0.4018
Tin Tam T T 2 0.01417 in am , GT GT
Tin Tam , GT
(57)
19
420
Tin Tam , GT
el nanofluid 0.1363 0.4310
(58)
421 422 423 424
Figure 12. Collector performance operating with water and nanofluid a) Thermal efficiency b) Electrical efficiency c) Total efficiency d) Exergetic efficiency
425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441
Figure 13 illustrates the collector performance for various flow rates. This figure regards the operation with nanofluid. It is essential to state that the flow rate of 3 L/min has been used up to this point. According to figure 13a, the thermal efficiency is getting greater with higher flow rate and 3 L/min is a satisfying value for achieving high performance. Higher flow rate leads to lower mean fluid temperature and consequently to lower absorber temperature. This situation leads to lower thermal losses and the thermal efficiency is finally getting higher. Similar results are obtained for the electrical efficiency in figure 13b. Higher flow rate leads to higher amount of cooling fluid to flow and higher amounts of heat are taken from the system; fact that increases the performance of the PV cell. The flow rate of 3 L/min is also a satisfying value for taking an adequate electrical output. The total efficiency (figure 13c) has similar behavior with the thermal and the electrical efficiency. On the other hand, the exergetic efficiency curves in figure 13d seem to be totally difference. The curves of 320 K leads to higher exergetic performance for all the flow rates, while the curve of 360 K leads to the lowest exergetic performance due to the extremely low thermal performance in this inlet temperature. For the inlet temperature levels of 320 K, 340 K and 360 K, higher flow rate leads to higher exergetic performance. Only for 300 K 20
442 443 444
higher flow rate decreases the exergetic performance. In any case, the flow rate of 3 L/min can be assumed to be a suitable selection exergetically because the majority of the operation cases (inlet temperature levels) operate ideally with this flow rate.
445 446 447 448
Figure 13. Collector performance operating with nanofluid (φ=2%) for various flow rates and inlet temperatures a) Thermal efficiency b) Electrical efficiency c) Total efficiency d) Exergetic efficiency
449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464
3.2 Daily performance of the solar collector during the year In this subsection, the daily performance of the hybrid PV coupled with a storage tank is investigated, Various storage tanks from 50 L to 300 L are examined and they are evaluated with energetic and exergetic criteria. Water and nanofluid are both examined under the same operating conditions in order to determine the monthly and yearly enhancement for operation with nanofluid. More specifically, one typical day for every month is examined and by using twelve typical days the yearly performance is found. Figures 14 shows the yearly thermal, electrical and exergetic output for various storage tank volumes when the collector operates with water. Higher storage tank volume increases the electrical and the thermal output. However, the exergetic efficiency is maximized for the storage tank of 150 L and thus this storage tank can be selected as the most appropriate solution. Moreover, the mean temperature inside the storage tank in the end of the day is depicted in the same figure. Higher storage tank volume leads to lower mean temperature and for the case of 150 L, this temperature is about 315 K. This temperature level is ideal for application as space heating and domestic hot water production and so the selection of the 150 L tank is validated 21
2000
340
1800
335
1600
330 Yearly thermal output Yearly electrical output Yearly exergetic output Mean heat temperature
1400 1200 1000
320 315
800
600
310
400
305
200
300 50
100
150
200
250
300
V (L)
471 472 473
325
Mean tank temperature (K)
again. Figure 15 shows the monthly thermal, electrical and exergetic output of the integrated system operating with water for the storage tank of 150 L. It is clear that the performance of the system is higher in the summer months due to the higher solar potential in this period. Moreover, the thermal performance is the greatest useful output and the electrical output is the lowest. The exergetic output is always over the electrical output but with a relative low difference.
Yearly outputs (kWh)
465 466 467 468 469 470
Figure 14. Water case yearly outputs (thermal, electrical, exergetic) and mean storage tank temperature in the end of the day for various storage tank volumes
V = 150 L
December November October September August July June May April March February January 0,0
1,0
2,0
3,0
4,0
5,0
6,0
Daily output (kWh) 474 475 476
Daily exergetic output
Daily electricity output
Daily thermal output
Figure 15. Monthly useful outputs for storage tank of 150 L with water as working fluid 22
2000
340
1800
335
1600
330
Yearly thermal output Yearly electrical output Yearly exergetic output Mean heat temperature
1400 1200 1000
325 320
800
315
600 400
310
200
305 50
100
150
200
250
Mean tank temperature (K)
Figures 16 and 17 regard operation with nanofluid. Similar results are extracted between figures 14 and 16 with the storage tank volume of 150 L to be again the optimum solution exergetically. Moreover, in this case the mean nanofluid temperature is about 317 K, a value close to 315 K of the water case. Figure 17 shows similar results as figure 15 with thermal efficiency to be the highest useful output in yearly basis. Moreover, it is useful to be said that July is the month with the highest useful outputs, a result which is obtained both by figures 15 and 17.
Yearly outputs (kWh)
477 478 479 480 481 482 483
300
484
V (L)
485 486 487
Figure 16. Nanofluid case yearly outputs (thermal, electrical, exergetic) and mean storage tank temperature in the end of the day for various storage tank volumes
V = 150 L December November October September August July June May April March February January 0,0
1,0
2,0
3,0
4,0
5,0
6,0
Daily output (kWh) Daily exergetic output
Daily electricity output
Daily thermal output
488 489 490
Figure 17. Monthly useful outputs for storage tank of 150 L with nanofluid as working fluid 23
491 492 493 494 495 496 497 498 499 500 501 502 503
Table 5 includes the results of yearly performance for the examined storage tank volumes and for the cases of water and nanofluid. Moreover, figure 18 depicts the enhancements in thermal, electrical and exergetic efficiency for the case of nanofluid compared to water case. Both table 5 and figure 18 prove that higher storage tank leads to higher yearly enhancement. The maximum thermal and electrical outputs are observed for the tank of 300 L, while the higher exergetic efficiency for the storage tank of 150 L. The thermal enhancement of the thermal efficiency is ranged from 1.80% to 5.42%, for the electrical efficiency from 1.41% to 3.34% and for the exergetic efficiency from 2.05% to 3.34%. The enhancement in the electrical efficiency is the lowest compared to the other enhancements, a result which proves that the use of nanofluids mainly leads to the thermal enhancement of the collector performance. For the case of 150 L, which is the optimum exergetically, the thermal enhancement is 4.35%, the electrical is 1.49% and the exergetic is 3.19%.
504
Table 5. Yearly useful outputs for water and nanofluid Storage tank volume – V (L) Yearly output Fluid (kWh) 50 100 150 200 250 300 Water 911 1325 1548 1687 1781 1849 Thermal Nanofluid 927 1372 1615 1768 1873 1950 Water 411 442 459 469 475 480 Electrical Nanofluid 417 449 466 476 483 488 Water 534 580 588 587 583 579 Exergetic Nanofluid 544 596 607 607 603 598
505
Yearly enhancement
6%
Yearly thermal enhancement Yearly electrical enhancement Yearly exergetic enhancement
5%
5,42%
5,19% 4,86%
4,35%
4%
3,51%
3,19%
3,28%
3,35%
3,34%
2,85%
3% 2,05%
2% 1,80%
1,41%
1,42%
1,49%
1,56%
1,63%
1,68%
50
100
150
200
250
300
1% 0%
506
V (L)
507 508
Figure 18. Yearly thermal, electrical and exergetic enhancement with the use of nanofluid
509 510 511
In the next part of this analysis, the daily performance for July is presented. Figure 19 illustrates the daily variation of the mean storage tank temperature level for three storage tanks volumes (50 L, 150 L, and 300 L). Moreover the incident solar 24
irradiation on the collector level is depicted in the same figure, as well as the ambient temperature. Results for water and nanofluid operation are given in this figure with the nanofluid to reach to higher temperature levels. This result can be explained by two reasons. The first one is the lower specific thermal capacity of the nanofluid (see table 2) and the second the higher performance for operation with nanofluid (see figure 12). Moreover, figure 19 proves that higher storage tank leads to lower temperature level inside it, a result which also has been extracted from figures 15 and 17 for yearly operation. For the storage tank of 50 L, the nanofluid temperature in the end of the day is 352.8 K, while the water case it is 351.5 K. For the storage tank of 150 L, the nanofluid and the water temperatures are 332.3 K and 330.7 K respectively, while for 300 L are 319.9 K and 318.8 K respectively.
Solar irradiation - GT (W/m2)
Solar irradiation V = 150 L (Water) V = 150 L (Nanofluid)
Ambient temperature V = 300 L (Water) V = 300 L (Nanofluid)
V = 50 L (Water) V = 50 L (Nanofluid)
800
360
700
350
600
340
500
330
400 320
300
310
200
Temperature (K)
512 513 514 515 516 517 518 519 520 521 522
300
100 0
290 4
6
8
10
12
14
16
18
20
Daily hours 523 524
Figure 19. Daily storage tank temperature variation in July
525 526 527 528 529 530 531 532 533 534 535 536
Figure 20 shows the daily variation of the thermal and electrical outputs, as well as the daily variation of the electrical and thermal efficiency of the collector. It is essential to state that the thermal efficiency of the collector takes into account the hybrid PV only, while the thermal efficiency of the system, which has been examined in the previous figures, takes into account also the storage tank. Three storage tanks (50 L, 150 L and 300 L) are examined in these figures for operation with water and nanofluid. Figures 20a, 20b and 20c are devoted for water case and figure 20d, 20e and 20f for nanofluid case. Similar results can be taken compared the figures 20a, 20b and 20c to 20d, 20e and 20f respectively, with the performance with nanofluid to be higher. The electrical performance is similar for the three examined storage tank volumes. However, the thermal efficiency is influenced by the storage tank volume by a great way. The blue lines in figures 20a, 20b and 20c have extremely different 25
537 538 539 540 541 542 543
behavior. The slopes of these curves are more intense in cases with lower storage tank volume. Lower storage tank volume leads to higher fluid temperature level, in a relative small time period, and thus the thermal performance is getting lower. This result makes the system to stop producing useful heat earlier in the cases of smaller storage tank. More specifically, the system stop producing useful thermal output at 15:00 for the storage tank of 50 L, at 17:00 for 150 L and at 18:00 for 300 L, while the electrical production stops about at 19:00, close to the sunset, in all these cases.
544 545 546
Figure 20. Daily performance of the system in July for operation with water (a, b, c) and with nanofluid (d, e, f)
547 548 549 550 551
In the last part of this subsection, monthly results about the system performance for the storage tank of 150 L are given. Table 6 includes thermal, electrical, total and exergetic efficiency for water and nanofluid cases. These results regard monthly performance, as well as the weight average yearly performance. The thermal efficiency is varied form 40% in June to 45.5% to December with yearly mean value 26
552 553 554 555 556 557 558 559 560 561 562
equal to 42.0% for water case. For nanofluid, the mean value is 43.8% with maximum 47.7% in December and minimum 41.6% in June. The electrical efficiency is varied form 12.2% in June to 12.7% to December with yearly mean value equal to 12.4% for water case. For nanofluid, the mean value is 12.6% with maximum 12.9% in December and minimum 12.4% in June. The total efficiency is varied form 52.2% in June to 58.2% to December with yearly mean value equal to 54.4% for water case. For nanofluid, the mean value is 56.4% with maximum 60.5% in December and minimum 54.0% in June. The exergetic efficiency is maximized in August with 18.5% for water and 19.1% for nanofluid. It is minimized in January with 14.8% for water and 15.3% for nanofluid, while the mean yearly value is 17.1% for water and 17.7% for nanofluid.
563 564
Table 6. Monthly efficiencies comparison between water and nanofluid for the storage tank of 150 L Water Nanofluid Month ηth,sys ηel,sys ηtot,sys ηex,sys ηth,sys ηel,sys ηtot,sys ηex,sys 0.448 0.126 0.574 0.148 0.469 0.128 0.600 0.153 January 0.433 0.125 0.558 0.154 0.453 0.127 0.580 0.159 February 0.420 0.124 0.544 0.162 0.438 0.126 0.564 0.167 March 0.409 0.124 0.533 0.170 0.426 0.125 0.552 0.175 April 0.402 0.123 0.525 0.176 0.419 0.125 0.543 0.181 May 0.400 0.123 0.522 0.181 0.416 0.124 0.540 0.186 June 0.402 0.122 0.525 0.184 0.419 0.125 0.543 0.190 July 0.410 0.123 0.533 0.185 0.427 0.125 0.553 0.191 August 0.124 0.546 0.180 0.440 0.126 0.566 0.186 September 0.421 0.435 0.125 0.561 0.171 0.456 0.127 0.583 0.176 October 0.126 0.576 0.158 0.471 0.128 0.599 0.163 November 0.449 0.127 0.582 0.149 0.477 0.129 0.605 0.154 December 0.455 0.420 0.124 0.544 0.171 0.438 0.126 0.564 0.177 Yearly
565 566 567 568 569 570 571 572
Figure 21 depicts the monthly enhancements for the four examined efficiencies. It is generally obvious that the enhancements are greater in winter months from October to February. At these months, the system output is relative low (see figures 15 and 17) and so the enhancement margin is greater by the use of nanofluids at the period. Only the exergetic efficiency presents a small different performance with also relative high enhancement in August and in September. In any case, the enhancement is similar among the months and close to the mean yearly value. So, it is proved that nanofluids can increase the hybrid PV performance during all the year period.
27
Thermal
Electrical
Total
Exergetic
Monthly enhancement
6% 5% 4% 3%
2% 1% 0% 1
2
3
4
5
6
7
8
9
10
11
12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 573
Months
574 575
Figure 21. Monthly enhancement with the use of nanofluid for the storage tank of 150 L volume
576 577 578 579 580 581 582 583 584
4. Conclusions In this study, a hybrid PV operating with water and nanofluid (Water + Cu) is examined in monthly and yearly basis. A detailed thermal model for the collector is developed in EES and it is validated with literature experimental results. The nanofluid is found to lead to higher thermal performance in all the operating conditions. The mainly examined nanofluid concentration is 2% and the flow rate is 3 L/min, two parameters which are also examined parametrically. The performance analysis proved high thermal and electrical enhancement with nanofluid utilization when the collector operates with lower inlet temperatures.
585 586 587 588 589 590
In the yearly performance of the collector integrated with storage tank, the storage tank volume of 150 L was found to be the most suitable choice exergetically. Moreover, it is found that higher storage tank volume leads to higher thermal and electrical performance but the thermal output is given in lower temperature levels. With the storage tank of 150 L, the useful heat is produced close to 315 K; a satisfying temperature level for space heating and domestic hot water purposes.
591 592 593 594 595 596 597 598
For the storage tank of 150 L, the yearly thermal enhancement is found to be 4.35%, while the electrical and the exergetic is calculated at 1.49% and 3.19% respectively. More specifically, the mean yearly thermal efficiency reach to 43.8% with the use of nanofluid compared to 42.0% in water case. The electrical efficiency increases from 12.4% to 12.6%, the total efficiency from 54.4% to 56.4% and the exergetic efficiency from 17.1% to 17.7%. In the monthly analysis, it is found that higher thermal and electrical enhancements are achieved in winter because in this time period the thermal output is lower and there is great margin for improvement. 28
599 600 601 602 603 604
Finally, it can be said that the examined hybrid PV with a storage tank can produce thermal energy of 1548 kWh with water and 1615 kWh with nanofluid in a yearly basis. The electrical production is calculated to 459 kWh with water and 466kWh with nanofluid. These results indicate the use of nanofluid in hybrid PV, especially in applications with high thermal demand because the thermal enhancement is obviously higher than the electrical.
605 606
Nomenclature Ac Collecting area, m2
607
a1
1st coefficient of equation 20, -
608
a2
2nd coefficient of equation 20, -
609
b
Reference temperature coefficient of PV, K-1
610
cp
Specific heat capacity coefficient, J/kgK
611
DT
Storage tank diameter, m
612
DR
Daily range, K
613
din
Inner tube diameter, m
614
dout
Outer tube diameter, m
615
E
Daily energy, kWh
616
Ex
Exergy flow, W
617
HT
Daily incident solar irradiation on the collector level, kWh/m2
618
GT
Incident solar irradiation, W/m2
619
GT,max Maximum daily solar irradiation, W/m2
620
g
Gravity acceleration ( = 9.81 m/s2)
621
hf
Heat transfer coefficient in the working fluid, W/m 2K
622
hin
Heat convection coefficient from plate to cover, W/m2 K
623
hout
Heat convection coefficient from cover to ambient, W/m2 K
624
k
Thermal conductivity, W/mK
625
L
Collector length, m
626
LT
Storage tank height, m
627
mc
Mass flow rate in the collector, kg/s
29
628
N
Number of risers, -
629
ND
Day duration, h
630
Nu
Nusselt, -
631
Pel
Electricity production, W
632
PF
Packing factor, -
633
Q
Heat, W
634
Ra
Raleigh, -
635
Re
Reynolds, -
636
T
Temperature, K
637
t
Time, s
638
Th
Daily time, h
639
UT
Storage tank thermal loss coefficient, W/m2 K
640
V
Storage tank volume, L
641
Vc
Collector flow rate, L/min
642
VT
Storage tank volume, m3
643
Vw
Wind speed, m/s
644
Z
Daily exergy, kWh
645 646
Greek symbols α Absorbance, -
647
β
Thermal expansion coefficient, K-1
648
βcol
Collector slope, o
649
δ
Distance, m
650
Δt
Time step, s
651
ε
Emittance, -
652
η
Efficiency, -
653
μ
Dynamic viscosity, Pa s
654
ν
Kinematic viscosity, m2/s
30
655
ρ
Density, kg/m3
656
σ
Stefan–Boltzmann constant [= 5.67 ∙ 10-8 W/m2 K4]
657
τ
Cover transmittance, -
658
φ
Nanoparticle concentration, -
659
φ0
Latitude, o
660 661
Subscripts and superscripts Air Ambient air
662
am
663
am,m Mean ambient
664
AT1
Outer area of the first zone of storage tank
665
AT2
Outer area of the second zone of storage tank
666
AT3
Outer area of the third zone of storage tank
667
back
Back side of the collector
668
bs
Base fluid
669
c
Cover
670
cell
PV cell
671
el
Electrical
672
el,sys System electrical
673
ex
674
ex,sys System exergetic
675
f
Fluid
676
fm
Mean fluid
677
in
Inlet
678
ins
Insulation
679
loss
Thermal losses
680
NEW New time step
681
nf
Ambient
Exergetic
Nanofluid
31
682
np
683
OLD Old time step
684
out
Outlet
685
p
Plate
686
pc
Plate-cover
687
PV
Photovoltaic cell
688
ref
Reference
689
s
Solar
690
sky
Equivalent Sky
691
st
Stored
692
sun
Outer layer of Sun
693
s1
First zone of storage tank
694
s2
Second zone of storage tank
695
s3
Third zone of storage tank
696
s,end Mean storage tank temperature in the end of day
697
s,start Mean storage tank temperature in the start of day
698
tot,sys System total
699
th
700
th,sys System thermal
701
top
Top side of the collector
702
tot
Total
703
u
Useful
704 705
Abbreviations CPC Compound parabolic concentrator
706
PV
Photovoltaic
707
PVT
Thermal Photovoltaic
Nanoparticle
Thermal
708 709 32
710 711 712
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