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Evaluating the environmental parameters affecting the performance of photovoltaic thermal system using nanofluid
Applied Thermal Engineering 115 (2017) 178–187
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Evaluating the environmental parameters affecting the performance of photovoltaic thermal system using nanofluid Y. Khanjari, A.B. Kasaeian ⇑, F. Pourfayaz Department of Renewable Energies, Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran
h i g h l i g h t s Using nanofluid in photovoltaic thermal system is studied theoretically. The examined factors consist of inlet fluid temperature and absorbed solar radiation. The efficiency, heat transfer coefficient and temperature in different sections are investigated. Al2O3-water nanofluid has better performance than pure water.
a r t i c l e
i n f o
Article history: Received 27 September 2016 Revised 19 November 2016 Accepted 20 December 2016 Available online 28 December 2016 Keywords: PV/T Al2O3-water nanofluid CFD Solar radiation
a b s t r a c t PV/T is a hybrid system which combines photovoltaic cells and solar collector. It can produce renewable electricity and heat, simultaneously. The aim of the present work is to study the effects of two environmental parameters on the performance of system. Also, the performance of pure water and Al2O3-water nanofluid are compared. The conduction and convection heat transfer are considered by CFD method. The mass, momentum, and energy equations are solved using the ANSYS Fluent. The second order upwind is selected as an interpolation scheme and the pressure-based solver is used for this laminar model. The pressure-velocity coupling method is the SIMPLE. Also, the gradients of the solution variables are determined by the least square cell based. The effects of solar radiation and fluid inlet temperature on the performance are modeled. Increasing the solar radiation reduces electrical efficiency; then, the thermal efficiency becomes fixed after a first rise. Nevertheless, the thermal efficiency remains fixed; the electrical efficiency decreases with increasing the fluid inlet temperature. The findings indicate that the heat transfer coefficient and the efficiency of Al2O3-water nanofluid are greater than pure water. The numerical model is validated by comparing the simulation results with the experimental data in the literature. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Energy consumption has a significant effect on the human interactions with the surrounding environment. Whereas, the growth of the world energy demand in recent decades is very large. Solar energy is an available and sustainable choice to meet the energy demand in the future. Moreover, by substituting solar energy, the challenges including finitude of fossil fuels and the environmental pollution related to conventional resources are eliminated. A report of the International Energy Agency suggests that a quarter of the energy usage and supply may be derived from solar power by 2050 [1].
⇑ Corresponding author. E-mail address: [email protected] (A.B. Kasaeian). http://dx.doi.org/10.1016/j.applthermaleng.2016.12.104 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
The solar energy can be applied in two different categories: solar thermal systems and photovoltaics. In a solar thermal system, solar energy converts to thermal energy, whereas in a photovoltaic case, electricity is directly produced from solar radiation. In a photovoltaic module, the electrical efficiency of the system decreases as the temperature of the module increases. In fact, a photovoltaic system uses a certain part of solar radiation for electricity production and the remainder is wasted in the form of heat. Therefore, with the circulation of a cold fluid through the system, the waste heat of photovoltaic module can be removed; consequently, higher electrical efficiency may be obtained. The combination of thermal and electrical sections constructs a new hybrid device called ‘‘photovoltaic thermal” energy system (PV/T). Using this combination, cogeneration of renewable power and heat is happened in a PV/ T. Plus the greater energy performance of the system, the space occupied by a hybrid system is reduced.
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Nomenclature P A Cp G h _ m P PV U T wt
packing factor area (m2) specific heat capacity (kJ/kg K) solar radiation intensity (W/m2) convection heat transfer coefficient (W/m2 K) mass flow rate (kg/s) pressure (N/m2) photovoltaic fluid velocity (m/s) temperature (K) weight fraction
Subscript f nf p ref ave cell i g atm
base fluid nano fluid nano particle reference average solar cell counter glass cover atmosphere
Many works have been carried out on the research and technological development of PV/T systems [2–6]. Also, some experimental tests for design development, theoretical methods for improving the thermal and electrical performance, and efforts for commercialization of PV/T were done in this area [7–9]. Many experimental and theoretical studies have been carried out regarding photovoltaic thermal collectors. The performance of nine different PV/T systems were considered and compared by Zondag et al. [10]. In Hong Kong, Chow et al. [11] examined two glazed and unglazed PV/T systems, with the construction design of sheet and tube. Their investigations were done based on both first and second law of thermodynamics. The results of energy analysis revealed that the glazed design was always appropriate, whereas the finding of their exergy analysis claimed that the use of unglazed design was more optimized. A thermal model was developed by Siddiqui et al. [12] to consider PV modules with and without cooling section. The effect of the environmental factors such as ambient temperature and absorbed solar radiation on the performance of PV panels were analyzed. Also, the effects of the inlet velocity, inlet temperature, and thermal contact resistance were studied. A full-scale BIPV/T collector was investigated by Corbin and Zhai [13] to determine the effects of utilizing cooling system on both electrical and thermal efficiency. Computational fluid dynamics (CFD) method was used to simulate the represented system. Additionally, the variations of some factors including cell temperature, outlet temperature, and solar insolation were examined via implementing a parametric analysis. A simulation model was developed by Cerón et al. [14] in which different heat transfer mechanisms were simultaneously taken into account. In this study, the fluid flow pattern, the absorber temperature field and the distribution of heat flux were studied. The heat transfer results were validated against common experimental correlations available in the literature, and the Nusselt number for water fluid inside the tubes was derived. Perino et al. [15] installed experimental PV/T prototypes, and represented a simulation model for the mentioned PV/T systems in the TRNSYS, for both steady-state and transient conditions. The energetic and exergetic performance of PV/T system was evaluated. A reference efficiency of 72.8% and electrical
est obs x n MAPE k g d Re Pr Gr Ra Ri
estimated observed value (observed or estimated) number of the values mean absolute percentage error conductivity (W/m K) gravity acceleration (N/kg) diameter (m) Reynolds number Prandtl number Grashof number Rayleigh number Richardson number
Greek symbols b temperature coefficient (K1) l viscosity (Pa s) h tilt angle of setup u volume fraction g efficiency q density (kg/m3) s transmitivity
efficiency of 10.5% were obtained using the mentioned PV/T system. Spertino et al. [16] investigated a mono-crystalline PV module to examine the effect of using water-cooling on the performance. Also, a theoretical model considering both thermal and electrical was represented. Using a low weight plastic-laminated sandwich, instead of glass, was tested. The results indicated that working fluid must be utilized according to the location and the season of the year. Tse et al. [17] evaluated the advantages of using water PV/T system in the office scale building. This system supported the electricity and hot water demand by a computer program. An economic analysis was also carried out to consider the time value of money. Study of a bi-fluid PV/T system was implemented by Jarimi et al. [18], and the two-dimensional steady-state model was performed using MATLAB. The tests were conducted in steady-state conditions under a solar simulator at the Solar Energy Research Lab UiTM Perlis, Malaysia. Three fluid modes of air, water, and combination of air-water were operated in the tests. Many experimental and numerical investigations have been done in the literature to improve the performance of the conventional coolants such as water or air used in PV/T systems. Using nanofluids as a coolant in PV/T systems has not been completely developed. The heat transfer performance can be enhanced by improving the thermo-physical properties, and dispersing nanoparticles lead to the increase in thermal conductivity [19]. Thus, utilizing nanofluid, instead of conventional fluids such as water, can be an advantageous option. It shall be noted that many original types of research have been implemented on the influence of using nanofluid in solar systems [20–27]. However, a few number of theoretical studies focused on using nanofluids in PV/T systems, among which we can point to some relevant references such as [28,29]. Sardarabadi et al. [28] investigated the effect of using SiO2 nanoparticles in a PV/T system experimentally. The electrical and thermal efficiencies were considered based on the first and second laws of thermodynamics. The results indicated that the thermal energy efficiency of using 1 wt% and 3 wt% nanofluids were increased by 7.6% and
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12.8%, respectively. The potential for size reduction of flat plate solar thermal collector and its proportional energy and cost saving in the case of using different nanofluids was studied by Faizal et al. [30]. The application of Al2O3, SiO2, TiO2, CuO nanoparticles was analyzed in this work. They declared that the higher density and lower specific heat of nanoparticles caused a better thermal performance. Mohammad Zadeh et al. [31] represented a numerical methodology for modeling and optimization, in the case of using Al2O3/synthetic oil nanofluid, in a parabolic trough collector. The effects of the volume fraction of nanoparticle on mixed convection heat transfer rate in a fully-developed turbulent flow were considered. In an experimental investigation, the application of Al2O3-waternanofluid in a flat plate solar collector was studied by Yousefi et al. [32]. The variation of two parameters including mass flow rate and nanoparticle mass fraction were analyzed. Their results claimed that adding 0.2% (wt) Al2O3 leads to an efficiency enhancement of 28.3%. The heat transfer and entropy generation of Al2O3-water nanofluid in a flat plate solar collector were examined by Mahian et al. [33]. They considered the effects of tube roughness, nanoparticle diameter, and two different thermo-physical models. The output data were represented in the form of Nusselt number, heat transfer coefficient, the outlet temperature of the collector, entropy generation, and Bejan number. They concluded that the entropy generation decreases with increasing the volume fraction of the nanoparticle. The mixed convection heat transfer of an Al2O3-waternanofluid system in a horizontal tube with uniform heat flux was considered by Akbari and Behzadmehr [34]. Their results show that increasing the Al2O3 nanoparticles from 2% to 4% causes in heat transfer coefficient rising from 9% to 15%, respectively. In a numerical survey, Tse et al. [17] studied the performance of Al2O3-water nanofluid in a circular tube in constant heat flux. For defining the nanoparticle behavior in the base fluid, both single-phase and two-phase models were applied. The maximum difference between the heat transfer coefficient of the single-phase, and two-phase models were just 11%. The previous research studies in the literature indicate that the previous numerical investigations for PV/T systems were carried out by solving energy balance equations for each particular case. Whereas, the CFD method is rarely used for simulating the behavior of PV/T systems. To conduct a comparative study, the CFD method was applied in the present investigation. As discussed above, only a limited number of experimental works are done about the application of nanofluid in PV/T systems. Utilizing nanofluid instead of pure water was studied numerically in other solar systems such as parabolic trough collectors, solar stills or flat plate collectors [35,36,25,37]. In addition, the effects of two environmental parameters including the absorbed solar radiation and the fluid input temperature on the performance of the system, is focused in the present work. The aim of this work is to study the effects of two environmental parameters on the efficiency and heat transfer performance of a water-cooled PV/T system using the numerical method of CFD. The effects of using Al2O3-water nanofluid, instead of water, as working fluid is also investigated theoretically in the ANSYS Fluent software. Finally, the simulation results are compared with the data of experimental works.
2. Thermo-physical properties Pure water is applied as the base fluid in the current investigation. The thermo-physical properties of water are considered as a function of temperature as followings [38,39]:
qf ¼ 4:48 103 T2 þ 999:9
ð1Þ
lf
ð2Þ
2 ! 1150 690 103 þ ¼ exp 1:6 T T
kf ¼ 8:01 106 T2 þ 1:94 103 T þ 0:563 Cpf ¼ 4:1855 103 0:966185 þ 0:0002874
5:26 !! T þ 100 100
þ ð0:011160 10ð0:036TÞ Þ
ð3Þ
ð4Þ
Adding nanoparticles to base fluid improves the thermophysical properties of the attained nanofluid. To obtain the thermal conductivity of nanofluid, following theoretical model is used [40]:
knf ¼ kf
ks þ 2kf 2ð1 þ bÞ3 ðks kf Þu ks þ 2kf þ ð1 þ bÞ3 ðks kf Þu
ð5Þ
In this conductivity model, the effects of the nanoparticle volume fraction and the properties of the base fluid are considered. The physical principle of the two-phase mixture is used for obtaining the density and specific heat of the nanofluid. The density, viscosity and heat capacity of nanofluid are determined by the following equations [41,42]:
qnf ¼ ð1 uÞqf þ uqs for u < 0:05; lnf ¼ ð1 þ 2:5uÞlf ð1 uÞqf Cpf þ uqs Cps Cpnf ¼ qnf
ð6Þ ð7Þ ð8Þ
As it can be seen in the previous equations, rising the nanoparticles volume fraction results in increasing and decreasing the density and specific heat of nanofluid, respectively. Also, the viscosity and thermal conductivity of nanofluids increase when the volume fraction of nanoparticles increases [43,44]. The thermo-physical properties of Al2O3 are gathered in Table 1 [45]. 3. Numerical modeling The nanofluid flow behavior through a water PV/T system was numerically simulated and compared with pure water. The represented PV/T model is composed of a glazing section, a PV panel and a sheet-and-tube collector with five identical riser tubes. To decrease the computational effort in the modeling process, the number of riser tubes in PV/T model can be reduced into just one, instead of five [46–48]. Therefore, the flow rate in each riser is assumed as 1/5 of the total mass flow rate in the proposed system. Thus, the velocity and temperature distributions can be generalized to whole the system. Consequently, the proposed model consists of a water riser tube and an absorber plate to consider the conduction and convection heat transfer mechanisms. The bodies of the absorber plate and the fluid tube are simulated entirely, whereas the effects of the glazing section and the photovoltaic panel are applied in boundary conditions. The amount of the absorbed solar radiation is mainly related to the transmittance of glass, the absorbtance of the photovoltaic panel and the absorber plate material. The geometry is created in the CATIA software, and the mesh generation and solution analysis are carried out in the ANSYS Workbench. For better understanding, the geometry
Table 1 Values for the thermo-physical properties of Al2O3 nanoparticles. Property
Al2O3 nanoparticles
Density (kg/m3) Conductivity (W/m K) Specific Heat (J/kg K)
3970 40 765
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In the CFD process, the domain of current model is discretized and then the conservation laws are solved by the finite volume method. The pressure-based solver is preferred to the densitybased solver in this work, and the SIMPLE scheme is applied for the velocity–pressure coupling. The selected interpolation scheme for the convection and diffusion terms is the second order upwind. The gradients of the solution variable at the cell center are determined by the least square cell based. The conjugate heat transfer is employed in the CFD procedure. The solution convergence happens whenever the residuals of velocity, continuity, and energy reach below 10e4, 10e3, and 10e6, respectively. The nontransient conservation laws are represented as followings: Continuity Equation Momentum Equation Energy Equation
Fig. 1. Geometry of current study.
rðqnf U nf Þ ¼ 0 r ðqnf U nf U nf Þ ¼ rP þ rs þ qnf g r ðqnf U nf C pnf TÞ ¼ r ðknf rTÞ
To characterize the flow, whether laminar or turbulent, the Reynolds and Grashof numbers are calculated for the forced and natural convection, respectively. Also, the Richardson number expresses whether the fluid flow is natural, forced or mixed. Since the fluid passing tube has low velocity (below 0.1 m/s), the buoyancy force effect is an essential factor in this investigation. Some of the relevant dimensionless numbers for Al2O3-water nanofluid in the volume fractions of 1% and 2% are tabulated in Table 3. It should be notified that the gravitational acceleration can affect the buoyancy force and convection terms. Therefore, the gravitational acceleration shall be activated in the ANSYS Fluent. The gravity acceleration is defined in the form of vectors, as below: Fig. 2. Schematic picture of the whole system.
of current study and a schematic picture of whole system are illustrated in Figs. 1 and 2, respectively. Table 2 represents the related dimensions and the characteristics of the model. The fluid flow is assumed to be steady, incompressible and uniform. The literature review shows that there is only 0.2% discrepancy between the steady and transient solutions [49]. To prevent ineffective calculations, the steady-state condition is chosen for current research. Also, a fully developed laminar flow is taken in the simulation. A thermal equilibrium exists between the base fluid and nanoparticles; therefore, the nanofluid is assumed to be single phase. The mentioned assumption is common in the literature [50–53]. The temperature distribution in the photovoltaic panel and absorber plate is supposed to be approximately the same [54,46].
g x ¼ gSinh gy ¼ 0 g z ¼ þgCosh Finally, it is deduced that the flow regime of this study is laminar and mixed. In the mesh generation procedure, the absorber plate and fluid body are meshed with the sweep and tetrahedrons elements, respectively. Also, an inflation method is applied in the fluid body near the riser wall to provide a boundary layer. Totally, 882,722 elements are generated in the meshing process of whole domain, and a grid study is carried out to prove the accuracy of results. Four different grids with the element numbers of 882,722, 921,507, 1,075,904 and 1,449,128 are evaluated. The maximum outlet velocity, the outlet temperature, and the average heat transfer coefficient are monitored for both pure water and Al2O3-water nanofluid, in each of the mentioned grids. The maximum percent-
Table 2 Dimensions and characteristics for different sections. Risers tubes
Absorber plate
Photovoltaic panel
Number: 5 Thickness: 0.001 (m) Outer diameter: 0.01 (m) Length: 2 (m) Spacing: 0.2 (m)
Length: 2 (m) Width: 1 (m) Thickness: 0.002 (m)
gr = 12% at 0 °C
Glass
Number of cells: 60
Length: 1.64 (m) Width: 0.99 (m) Absorptance: 0.9 Emissivity: 0.88
1
br = 0.0045 °C
Emissivity: 0.88
Table 3 Dimensionless numbers in constant velocity for Al2O3-water nanofluids (Absorbed Radiation on Plate ¼ 570:24 mW2 ; dp ¼ 50 nm; T inlet ¼ 303:15 KÞ. lC p
u (%)
Pr ¼
1 2
3.9321 3.8215
k
V
Re ¼ qlVD
Gr ¼ q
0.06377
965.1246 969.6174
0.9940 1.0023
2
gcoshbðT out T in ÞL3
l2
105
Ra ¼ Gr Pr 105
Gr Ri ¼ Re 2
3.9087 3.8307
0.1067 0.1066
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age of the parameter change due to mesh refinement is just 2.20% [29]. Therefore, the results of different grid sizes are identical approximately. Thus, the grid with 882,722 elements is the most appropriate domain for the present simulation study. To achieve a unique solution in a numerical simulation, the best boundary conditions must be selected appropriately and activated in the ANSYS Fluent. The ‘velocity inlet’ boundary condition is applied to the inlet area of the tube. Also, the fluid inside the tube is incompressible. Thus, the ‘pressure outlet’ boundary condition is utilized at the outlet of the tube. The no-slip wall and impermeable boundary conditions have been specified over the walls. The absorbed heat flux is obtained by the following equation:
Absorbed heat flux on plate ¼ Gt sg að1 gÞ
ð9Þ
The absorbed heat flux is imposed to the wall boundary conditions of the plate in the ANSYS Fluent. The back surface of the absorber plate and the external face of the tube are assumed to be adiabatic. Consequently, the zero heat flux wall boundary condition is used for simulation in the software. Following equations express the boundary conditions at the inlet of the tube in mathematical form:
ux ¼ uin uy ¼ uz ¼ 0 T ¼ Tin In addition, the boundary condition at the outlet of the tube is:
P ¼ Patm ðstatic pressureÞ Furthermore, the following mathematical equations were used as the boundary conditions at the fluid–solid interface:
ux ¼ uz ¼ uy ¼ 0 q ¼ kdT=dz ¼ hðT Tbulk Þ The thermal and electrical efficiencies of the PV/T system can be computed with following equations:
gthermal ¼ P¼
_ w Cpw ðT out T in Þ m Gt AP
APV AP ¼ gref ½1 bðTcell Tref Þ
gPV gelectrical ¼ P:gPV
ð10Þ ð11Þ
Fig. 3. Validation of the PV/T simulation.
ence [55] are entered as the input data for current simulation, while other related factors are kept fixed. As mentioned before, same operational conditions are imposed in the model simulation, such as solar radiation in the range of 470–542 W/m2, the inlet temperature in the range of 32–46 °C, and the mass flow rate of 0.00136 kg/s (all exactly same as Selmi et al.). The outlet water temperature of the system is illustrated versus time of day for both current simulation and data attained in reference [55]. The obtained curves are indicated in Fig. 3 to prove the validation of the present simulation model. It is found that the temperature difference between the water inlet temperature and outlet water temperature is approximately fixed. As it can be seen in Fig. 3, the same trend is obtained for both sets of data. The error formulation of MAPE is computed precisely to find how accurate the results of validation are. In the other words, the difference of present model outputs and the experimental results are evaluated by a statistical test. The MAPE is calculated by the following equations:
ð12Þ ð13Þ
4. Validation Two different sets of data from literature are selected to validate the current numerical study. The first one is related to a flat plate solar energy collector and the second one is allocated to a comparison study between an important heat transfer correlation of Al2O3-water nanofluid in a tube and riser tube of the present simulation model. 4.1. Water PV/T The numerical CFD model of the PV/T system is validated by comparing the current results with the findings of a research in literature [55]. In fact, the model outputs are compared with an experimental set of data measured in a real system. In order to build a correct method of validation, the current basic simulation model is driven with new set of operational conditions and the input parameters corresponding to the Selmi et al. research [55]. To perform a comparison study, the solar radiation variation, the inlet temperature variation and the mass flow rate used in refer-
MAPE ¼
n 1X jðxobs:i xest:i Þ=xobs:i j n i¼1
ð14Þ
The computed result of MAPE in Fig. 3 is 7.46%. Thus, a good agreement between the experimental and the numerical results is observed. It shall be noted that two successful validation procedures for current model had been carried out and reported in reference [29]. 4.2. Al2O3-water nanofluid in the tube The heat transfer coefficient of Al2O3-water nanofluid with the volume fraction of 5% inside the tube is computed by a common correlation in the literature, the Shah equation [44]. The output heat transfer coefficient obtained from the numerical simulation is also plotted. For the purpose of validation, the results of correlation and simulation are compared with each other. The validation of current simulation results versus Shah Correlation is illustrated in Fig. 4 for various dimensionless lengths of tube. The simulation results are in suitable concordance with the theoretical ones, as can be seen in Fig. 4. This procedure had been conducted and detailed in reference [29].
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Fig. 4. Validation of using nanofluid in PV/T system [29]. Fig. 5. Variation of the outlet temperature versus inlet temperature for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
5. Results and discussion The heating performance of the fluid and the collector cooling process are mainly affected by the value of the inlet fluid flow temperature. In many cases, increasing the inlet fluid flow temperature causes the reduction in the efficiency parameters. The mentioned reduction for thermal efficiency is possible while decreasing of electrical and overall efficiencies is definite [56]. Decision making about the value of inlet fluid flow temperature strongly depends on the amount of the absorbed solar radiation. At the highly absorbed solar radiation levels, the cooling impact of fluid flow with high inlet temperature is considerable. In the other words, the inlet fluid flow with high temperature can participate in heat recovery effectively, provided that high absorbed solar radiation is available. While in the low absorbed solar radiation levels, the high inlet fluid flow temperature increases the temperature of photovoltaic panel conversely. The high inlet fluid flow temperature leads to electrical efficiency fall, instead of improving the cooling effect. Whereas, the low inlet fluid flow temperatures cause in an efficient cooling at all solar radiation values. Thus, the lower inlet fluid flow temperature provides suitable circumstances for the performance of the current solar system. It shall be expressed that raising the fluid inlet temperature passing the tube has a remarkable effect on the heat transfer characteristics of the system. In the current investigation, the fluid inlet temperature has been changed from 20 °C to 50 °C in the constant absorbed solar radiation of 600 W/m2, fluid velocity of 0.06377 m/s and tilt angle of 35°. The obtained results of pure water are compared to Al2O3water nanofluid with the volume fraction of 2%. The variations of the outlet temperature versus the inlet temperature for both pure water and Al2O3-water nanofluid (u ¼ 2%Þ are indicated in Fig. 5. As it can be seen, there is a direct dependency between the inlet and outlet fluid temperatures. It is evident that the higher inlet fluid temperature leads to the greater outlet fluid temperature, proportionally. Furthermore, the Al2O3-water nanofluid plot is placed over the curve of pure water. It means that Al2O3-water nanofluid (u ¼ 2%Þ plays a more successful role than pure water in removing excess heat from the photovoltaic panel. Therefore, 3 °C temperature difference between nanofluid and pure water is observed in the current system. The absorber plate temperature is mainly influenced by the absorbed solar radiation and fluid inlet temperature. The variations
Fig. 6. Variation of the absorber plate temperature versus inlet temperature for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
of absorber plate temperature versus the fluid inlet temperature for Al2O3-water nanofluid and pure water are shown in Fig. 6. Greater inlet fluid temperature would lead to higher absorber plate temperature. Fig. 6 indicates that, by using Al2O3-water nanofluid instead of pure water, the absorber plate temperature decreases about 1 °C. The variations of the efficiencies terms versus the inlet water temperature are displayed in Fig. 7. As mentioned before in Section 3, the temperatures of the photovoltaic panel and absorber plate have been assumed to be the same. Thus, increasing the absorber plate temperature (Fig. 6) results in photovoltaic panel temperature rise. Consequently, electrical efficiency fall is expected to happen in such conditions, based on Eq. (12). It is apparent that the inlet fluid temperature rise would have undesirable effects on the absorber plate temperature and subsequently, the electrical efficiency. It shall be noted that utilizing nanofluid instead of pure water helps the system to face with less electrical efficiency fall. As it can be observed in Fig. 7, the electrical efficiency of the system using Al2O3-water nanofluid is 1% more than pure water.
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Fig. 7. Variation of efficiencies versus the fluid inlet temperature for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
As represented previously in Section 3, the thermal efficiency is calculated by Eq. (10). Fig. 7 demonstrates that the thermal efficiency remains approximately fixed with respect to increasing the fluid inlet temperature. It shall be noticed that increasing the fluid inlet temperature has a direct effect on the outlet temperature. Consequently, the difference between the inlet and outlet temperatures is approximately fixed. Therefore, the thermal efficiency is expected to be fixed in the constant absorbed solar radiation. Also, it is inferred from Fig. 7 that Al2O3-water nanofluid is slightly more efficient than pure water. The heat transfer coefficient is affected by several parameters including the heat flux on the tube, the tube wall temperature and the bulk temperature of the fluid passing the tube. In a low inlet fluid temperature, a more significant temperature gradient is found between the fluid passing the tube and the tube wall. Whereas, with increasing the fluid inlet temperature, the temperature gradient sounds to be weaker. Therefore, in the low inlet fluid temperature, the heat transfer coefficient varies significantly. In the greater inlet fluid temperature, the operational temperature of the PV/T system rises. This increase results in slight improvement of the heat transfer coefficient. In the other hand, the average heat transfer coefficient is dependent on the thermo-physical properties of fluid. As mentioned before, adding fine nanoparticles in base fluid increases the heat transfer coefficient via the Brownian motions and thermal conductivity increase [44]. Thus, it is found that the heat transfer coefficient of nanofluid is greater than pure water. Fig. 8 illustrates the variation of the average heat transfer coefficient versus the fluid inlet temperature. Fig. 8 also reveals that, in comparison to pure water, the higher heat transfer coefficients are achieved by using Al2O3-water nanofluid. The increase percentage of heat transfer coefficient for Al2O3-water nanofluid (u ¼ 2%Þ in comparison with pure water reaches to a considerable value of 24%. The most essential effect on the heating of the fluid is attributed to absorbed solar radiation. As long as the solar radiation arrives at the photovoltaic panel, a portion of the entered solar energy converts to electrical energy. The electricity production content is correspondent to the photovoltaic panel efficiency. The remainder of the entered radiation passes the photovoltaic panel and reaches to the collector. Consequently, the absorbed solar radiation by the sheet-and-tube collector transmits to the fluid. So, fluid heating
Fig. 8. Variation of the heat transfer coefficient versus inlet temperature for Al2O3water nanofluid (u ¼ 2%Þ and pure water.
Fig. 9. Variation of the fluid outlet temperature versus absorbed solar radiation for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
Y. Khanjari et al. / Applied Thermal Engineering 115 (2017) 178–187
and panel cooling is occurred as a result of the above-mentioned process. The performance of Al2O3-water nanofluid (u ¼ 2%Þ and pure water versus variations of absorbed solar radiation are analyzed in a comparison study. In this section, the absorbed solar radiation is changed from 200 W/m2 to 800 W/m2, in constant inlet fluid velocity of 0.06377 m/s and fluid inlet temperature of 303.15 K. The variations of the fluid outlet temperature versus absorbed solar radiation are shown in Fig. 9. As the absorbed solar radiation increases, the fluid outlet temperature grows. According to Fig. 9, the outlet temperature of Al2O3-water nanofluid (u ¼ 2%Þ is greater than the outlet temperature attained by pure water. As much as the absorbed solar radiation goes up, the outlet temperature difference between nanofluid and pure water tends to greater values. For instance, in an absorbed solar radiation of 200 W/m2, the outlet temperature difference between nanofluid and pure water is just 1 K, while this value reaches to 5 K for the absorbed solar radiation of 800 W/m2. It is obvious that nanofluid is more efficient than pure water in the fluid heating procedure. Furthermore, in the higher absorbed solar radiation levels, nanofluid can provide a better cooling effect, in comparison with pure water.
Fig. 10. Variation of the absorber plate temperature versus the absorbed solar radiation for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
185
Fig. 10 illustrates the variations of the absorber plate temperature with respect to the absorbed solar radiation for both working fluids, including Al2O3-water nanofluid and pure water. It is found that a direct dependency exists between the absorber plate temperature and the absorbed solar radiation. It shall be noted that the absorber plate temperature, in the case of using nanofluid, is lower than pure water. Nevertheless, the maximum temperature difference between the outlet temperature of nanofluid and pure water is at most 3 K; this reveals more efficient cooling ability of nanofluid in comparison with pure water. As it was demonstrated by Eq. (12) in Section 2, the electrical efficiency of the photovoltaic panel decreases, when the cell temperature increases. In fact, the higher levels of absorbed solar radiation results in greater temperatures for both absorber plate and photovoltaic panel; eventually, the electrical energy efficiency of PV/T system reduces. Also, using nanofluid instead of pure water decreases the electrical efficiency loss. The descending trend of electrical efficiency with respect to the variations of the absorbed solar radiation for Al2O3-water nanofluid and pure water is indicated in Fig. 11. Therefore, it is concluded that the high absorbed solar radiation is not necessarily the best choice for the current system. It should be notified that the effect of using nanofluid, in comparison with pure water, is more sensible in greater values of the absorbed solar radiation. To clarify this fact, the increase percentage of electrical efficiency is computed for the absorbed solar radiation of 800 W/m2. In the absorbed solar radiation of 800 W/ m2, the increase percentage of electrical efficiency is approximately 1%. While, in the absorbed solar radiation below 800 W/ m2, increase percentage of electrical efficiency is clearly lower than 1%. Fig. 11 also displays the variation of thermal efficiency versus the absorbed solar radiation. In constant values of fluid inlet temperature, thermal efficiency is mainly dependent on the fluid outlet temperature and absorbed solar radiation. At the low absorbed solar radiation, an ascending trend for thermal efficiency is observed. While in the medium and high absorbed solar radiations, thermal efficiency remains fixed approximately. The reason may be due to the simultaneous increase of the absorbed solar radiation and the outlet temperature. In fact, the outlet temperature increases with increasing the absorbed solar radiation and consequently, the thermal efficiency remains fixed. This fact can also be proved by Eq. (10). A significant difference value of 10% is observed between thermal efficiencies of Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
Fig. 11. Variation of efficiencies versus the absorbed solar radiation for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
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Fig. 12. Variation of heat transfer coefficient versus the absorbed solar radiation for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
The variations of the average heat transfer coefficient versus the absorbed solar radiation for Al2O3-water nanofluid and pure water are illustrated in Fig. 12. The heat transfer coefficient is mainly influenced by the heat transfer characteristics; In fact, it is not dependent on the environmental factors such as absorbed solar radiation. Therefore, increasing the absorbed solar radiation does not have a significant effect on the heat transfer performance of the PV/T system. According to Fig. 12, the heat transfer coefficient of Al2O3-water nanofluid and pure water, in the case of increasing the absorbed solar radiation, remains approximately fixed. Fig. 12 also shows that the greater heat transfer coefficient is achieved by using Al2O3-water nanofluid than pure water in the same conditions. The heat transfer coefficient of Al2O3-water nanofluid is 10% higher than pure water. 6. Conclusion The purpose of present study is establishing a simulation model to consider the behavior of nanofluid in a water PV/T system via computational fluid dynamics method. Also, effects of different parameters on efficiency and performance of the system are investigated numerically. The performance of the PV/T system versus variations of absorbed solar radiation on the plate and fluid inlet temperature are analyzed for both pure water and Al2O3-water nanofluid. In the case of increasing in both absorbed solar radiation and fluid inlet temperature, the outlet temperature and absorber plate temperature increase. While the electrical efficiency decreases by increasing the absorbed solar radiation and fluid inlet temperature. The obtained results prove the superiority of Al2O3water nanofluid to pure water in PV/T system. Furthermore, by increasing absorbed solar radiation, thermal efficiency becomes fixed after a primary rise. Also, rising the inlet temperature leads to remaining the thermal efficiency at a fixed value. References [1] I.E. Agency, How Solar Energy could be the Largest Source of Electricity by Midcentury. 2014; Available from:. [2] I. Guarracino et al., Dynamic coupled thermal-and-electrical modelling of sheet-and-tube hybrid photovoltaic/thermal (PVT) collectors, Appl. Therm. Eng. 101 (2016) 778–795.
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Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Evaluating the environmental parameters affecting the performance of photovoltaic thermal system using nanofluid Y. Khanjari, A.B. Kasaeian ⇑, F. Pourfayaz Department of Renewable Energies, Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran
h i g h l i g h t s Using nanofluid in photovoltaic thermal system is studied theoretically. The examined factors consist of inlet fluid temperature and absorbed solar radiation. The efficiency, heat transfer coefficient and temperature in different sections are investigated. Al2O3-water nanofluid has better performance than pure water.
a r t i c l e
i n f o
Article history: Received 27 September 2016 Revised 19 November 2016 Accepted 20 December 2016 Available online 28 December 2016 Keywords: PV/T Al2O3-water nanofluid CFD Solar radiation
a b s t r a c t PV/T is a hybrid system which combines photovoltaic cells and solar collector. It can produce renewable electricity and heat, simultaneously. The aim of the present work is to study the effects of two environmental parameters on the performance of system. Also, the performance of pure water and Al2O3-water nanofluid are compared. The conduction and convection heat transfer are considered by CFD method. The mass, momentum, and energy equations are solved using the ANSYS Fluent. The second order upwind is selected as an interpolation scheme and the pressure-based solver is used for this laminar model. The pressure-velocity coupling method is the SIMPLE. Also, the gradients of the solution variables are determined by the least square cell based. The effects of solar radiation and fluid inlet temperature on the performance are modeled. Increasing the solar radiation reduces electrical efficiency; then, the thermal efficiency becomes fixed after a first rise. Nevertheless, the thermal efficiency remains fixed; the electrical efficiency decreases with increasing the fluid inlet temperature. The findings indicate that the heat transfer coefficient and the efficiency of Al2O3-water nanofluid are greater than pure water. The numerical model is validated by comparing the simulation results with the experimental data in the literature. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Energy consumption has a significant effect on the human interactions with the surrounding environment. Whereas, the growth of the world energy demand in recent decades is very large. Solar energy is an available and sustainable choice to meet the energy demand in the future. Moreover, by substituting solar energy, the challenges including finitude of fossil fuels and the environmental pollution related to conventional resources are eliminated. A report of the International Energy Agency suggests that a quarter of the energy usage and supply may be derived from solar power by 2050 [1].
⇑ Corresponding author. E-mail address: [email protected] (A.B. Kasaeian). http://dx.doi.org/10.1016/j.applthermaleng.2016.12.104 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
The solar energy can be applied in two different categories: solar thermal systems and photovoltaics. In a solar thermal system, solar energy converts to thermal energy, whereas in a photovoltaic case, electricity is directly produced from solar radiation. In a photovoltaic module, the electrical efficiency of the system decreases as the temperature of the module increases. In fact, a photovoltaic system uses a certain part of solar radiation for electricity production and the remainder is wasted in the form of heat. Therefore, with the circulation of a cold fluid through the system, the waste heat of photovoltaic module can be removed; consequently, higher electrical efficiency may be obtained. The combination of thermal and electrical sections constructs a new hybrid device called ‘‘photovoltaic thermal” energy system (PV/T). Using this combination, cogeneration of renewable power and heat is happened in a PV/ T. Plus the greater energy performance of the system, the space occupied by a hybrid system is reduced.
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Nomenclature P A Cp G h _ m P PV U T wt
packing factor area (m2) specific heat capacity (kJ/kg K) solar radiation intensity (W/m2) convection heat transfer coefficient (W/m2 K) mass flow rate (kg/s) pressure (N/m2) photovoltaic fluid velocity (m/s) temperature (K) weight fraction
Subscript f nf p ref ave cell i g atm
base fluid nano fluid nano particle reference average solar cell counter glass cover atmosphere
Many works have been carried out on the research and technological development of PV/T systems [2–6]. Also, some experimental tests for design development, theoretical methods for improving the thermal and electrical performance, and efforts for commercialization of PV/T were done in this area [7–9]. Many experimental and theoretical studies have been carried out regarding photovoltaic thermal collectors. The performance of nine different PV/T systems were considered and compared by Zondag et al. [10]. In Hong Kong, Chow et al. [11] examined two glazed and unglazed PV/T systems, with the construction design of sheet and tube. Their investigations were done based on both first and second law of thermodynamics. The results of energy analysis revealed that the glazed design was always appropriate, whereas the finding of their exergy analysis claimed that the use of unglazed design was more optimized. A thermal model was developed by Siddiqui et al. [12] to consider PV modules with and without cooling section. The effect of the environmental factors such as ambient temperature and absorbed solar radiation on the performance of PV panels were analyzed. Also, the effects of the inlet velocity, inlet temperature, and thermal contact resistance were studied. A full-scale BIPV/T collector was investigated by Corbin and Zhai [13] to determine the effects of utilizing cooling system on both electrical and thermal efficiency. Computational fluid dynamics (CFD) method was used to simulate the represented system. Additionally, the variations of some factors including cell temperature, outlet temperature, and solar insolation were examined via implementing a parametric analysis. A simulation model was developed by Cerón et al. [14] in which different heat transfer mechanisms were simultaneously taken into account. In this study, the fluid flow pattern, the absorber temperature field and the distribution of heat flux were studied. The heat transfer results were validated against common experimental correlations available in the literature, and the Nusselt number for water fluid inside the tubes was derived. Perino et al. [15] installed experimental PV/T prototypes, and represented a simulation model for the mentioned PV/T systems in the TRNSYS, for both steady-state and transient conditions. The energetic and exergetic performance of PV/T system was evaluated. A reference efficiency of 72.8% and electrical
est obs x n MAPE k g d Re Pr Gr Ra Ri
estimated observed value (observed or estimated) number of the values mean absolute percentage error conductivity (W/m K) gravity acceleration (N/kg) diameter (m) Reynolds number Prandtl number Grashof number Rayleigh number Richardson number
Greek symbols b temperature coefficient (K1) l viscosity (Pa s) h tilt angle of setup u volume fraction g efficiency q density (kg/m3) s transmitivity
efficiency of 10.5% were obtained using the mentioned PV/T system. Spertino et al. [16] investigated a mono-crystalline PV module to examine the effect of using water-cooling on the performance. Also, a theoretical model considering both thermal and electrical was represented. Using a low weight plastic-laminated sandwich, instead of glass, was tested. The results indicated that working fluid must be utilized according to the location and the season of the year. Tse et al. [17] evaluated the advantages of using water PV/T system in the office scale building. This system supported the electricity and hot water demand by a computer program. An economic analysis was also carried out to consider the time value of money. Study of a bi-fluid PV/T system was implemented by Jarimi et al. [18], and the two-dimensional steady-state model was performed using MATLAB. The tests were conducted in steady-state conditions under a solar simulator at the Solar Energy Research Lab UiTM Perlis, Malaysia. Three fluid modes of air, water, and combination of air-water were operated in the tests. Many experimental and numerical investigations have been done in the literature to improve the performance of the conventional coolants such as water or air used in PV/T systems. Using nanofluids as a coolant in PV/T systems has not been completely developed. The heat transfer performance can be enhanced by improving the thermo-physical properties, and dispersing nanoparticles lead to the increase in thermal conductivity [19]. Thus, utilizing nanofluid, instead of conventional fluids such as water, can be an advantageous option. It shall be noted that many original types of research have been implemented on the influence of using nanofluid in solar systems [20–27]. However, a few number of theoretical studies focused on using nanofluids in PV/T systems, among which we can point to some relevant references such as [28,29]. Sardarabadi et al. [28] investigated the effect of using SiO2 nanoparticles in a PV/T system experimentally. The electrical and thermal efficiencies were considered based on the first and second laws of thermodynamics. The results indicated that the thermal energy efficiency of using 1 wt% and 3 wt% nanofluids were increased by 7.6% and
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12.8%, respectively. The potential for size reduction of flat plate solar thermal collector and its proportional energy and cost saving in the case of using different nanofluids was studied by Faizal et al. [30]. The application of Al2O3, SiO2, TiO2, CuO nanoparticles was analyzed in this work. They declared that the higher density and lower specific heat of nanoparticles caused a better thermal performance. Mohammad Zadeh et al. [31] represented a numerical methodology for modeling and optimization, in the case of using Al2O3/synthetic oil nanofluid, in a parabolic trough collector. The effects of the volume fraction of nanoparticle on mixed convection heat transfer rate in a fully-developed turbulent flow were considered. In an experimental investigation, the application of Al2O3-waternanofluid in a flat plate solar collector was studied by Yousefi et al. [32]. The variation of two parameters including mass flow rate and nanoparticle mass fraction were analyzed. Their results claimed that adding 0.2% (wt) Al2O3 leads to an efficiency enhancement of 28.3%. The heat transfer and entropy generation of Al2O3-water nanofluid in a flat plate solar collector were examined by Mahian et al. [33]. They considered the effects of tube roughness, nanoparticle diameter, and two different thermo-physical models. The output data were represented in the form of Nusselt number, heat transfer coefficient, the outlet temperature of the collector, entropy generation, and Bejan number. They concluded that the entropy generation decreases with increasing the volume fraction of the nanoparticle. The mixed convection heat transfer of an Al2O3-waternanofluid system in a horizontal tube with uniform heat flux was considered by Akbari and Behzadmehr [34]. Their results show that increasing the Al2O3 nanoparticles from 2% to 4% causes in heat transfer coefficient rising from 9% to 15%, respectively. In a numerical survey, Tse et al. [17] studied the performance of Al2O3-water nanofluid in a circular tube in constant heat flux. For defining the nanoparticle behavior in the base fluid, both single-phase and two-phase models were applied. The maximum difference between the heat transfer coefficient of the single-phase, and two-phase models were just 11%. The previous research studies in the literature indicate that the previous numerical investigations for PV/T systems were carried out by solving energy balance equations for each particular case. Whereas, the CFD method is rarely used for simulating the behavior of PV/T systems. To conduct a comparative study, the CFD method was applied in the present investigation. As discussed above, only a limited number of experimental works are done about the application of nanofluid in PV/T systems. Utilizing nanofluid instead of pure water was studied numerically in other solar systems such as parabolic trough collectors, solar stills or flat plate collectors [35,36,25,37]. In addition, the effects of two environmental parameters including the absorbed solar radiation and the fluid input temperature on the performance of the system, is focused in the present work. The aim of this work is to study the effects of two environmental parameters on the efficiency and heat transfer performance of a water-cooled PV/T system using the numerical method of CFD. The effects of using Al2O3-water nanofluid, instead of water, as working fluid is also investigated theoretically in the ANSYS Fluent software. Finally, the simulation results are compared with the data of experimental works.
2. Thermo-physical properties Pure water is applied as the base fluid in the current investigation. The thermo-physical properties of water are considered as a function of temperature as followings [38,39]:
qf ¼ 4:48 103 T2 þ 999:9
ð1Þ
lf
ð2Þ
2 ! 1150 690 103 þ ¼ exp 1:6 T T
kf ¼ 8:01 106 T2 þ 1:94 103 T þ 0:563 Cpf ¼ 4:1855 103 0:966185 þ 0:0002874
5:26 !! T þ 100 100
þ ð0:011160 10ð0:036TÞ Þ
ð3Þ
ð4Þ
Adding nanoparticles to base fluid improves the thermophysical properties of the attained nanofluid. To obtain the thermal conductivity of nanofluid, following theoretical model is used [40]:
knf ¼ kf
ks þ 2kf 2ð1 þ bÞ3 ðks kf Þu ks þ 2kf þ ð1 þ bÞ3 ðks kf Þu
ð5Þ
In this conductivity model, the effects of the nanoparticle volume fraction and the properties of the base fluid are considered. The physical principle of the two-phase mixture is used for obtaining the density and specific heat of the nanofluid. The density, viscosity and heat capacity of nanofluid are determined by the following equations [41,42]:
qnf ¼ ð1 uÞqf þ uqs for u < 0:05; lnf ¼ ð1 þ 2:5uÞlf ð1 uÞqf Cpf þ uqs Cps Cpnf ¼ qnf
ð6Þ ð7Þ ð8Þ
As it can be seen in the previous equations, rising the nanoparticles volume fraction results in increasing and decreasing the density and specific heat of nanofluid, respectively. Also, the viscosity and thermal conductivity of nanofluids increase when the volume fraction of nanoparticles increases [43,44]. The thermo-physical properties of Al2O3 are gathered in Table 1 [45]. 3. Numerical modeling The nanofluid flow behavior through a water PV/T system was numerically simulated and compared with pure water. The represented PV/T model is composed of a glazing section, a PV panel and a sheet-and-tube collector with five identical riser tubes. To decrease the computational effort in the modeling process, the number of riser tubes in PV/T model can be reduced into just one, instead of five [46–48]. Therefore, the flow rate in each riser is assumed as 1/5 of the total mass flow rate in the proposed system. Thus, the velocity and temperature distributions can be generalized to whole the system. Consequently, the proposed model consists of a water riser tube and an absorber plate to consider the conduction and convection heat transfer mechanisms. The bodies of the absorber plate and the fluid tube are simulated entirely, whereas the effects of the glazing section and the photovoltaic panel are applied in boundary conditions. The amount of the absorbed solar radiation is mainly related to the transmittance of glass, the absorbtance of the photovoltaic panel and the absorber plate material. The geometry is created in the CATIA software, and the mesh generation and solution analysis are carried out in the ANSYS Workbench. For better understanding, the geometry
Table 1 Values for the thermo-physical properties of Al2O3 nanoparticles. Property
Al2O3 nanoparticles
Density (kg/m3) Conductivity (W/m K) Specific Heat (J/kg K)
3970 40 765
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In the CFD process, the domain of current model is discretized and then the conservation laws are solved by the finite volume method. The pressure-based solver is preferred to the densitybased solver in this work, and the SIMPLE scheme is applied for the velocity–pressure coupling. The selected interpolation scheme for the convection and diffusion terms is the second order upwind. The gradients of the solution variable at the cell center are determined by the least square cell based. The conjugate heat transfer is employed in the CFD procedure. The solution convergence happens whenever the residuals of velocity, continuity, and energy reach below 10e4, 10e3, and 10e6, respectively. The nontransient conservation laws are represented as followings: Continuity Equation Momentum Equation Energy Equation
Fig. 1. Geometry of current study.
rðqnf U nf Þ ¼ 0 r ðqnf U nf U nf Þ ¼ rP þ rs þ qnf g r ðqnf U nf C pnf TÞ ¼ r ðknf rTÞ
To characterize the flow, whether laminar or turbulent, the Reynolds and Grashof numbers are calculated for the forced and natural convection, respectively. Also, the Richardson number expresses whether the fluid flow is natural, forced or mixed. Since the fluid passing tube has low velocity (below 0.1 m/s), the buoyancy force effect is an essential factor in this investigation. Some of the relevant dimensionless numbers for Al2O3-water nanofluid in the volume fractions of 1% and 2% are tabulated in Table 3. It should be notified that the gravitational acceleration can affect the buoyancy force and convection terms. Therefore, the gravitational acceleration shall be activated in the ANSYS Fluent. The gravity acceleration is defined in the form of vectors, as below: Fig. 2. Schematic picture of the whole system.
of current study and a schematic picture of whole system are illustrated in Figs. 1 and 2, respectively. Table 2 represents the related dimensions and the characteristics of the model. The fluid flow is assumed to be steady, incompressible and uniform. The literature review shows that there is only 0.2% discrepancy between the steady and transient solutions [49]. To prevent ineffective calculations, the steady-state condition is chosen for current research. Also, a fully developed laminar flow is taken in the simulation. A thermal equilibrium exists between the base fluid and nanoparticles; therefore, the nanofluid is assumed to be single phase. The mentioned assumption is common in the literature [50–53]. The temperature distribution in the photovoltaic panel and absorber plate is supposed to be approximately the same [54,46].
g x ¼ gSinh gy ¼ 0 g z ¼ þgCosh Finally, it is deduced that the flow regime of this study is laminar and mixed. In the mesh generation procedure, the absorber plate and fluid body are meshed with the sweep and tetrahedrons elements, respectively. Also, an inflation method is applied in the fluid body near the riser wall to provide a boundary layer. Totally, 882,722 elements are generated in the meshing process of whole domain, and a grid study is carried out to prove the accuracy of results. Four different grids with the element numbers of 882,722, 921,507, 1,075,904 and 1,449,128 are evaluated. The maximum outlet velocity, the outlet temperature, and the average heat transfer coefficient are monitored for both pure water and Al2O3-water nanofluid, in each of the mentioned grids. The maximum percent-
Table 2 Dimensions and characteristics for different sections. Risers tubes
Absorber plate
Photovoltaic panel
Number: 5 Thickness: 0.001 (m) Outer diameter: 0.01 (m) Length: 2 (m) Spacing: 0.2 (m)
Length: 2 (m) Width: 1 (m) Thickness: 0.002 (m)
gr = 12% at 0 °C
Glass
Number of cells: 60
Length: 1.64 (m) Width: 0.99 (m) Absorptance: 0.9 Emissivity: 0.88
1
br = 0.0045 °C
Emissivity: 0.88
Table 3 Dimensionless numbers in constant velocity for Al2O3-water nanofluids (Absorbed Radiation on Plate ¼ 570:24 mW2 ; dp ¼ 50 nm; T inlet ¼ 303:15 KÞ. lC p
u (%)
Pr ¼
1 2
3.9321 3.8215
k
V
Re ¼ qlVD
Gr ¼ q
0.06377
965.1246 969.6174
0.9940 1.0023
2
gcoshbðT out T in ÞL3
l2
105
Ra ¼ Gr Pr 105
Gr Ri ¼ Re 2
3.9087 3.8307
0.1067 0.1066
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age of the parameter change due to mesh refinement is just 2.20% [29]. Therefore, the results of different grid sizes are identical approximately. Thus, the grid with 882,722 elements is the most appropriate domain for the present simulation study. To achieve a unique solution in a numerical simulation, the best boundary conditions must be selected appropriately and activated in the ANSYS Fluent. The ‘velocity inlet’ boundary condition is applied to the inlet area of the tube. Also, the fluid inside the tube is incompressible. Thus, the ‘pressure outlet’ boundary condition is utilized at the outlet of the tube. The no-slip wall and impermeable boundary conditions have been specified over the walls. The absorbed heat flux is obtained by the following equation:
Absorbed heat flux on plate ¼ Gt sg að1 gÞ
ð9Þ
The absorbed heat flux is imposed to the wall boundary conditions of the plate in the ANSYS Fluent. The back surface of the absorber plate and the external face of the tube are assumed to be adiabatic. Consequently, the zero heat flux wall boundary condition is used for simulation in the software. Following equations express the boundary conditions at the inlet of the tube in mathematical form:
ux ¼ uin uy ¼ uz ¼ 0 T ¼ Tin In addition, the boundary condition at the outlet of the tube is:
P ¼ Patm ðstatic pressureÞ Furthermore, the following mathematical equations were used as the boundary conditions at the fluid–solid interface:
ux ¼ uz ¼ uy ¼ 0 q ¼ kdT=dz ¼ hðT Tbulk Þ The thermal and electrical efficiencies of the PV/T system can be computed with following equations:
gthermal ¼ P¼
_ w Cpw ðT out T in Þ m Gt AP
APV AP ¼ gref ½1 bðTcell Tref Þ
gPV gelectrical ¼ P:gPV
ð10Þ ð11Þ
Fig. 3. Validation of the PV/T simulation.
ence [55] are entered as the input data for current simulation, while other related factors are kept fixed. As mentioned before, same operational conditions are imposed in the model simulation, such as solar radiation in the range of 470–542 W/m2, the inlet temperature in the range of 32–46 °C, and the mass flow rate of 0.00136 kg/s (all exactly same as Selmi et al.). The outlet water temperature of the system is illustrated versus time of day for both current simulation and data attained in reference [55]. The obtained curves are indicated in Fig. 3 to prove the validation of the present simulation model. It is found that the temperature difference between the water inlet temperature and outlet water temperature is approximately fixed. As it can be seen in Fig. 3, the same trend is obtained for both sets of data. The error formulation of MAPE is computed precisely to find how accurate the results of validation are. In the other words, the difference of present model outputs and the experimental results are evaluated by a statistical test. The MAPE is calculated by the following equations:
ð12Þ ð13Þ
4. Validation Two different sets of data from literature are selected to validate the current numerical study. The first one is related to a flat plate solar energy collector and the second one is allocated to a comparison study between an important heat transfer correlation of Al2O3-water nanofluid in a tube and riser tube of the present simulation model. 4.1. Water PV/T The numerical CFD model of the PV/T system is validated by comparing the current results with the findings of a research in literature [55]. In fact, the model outputs are compared with an experimental set of data measured in a real system. In order to build a correct method of validation, the current basic simulation model is driven with new set of operational conditions and the input parameters corresponding to the Selmi et al. research [55]. To perform a comparison study, the solar radiation variation, the inlet temperature variation and the mass flow rate used in refer-
MAPE ¼
n 1X jðxobs:i xest:i Þ=xobs:i j n i¼1
ð14Þ
The computed result of MAPE in Fig. 3 is 7.46%. Thus, a good agreement between the experimental and the numerical results is observed. It shall be noted that two successful validation procedures for current model had been carried out and reported in reference [29]. 4.2. Al2O3-water nanofluid in the tube The heat transfer coefficient of Al2O3-water nanofluid with the volume fraction of 5% inside the tube is computed by a common correlation in the literature, the Shah equation [44]. The output heat transfer coefficient obtained from the numerical simulation is also plotted. For the purpose of validation, the results of correlation and simulation are compared with each other. The validation of current simulation results versus Shah Correlation is illustrated in Fig. 4 for various dimensionless lengths of tube. The simulation results are in suitable concordance with the theoretical ones, as can be seen in Fig. 4. This procedure had been conducted and detailed in reference [29].
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Fig. 4. Validation of using nanofluid in PV/T system [29]. Fig. 5. Variation of the outlet temperature versus inlet temperature for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
5. Results and discussion The heating performance of the fluid and the collector cooling process are mainly affected by the value of the inlet fluid flow temperature. In many cases, increasing the inlet fluid flow temperature causes the reduction in the efficiency parameters. The mentioned reduction for thermal efficiency is possible while decreasing of electrical and overall efficiencies is definite [56]. Decision making about the value of inlet fluid flow temperature strongly depends on the amount of the absorbed solar radiation. At the highly absorbed solar radiation levels, the cooling impact of fluid flow with high inlet temperature is considerable. In the other words, the inlet fluid flow with high temperature can participate in heat recovery effectively, provided that high absorbed solar radiation is available. While in the low absorbed solar radiation levels, the high inlet fluid flow temperature increases the temperature of photovoltaic panel conversely. The high inlet fluid flow temperature leads to electrical efficiency fall, instead of improving the cooling effect. Whereas, the low inlet fluid flow temperatures cause in an efficient cooling at all solar radiation values. Thus, the lower inlet fluid flow temperature provides suitable circumstances for the performance of the current solar system. It shall be expressed that raising the fluid inlet temperature passing the tube has a remarkable effect on the heat transfer characteristics of the system. In the current investigation, the fluid inlet temperature has been changed from 20 °C to 50 °C in the constant absorbed solar radiation of 600 W/m2, fluid velocity of 0.06377 m/s and tilt angle of 35°. The obtained results of pure water are compared to Al2O3water nanofluid with the volume fraction of 2%. The variations of the outlet temperature versus the inlet temperature for both pure water and Al2O3-water nanofluid (u ¼ 2%Þ are indicated in Fig. 5. As it can be seen, there is a direct dependency between the inlet and outlet fluid temperatures. It is evident that the higher inlet fluid temperature leads to the greater outlet fluid temperature, proportionally. Furthermore, the Al2O3-water nanofluid plot is placed over the curve of pure water. It means that Al2O3-water nanofluid (u ¼ 2%Þ plays a more successful role than pure water in removing excess heat from the photovoltaic panel. Therefore, 3 °C temperature difference between nanofluid and pure water is observed in the current system. The absorber plate temperature is mainly influenced by the absorbed solar radiation and fluid inlet temperature. The variations
Fig. 6. Variation of the absorber plate temperature versus inlet temperature for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
of absorber plate temperature versus the fluid inlet temperature for Al2O3-water nanofluid and pure water are shown in Fig. 6. Greater inlet fluid temperature would lead to higher absorber plate temperature. Fig. 6 indicates that, by using Al2O3-water nanofluid instead of pure water, the absorber plate temperature decreases about 1 °C. The variations of the efficiencies terms versus the inlet water temperature are displayed in Fig. 7. As mentioned before in Section 3, the temperatures of the photovoltaic panel and absorber plate have been assumed to be the same. Thus, increasing the absorber plate temperature (Fig. 6) results in photovoltaic panel temperature rise. Consequently, electrical efficiency fall is expected to happen in such conditions, based on Eq. (12). It is apparent that the inlet fluid temperature rise would have undesirable effects on the absorber plate temperature and subsequently, the electrical efficiency. It shall be noted that utilizing nanofluid instead of pure water helps the system to face with less electrical efficiency fall. As it can be observed in Fig. 7, the electrical efficiency of the system using Al2O3-water nanofluid is 1% more than pure water.
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Fig. 7. Variation of efficiencies versus the fluid inlet temperature for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
As represented previously in Section 3, the thermal efficiency is calculated by Eq. (10). Fig. 7 demonstrates that the thermal efficiency remains approximately fixed with respect to increasing the fluid inlet temperature. It shall be noticed that increasing the fluid inlet temperature has a direct effect on the outlet temperature. Consequently, the difference between the inlet and outlet temperatures is approximately fixed. Therefore, the thermal efficiency is expected to be fixed in the constant absorbed solar radiation. Also, it is inferred from Fig. 7 that Al2O3-water nanofluid is slightly more efficient than pure water. The heat transfer coefficient is affected by several parameters including the heat flux on the tube, the tube wall temperature and the bulk temperature of the fluid passing the tube. In a low inlet fluid temperature, a more significant temperature gradient is found between the fluid passing the tube and the tube wall. Whereas, with increasing the fluid inlet temperature, the temperature gradient sounds to be weaker. Therefore, in the low inlet fluid temperature, the heat transfer coefficient varies significantly. In the greater inlet fluid temperature, the operational temperature of the PV/T system rises. This increase results in slight improvement of the heat transfer coefficient. In the other hand, the average heat transfer coefficient is dependent on the thermo-physical properties of fluid. As mentioned before, adding fine nanoparticles in base fluid increases the heat transfer coefficient via the Brownian motions and thermal conductivity increase [44]. Thus, it is found that the heat transfer coefficient of nanofluid is greater than pure water. Fig. 8 illustrates the variation of the average heat transfer coefficient versus the fluid inlet temperature. Fig. 8 also reveals that, in comparison to pure water, the higher heat transfer coefficients are achieved by using Al2O3-water nanofluid. The increase percentage of heat transfer coefficient for Al2O3-water nanofluid (u ¼ 2%Þ in comparison with pure water reaches to a considerable value of 24%. The most essential effect on the heating of the fluid is attributed to absorbed solar radiation. As long as the solar radiation arrives at the photovoltaic panel, a portion of the entered solar energy converts to electrical energy. The electricity production content is correspondent to the photovoltaic panel efficiency. The remainder of the entered radiation passes the photovoltaic panel and reaches to the collector. Consequently, the absorbed solar radiation by the sheet-and-tube collector transmits to the fluid. So, fluid heating
Fig. 8. Variation of the heat transfer coefficient versus inlet temperature for Al2O3water nanofluid (u ¼ 2%Þ and pure water.
Fig. 9. Variation of the fluid outlet temperature versus absorbed solar radiation for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
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and panel cooling is occurred as a result of the above-mentioned process. The performance of Al2O3-water nanofluid (u ¼ 2%Þ and pure water versus variations of absorbed solar radiation are analyzed in a comparison study. In this section, the absorbed solar radiation is changed from 200 W/m2 to 800 W/m2, in constant inlet fluid velocity of 0.06377 m/s and fluid inlet temperature of 303.15 K. The variations of the fluid outlet temperature versus absorbed solar radiation are shown in Fig. 9. As the absorbed solar radiation increases, the fluid outlet temperature grows. According to Fig. 9, the outlet temperature of Al2O3-water nanofluid (u ¼ 2%Þ is greater than the outlet temperature attained by pure water. As much as the absorbed solar radiation goes up, the outlet temperature difference between nanofluid and pure water tends to greater values. For instance, in an absorbed solar radiation of 200 W/m2, the outlet temperature difference between nanofluid and pure water is just 1 K, while this value reaches to 5 K for the absorbed solar radiation of 800 W/m2. It is obvious that nanofluid is more efficient than pure water in the fluid heating procedure. Furthermore, in the higher absorbed solar radiation levels, nanofluid can provide a better cooling effect, in comparison with pure water.
Fig. 10. Variation of the absorber plate temperature versus the absorbed solar radiation for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
185
Fig. 10 illustrates the variations of the absorber plate temperature with respect to the absorbed solar radiation for both working fluids, including Al2O3-water nanofluid and pure water. It is found that a direct dependency exists between the absorber plate temperature and the absorbed solar radiation. It shall be noted that the absorber plate temperature, in the case of using nanofluid, is lower than pure water. Nevertheless, the maximum temperature difference between the outlet temperature of nanofluid and pure water is at most 3 K; this reveals more efficient cooling ability of nanofluid in comparison with pure water. As it was demonstrated by Eq. (12) in Section 2, the electrical efficiency of the photovoltaic panel decreases, when the cell temperature increases. In fact, the higher levels of absorbed solar radiation results in greater temperatures for both absorber plate and photovoltaic panel; eventually, the electrical energy efficiency of PV/T system reduces. Also, using nanofluid instead of pure water decreases the electrical efficiency loss. The descending trend of electrical efficiency with respect to the variations of the absorbed solar radiation for Al2O3-water nanofluid and pure water is indicated in Fig. 11. Therefore, it is concluded that the high absorbed solar radiation is not necessarily the best choice for the current system. It should be notified that the effect of using nanofluid, in comparison with pure water, is more sensible in greater values of the absorbed solar radiation. To clarify this fact, the increase percentage of electrical efficiency is computed for the absorbed solar radiation of 800 W/m2. In the absorbed solar radiation of 800 W/ m2, the increase percentage of electrical efficiency is approximately 1%. While, in the absorbed solar radiation below 800 W/ m2, increase percentage of electrical efficiency is clearly lower than 1%. Fig. 11 also displays the variation of thermal efficiency versus the absorbed solar radiation. In constant values of fluid inlet temperature, thermal efficiency is mainly dependent on the fluid outlet temperature and absorbed solar radiation. At the low absorbed solar radiation, an ascending trend for thermal efficiency is observed. While in the medium and high absorbed solar radiations, thermal efficiency remains fixed approximately. The reason may be due to the simultaneous increase of the absorbed solar radiation and the outlet temperature. In fact, the outlet temperature increases with increasing the absorbed solar radiation and consequently, the thermal efficiency remains fixed. This fact can also be proved by Eq. (10). A significant difference value of 10% is observed between thermal efficiencies of Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
Fig. 11. Variation of efficiencies versus the absorbed solar radiation for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
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Fig. 12. Variation of heat transfer coefficient versus the absorbed solar radiation for Al2O3-water nanofluid (u ¼ 2%Þ and pure water.
The variations of the average heat transfer coefficient versus the absorbed solar radiation for Al2O3-water nanofluid and pure water are illustrated in Fig. 12. The heat transfer coefficient is mainly influenced by the heat transfer characteristics; In fact, it is not dependent on the environmental factors such as absorbed solar radiation. Therefore, increasing the absorbed solar radiation does not have a significant effect on the heat transfer performance of the PV/T system. According to Fig. 12, the heat transfer coefficient of Al2O3-water nanofluid and pure water, in the case of increasing the absorbed solar radiation, remains approximately fixed. Fig. 12 also shows that the greater heat transfer coefficient is achieved by using Al2O3-water nanofluid than pure water in the same conditions. The heat transfer coefficient of Al2O3-water nanofluid is 10% higher than pure water. 6. Conclusion The purpose of present study is establishing a simulation model to consider the behavior of nanofluid in a water PV/T system via computational fluid dynamics method. Also, effects of different parameters on efficiency and performance of the system are investigated numerically. The performance of the PV/T system versus variations of absorbed solar radiation on the plate and fluid inlet temperature are analyzed for both pure water and Al2O3-water nanofluid. In the case of increasing in both absorbed solar radiation and fluid inlet temperature, the outlet temperature and absorber plate temperature increase. While the electrical efficiency decreases by increasing the absorbed solar radiation and fluid inlet temperature. The obtained results prove the superiority of Al2O3water nanofluid to pure water in PV/T system. Furthermore, by increasing absorbed solar radiation, thermal efficiency becomes fixed after a primary rise. Also, rising the inlet temperature leads to remaining the thermal efficiency at a fixed value. References [1] I.E. Agency, How Solar Energy could be the Largest Source of Electricity by Midcentury. 2014; Available from:
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