Open access peer-reviewed chapter

Exergy in Photovoltaic/Thermal Nanofluid-Based Collector Systems

Written By

Amin Farzanehnia and Mohammad Sardarabadi

Submitted: 18 January 2019 Reviewed: 25 February 2019 Published: 23 October 2019

DOI: 10.5772/intechopen.85431

From the Edited Volume

Exergy and Its Application - Toward Green Energy Production and Sustainable Environment

Edited by Muhammad Aziz

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This chapter focuses on the exergy analysis of photovoltaic/thermal (PVT) systems using nanofluid. The PVT hybrid systems are designed to harness solar energy more efficiently. The thermodynamic theory of exergy in PVT systems is explained in details. The existing researches used various models to perform the exergy analysis for performance evaluation of the PVT systems. These models and formulations are compared with each other to achieve a widely used theory for a better comparison of the results. The exergy analysis is an effective tool to evaluate the performance of PVT systems. The exergy efficiency enhancement in PVT systems and the effect of nanofluid from the literature are presented. The literature survey suggests that the increase in the flow rate increases the exergy efficiencies in collector-based PVT. Using nanofluid as optical filters of solar radiation results in higher exergy efficiencies compared to collector-based PVT systems. According to the recent publications, the long-term thermophysical stability of nanofluid and cost-based exergy analysis still require further investigations.


  • PVT
  • photovoltaic/thermal
  • solar energy
  • nanofluids
  • exergy
  • nanoparticles

1. Introduction

Solar energy is a proven alternative for fossil fuels due to its sustainability and availability. The ever-reducing investment costs of solar system installation made this technology highly popular. The use of solar energy is a great method for mitigating the environmental and health problems presented by nonrenewable energy sources in the long term. Photovoltaic (PV) systems and hybrid photovoltaic/thermal (PVT) systems are the major tools for solar radiation to electrical and thermal energy conversion. The PVT systems are a combination of PV and solar collector to produce electricity and heat simultaneously. These hybrid systems have the benefits of increasing the electrical efficiency of the PV, obtaining thermal energy, and avoiding thermal degradation of PV solar panels [1]. Figure 1 shows the schematic of a PVT system. The diagram of the PVT system with a water-based sheet and tube thermal collector is presented in Figure 2. It is shown that by reducing 1°C in PV cell temperature, the electrical efficiency increases by 0.4–0.5% [2]. For amorphous silicon (a-Si), this increase is smaller about 0.25%/°C [3]. Additionally, the combination of solar collector and PV technologies has the advantages of reducing material usage, time of installation, and space required [4]. It is therefore necessary to evaluate the efficiency of PV and PVT systems to improve the design and usage of the systems, moreover, to help researches to make decisions on the usage and improvement of efficient systems.

Figure 1.

The schematics of a PVT system.

Figure 2.

The diagram of a PVT system with a water-based sheet and tube thermal collector.

Regarding the working fluid, PVT systems are classified under three groups of air-based PVT collector [5, 6], water-based PVT collector [7, 8], and a combination of air/water PVT collector [9, 10]. The PVT systems are mainly employed for low-temperature applications including space heating and air/water preheating in domestic buildings [11]. The type of working fluid is of primary significance to achieve energy-efficient systems compared to conventional fluids. The use of nanofluids due to their advanced thermal properties is gaining more and more attention [12]. Nanofluids are able to increase the efficiency of solar systems due to their augmented heat transfer properties such as thermal conductivity [13].

Exergy is an important means to evaluate the efficient use of the PV and PVT systems. The term exergy is defined as the maximum theoretical work potential of a system that interacts with an environment with constant conditions. In other words, exergy is defined as the energy that is available to be used. Therefore, one can evaluate the performance of a system by using the exergetic (second law) of thermodynamics.


2. Theory

The performance of PVT systems could be analyzed by the second law of thermodynamics (exergy analysis). In contrast to energy analysis, the exergy analysis takes the quality of energies into consideration. As mentioned before, the output energy of a PVT system is distributed over two forms of thermal and electrical energies. However, the quality of electrical energy is different from that of thermal energy. The electrical energy is equivalent to the available work, while only a part of thermal energy could be exploited as available work.

2.1 Energy analysis

Prior to performing the exergy analysis, the absorbed solar irradiation and output thermal and electrical power of PVT are required to be found. The PVT system is considered as control volume and is assumed to be in semi-steady state condition. The solar irradiation absorbed by PVT is calculated by [14]:

E ̇ sun = G T ̇ A PV τ g α cell E1

where G T ̇ is the total solar irradiation, A PV is the PV area, τ g is transmissivity of the glass layer over the PV module, and α cell absorptivity of PV cells. The output energy from the thermal collector is given by:

E ̇ th = m ̇ C p T out T in E2

In Eq. (2) the term m ̇ refers to the mass flow rate of the coolant fluid in the thermal collector of PVT system, C p is the specific heat capacity, and the T in and T out are the inlet temperature and the outlet temperature of the coolant fluid, respectively.

In the condition where the coolant fluid is a nanofluid, the specific heat capacity of nanofluid is expressed as either Eq. (3) or (4) [15]:

C p . nf = φ C p , np + 1 φ C p , np E3
C p . nf = φ ρ C p np + 1 φ ρ C p bf ρ nf E4

where the subscripts nf , np , and bf denote nanofluid, nanoparticles, and base fluid, respectively. In the above equations, ρ is the density of the corresponding materials. The term φ is the volume fraction of nanoparticles which is given by:

φ = m np ρ np m np ρ np + m bf ρ bf E5

where m np and m bf refer to the mass of nanoparticles and base fluid, respectively. The density of nanofluid ρ nf in Eq. (4) is simply given by the two-phase mixture principle:

ρ nf = φ ρ np + 1 φ ρ bf E6

Equation (4) is proposed more in the literature than Eq. (3) due to the better agreement with the experimental results [15, 16, 17].

The main output of a PV module is the electrical energy output which is given by [18]:

E ̇ el = V oc × I sc × FF E7

where V oc , I sc , and FF are the open circuit voltage, short circuit current, and fill factor, respectively.

2.2 Exergy analysis

For better understanding, the diagram of exergy flows belonging to a PVT system is shown in Figure 3. The first step to investigate the performance of PVT system from exergy viewpoint is to consider the PVT system as a control volume. It is assumed that the system is in semi-steady condition.

Figure 3.

The exergy flow diagram of a PVT system.

The exergy balance of a PVT system is expressed as:

Ex ̇ in = Ex ̇ out + Ex ̇ dest E8

where Ex ̇ in is inlet exergy, Ex ̇ out is the outlet exergy, and Ex ̇ dest is the exergy loss or destruction due to the irreversibility.

The term Ex ̇ in is the net input exergy rate. In solar systems such as PVT, the input energy is the solar radiation that reaches the system; therefore, the input exergy is equal to the exergy of incident solar irradiation to the system ( Ex ̇ sun ):

Ex ̇ in = Ex ̇ sun E9

The net output exergy ( Ex ̇ out ) of PVT systems consists of thermal exergy ( Ex ̇ th ) and electrical exergy ( Ex ̇ el ):

Ex ̇ out = Ex ̇ th + Ex ̇ el E10

Considering that the thermal exergy is equal to the difference of flow exergy at the outlet and inlet of the collector ( Ex ̇ th = Ex ̇ mass . out E ̇ x mass . in ), the exergy balance becomes (Eqs. 8–10):

Ex ̇ sun = Ex ̇ th + Ex ̇ el + E ̇ x dest E11

Many methods have been proposed to evaluate the exergy of the solar irradiation. The three following equations are the most commonly used equations for the exergy of absorbed solar irradiation by the PVT proposed, respectively, by Jeter [19], Spanner [20], and Petala [21]:

E x ̇ sun = E ̇ sun 1 T amb T sun E12
E x ̇ sun = E ̇ sun 1 4 T amb 3 T sun E13
E x ̇ sun = E ̇ sun 1 4 T amb 3 T sun + 1 3 T amb T sun 4 E14

where T amb is the ambient temperature and T sun is the surface temperature of the sun as a blackbody. Although it is hotter inside, the sun temperature could be estimated at its surface where the emissions occur and is approximated as a blackbody at 5770 K. The results from Eqs. (12)(14) differ from each other less than 2% [22]. However, the literature review by Kalogirou [23] indicates that Eq. (14) (Petala equation) is proposed and used more often than the other two equations.

The output thermal exergy of the PVT system ( Ex ̇ th ) is given by both Eqs. (15) and (16) [24, 25]:

Ex ̇ th = E ̇ th 1 T amb T out E15
Ex ̇ th = m ̇ h out h in T amb s out s in = m ̇ C p T out T in T amb ln T out T in E16

where h out and s out are the fluid enthalpy and entropy at the outlet of the collector. Similarly, h in and s in are the fluid enthalpy and entropy at the inlet of the collector.

Equation (15) derives the exergy based on a series of imaginary heat engine that operates between source temperature of T out and the sink temperature of T amb . Thus, the thermal exergy is the available work extracted from a Carnot efficiency heat engine between the outlet fluid temperature and ambient temperature. Equation 16 is often encountered in the literature [24, 26].

The electrical energy output is equivalent to the electrical exergy. The electrical energy could be 100% converted to work. Therefore, the electrical exergy of a passive PVT is expressed as:

Ex ̇ el = E ̇ el E17

However, the electrical exergy of an active PVT system is defined as the difference between electrical power and the required pumping power Eq. (18) [27]. Nevertheless, some studies do not consider the pumping power and simply use Eq. (17) [11]:

Ex ̇ el = E ̇ el E ̇ pump E18

where E ̇ pump is the electrical power consumption of the pump, which can be expressed as [28]:

E ̇ pump = m ̇ P ρ η p E19

where η p is the pump efficiency. Thermal and electrical exergy efficiencies based on second law are given as:

ε th = Ex ̇ th Ex ̇ sun × 100 E20
ε el = Ex ̇ el Ex ̇ sun × 100 E21

The overall exergy efficiency could be given as follows:

ε total Ex ̇ th + Ex ̇ el Ex ̇ sun = t 2 t 1 A c Ex ̇ " th + A PV Ex ̇ " el dt A c t 2 t 1 Ex ̇ " sun dt = ε th + r ε el E22

where A PV and A c are the PV panel and collector areas, respectively. Ex ̇ " th is the rate of the output thermal exergy per unit area of collector, Ex ̇ " el is the rate of electrical exergy per unit area of PV module, and Ex ̇ " sun is the rate of solar irradiation exergy per unit area of collector. The term r is the packing factor and defined as the area of PV panel to the collector ( r = A PV / A c ). Therefore, when the packing factor is equal to 1, the overall exergy is simply the sum of thermal and electrical exergy efficiencies.

It worth mentioning that the exergy destruction term Ex ̇ dest in Eqs. (8) and (11) is due to heat transfer losses and frictional losses in the collector tube. In the active PVT systems, in addition to heat transfer exergy loss, there is another exergy loss due to head or frictional loss in the collector tube, which can be derived by:

E ̇ loss , fr = m ̇ P ρ T amb . ln T out T in T out T in E23

where P is the pressure drop along the collector and ρ is the fluid density. The rate of entropy generation by irreversibility in the control volume could be calculated as:

S ̇ gen = E ̇ x dest T amb E24

where the E ̇ x dest is the total rate of exergy destruction which is the sum of exergy destruction due to the heat transfer loss and due to pressure drop in the collector tube and is given by Eq. (11).


3. Development of nanofluid-based PVT

The PVT system is employed to produce electrical and thermal energies simultaneously. The study of PVT water-based collectors has been limited in the literature due to the small market size. Also, most literature is focused on custom-made PVT systems [4]. However, now there are various configurations of commercialized PVT available, and these systems became popular [29, 30]. As the market size increases, it is necessary to evaluate and enhance the performance of PVT systems. Recently, the nanofluids are used in the PVT systems as working fluid or as optical filters resulting in increased efficiency of the systems. There are several reviews published on the topic of nanofluid PVT in the last couple of years such as by Said et al. [31], by Yazdanifard et al. [27], by Al-Shamani et al. [12], and by Ali et al. [32].

Sardarabadi et al. [14] performed an experimental investigation on silica/water nanofluid PVT systems based on first and second laws of thermodynamics. The mass flow rates 20, 30, and 40 L/h were studied, and the optimum mass flow rate for the working fluid was determined. The thermal exergy efficiency of the system was much smaller than the electrical efficiency. This was attributed to the small temperature difference between outlet and ambient temperatures. The results indicated that using thermal collector with the PV module increases the overall efficiency. Also using nanofluid enhances the energy efficiency of the system. However, comparing the results from the second law to the first law of thermodynamics, it was shown that although the thermal and overall efficiency from the first law viewpoint is high, the thermal exergetic and therefore overall efficiency were low (Table 1). This was due to the low-quality (low temperature) thermal energy in PVT systems.

Ref. Working fluid type Concentrations Flow rate Amb. temp. (°C) Exergy efficiencies (%)
Thermal Electrical Overall
[14] Without cooling 33 0 11.53 11.53
Pure water 0 30 L/h 1.23 12.47 13.54
SiO2/water 1 wt% 1.48 12.57 13.85
SiO2/water 3 wt% 1.68 12.59 14.02
[33] Ag/water 2 and 4 wt% 0.0085, 0.016, and 0.029 kg/s corresponding to laminar, transient, and turbulent regimes 25 4 wt%, turbulent regime: 50 and 30% improvements in exergy efficiency compared to water coolant
[34] Without cooling 0 10.9 10.9
PVT pure water 0 30 kg/h 0.50 11.73 12.23
PVT ZnO/water 0.2 wt% 0.51 11.78 12.29
PVT/PCM Pure water 0 0.87 12.30 13.17
PVT/PCM ZnO/water 0.2 wt% 1.08 12.35 13.42
[35] Without cooling 11.7
Pure water 15 (l/min) 12.5
Al2O3/methanol 1, 1.5, and 2 wt% 12.7 for the optimum conditions
[24] Without cooling 0 10.29 10.29
Pure water 30 kg/h 0.72 10.84 11.56
TiO2/water 0.2 wt% 0.91 11.02 11.93
ZnO/water 0.2 wt% 1.18 10.99 12.17
Al2O3/water 0.2 wt% 1.01 10.87 11.88
[36] Au/Duratherm S 0.05 kg/s 19 41.3
ITO/Duratherm S 42.3
[37] Ag/water 0.001–1.5 vol.% 0.08 kg/s By increasing nanofluid volume fraction
for GaAs cells: 24.2–30% For Si cells: 19.8–24.4%

Table 1.

List of studies on the PVT nanofluid collector-based systems.

Moradgholi et al. [35] studied two-phase closed thermosyphon (TPCT) PVT system using Al2O3/methanol nanofluid as the working fluid. They studied the effects of various mass fractions of nanoparticles 1, 1.5, and 2 wt%, and also the effect of filling ratio (the working fluid volume to the evaporating section volume) was studied. The optimum values of thermal and electrical performance of the system were obtained at the mass concentration of 1.5 wt% and the filling ratio of 50%. The average overall exergy efficiency was 11.7, 12.5, and 12.7% for PV module, PVT module with base fluid, and PVT module with nanofluid, respectively.

Sardarabadi et al. [34] studied the effects of both ZnO/water nanofluid and phase-change material (PCM) as a coolant in photovoltaic thermal systems. They used a PV module as a reference point and performed energy and exergy analysis on PV, PVT, and PVT with PCM systems with water and ZnO/water nanofluid as working fluids. An increase of nearly twice in the thermal exergy output was observed using PCM in PVT modules. This was also shown in other studies [26] and is because the heat generated in PV cells is absorbed in PCM and could be used as thermal energy. Also, the overall exergy efficiency of 10% was found for the PV module, whereas the PVT module and PVT module with PCM using nanofluid had an efficiency of 12.29 and 13.42%, respectively.

Sardarabadi et al. [24] studied the effects of using metal-oxides/water nanofluids on a PVT system from energy and exergy viewpoints. The Al2O3, TiO2, and ZnO nanoparticles with the mass fraction of 0.2 wt% were considered. It was shown that the ZnO/water nanofluid had the highest energy and exergy efficiencies and TiO2/water had the highest electrical exergy efficiency than other systems. The average overall exergy efficiency for the PV, PVT/water, PVT/TiO2, PVT/ZnO, and PVT/Al2O3 was 10.29, 11.56, 11.93, 12.17, and 11.88%, respectively.

Brekke et al. [36] proposed a performance model of a concentrating hybrid PVT system utilizing selective spectral nanofluid absorption. The proposed system used nanofluid to absorb the portion of the solar spectrum not efficiently exploited by the PV module. Two common PV cell materials of crystalline silicon (c-Si) and gallium arsenide (GaAs) were used in their numerical study. The heat transfer fluid of Duratherm S and gold nanoparticles were considered for c-Si, and indium tin oxide (ITO) nanoparticles were considered for GaAs PV module. The GaAs exhibited higher exergy efficiency due to higher PV efficiency of this cell; however, this results in the reduction of thermal exergy percentage of these cells because a smaller portion of thermal energy is absorbed by the spectral fluid. The results of exergy efficiency of previous studies are summarized in Table 1.


4. Conclusion

This chapter addresses the exergy in photovoltaic/thermal systems that contain nanofluid-based collector. These systems provide both thermal and electrical energies. The comprehensive theory of exergy analysis in these systems is elaborated. It is shown that existing researches used various models to perform the exergy analysis for performance evaluation of the photovoltaic/thermal systems. These models are compared with each other to achieve a widely used theory for a better comparison of the results. The literature survey on nanofluid in PVT indicates that the overall exergy efficiency is generally in the range of 10–14% for PVT collectors. The increasing flow rate and transition to turbulent flow increase exergy efficiency. When using nanofluid as optical filters, higher exergy efficiencies were observed. The performance of PVT systems could be analyzed by exergy analysis. Despite the benefits of nanofluid PVT system, barriers to the development of these systems are agglomeration, required pumping power, and pipe erosions. Additionally, the use of nanofluid collectors and optical filters brings much cost to the system. Therefore future investigation is required on exergy-based cost analysis, nanofluid stability, and optimization of PVT systems.


A area (m2)
C P specific heat capacity (J kg−1 K−1)
Eenergy ( J )
Exexergy ( J )
E ̇ power (W)
FF fill factor
G ̇ solar irradiation rate (W m−2)
I electrical current (A)
m ̇ mass flow rate (kg s−1)
k thermal conductivity (W m−1 K−1)
P pressure (Pa)
T temperature (K)
V velocity (m/s)
r packing factor
α absorptivity
ε exergy efficiency (%)
ρ density (kg m−3)
τ transmissivity
ϕnanoparticles volume fraction
amb ambient
bf base-fluid
dest destruction
el electrical
in inlet
n nanoparticle
nf nanofluid
oc open circuit
out outlet
ov overall
t total
sc short circuit
th thermal


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Written By

Amin Farzanehnia and Mohammad Sardarabadi

Submitted: 18 January 2019 Reviewed: 25 February 2019 Published: 23 October 2019