Solar Energy 135 (2016) 222–231

Contents lists available at ScienceDirect

Solar Energy
journal homepage: www.elsevier.com/locate/solener

Exergy analysis of photovoltaic thermal (PVT) compound parabolic

concentrator (CPC) for constant collection temperature mode
Deepali Atheaya a,⇑, Arvind Tiwari b, G.N. Tiwari a
a
Centre for Energy Studies, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 11 00 16, India
b
Department of Electrical Engineering, College of Engineering, Qassim University, P.O Box-6677, Buraydah 51452, Saudi Arabia

a r t i c l e i n f o a b s t r a c t

Article history: In this communication, an attempt has been made to evaluate exergy of photovoltaic thermal compound
Received 9 April 2015 parabolic concentrator (PVT-CPC) water collector system [case (i)] for constant collection temperature
Received in revised form 12 April 2016 mode of operation. The performance of PVT-CPC water collector systems can be analyzed in two modes
Accepted 30 May 2016
namely (i) constant mass flow rate and (ii) constant collection temperature. In the present analysis, an
Available online 7 June 2016
analytical expression for mass flow rate and electrical efficiency of PV module for partially covered
PVT-CPC water collector system [case (i)] have been developed to determined the performance under
Keywords:
constant collection temperature mode. Such system will be most useful for thermal space heating of
Constant collection temperature
Compound parabolic concentrator
buildings to conserve fossil fuel to save environment. The comparison of proposed system with fully
Exergy covered PVT-CPC water collectors [case (ii)], conventional CPC water collectors [case (iii)] and partially
covered PVT water collectors [case (iv)] have also been carried out for climatic condition of New Delhi.
Based on computation, it has been found that for fully covered PVT-CPC water collector system [case
(ii)] (a) at high operating temperatures, instantaneous thermal efficiency has lower value in comparison
with constant mass flow rate condition; (b) at high concentration ratio (C = 5), higher operating temper-
ature is achieved. The analytical expression of the electrical efficiency of the proposed system is also
derived. An overall thermal and exergy analysis of PVT-CPC water collector system in terms of energy
degraded into the environment and exergy destruction have also been carried out.
Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction exit operating outlet fluid temperature (Too), the mass flow rate
should be controlled by using appropriate temperature sensor for
For the conservation of conventional fossil fuels available to a known insolation (solar intensity). Sodha et al. (1981) have stud-
human kind, there is a need to search an alternative energy source ied the performance of forced circulation solar water heating sys-
locally available to meet our energy requirements. Basically, solar tem with and without heat exchanger for constant collection
energy is directly responsible to produce renewable energy sources temperature mode. Sinha and Tiwari (1992) investigated the ther-
and indirectly for non-renewable energy sources (fossil fuel). One mal performance of commercial solar hot water system for con-
of easiest way to use solar energy is in the form of hot water stant delivery temperatures. It was reported that when constant
through flat plate collector. It is also known that flat plate collec- delivery temperature increases then the time in which the system
tors (FPC’s) give better performance under forced mode of opera- operates also reduces. In this direction the same concept was
tion in larger hot water system for industrial applications. For applied by Tiwari et al. (2009) for an exergy analysis of integrated
sustainable forced mode of operation of flat plate collector, photo- photovoltaic thermal solar water heater under constant collection
voltaic thermal (PVT) flat plate collectors have been developed. temperature modes and the results were also compared with con-
There are lots of works carried out by many researchers in the area stant flow rate mode. It was observed that the overall daily thermal
of photovoltaic thermal (PVT) flat plate collectors. However, there efficiency of integrated photovoltaic thermal system (IPVTS)
is a variation in operating outlet fluid temperature (Tfo) using such increased with the increase in constant mass flow rate and
system (PVT-FPC) for a given mass flow rate. To achieve constant decreased with increase of constant collection temperature. Alta
et al. (2010) have found that the thermal efficiencies of the finned
air collectors were high as compared to air collector without fin.
⇑ Corresponding author. The irreversibility was found to be highest in air collector without
E-mail address: datheaya@gmail.com (D. Atheaya).

http://dx.doi.org/10.1016/j.solener.2016.05.055
0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.
 D. Atheaya et al. / Solar Energy 135 (2016) 222–231 223

Nomenclature

A area (m2) U t;pa total (top and bottom) overall heat transfer coefficient
Aa total aperture area (m2) (Aa = Aam + Aac) from plate to ambient (W/m2 K)
Aam aperture area over PV module (m2) U L1 overall heat transfer coefficient from blackened surface
Aac aperture area over glazed portion (m2) to ambient (W/m2 K)
Ar total receiver area (m2) go efficiency at standard test condition (It = 1000 W/m2,
Arm receiver area covered by PV module (m2) To = 25 °C)
Arc receiver area covered by glass (m2) bo temperature coefficient of efficiency (K1)
b breadth of receiver (m)
bo breadth of aperture area of glass (m) Greek letters
cf specific heat of fluid (J/kg K) a absorptivity
C concentration ratio, dimensionless b packing factor
dx elemental length (m) q reflectivity
_
Ex exergy (kW h) s transmittivity
F0 flat plate collector efficiency factor gi instantaneous thermal efficiency
FR flow rate factor, dimensionless ðasÞeff product of effective absorptivity and transmittivity
h heat transfer coefficient (W/m2 K) g thermal efficiency
Lrm length of receiver covered by PV module (m)
Lrc length of receiver covered by glass (m)
Subscript
Lr total length of the aperture area (m) a ambient
Len energy loss (kW h) c solar cell
Lex exergy loss (kW h) eff effective
PF1 first penalty factor due to glass cover
f fluid
PF 2 second penalty factor due to absorber/receiver plate fi inlet fluid
PFc penalty factor due to glass cover for the portion covered fo outlet fluid
by glazing g glass
It total radiation (W/m2)
m module
Ib beam radiation (W/m2) p plate
m_f mass flow rate of water in (kg/s)
T oo constant collection temperature (°C)
U t;ca overall heat transfer coefficient from solar cell to ambi- Abbreviations
ent through glass cover (W/m2 K) PV photovoltaic
CPC compound parabolic concentrator
U t;cp overall heat transfer coefficient from solar cell to plate
(W/m2 K) PVT photovoltaic thermal
PVT-CPC photovoltaic thermal compound parabolic concentrator

fins. Tiwari et al. (2011) have reviewed analytical work on PVT Bouadila et al. (2014) studied energy and exergy analyses of
technology which includes an overall thermal performance, exergy solar air heaters with and without latent heat storage materials.
analysis, energy matrices and uniform annual cost (una cost) anal- They reported that the daily energy and exergy efficiencies varied
ysis including constant collection temperature mode. Saidur et al. between 32–45% and 13–25% respectively. Further, exergy analy-
(2012) studied the detailed exergy analysis of solar energy applica- ses of solar photovoltaic thermal (PVT) water collector with and
tions namely solar photovoltaic, solar heating devices, solar water without collection cum storage were carried out by
desalination system, solar air conditioning and refrigerators, solar Sobhnamayan et al. (2014) and Ziapour et al. (2014). The PVT-
drying process and solar power generation. They have observed CPC system has a dual advantage firstly thermal energy and elec-
that the highest exergy destruction was in solar collectors in most tricity is produced and secondly the photovoltaic cell area
of the solar heating devices and solar air conditioning systems. decreases which leads to a decrease in system cost. Nowadays in
Ceylan (2012) analyzed a temperature controlled (constant tem- most of the industries the requirement of hot water at a constant
perature mode) solar water heater by using the concept of energy temperature is growing in abundance. Therefore, in this paper, an
(first law of thermodynamics) and exergy (second law of thermo- attempt has been made to an overall energy and exergy analyses
dynamics). It was experimentally observed that the temperature of photovoltaic thermal (PVT) compound parabolic concentrator
controlled solar water heater (TCSWH) and thermo-siphon water (CPC) under constant collection temperature mode which can be
system for the control device set to 45 °C. An average energy effi- utilized for industrial applications. These analyses have been car-
ciency of TCSWH thermo-siphon system was reported as 65% and ried out for the climatic and design parameters used by Atheaya
60% respectively. Later on, Mishra and Tiwari (2013) have et al. (2015). Comparison of partially covered PVT-CPC water col-
extended the work of constant collection temperature for N- lector system [case (i)] has also been made with fully covered
photovoltaic thermal (PVT) flat plate collectors connected in series. PVT-CPC water collector system [case (ii)], conventional CPC water
They concluded that for N-photovoltaic thermal (PVT) flat plate collector system [case (iii)] and partially covered PVT water collec-
collectors connected in series, there was not much difference in tor system [case (iv)].
overall performance for placing semi-transparent PV either above
portion or below portion of flat plate collector (FPC) in any mode
of operation. Recently, Ceylan et al. (2014) have seen the effect of 2. Photovoltaic thermal compound parabolic concentrator
temperature controlled cooling on performance of photovoltaic system
module solar collector. It was observed that electrical efficiency
with cooling effect has maximum value of 13% in comparison with The photovoltaic thermal compound parabolic concentrator
electrical efficiency without cooling as expected. considered in this present study [case (i)] was proposed by
224 D. Atheaya et al. / Solar Energy 135 (2016) 222–231

Fig. 1a. Cross sectional side view of proposed partially covered PVT-CPC water collector system showing constant collection temperature [case (i)] (Aa > Ar; Lrm = 1m;
Lrc = 1m).

Fig. 1b. Cut sectional front view at x–x0 of proposed partially covered PVT-CPC water collector system [case (i)].

Atheaya et al. (2015) to develop an analytical characteristic get the water at a constant collection temperature ðT oo Þ by varying
equation of the partially covered PVT-CPC system. Here in this sys- the mass flow rate of water throughout the system. This heated
tem a photovoltaic thermal system is integrated with compound water at a constant temperature is used for various processes in
parabolic concentrator. Fig. 1a shows side view of proposed par- chemical industries. The outlet fluid which exits below the semi-
tially covered PVT-CPC water collector system showing constant transparent PV module becomes inlet of glazed receiver system.
collection temperature ðT oo Þ. The beam radiation falls on aperture The prime objective of this research work is to have a high constant
area Aa (Fig. 1b) of the partially covered PVT-CPC system and it gets water temperature at the outlet of the system. However if the
reflected from the reflector and finally comes to the receiver sur- system operates in forced mode it is easier to continuously
face and gets absorbed there. A tube in plate glazed partially cov- deliver water at constant temperature because for this we need
ered flat plate collector is taken as receiver of area Ar (Fig. 1c). extra source of electricity to run the pump which can be
This tube in plate is insulated from all the sides. Heat gets trans- achieved by using PV module. The cases which are investigated
ferred from the PV module’s non packing area which is placed in the paper are
above the half surface of receiver plate. The other half surface of
the receiver plate is glazed. There is also some heat transfer from [case (i)]: Partially covered PVT-CPC water collector system for
solar cell to the receiver plate and in return the water which flows constant collection temperature mode. (In half of the
below the receiver plate gets heated. The electrical energy is gen- receiver plate PV modules are pasted and in another half glazing
erated from the PV module of the partially covered PVT-CPC water is done on the receiver absorber plate in this case;
collector system. At the outlet of the above mentioned system we Aa ¼ 2 m2 ; Ar ¼ 1 m2 ).
 D. Atheaya et al. / Solar Energy 135 (2016) 222–231 225

Fig. 1c. Cut sectional front view at y–y0 of proposed partially covered PVT-CPC water collector system [case (i)].

[case (ii)]: Fully covered PVT-CPC water collector system for outlet fluid temperature of system ðT oo Þ will be kept constant with
constant collection temperature mode. (Only PV module is pre- the time during the day by varying the mass flow rate.
sent on the receiver absorber plate in this case).
Aa ¼ 2 m2 ; Ar ¼ 1 m2 ðArm ¼ 1 m2 ; Arc ¼ 0Þ
[case (iii)]: Conventional CPC water collector system for con- 3.1.1. Partially covered PVT-CPC water collector system [case (i)]
stant collection temperature mode. (Glazing is done and PV Following Atheaya et al. (2015), the analytical expression for
module is absent on the receiver absorber plate in this case; the outlet fluid temperature of partially covered PVT-CPC water
Aa ¼ 2 m2 ; Ar ¼ 1 m2 ðArm ¼ 0; Arc ¼ 1 m2 Þ.) collector system for constant mass flow rate ðm _ f Þ is given by
Eq. (1) determines the outlet fluid temperature for a variable solar

2h in o3
PF 2 ðasÞm;eff Ib Arm U l;m F rm
h in o þ T n 0 o
PF ðasÞ I Arc U l;c F rc 6 U l;m a _ f cf
m 7 F U l;c Arc
T fo1 ¼ c U c;eff b þ T a m _ f cf þ4 n 0 o 5 exp m_ f cf
l;c F U l;m Arm
þT fi exp _ f cf
m
ð1Þ
_ f cf
h n 0 oi _ f cf
h n 0 oi
m F U l;c Arc m F U l;m Arm
where F rc ¼ U Arc 1  exp m_ c ; F rm ¼ U Arm 1  exp _ c
m
l;c f f l;m f f

[case (iv)]: Partially covered PVT water collector system for con-
stant collection temperature mode. (The compound parabolic
concentrator is absent in this case, Aa ¼ 2 m2 ; Ar ¼ 2 m2 .) intensity and constant massflow rate. The various assumptions
under which Eq. (1) was derived are as follows:
3. Thermal modeling
(1) The partially covered PVT-CPC water collector system was in
3.1. Constant collection temperature mode quasi steady state.
(2) The ohmic losses in the solar cells and the photovoltaic mod-
The output temperature of a solar collector device is sensitive to ules were negligible.
the mass flow rate variation. When the mass flow rate is low the (3) One dimensional heat flow was considered.
high output temperature of working fluid can be obtained at a (4) The heat capacity of solar cells and glass cover were
given solar intensity (beam radiation). In order to use the solar neglected.
devices for commercial purposes for eg. chemical factories, (5) The temperature was uniform across the thickness of solar
manufacturing plants etc. a constant temperature of working fluid cells and glass cover.
is required for the proper functioning of the processes. The final
226 D. Atheaya et al. / Solar Energy 135 (2016) 222–231

However, inorder to get constant outlet fluid temperature for 3.2. Analytical expression for the electrical efficiency determination
variable intensity, there is a need to vary mass flow rate. Now, under constant collection temperature mode
our attempt in this paper is to evaluate variable mass flow rate
for constant temperature, Too. The solar cell temperature ðT c Þ and absorber plate temperature
For constant collection temperature, the outlet fluid tempera- ðT p Þ can be calculated by using the expressions given by Atheaya
ture of partially covered PVT-CPC water collector system for con- et al. (2015) which are as follows:
stant mass flow rate ðm _ f Þ, Eq. (1) should be considered as
ðasÞ1;eff Ib þ U t;ca T a þ U t;cp T p
constant i.e. T fo1 ¼ T oo . Tc ¼ ð6Þ
In this case for known constant T oo and Ib , the solution of above
U t;ca þ U t;cp
equation will be the mass flow rate at which ½T oo  f ðm _ f Þ ¼ 0. The
numerical values of the mass flow rate for a known constant collec- ðasÞ2;eff Ib þ PF 1 ðasÞ1;eff Ib þ U L1 T a þ F 0 hpf T oo
Tp ¼ ð7Þ
tion temperature ðT fo1 ¼ T oo Þ and Ib was determined by the Itera- F 0 hpf þ U L1
tion method. The above expression ðT fo1 ¼ T oo Þ can also be solved
The expression of solar cell efficiency ðgc Þ of photovoltaic
by Computational Fluid Dynamics (CFD) analysis as suggested by
module as given by Evans (1981) and Schott (1985) which is as
Giangaspero and Sciubba (2013).
follows:
gc ¼ go ½1  bo ðT c  T o Þ ð8Þ
3.1.2. For fully covered PVT-CPC water collector system [case (ii)]
In this system the receiver area is entirely covered with PV By substituting the values of solar cell temperature ðT c Þ and
module. Therefore in this very system in Eq. (1), Arc ¼ 0. absorber plate temperature ðT p Þ from Eqs. (6) and (7) in Eq. (8)
The outlet fluid temperature at the end of the fully covered PVT- the analytical expression of solar cell efficiency for the partially
CPC collector for constant mass flow rate ðm _ f Þ is given by covered PVT-CPC water collector system [case (i)] operating under
constant collection temperature mode is given by
   0  2 8  93
PF 2 ðasÞm;eff Ib F U l;m Arm > b qs b Aam I F 0 hpf þ U L1 þ PF 1  U t;cp >
T oo ¼ þ T a 1  exp þ T fi 6 >  o g c Arm b
>  >
>7
U l;m m_ f cf 6 >
> þ U t;cp ðasÞ2:eff Ib þ T a U t;ca F 0 hpf þ U t;ca U L1 >
>7
 0  6 >
> >
>7
6 >
< þU F 0 h T  T U þ U   0 >
=7
F U l;m Arm t;cp F hpf þ U L1
 exp
_ f cf
ð2Þ go 6
61  bo
t;cp pf oo o t;ca
ðUt;ca þUt;cp ÞðF 0 hpf þUt;cp Þ
7
7
m 6 >
> >
>7
6 >
> >
>7
6 >
> >
>7
From the above Eq. (3) the following expression for mass flow 4 >
> >
>5
: ;
rate is given by
gc ¼ go bo qsg bc AAam I ðF 0 hpf þU L1 þPF 1 U t;cp Þ
F 0 U l;m Arm 1 rm b

_f ¼ h n
m  oi n  o ðUt;ca þUt;cp ÞðF 0 hpf þUt;cp Þ
PF 2 ðasÞm;eff Ib PF 2 ðasÞm;eff Ib
cf ln T fi  U
þ Ta  ln T oo  U
þ Ta ð9Þ
l;m l;m

ð3Þ The electrical efficiency gm of photovoltaic module system by

Tiwari et al. (2011) is given as follows:
From Eq. (3) we can determine the different mass flow rate val-
ues for a known constant collection temperature ðT fo1 ¼ T oo Þ. gm ¼ sg bc gc ð10Þ
Substituting the above Eq. (9) in Eq. (10) we get the expression
3.1.3. For conventional CPC water collector system [case (iii)] for the electrical efficiency of partially covered PVT-CPC system
In this system the receiver area is entirely covered with glass under constant collection mode which is as follows:
therefore in Eq. (1); ðArm ¼ 0Þ. 2 8  93
>
> bo qsg bc AAam Ib F 0 hpf þ U L1 þ PF 1  U t;cp >
>
The outlet fluid temperature at the end of the conventional CPC 6 >
>  rm
  >
>7
6 >
> >
>7
collector for constant mass flow rate ðm _ f Þ is given by 6 >
> þ U t;cp ðasÞ2:eff Ib þ T a U t;ca F 0 hpf þ U t;ca U L1 >
>7
6 >
> >
>7
    0  6 < þU F 0 h T  T U þ U
>  0
F h þU
>
=7
PF c ðasÞc;eff Ib Arc U l;c F rc F U l;c Arc go 6
61  bo
t;cp pf oo o t;ca t;cp pf L1 7
7
T oo ¼ þ Ta þ T fi exp ð4Þ 6 >
> ðUt;ca þUt;cp ÞðF 0 hpf þUt;cp Þ >
>7
U l;c m _ f cf _ f cf
m 6 >
> >
>7
6 >
> >
>7
6 >
> >
>7
4 >
> >
>5
Solving the above Eq. (4) we get the following expression >
: >
;
gm ¼ sg bc
F 0 U l;c Arc 1
go bo qsg bc AAam I ðF 0 hpf þU L1 þPF 1 U t;cp Þ
rm b
_f ¼
m hn  oi n  o ðUt;ca þUt;cp ÞðF 0 hpf þUt;cp Þ
PF c ðasÞc;eff Ib PF c ðasÞc;eff Ib
cf ln T fi  U
þ Ta  ln T oo  U
þ Ta
l;c l;c
ð11Þ
ð5Þ
From the above Eq. (5) the different mass flow rate values 3.3. Overall thermal and exergy analysis
can be computed for a particular constant collection temperature,
T oo . The useful daily electrical energy available (kW h) from the par-
tially covered PVT-CPC water collector system is given as follows:
3.1.4. Partially covered PVT water collector system [case (iv)] X
t¼n

In this case the CPC is absent and by following Atheaya et al. Eel ¼ gm Ib qAam ð12Þ
t¼1
(2015) we know Aa ¼ Ar ; Lrm ¼ 0:605 m; Lrc ¼ 1:395 m.
The case (iv) can be investigated by using Eq. (1) and itera- where n is the number of hours the working fluid (water) is used
tion method. Also we can determine the different mass flow from the system.
rate values for a particular known constant collection The daily thermal energy available (kW h) from the partially
temperature. covered PVT-CPC water collector system is given as follows:
 D. Atheaya et al. / Solar Energy 135 (2016) 222–231 227

X X X
X
t¼n _ inputs ¼
Ex _ outputs þ
Ex _ Total;Destruction
Ex ð23Þ
Q_ th ¼ _ f cf  ðT oo  T fi Þ
m ð13Þ
t¼1 The above expression can be written as follows:
where n is the number of hours the working fluid is used from the X X X
_ Total;Destruction ¼
Ex _ inputs 
Ex _ outputs
Ex
system.
¼ ExergylossðLex Þ ð24Þ
3.3.1. Overall exergy analysis
The above total exergy destruction is calculated in the next
Following Hepbasli (2008), the thermal exergy of the partially
section.
covered PVT-CPC water collector system [case (i)] under constant
collection mode ðT fo1 ¼ T oo Þ can be written as
3.5. Exergy destruction (irreversible entropy generation) of the
ðT þ 273Þ partially covered PVT-CPC water collector system
E_ xc ¼ m
_ f cf ðT oo  T fi Þ  m
_ f cf ðT a þ 273Þ ln oo ðWÞ ð14Þ
ðT fi þ 273Þ
The concept of exergy destruction is helpful in evaluating the
Following Petela (2003) and Szargut (2003) and the solar radia- thermal performance of the system. It is beneficial to determine
tion exergy can be expressed by the exergy destruction of the various components of the system.
" #
4 Agrawal and Tiwari (2012) suggested that the exergy destruction
_Exsun ¼ Ib 1  4 T a þ T a ð15Þ or irreversibility’s associated with the system should be minimized
3 Ts Ts
to improve the system’s performance. Following Rosen and Dincer
where T a is the surrounding temperature in Kelvin and (2003) for any system operating in a steady state process the
T s ¼ T sun ¼ 6000 K. energy degraded into the environment and exergy destruction
Thermal exergy efficiency is defined as the ratio of thermal are given as follows:
exergy output to the thermal exergy input. Energy degraded into the environment; Len
X X
E_ xc ¼ Energy  Energy ð25Þ
Overall thermal exergy efficiency ¼ ð16Þ
Aa E_ xsun inputs outputs

And the useful electrical exergy of the partially covered PVT- and
CPC water collector system from the PV module for constant col- X X
Exergy destruction; Lex ¼ Exergy  Exergy ð26Þ
lection temperature mode in Watts is given as follows: outputs
inputs

E_ el ¼ gm Ib qAam ð17Þ where the summation represents overall inputs and outputs in a
Electrical exergy efficiency is basically the electrical efficiency, gm system per day.

Electrical exergy efficiency ¼ gm ð18Þ

4. Results and discussion
The overall exergy efficiency of partially covered PVT-CPC water
collector systems under constant collection mode can be deter- The design and climatic parameters of the partially covered
mined by adding both the thermal exergy efficiency and electrical PVT-CPC system used by Atheaya et al. (2015) is used to carry
exergy efficiency. out the numerical computations of the present study. The various
design parameters of partially covered PVT-CPC water collector
E_ xc
So overall exergy efficiency ¼ ðgm Þ þ ð19Þ system has been given in Table 1.
Aa E_ xsun Fig. 2. illustrates the mass flow rate variation with respect to
time for partially covered PVT-CPC water collector system with
constant collection temperature. It is observed that as the constant
3.4. Exergy destruction of the system components
collection temperature is increased from 30 °C to 60 °C there is a
significant decrease in mass flow rate of water. This is because
There are two components of partially covered PVT-CPC water
the transfer of thermal energy will be more at low mass flow rates
collector system namely first is semi-transparent PV module and
secondly the other is conventional CPC collector. Following
Table 1
Tiwari and Mishra (2011), the overall exergy balance for the
Various design parameters of partially covered PVT-CPC water collector system
semi-transparent PV module is as follows: Atheaya et al. (2015).
X X X
_ input;PV ¼
Ex _ Electrical þ
Ex _ Destruction PV
Ex ð20Þ Parameters Values
Aa, Aam, Aac 2 m2, 1 m2, 1 m2
Further, the overall exergy balance exergy for the conventional Arc, Arm, Ar 0.5 m2, 0.5 m2, 1 m2
CPC collector is as follows Lrm, Lrc 1 m, 1 m
X X X bo, b 1 m, 0.5 m
_ input;CPC;Collector ¼
Ex _ Thermal þ
Ex _ Destruction CPC;Collector
Ex ð21Þ F0 , Frc, Frm 0.9680, 0.8693, 0.8110
Inclination angle 30°
The overall exergy balance for the combined system is obtained go, bo, q 0.15, 0.0045/K, 0.84
by the summation of Eqs. (20) and (21) and we get the following Kg, Ki, Kp 0.816 W/m K, 0.166 W/m K, 64 W/m K
expression Lg, Li, Lp 0.003 m, 0.100 m, 0.002 m
X X PF1, PF2, PFc 0.3782, 0.9512, 0.9842
_ input;PV þ
Ex _ input;CPC;Collector
Ex hpf 100 W/m2
X X hi, hi1, ho 5.7 W/m2, 5.8 W/m2, 9.5 W/m2
¼ _ Electrical þ
Ex _ Thermal
Ex ac, ap, cf 0.9, 0.8, 4179 J/kg K
X X  UL1, Ul,c 3.47 W/m2K, 4.7 W/m2K
þ _ Destruction PV þ
Ex _ Destruction CPC;Collector
Ex ð22Þ Ul,m, Ut,pa 7.87 W/m2K, 4.8 W/m2K
Ut,ca, Ut,cp 9.17 W/m2K, 5.58 W/m2K
sg, bc 0.95, 0.89
The above Eq. (22) can be further rewritten as follows:
228 D. Atheaya et al. / Solar Energy 135 (2016) 222–231

which leads to high collection temperature of water. This is in

0.009 o
30 C accordance with the results obtained by Abdullah and Bassiouny
o
40 C (2014). The hourly variation of mass flow rate for constant collec-
0.008 o
50 C
o
tion temperature of 50 °C for partially covered PVT-CPC water col-
60 C
0.007 lector [case (i)], fully covered PVT-CPC water collector [case (ii)],
Mass flow rate, kg/sec

conventional CPC water collector system [case (iii)] and partially

0.006 covered PVT water collector system [case (iv)] is shown in Fig. 3.
From the figure it is observed that the variation of mass flow rate
0.005 with time for a given constant collection temperature ðT oo Þ have
lower value in the case of fully covered PVT-CPC water collector
0.004 system due to lower value of Ib through non packing area at recei-
ver. It is due to the fact that thermal energy associated with recei-
0.003
ver/absorber in case (ii) is least. Fig. 4 shows the hourly variation of
thermal, electrical and overall exergy efficiency (Eqs. (16), (18) and
0.002
(19)). As the constant collection temperature (Too) is increased
08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 from 30 °C to 60 °C there is an increase in thermal exergy and this
Time, hour can be verified from Eq. (14). Further, the electrical efficiency
decreases with the increase of temperature (Eq. (8)) so the electri-
Fig. 2. Variation of mass flow rate with respect to time for partially covered PVT- cal exergy shows a decreasing trend. The above findings are in
CPC water collector system [case (i)] when constant collection temperature is
accordance to the results reported by Chow et al. (2009). However
varied from 30 °C to 60 °C.
the overall exergy efficiency increases due to the dominance of
thermal exergy. It is also noted that overall exergy efficiency at col-
lection (60 °C) is highest due the decrease in electrical exergy effi-
0.009 o

ciency ðg Þ and increase in thermal exergy efficiency ðE_ xc Þ.

At 50 C constant collection temperature
Conventional CPC water collector m
0.008 Partially covered PVT-CPC water collector Fig. 5 shows the hourly variation of solar cell temperature ðT c Þ
0.007
Partially covered PVT water collector
in °C, solar cell efficiency ðgc Þ and the module efficiency ðgm Þ at dif-
Fully covered PVT-CPC water collector
ferent constant collection temperatures which are 30 °C, 40 °C,
Mass flow rate, kg/sec

0.006
50 °C and 60 °C respectively. It can be seen that solar cell temper-
0.005 ature increases till 1 pm and then it decreases afterwards. As the
0.004
constant collection temperature increases the solar cell tempera-
ture, T c decreases because of the electrical energy losses at higher
0.003 temperatures. The maximum Tc is 97 °C at constant collection tem-
0.002 perature 30 °C and the minimum T c is 81 °C at constant collection
temperature 60 °C (1 pm). The module and the solar cell ðgm ; gc Þ
0.001
efficiencies decrease till 1 pm and then again increases further. It
0.000 is observed that as constant collection temperature is increased
08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00
from 30 °C to 60 °C the module and solar cell efficiencies decrease.
Time, hour
The fully covered PVT-CPC water collector system [case (ii)]
Fig. 3. Hourly variation of mass flow rate at constant collection temperature (50 °C)
gives the maximum daily electrical energy (Fig. 6) then the par-
for partially covered PVT-CPC water collector [case (i)], fully covered PVT-CPC water tially covered PVT-CPC water collector system [case (i)] owing to
collector [case (ii)], conventional CPC water collector system [case (iii)] and maximum area covered by PV module in earlier case. Similarly
partially covered PVT water collector system [case (iv)]. because the area of PV module in partially covered PVT water col-
lector system [case (iv)] is less than the partially covered PVT CPC
water collector system therefore the generation is electrical energy
is also least in case (iv).

20

18 100 0.15
Overall exergy efficiency
o
Eel(30 C)
16 o 90
Exc(30 C) Tc 0.14
Electrical Efficiency, in fraction

o
Exergy efficiency, in percentage

Ex (30 C)
14 o 80
Eel (40 C) o o
(Too= 30 C) (Too= 30 C)
0.13
Solar cell Temperature, C

o c m

12
Exc (40 C)
70 o o
o

o (Too=40 C) (Too=40 C)
Ex (40 C) c m
o o
o (Too=50 C) (Too=50 C)
Eel (50 C) 60 c m
10 Electrical Exergy efficiency
Exc (50 C)
o o
(Too=60 C) (Too=60 C)
o 0.12
c m

50
o
Ex (50 C)
8 o
Eel (60 C)
0.11
Thermal exergy efficiency Exc (60 C)
o
40 c
6 o
Ex (60 C)
30 0.10
4 o
Too=30 C
20 o
Too=40 C
2 o m 0.09
10 Too=50 C
o
Too=60 C
0
0 0.08
8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00
Time, hour Time, hour

Fig. 4. Hourly variation of thermal exergy efficiency (Exc), electrical exergy Fig. 5. Hourly variation of solar cell temperature (Tc), solar cell efficiency (gc)
efficiency (Eel) and overall exergy efficiency (Ex) at constant collection temperatures electrical efficiency (gm) for partially covered PVT-CPC water collector system [case
(30–60 °C) for partially covered PVT-CPC water collector system [case (i)]. (i)] for different constant collection temperatures.
 D. Atheaya et al. / Solar Energy 135 (2016) 222–231 229

1.50 PVT-CPC system were obtained for 8 h (8 am–4 pm). Further,

60 °C constant collection temperature was obtained for 6 h
1.25 Partially covered PVT-CPC watercollector system (10 am–4 pm) (Ref. Fig. 2). For conventional CPC water collector sys-
Fully covered PVT-CPC water collector system tem [case (iii)] the available daily thermal energy is maximum and it
Daily Electrical Energy, kWh

Partially covered PVT water collector system

decreases from 30 °C to 60 °C. For fully covered PVT-CPC water col-
1.00
lector system it is obvious that the thermal energy is least and it
decreases as constant collection temperature is increased. For par-
0.75 tially covered PVT water collector [case (iv)] at 30 °C it is observed
that the thermal energy is initially more than the partially covered
0.50 PVT-CPC water collector system[case (i)] and then it reduces.
Fig. 8 illustrates the hourly variation of concentration ratio
0.25
(C = Aa/Ar, C = 1–5) and the outlet fluid temperature for fully cov-
ered PVT-CPC water collector system when the mass flow rate is
constant and equal to 0.025 kg/s. It is further noted that as the con-
0.00
centration ratio is increased from 1 to 5 the outlet fluid tempera-
20 30 40 50 60 70
Constant collection Temperature To, C
o ture increases. The obtained results are in accordance with Li
et al. (2013). It is also observed that the outlet fluid temperature
Fig. 6. Daily electrical energy in kW h for different constant collection tempera- increases firstly till 1 pm because the beam radiation increases
tures 30 °C, 40 °C, 50 °C and 60 °C for [case (i)], [case (ii)] and [case (iv)]. and then it decreases due to reduced beam radiation afterwards.
Fig. 9 shows the characteristic curve for fully covered PVT-CPC
water collector system [case (ii)] for constant mass flow rate
10
(0.025 kg/s) and constant collection temperatures namely 40 °C,
9 Partially covered PVT-CPC water collector system 50 °C, 60 °C and 100 °C. The characteristic equations for the above
Fully covered PVT-CPC water collector system cases are given as follows:
8 Conventional CPC water collector system
Partially covered PVT water collector system
Daily Thermal energy, kWh

7 (a) For [case (ii)], constant mass flow rate (0.025 kg/s)
 
6 Tm  Ta
gth ðin fractionÞ ¼ 0:43  4:90
5 Ib
4  
Tm  Ta
gth ðin percentageÞ ¼ 43  490
3 Ib
2 (b) For [case (ii)], 40 °C
1
 
Tm  Ta
gth ðin fractionÞ ¼ 0:28  2:7
0 Ib
20 30 40 50 60 70
 
Constant collection temperature, C
o
Tm  Ta
gth ðin percentageÞ ¼ 28  270
Ib
Fig. 7. Daily thermal energy in kW h for different constant collection temperatures
30 °C, 40 °C, 50 °C and 60 °C for [case (i)], [case (ii)], [case (iii)], and [case (iv)] (c) For [case (ii)], 60 °C
respectively.  
Tm  Ta
gth ðin fractionÞ ¼ 0:25  1:58
Ib
C=1, Aa=1,Ar=1
100 mf=0.025 kg/sec
C=2, Aa=2,Ar=1
90 C=3, Aa=3,Ar=1
C=4, Aa=4,Ar=1
50
80 C=5, Aa=5,Ar=1
Outlet fluid temperature T fo , C

Constant mass flow rate (0.025kg/sec)

o

o
70 Constant collection temperature (To=40 C)
o
Constant collection temperature (To=60 C)
60 40 o
Constant collection temperature (To=80 C)
o
50 Constant collection temperature (To=100 C)

C=5
, in percentage

40 30

30

20 20
i,th

10

0
10
08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
Time, hour

Fig. 8. Effect of concentration ratio (C) for fully covered PVT-CPC water collector 0
system [case (ii)] with respect to time. 0.00 0.02 0.04 0.06 0.08 0.10
o 2
(Tm-Ta)/Ib, Cm /W

Fig. 7 gives the daily thermal energy in kW h at different constant Fig. 9. Characteristic curve for fully covered PVT-CPC water collector system for (a)
collection temperatures for various cases. The constant collection constant flow rate (0.025 kg/s), (b) constant collection temperature To = 40 °C, 60 °C,
temperature in the range of (30–40 °C) for partially covered 80 °C, 100 °C when concentration ratio is 5.
230 D. Atheaya et al. / Solar Energy 135 (2016) 222–231

Table 2 1. For partially covered PVT-CPC water collector system [case (i)],
Values of gain factor and loss term for various cases. the mass flow rate of water is found to decrease with the
S. Fully covered PVT-CPC water collector Gain Loss increase of the constant collection temperature.
No System factor term 2. It is observed that fully covered PVT-CPC water collector system
1 Constant mass flow rate (0.025 kg/s) 0.43 4.90 [case (ii)] has low mass flow rates as compared to [case (i)],
2 Constant collection temperature (To = 40 °C) 0.28 2.70 [case (iii)] and [case (iv)] for a given constant collection temper-
3 Constant collection temperature (To = 60 °C) 0.25 1.58 ature (50 °C).
4 Constant collection temperature (To = 80 °C) 0.21 1.04
5 Constant collection temperature 0.17 0.71
3. The daily electrical energy is more in fully covered PVT-CPC
(To = 100 °C) water collector system [case (ii)] as expected.
4. The instantaneous thermal efficiency for fully covered PVT-CPC
water collector system at different constant collection temper-
  atures is predicted and compared with the constant mass flow
Tm  Ta
gth ðin percentageÞ ¼ 25  158 rate mode.
Ib
5. The fully covered PVT-CPC water collector system [case (ii)] is
(d) For [case (ii)], 80 °C recommended from the electrical energy point of view (Fig. 6)
  while from the thermal point of view conventional CPC water
Tm  Ta
gth ðin fractionÞ ¼ 0:21  1:04 collector system [case (iii)] is the best (Fig. 7). The above results
Ib
are in agreement with Atheaya et al. (2015).
 
Tm  Ta
gth ðin percentageÞ ¼ 21  104
Ib
Appendix A
(e) For [case (ii)], 100 °C
  In the thermal modeling of partially covered PVT-CPC water col-
Tm  Ta
gth ðin fractionÞ ¼ 0:17  0:71 lector system the following relations are used:
Ib
Aa
  C¼
Tm  Ta Ar
gth ðin percentageÞ ¼ 17  71
Ib and
where T m ¼ ðT oo þ T fi Þ=2.  Aam
ðasÞ1;eff ¼ q ac sg bc  gm
Arm
The gain factor and loss terms are mentioned in Table 2. The
energy degraded into the environment and exergy destruction For fully covered PVT-CPC water collector system
per day for partially covered PVT-CPC system has been calculated Aac ¼ 0; Arc ¼ 0
by using Eqs. (25) and (26) and it can be minimized by increasing Therefore ðasÞ1;eff ¼ qðac sg bc  gm ÞC
the thermal and electrical efficiency of partially covered PVT-CPC  1
water collector. Table 3 shows the values of Len and Lex as Lg 1
U t;ca ¼ þ
6.05 kW h and 10.08 kW h respectively. K g ho
 1
5. Validation Lg 1
U t;cp ¼ þ
K g hi
The validation of model proposed by Atheaya et al. (2015) for
constant collection temperature as a special case (see Section 3.1.2) ho ¼ 5:7 þ 3:8V; V ¼ 1 m=s
has been carried out and it has been observed that computational
results are in accordance as obtained by Mishra and Tiwari (2013). hi ¼ 2:8 þ 3V
The decreasing trend of instantaneous thermal efficiency is same Also,
as for collectors fully covered by semitransparent PV module
ðT oo ¼ 40  CÞ obtained by Mishra and Tiwari (2013) and Sodha Aam
ðasÞ2;eff ¼ qap s2g ð1  bc Þ
et al. (1981). Arm
For fully covered PVT-CPC water collector system
6. Conclusions
ðasÞ2;eff ¼ qap s2g ð1  bc ÞC
In the present study, the partially covered PVT-CPC system
U t;cp
[case (i)] is studied under constant collection temperature. The PF1 ¼
other cases which are discussed along with the previous system U t;cp þ U t;ca
are fully covered PVT-CPC water collector system [case (ii)], con-
ventional CPC water collector system [case (iii)] and partially cov- U t;ca  U t;cp
U L1 ¼
ered PVT water collector system [(case iv)]. The following ðU t;ca þ U t;cp Þ
conclusions are drawn from the present studies.

Table 3
Values of energy degraded into the environment (Len) and exergy destruction (Lex) for partially covered PVT-CPC water collector system.
P P P P
System inputs Energy outputs Energy Len inputs Exergy outputs Exergy Lex
(kW h) (kW h) (kW h) (kW h) (kW h) (kW h)
Partially covered PVT-CPC water collector system 10.8 4.75 6.05 10.9 0.82 10.08
 D. Atheaya et al. / Solar Energy 135 (2016) 222–231 231

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