Renewable Energy 109 (2017) 168e187

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Renewable Energy
journal homepage: www.elsevier.com/locate/renene

Numerical studies on thermal and electrical performance of a fully

wetted absorber PVT collector with PCM as a storage medium
Ankita Gaur a, *, Christophe Me
zo a, **, Ste

ne
phanie Giroux–Julien b
a ^timent H

University Savoie Mont-Blanc, LOCIE UMR CNRS 5271, Campus Scientifique Savoie Technolac - Ba elios, Avenue du Lac L

eman, F-73376, Le
Bourget-du-Lac, France
b ^timent Carnot, Avenue de la Physique, F-69621, Vileurbanne,
University Claude Bernard Lyon 1, CETHIL UMR CNRS 5008, Campus LyonTech La Doua - Ba
France

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

Article history: A detailed mathematical models is developed for a fully wetted absorber photovoltaic thermal (PVT)
Received 15 September 2016 collector with and without phase change material (PCM) under its absorber channel. Thermal and
Received in revised form electrical investigations were carried out using PCM OM37 for typical winter and summer days in Lyon,
21 January 2017
France. The system is analyzed under energy and exergy performances. PCM incorporation in a water PVT
Accepted 28 January 2017
Available online 4 February 2017
absorber improves the performance of system in terms of electrical and thermal parameters. Enhanced
electrical and thermal energy is attributed to dissipation of excess heat of PV module by latent heat
absorption mechanism that reduces the PV module temperature and release heat at the night as well,
Keywords:
PV modules
provides better electrical and thermal stabilities to the system. Overall thermal energy and overall exergy
Photovoltaic thermal system of PVT system for a winter day as well as for a typical summer day, are found to be strongly in favor of
Mass of PCM adding PCM. The effects of mass of PCM on module temperature, outlet water temperature, and PV
Exergy module electrical efficiency, have also been investigated. During sunshine hours, increment in the PCM
mass up to its optimal value decreases temperature resulting in higher electrical efficiency and also
allows providing higher water temperature at the nighttime.
© 2017 Elsevier Ltd. All rights reserved.

1. Introduction some cooling techniques like air cooling and water cooling. An
increment in electrical yield by water flow on the front of the PV
There is an urgent need of development of renewable energy modules based on crystalline and multi crystalline Si, has been
sources due to rapid growing demand of energy. In our modern observed before [3,4]. The extracted surplus heat of PV module can
society, inadequate supply of conventional energy sources is a be used to fulfil the need of thermal energy for industrial and
critical challenge. Emission of carbon di oxide and other pollution residential sectors. Such system is known as photovoltaic thermal
from the fossil fuels is another a major issue as it is causing climate (PVT) technology: a single unit that can increase the efficiency of PV
change [1]. module by using solar thermal system. In 1978 the first design and
Solar energy is one of the fastest growing sources of renewable performance of a PVT collector was presented, where water and air
energy. There are numerous foremost directions for solar technol- were used as a cooling fluid [5]. Since then a significant amount of
ogy growth such as Photovoltaic (PV) panel which directly convert theoretical and experimental research on PVT systems has been
the solar energy into electrical energy. It is a most mature tech- carried out [6e15]. A theoretical analysis via use of modified hotel
nology but unfortunately typically power of PV module decreases whillier model was presented by Florschuetz [16]. Further Lalovic
with 0.2e0.5%/
C increase of temperature [2]. Therefore to maxi- et al. conducted a theoretical analysis on PVT water collector and
mize the performance of PV module its temperature regulation is suggested that such system can be useful as pre heater for domestic
strongly needed which is usually done by cooling the PV module via hot water services [17]. Garg at al. also presented the same facets of
a PVT water collector [18].
Van Heiden et al. [19]. suggested that PVT systems could be a
cost effective solution for applications where roof area is limited.
* Corresponding author.
** Corresponding author. He et al. [20]. carried out a research on PVT system in which natural
E-mail address: ankita.gaur@univ-smb.fr (A. Gaur). convection was used to circulate the cold water. They found the

http://dx.doi.org/10.1016/j.renene.2017.01.062
0960-1481/© 2017 Elsevier Ltd. All rights reserved.
 A. Gaur et al. / Renewable Energy 109 (2017) 168e187 169

thermal efficiency lesser than a conventional thermosyphon solar For incidence of the maximum solar radiation, the PV module in
water heater but the energy saving efficiency was found to be northern hemisphere are placed south oriented, having inclination
greater. with horizontal surface equal to the latitude of the system's station
The same hybrid system was dynamically modelled by Chow [42,43]. Since the present study is carried out for climatic condi-
et al. [21]. They suggested that the performance of the system can tions of Lyon which is located at 45.7600
N, 4.8400
E in France
be enhanced by insertion of PV cells on the lower portion of col- therefore PV module is considered to be south oriented and in-
lector. Kalogirou and Tripanagnostopoulos [22] stated that PVT is clined at an angle of 45
to the horizontal.
economically feasible for industrial applications in a Mediterranean A thin layer of PCM below the water tubes of a water collector
environment. will store a substantial quantity of heat within PCM during sun-
Assoa et al. [23] presented a steady-state two-dimensional shine and at the night duration, solidification cause the discharging
thermal model for PVT collector based on sheet-and-tube concept of stored heat that will keep the water warm even at night too.
whereas the experimental study was carried out by Zondag et al.
[24]. Dupeyyrat et al. [25] performed an experiment on PVT col- 2. Thermal analysis
lector to enhance its performance. They found the global efficiency
of PVT collector more than 87%. Touafek et al. [26] studied the PVT A schematic diagram of the anticipated fully wetted absorber
system and PV module separately and found the thermal system type unglazed PVT water collector with PCM is depicted in Fig. 1.
cause improvement in efficiency of PV collector. The present fully wetted absorber type PVT collector set up
Shyam et al. [27,28] investigated the N-PVT water collectors consists of a frameless mono-crystalline semitransparent PV panel
connected in series and validated their thermal model with rated at 110 W, having efficiency 18% under standard test conditions
experimental studies. They found the collector partially covered by (STC). The photovoltaic parameters of the PVT system at STC are
semitransparent PV module at inlet of PVT water collector gives shown in Table 1. The detailed structure of fully wetted absorber
better result compared to that covered by PV module at outlet of type PVT collector with PCM is presented in Fig. 2(a).
the collector. However they have concluded that both configuration PV modules used in present PVT collector considered to be
give similar results for large number of collectors connected in semitransparent as higher efficiency is obtained using semi-
series. An experimental study was carried out by Jin et al. [29] on transparent or bi glass PV modules due to the solar radiation inci-
water type glazed and unglazed PV thermal collector. They dent on non packing area of PV module is transmitted through the
concluded that the unglazed PVT collector results in lower thermal glass however absorbed by the blackened plate [44,45]. Hence heat
efficiency and higher thermal efficiency as compared to the glazed is convected to the water from back PV cells as well as from top
PVT collector. surface of the blackened plate.
Further Jin et al. [30] performed an experiment on unglazed The area of the PVT collector is 2 m2 which is connected with an
liquid PVT collector with a sheet and tube type of absorber and insulated water tank of capacity 100 L. A DC pump of the capacity
other with fully wetted absorber type. They observed that the PVT 24 W was used to force the flow of water which is operated by the
collector with fully wetted absorber are more efficient. PV module itself.
Solar water heating system is a superior technology that has In order to maximize the heat transfer area fully wetted channel
been widely realized for domestic and industrial applications. approach of collector has been used that reduce the thermal
Though, still research is being carried out on unglazed PVT water resistance between water and collector fluid by allowing rectan-
collectors to improve its performance in both senses i.e. electrical gular shape channel for water flow [46]. There is no absorber sheet
and thermal. Recently some of the important studies have been in fully wetted absorber collector as PV module itself makes one
done on the use of phase change materials with PVT systems for face of channel. The heat is transferred from back surface of PV
minimizing the temperature of PV module [31e38]. PCM can store a module to the flowing water.
high latent heat due to phase change occurs and having a melting In fully wetted absorber type PVT water collector, a good ther-
point suitable for the application. Therefore in PVT water collector mal transfer improves the useful thermal output and reduces the
PCM can regulate the temperature of PV module by absorbing the temperature difference between the PV cells and the fluid (water)
heat on melting and can extend the duration of water heating as results better cooling effect and electrical efficiency of PV module.
well by releasing heat on freezing. Rabin et al. [39] studied a solar The PVT collectors are considered to be made up of black painted
collector storage system using salt hydrate eutectic mixture as PCM. copper rectangular channel attached to each other and covered
They developed a mathematical model for charging process by with PV absorber as shown in Fig. 2. These collectors are thermally
considering the negligible natural convection. Chaabane et al. [40] protected with 50 mm glass wool insulation. The bottom and sides
presented a numerical study of an integrated collector storage solar of the PVT collector are perfectly insulated. A space is formed be-
water heater with two different PCM (myristic acid and RT-42 tween the insulation and absorber plate where PCM is filled via PVC
graphite) and three radii of this PCM layer. They found that the pipe that could be better for the volume dissemination at the time
highest water temperature corresponds to the lowest radius. of PCM melting. A bio-based Phase Change Material (PCM) OM37
Bouadila et al. [41] performed an experiment on an integrated solar was used which is an organic material having large amount of heat
latent storage collector with two PCM-filled cavities incorporating energy stored in the form of latent heat. It can be absorbed or
below the absorber. The results showed that the paraffin increased released when the materials change state from solid to liquid or
the performance of the solar collector at night. liquid to solid. Ingredients of OM 37 are from 100% bio based raw
This paper aims to understand the effect of integration of OM 37 materials which are non hazardous, biodegradable and non toxicis
as a phase change material on the electrical and thermal perfor- usually the most available and cheaper phase change material
mance of an unglazed fully wetted type absorber PVT water col- therefore in the present study OM 37 has been used. The properties
lector. For that purpose theoretical models have been developed of OM37 is also given in Table 1 [47].
and solved numerically for PVT water collector with incorporation The PV panel converts visible and ultraviolet parts of the solar
of PCM under the absorber channel, for charging and discharging spectrum into electricity but infrared part of spectrum and excess
approach. The results have also been compared with collector heat of PV module are absorbed by the fully wetted absorber. That
without PCM. The numerical calculations have been done for a excess heat is convectively transferred to the flowing water in
typical day of winter (20 Feb) and summer (8July) of Lyon, France. channel. The blackened absorber plate or channel absorbs solar
170 A. Gaur et al. / Renewable Energy 109 (2017) 168e187

Fig. 1. A schematic diagram of fully wetted absorber type unglazed PVT water collector.

Table 1 system.
Design parameters of PVT collector and used for the computation. Thermal network for charging and discharging mode of present
PV module Specific heat, Cpv 900 (J/kg K) fully wetted absorber type PVT water collector with PCM and
Thermal conductivity, kpv 140 (W/m K) without PCM have been shown in Fig. 3(a)e(c) respectively.
Emissivity, epv 0.93
PV module efficiency at STC 18%
Packing factor 0.89 3. Thermal model
Apv 2m2 (1  2)
apv 0.89 To write the energy balance equations for the components of
ab 0.9 fully wetted type absorber PVT water collector with integration of
Solar cell temperature coefficient 0.405 K-1
Absorber channel density 2702 (kg/m3)
PCM, the following assumptions have been considered;
Absorber thermal conductivity, Kp 310 (W/m K)
Absorber thermal thickness, Lp 0.0012 m  The heat capacitance of front and back glass of PV module,
Cw 4190 J/KgK absorber channel and insulating material are negligible as
m_ w 0.04 kg/s
compared to water and PCM.
OM 37 melting point Tm 37
C
Kpcm,s 0.5 w/mK  The glass is considered purely transparent.
Kpcm,l 0.44 w/m K  The rate of water flow is assumed to be constant,
Cpcm,l 1.76 kJ kg/K  The ohmic losses and side losses in PV modules are negligible.
Cpcm,s 2.27 kJ kg/K  There is a good contact of PCM with absorber channel.
Lpcm 211 kJ/kg
Density of pcm (solid) 960 kg/m3
 The temperature gradient through the thickness of PCM is
Density of pcm (liquid) 862 kg/m3 considered negligible and only an uniform average temperature
Insulation Thickness, Lin 0.05 m Tpcm, during the melting and solidification processes is
Insulation conductivity,Kin 0.030 (W/m K) considered.
Storage tank capacity Ctank 100 L
DC pump power 24 W

3.1. The PVT collector with the PCM (charging mode)

radiation through non packing area of PV module (direct gain) and
also from fully wetted absorber e.g from back side of PV module via The energy balance equations for components of PVT collector
convection (indirect gain). A fraction of thermal energy is trans- during sunshine hours can be written as follows:
ferred by convection to the water and rest is transmitted to the PCM
via conduction. When the temperature of wetted absorber channel  PV module:
becomes higher than that of the PCM heat is stored as a sensible
dTpv h   
heat until its melting point arrives. In the mean time PCM starts mpv Cpv ¼ apv tg IðtÞ  ht;pvw Tpv  Tw  hr;pvsky Tpv
melting and when entire melting of the PCM is finished, heat will dt
    
be stored in the melted PCM as a sensible heat. When solar radia-  Tsky  ht;pva Tpv  Ta  ht;pvb Tpv  Tb
tion decreases, the PVT collector component starts to cool down, i
the melted PCM releases heat to the absorber channel and hence to  hpv IðtÞ bApv
water until the PCM gets solidified. Therefore PCM supplies heat to
(1)
the water during the time of low intensity solar radiation as well as
during the night. Thus the thermal efficiency of unglazed PVT col-
lector is enhanced as water gets heated from the excess heat of PV In this equation, left hand side term indicates the energy
module and from PCM, also it can produce the hot water even at stored in PV module whereas on right hand side first term
night time. The heat from PV module is dissipated by the water and corresponds to the rate of absorbed solar radiation received by
PCM as well. Therefore along with thermal efficiency improvement, the PV module and the second term represents the overall heat
it is also an attempt to enhance the electrical efficiency of PVT transfer from solar cells of PV module to water through back
 A. Gaur et al. / Renewable Energy 109 (2017) 168e187 171

Fig. 2. a. PVT system using water storage tank. b. The flow of water over elementary area b dx of PVT system.

glass. The next consequent two terms corresponds to the radi-

ative and convective overall heat losses from PV module to the For fully developed laminar flow in rectangular channels with
sky and ambient through front glass respectively and the fifth constant heat flux condition (present case) the Nusselt number
term is convective heat loss to the blackened absorber plate (Nu) has been calculated using correlation suggested by Kays
whereas last term indicates electrical energy produced by PV and Crawford [49] as:
module.
In Eq. (1) ht;pvw is convective heat transfer coefficient from  
cells of PV module to water through back glass of module. Nu ¼ 8:235 11:893a þ3:76a2 5:814a3 þ5:361a4 2a5
" #1 (2)
1 Lbg
ht;pvw ¼ þ
hc;pvw Kbg where, a is the aspect ratio [¼channel height(b)/channel width(a)]
For non circular channel equivalent diameter can be calculated as

Convective heat transfer coefficient hc;pvw has been calcu-

lated using empirical relation for forced convective heat transfer ab
[48] as: De ¼ 4
2ða þ bÞ

Kw Nu
hc;pvw ¼ The rest heat transfer coefficients using in Eq. (1) have been
De
calculated as:
172 A. Gaur et al. / Renewable Energy 109 (2017) 168e187

Fig. 3. The thermal network of the PVT collector for (a) the charging mode (b) discharging mode and (c) without PCM.

" # " #
1 Lg 1 Lg Tsky is calculated using relation given by Swinbank [50] as;
ht;pvsky ¼ þ ht;pva ¼ þ
hr;pvsky Kg hc;pva Kg

hr;pvsky is calculated as [40]:

Tsky ¼ 0:0522Ta1:5
  
hr;pvsky ¼εpv sApv Tpv þTsky 2
Tpv 2
þTsky and
hc;pva ¼2:8þ3v The temperature dependent electrical efficiency of a PV
module can be written as [51].
 A. Gaur et al. / Renewable Energy 109 (2017) 168e187 173

Fig. 3. (continued).

Heat transfer coefficients from absorber channel to water has

  
hpv ¼ h0 1  b0 Tpv  T0 : (3) been calculated similarly as for pv module to water using Eq. (2).
 1
L
Also, ht;pvb ¼ ht;pvw and hcd;b/pcm ¼ Kpcm
pcm
:
 Fully wetted absorber channel:
 Water inside the fully wetted absorber channel:
  Referring to Fig. 2(b) in which an incremental area of collector
ab ð1 bÞt2g IðtÞAb
þ ht;pvb Tpv  Tb bAb
  is taken b dx, where b is width of the collector and dx is an
¼ hc;bw ðTb  Tw ÞAb þ hc;bpcm Tb  Tpcm Ab (4) incremental length along the collector. The heat gain transferred
to the water as it moves from x to x þ dx be given by:

Here, first term of right hand side corresponds to the energy : ;

absorbed by the blackened absorber plate via non packing area Q ¼ mw Cw dTw
of module and second term is overall heat gain form PV cells
through back glass whereas the left hand side indicates the heat here dTw is the change in water temperature for an incremental
transfer from the blackened absorber to the water via convec- length dx. The heat gain per unit area transferred to the water at a
;
;
tion and to PCM via conduction respectively. distance x from the inlet of collector is given by qw ¼ mwbCw dTw
dx
:
174 A. Gaur et al. / Renewable Energy 109 (2017) 168e187

Therefore The energy balance for the rate of thermal energy gain 3.2. PVT collector with PCM (discharging mode)
for cross sectional area bdx by water inside the absorber channel
can be written as: The energy balance equation for components of PVT collector
with PCM during off sunshine can be written as follows:
  ; dTw
ht;pv/w Tpv  Tw bdx þ hc;b/w ðTb  Tw Þbdx ¼ mw Cw dx  PCM
dx
(5)
(i) For Tpcm ¼ Tm þ VT
   
The terms of left hand side are the overall heat transfer to mpcm Lpcm ¼ Ut;pcma Tpcm  Ta Ab þ hc;pcmb Tpcm  Tb Ab
water from PV module and the absorber channel. The right hand
side term is for the rate of heat gain by the flowing water within
(11a)
absorber channel on integration the Tw from x ¼ 0 to x ¼ L one (ii) For Tpcm sTm
can get the average water temperature.
dTpcm    
 Phase change material (PCM): M ¼ Ut;pcm/a Tpcm  Ta Ab þ hc;pcm/p Tpcm  Tb Ab
dt
    (11b)
dTpcm where
hcd;bpcm Tb  Tpcm Ab ¼ M þ Ut;pcma Tpcm  Ta Ab
dt M ¼ mpcm Cl;pcm for Tpcm > Tm
(6) M ¼ mpcm Cs;pcm for Tpcm < Tm
where
In Eqs. (11a) and (11b) the heat is stored in PCM as a latent
M ¼ mpcm Cs;pcm for Tpcm < Tm
heat and thermal energy respectively which would be equal
M ¼ mpcm Lpcm for Tpcm ¼ Tm
to the overall heat loss to the ambient through insulation and
M ¼ mpcm Cl;pcm for Tpcm > Tm
convective heat transfer to the absorber channel.
The single term on the left side of Eq. (6) is the heat gain to
The heat transfer coefficient between the melted PCM and
the PCM from absorber channel and the first term on the
absorber channel is augmented by free convection and the
right hand side is thermal energy stored in PCM whereas the
following relation [52] has been used to estimate the Nus-
second term corresponds to the overall heat loss from PCM to
selet number for heat transfer coefficient.
the ambient through insulation.
Rayleigh number (Ra ¼ Gr*Pr)
Overall heat transfer coefficient Ut,pcm is determined as:
0:068
 1 l
L 1 Nu ¼ 0:133Ra0:326 0:0686
Ut;pcm/a ¼ in þ Drm
Kin hi
where Ra, Drm and l are the Rayleigh number, thickness of the PCM
From Eq. (4)) Tb is obtained as: and length of the absorber respectively.
Heat transfer from phase change material to water has been
considered through blackened metallic absorber channel/plate. The
t2 g ab ð1  bÞIðtÞ þ hc;bw Tw þ hcd;bpcm Tpcm þ ht:pvb bTpv
Tb ¼ overall heat transfer coefficient from phase change material to the
hc;bw þ hcd;bpcm þ ht:pvb b water will be equivalent heat transfer of conductive heat transfer
(7) coefficient of blackened absorber plate and convective heat transfer
from that plate to water.

Eqs. (1), (5) and (6) are solved analytically by using the method  Fully wetted absorbing channel:
of separation of variables and following expressions have been
  
obtained for the temperatures of PV module (Tpv), water (Tw) hc;pcmb Tpcm  Tb bdx ¼ hc;bw ðTb  Tw Þbdx þ hc;bpv Tb
and PCM (Tpcm) respectively: 
 Tpv bdx

f1 ðtÞ   (12)
Tpv ¼ 1  ea1 t þ Tpv0 ea1 t (8)
a1
Now in discharging mode the heat source will be the PCM.
Here in above equation, the term of right hand side is the
f2 ðtÞ  
Tw ¼ 1  ea2 t þ Tw0 ea2 t (9) convective heat gain to the absorber channel from PCM and the
a2 left members are the convective heat transfer from absorber
channel to the water and PV module respectively.
f3 ðtÞ  
Tpcm ¼ 1  ea4 t þ Tpcm0 ea3 t (10)  For PV module:
a3
  dTpv  
where f1 ðtÞ; f2 ðtÞ and f3 ðtÞ are the average values off1 ðtÞ; f2 ðtÞ, ht;bpv Tb  Tpv Apv ¼ mpv Cpv þ ht;pv/sky Tpv  Tsky Apv
dt
andf3 ðtÞ, which are functions of solar radiation, ambient tempera-  
þ ht;pv/a Tpv  Ta Apv
ture, sky temperature and heat transfer coefficients at time interval
dt and can be considered as constants. Tpv0 ; Tw0 and Tpcm0 are the (13)
initial values of temperatures of PV, module, water and PCM
respectively. The expressions of f1 ðtÞ, f2 ðtÞ, f3 ðtÞ, a1, a2, and a3 are During discharging, a convective heat transfer from absorber
given in Appendix I. channel to the PV module via water takes place and some of the
 A. Gaur et al. / Renewable Energy 109 (2017) 168e187 175

heat is stored by the PV module and rest is lost to the sky and
ambient via radiation and convection respectively. dTtan k  
Mw Cw ¼ ðUAÞw/a Ta  Tw;tan k (20)
From Eq. (12) the expression for Tb can be obtained as: dt
The solutions of Eqs. (19) and (20) were obtained as given below
hc;pcmb Tpcm þ hc;b/w Tw þ ht;pvb Tpv b
Tb ¼ (14) Eqs. (21) and (22) respectively:
hc;pcmb þ hc;bw þ bht;pvb
f6 ðtÞ  
Tw;tan k ¼ 1  ea6 t þ Tw;tan 0 ea6t (21)
Further by using method of separation of variables Eqs. (11) a6
and (13) are solved analytically as:
 
Tw;tan k2 ¼ Ta 1  ea7t þ Tw;tan 0 ea7t
f ðtÞ  
Tpcm ¼ 4 1  ea5 t þ Tpcm0 ea4 t (15)
a4
The expressions for f5 ðtÞ, a6 and a7 are given in Appendix I.

f5 ðtÞ  
Tpv ¼ 1  ea5 t þ Tpv0 ea5t (16)
a5 3.5. Overall electrical and thermal energy

The daily electrical energy in KWh of a PVT collector was ob-

The expressions forf4 ðtÞ f5 ðtÞ, a4 and a5 are given in Appendix
tained as:
I.
X
N1 h bA t IðtÞ
pv pv g
Eel;daily ¼ ; (22)
i¼1
1000
3.3. PVT collector without PCM
N1 is the number of sun shine hours per day.
The energy balance equations for PV module and water will be Net daily electrical energy for present system was calculated as:
similar as Eqs. (1) and (5) but for absorber channel heat loss
through insulation to the ambient would be from absorber channel Qel ¼ Eel;daily  Pw (23)
only. It can be written as follows:
Pw is power consumption by DC pump from PV module.
 Wetted absorber channel: Heat gain for water in storage tank was calculated as:
 
ab ð1  bÞt2g IðtÞAb þ ht;pvb Tpv  Tb bAb Qth ¼ Qw;tan k ¼ Mw Cw ðTw0  Twi Þ (24)
¼ hc;bw ðTb  Tw ÞAb þ Ut;ba ðTb  Ta ÞAb (17) During the day heat gain for the PVT collector without PCM has
also been calculated for the same Eq. (24) but for the night time
where temperature difference would be the difference of consecutive
" #1 water temperature in tank only.
0
Lin 1 The overall thermal energy was calculated as [53],
Ut;b/a ¼ þ
Kin hi
Qel  Pw
Qoverall;thermal ¼ Qth þ ; (25)
gm
From Eq. (17) the expression for Tb can be written as:
where gm is the conversion efficiency of thermal power plant which
t2 g ab ð1  bÞIðtÞ þ hc;bw Tw þ hcd;bpcm Tpcm þ h1 bTpv depends upon quality of coal (gm ¼ 0.38 for good quality of coal).
Tb ¼ To convert the thermal efficiency into equivalent electrical en-
hc;bw þ hcd;bpcm þ h1
ergy the Carnot efficiency factor [54] was used.
(18)
Ta þ 273
Qoverall;exergy ¼ Qel;daily þ Qth 1  ; (26)
The same methodology has also been adopted to solve the Two þ 273
Equations for PVT water collector without PCM.
where Ta and Two are ambient and water outlet temperature
respectively.
The daily electrical and thermal efficiencies of the present sys-
3.4. Water storage tank tem were calculated using the following relations:
P
The energy balance for the storage tank during the day can be Qel
written as follows: hel;daily ¼ 24hours
P (27)
Apvt b IðtÞ
24 hours
 dTw;tan k  
mw Cw ðTwo  Twi Þ ¼ Mw Cw þ ðUAÞw/a Tw;tan k  Ta
dt P
Qth
(19)
hth;daily ¼ 24hours
P (28)
There is no forced mode in PVT collector without PCM during Apvt IðtÞ
24 hours
the night time, In such case the energy balance for tank water can
be written as:
176 A. Gaur et al. / Renewable Energy 109 (2017) 168e187

4. Numerical analysis

To solve the above-mentioned mathematical equations, an

iteration method has been used in a computer program MathCad
15. A computer program was developed for calculation of solar
radiation on an inclined surface of 45
, using Liu and Jordan for-
mula [55,56]. Hence beam and diffuse radiations on the PVT col-
lector are required that were calculated using a correlation
between direct and diffuse radiation given by Sears et al. [57].
Further another computer program was developed to solve the
energy balance equations of present PVT water collector compo-
nents with and without PCM. For both the cases Mathcad15 pro-
gram has been run for 24 h period. At first the initial temperatures
of components of PVT collector, PCM and inlet water temperature
(Twi) were considered to be equal to ambient temperature at t ¼ 0.
Assuming a perfect insulation of the connecting pipes and the
storage tank, water temperature in tank (Tw,tank) has been consid-
ered to be inlet water temperature (Twi) for next hour. Fig. 4 shows
a detailed flowchart entailing the various steps to solve the math-
ematical model developed for the analysis of present PVT system.

5. Results and discussions

5.1. Solar radiation I(t) and ambient temperature (Ta)

Fig. 5 shows the calculated hourly I(t), incident on the PVT col-
lector at its inclination and Ta, on the typical winter (20 Feb) and
summer (8 July) days when evaluations were performed for Lyon,
France. I(t) first increased and then decreased with time and were
maximum 816.64 W/m2 at 12:00 h and 883.45 W/m2 at 13:00 h on
typical winter and summer days respectively. Similarly the Ta was
maximum 12.08
C at 15:00 h on a typical winter day and 24.09
C
at 17:00 h on a typical day of summer.

5.2. Temperatures of water and elements of the PVT system with

electrical efficiency

5.2.1. Without PCM

Fig. 6(a) shows the hourly variations in PV module temperature
(Tpv), outlet water temperature (Two), blackened absorber plate
temperature (Tb), water temperature in storage tank (Tw,tank) and
electrical efficiency of PV module (hpv) for a typical winter
(Fig. 6(a)) and summer (Fig. 6(b)) days.
It can be seen in the figures that the temperatures Tpv, Two, Tb,
and Tw,tank vary as dependent on the solar radiation, first increase
with increase of solar intensity and then decrease with decrease in
solar intensity over a 24 h period. The maximum values of Tpv, Two,
Tb, and Tw,tank were obtained at ~15:00 h for winter as 51.38
C,
51.71
C, 52.01
C, 44.64
C and at 13:00 h for summer day as
69.17
C, 69.37
C, 69.54
C and 63.98
C respectively which cor-
responds to maximum solar intensity (see Fig. 5). It is worth
mentioning the fact that, when the maximum water temperature of
51.71
C for winter day and of 69.2
C for summer day were ach-
Fig. 4. Flow chart for the analysis of present PVT system.
ieved, the inlet temperatures were 34.67
C and 49.79
C
respectively.
Here, Tpv and Two are almost the same at any instant of time. It is gain) results into a increment in its temperature. The channel water
due to the admirable heat transfer from the PV module to the water is also in direct contact with absorber. Fig. 6(a) and (b) also repre-
through the contact area of entire PV module as back surface of PV sent variation of PV module efficiency with time, where it
module itself forms one side of channel and water remains in the decreased and then increased with time. The minimum efficiencies
direct touch of PV module resulting very low temperature differ- of PV modules for a typical winter and summer days are observed
ence. Therefore the Tw of the fully wetted PVT collector is quite as 15.7% at ~12:00 h and 14.2% at 13:00 h respectively. This varia-
close to Tpv under the effectual convective heat transfer. However, a tion in module efficiencies can be understood by variation in
slight increment is observed in Tb. Since the absorber plate receives module temperatures which are maximum at ~12 h on winter day
thermal energy from PV cells (indirect gain) as well as via non and at ~13 h on summer day. It is because of the reduction in band
packing area of PV module (I(t) is transmitted through glass, direct gap energy with rise of cell operating temperature. The reduction in
 A. Gaur et al. / Renewable Energy 109 (2017) 168e187 177

Fig. 5. Hourly variation of solar intensity, I(t) and ambient temperature (Ta) on a typical day of winter (20 Feb) and summer (8 July) for Lyon, France.

band gap energy due to temperature rise increases the dark current thermal conductivity of PCM with faster heat transfer [59]. Few
which affects the cell voltage significantly. The reduction in cell Another approaches of macroscopic-capsules and micro-
voltage with rise in operating temperature is due to the rapid in- encapsulation to reduce the adverse effect of thermal conductiv-
crease in reverse saturation current I0 (Voc ¼ KT/q  log Isc/I0). ity have also been explored [60]. Macroscopic-capsules technique is
the most often used encapsulation method in which usually a
plastic module having a diameter of few centimeters, chemically
5.2.2. With PCM neutral for both the phase change material and the heat transfer
From Fig. 6, it is clearly seen that water gets heated during fluids is used. However micro-encapsulation is a quite new method
sunshine hours only. There is a fast drop in temperature of storage in which the PCM is encapsulated in a small shell of polymer ma-
water in tank overnight and in sunshine hours Tm is quite high terials with a diameter of micrometers (at the moment for paraf-
causing lower electrical efficiency. Further to enhance the over- fin's only) results a large heat-exchange surface. Using containment
night production of hot water and hpv with reduced Tm, the same can also increase the surface area by reducing the distance from the
system is studied using PCM OM 37 beneath on the collector. external heat source to the center of the PCM. therefore the heat has
Fig. 7(a) and (b) shows the hourly variations of Tpv, Tpcm,Two, Tb, to travel less distance which can increase the rate of heat transfer.
Tw,tank and hpv for a winter (Fig. 7(a)) and summer (Fig. 7(b)) days. One can observe from Figs. 6 and 7 that during night due to
The maximum values of Tpv, Tw, Tb, and Tw,tank were obtained at decreased ambient temperature with time the water temperature in
~12:00 h for winter as 46.78
C, 46.84
C, 46.89
C and 40.43
C and tank (Tw,tank) without PCM decreases faster than that of (Tw,tank)
at ~13:00 h for summer day as 53.86
C, 53.58
C, 53.34
C and with PCM. For night PCM will act as a heat source for water and
49.45
C respectively. decrease its temperature very slowly. In charging mode (during
Here, as the solar intensity increases, Tpcm increases due to the sunshine hours) the outlet temperatures are much higher than the
heat transfer from blackened absorber via conduction. It can be inlet temperature whereas during discharging mode there is no
seen that the PCM started to melt after 11 h on a typical winter day remarkable temperature difference between inlet and outlet water
and after 9 h on a summer day from the beginning of PVT collector temperature as water is receiving heat energy from PCM only but is
exposure to solar radiation. Afterwards, Tpcm remains almost worth to note the fact that, at ~5 h in the morning of winter and
constant from its temperatures of 43.9
C at~12 h in winter 41.23
C summer typical days, the outlet Two and Tw,tank were found to be
at~10 h on summer day till it melts completely then after sunset it 34.78
C, 31.67
C and 34.89
C, 33.15
C respectively, whereas for
decreases slowly in the discharging process of the heat stored without PCM the Tw,tank at ~5 h were 14.98
C for winter and 27.75
C
within the PCM. The time requisite for PCM in entire charging or for summer (Figs. 6 and 7). Hence hot water can be obtained in early
discharging depends on its thermal conductivity. PCM material morning when it is really needed to take shower or other uses.
suffer from poor thermal conduction, especially PCM based on
organic materials such as paraffin wax exhibit very low thermal
conductivity (~0.21 W/m K) which is an obstacle in phase change 5.2.3. Comparison of electrical efficiencies of PVT system with and
processes in energy systems [58]. This is also a challenge for bio- without PCM
based PCMs. An extensive research in that area is being carried Fig. 8 compares the PV module efficiencies of fully wetted
out to enhance the thermal conductivity of existing PCM by adding absorber PVT collector with and without PCM at different time
particles with high thermal conductivity. Thermally conductive intervals. For a typical day of summer daily average electrical effi-
additives such as expanded graphite, aluminum, copper and ciency of PV modules of PVT collector with PCM and without PCM
aluminum nitride have been investigated that improve the overall were found to be 16.30% and 15.40% respectively whereas for
178 A. Gaur et al. / Renewable Energy 109 (2017) 168e187

Fig. 6. (a). Hourly variation of Two, Tpv, Tb, Tw,tank, and electrical efficiency (ƞpv) of PVT collector without PCM for winter (20 Feb). (b). Hourly variation of Two, Tpv, Tb, Tw,tank, and
electrical efficiency (ƞpv) of PVT collector without PCM for summer (8 July).

winter it has been found to be 16.87% and 16.78% respectively. The absorber plate resulting reduced module temperature and
improvement in efficiency with PCM can be understood as the heat improved electrical efficiency. A maximum reduction of module
capacity of PCM is high. It stores excess heat of PV module via temperature with PCM for summer at12 h and at 13 h for winter
 A. Gaur et al. / Renewable Energy 109 (2017) 168e187 179

Fig. 7. (a). Hourly variation of Two, Tpv, Tb, Tw,tank, Tpcm and electrical efficiency (ƞpv) of PVT collector with PCM for winter (20 Feb). (b). Hourly variation of Two, Tpv, Tb, Tw,tank, Tpcm and
electrical efficiency (ƞpv) of PVT collector with PCM for summer (8 July).
180 A. Gaur et al. / Renewable Energy 109 (2017) 168e187

Fig. 8. Hourly variation of electrical efficiencies (ƞpv) of PVT collector with PCM and without PCM for winter (20 Feb) and summer (8 July).

day was observed up to ~16.04
C and ~5
C respectively. Hence for 5.2.4. Optimization of mpcm(kg) for the present PVT system
improvement of electrical efficiency point of view, use of PCM is Fig. 9 shows the effect of varying mass of PCM for 10 kg
quite effective. (dpcm ¼ 0.005 m), 20 Kg(dpcm ¼ 0.01 m), 30 Kg (dpcm ¼ 0.015),

Fig. 9. Variations of hourly temperatures (Two, and Tpcm), of the PVT collector with different masses of PCM.
 A. Gaur et al. / Renewable Energy 109 (2017) 168e187 181

Fig. 10. Variations of hourly module temperature (Tm) and electrical efficiency (ƞpv) of the PVT collector with different masses of PCM for summer (8 July).

40 Kg(dpcm ¼ 0.02) and 50 Kg (dpcm ¼ 0.025) on outlet water module and absorber plate. Therefore as the mass of PCM increases
temperature (Two) temperature and PCM temperature (Tpcm). It can up to a certain amount the heat capacity of PCM increases and it can
be seen that during the day time in sunshine hours when mass of store more amount of heat during the day time resulting lower
PCM increases from 10 Kg to 30 Kg the outlet temperature outlet temperature whereas in off sunshine, during night it acts as a
decreased whereas during the night time it increased with heat source and release more heat to the water with increase mass
increased mass of PCM. The reason behind this is that during the day but it was also observed that after an optimal mass and thickness of
time PCM remains in charging mode and acts as a heat sink for PV PCM (dpcm) it does not effective. It is seen from figure, for 10 kg of

Fig. 11. Variation of Tpv and (ƞpv) of fully wetted absorber for summer with different mass flow rate.
182 A. Gaur et al. / Renewable Energy 109 (2017) 168e187

Fig. 12. Hourly variation of thermal energy produced by present system with and without PCM for winter (20 Feb) day and summer day (8 July).

mass the values are lower than that of the values with 20 kg and interesting to see that after 30 kg of PCM if we increase more mass
30 kg which can be attributed as the PCM is completely in liquid then temperatures are found to be lesser than that of temperatures
state and the activation of the latent heat is not allowed. It is with 20 and 30 kg PCM. It can be understood as when thickness of

Fig. 13. Hourly variation of electrical energy produced by present system with and without PCM for winter (20 Feb) day and summer day (8July).
 A. Gaur et al. / Renewable Energy 109 (2017) 168e187 183

Fig. 14. The variation of thermal efficiencies of PVT collector with PCM and without PCM as a function of reduced temperature ðTwi  Ta =IðtÞÞ:

;
PCM is large enough then thermal resistance may be increases and water mw . The module temperature was observed to decrease with
thermal flow cannot pass through it perfectly and PCM will act as a ;
increment in mw causing higher electrical efficiency of PV module.
semi infinite material resulting less energy storage. It was observed ;
This is all because of more heat dissipation on increment of mw . For
that, as the PCM mass increased, temperature of PCM decreased ;
which is quite obvious because of the increased time taken by the very low mw of 0.0005 kg/sec the hpv and Tpv were found to be
;
PCM to attain its melting temperature. Heat required to melt the 58.02
C and 15.1%, whereas for very high mw of 0.075 kg/s the hpv
PCM must be equal to the product of its mass (mpcm) and latent and Tpv were found to be 25.29
C and 18% respectively. There is no
heat (L) i.e. H ¼ mpcm* Lpcm. Hence for excellent performance of benefit in increasing the mass flow rate beyond 0.04 kg/s.
PVT collector with PCM an optimal value of PCM thickness and mass
is required that was observed to be 0.015 (30 kg) mass for OM 37. 5.4. Thermal and electrical energy performances of the system

5.2.5. Effect of different mpcm on Tpv and hpv 5.4.1. Daily thermal energy and overall energy
Fig. 10 shows the effect of mass of PCM on Tpv and hpv It is clearly Fig. 12 compares the hourly thermal power of present PVT col-
seen from figure that hpv increases with increase of PCM mass and lector with PCM and without PCM for winter and summer day. It
Tpv decreases. The reason behind this is the increased mass of PCM was observed that during the day time PVT collector without PCM
increases its heat capacity that can store more amount of heat exhibited higher thermal energy due to high solar radiation and
resulting reduced Tpv and higher hpv. For present system melting ambient temperature but in evening solar radiation is low and in
point of PCM OM 37 is 37
C which has been found suitable for night PVT collector with PCM exhibited higher thermal energy.
winter (Feb) and summer (July) of climatic condition of Lyon The daily thermal energy and overall thermal energy from PVT
France. It was observed that during the summer it attains melting collector with PCM and without PCM for a winter (Feb) day were
temperature very quickly, though it was found to be good for found to be 8.74 kWh, 13.18 kWh and 5.32 kWh, 9.26 kWh
summer as well but it could be a problem for very high ambient respectively whereas for summer day (July) the thermal energy and
temperature and solar radiation. In such case the PCM will be overall thermal energy were found to be 9.21 kWh and 14.14 kWh
melted completely very rapidly and latent heat would not be for PVT with PCM and 6.499 kWh and 11.79 kWh for without PCM.
allowed. In such case heat can be stored as a sensible heat only. Also The overall thermal energy was observed higher in summer. As
the module temperature can reach very high resulting lower expected the length of the day in summer, when solar radiation is
electrical efficiency. This possibility of deterioration in the perfor- available is higher than that of the month of winter (Feb). On the
mance of present PVT collector can be minimized if it is operated at other hand the thermal efficiency was also calculated using Eq. (27)
relatively lower temperatures, which can be achieved by increasing for the fully wetted PVT with PCM and it was found to be 84.01% for
the mass flow rate during the summer to compensate for increased winter day (Feb) and 59.66% for summer day(July). The reason
ambient temperature and solar radiation. behind higher thermal efficiency in winter can be attributed as the
total length of solar radiation (power input) is lesser than that of
5.3. Effect of mass flow rate (kg/s) of water on Tpv and hpv the summer. Thermal energy with PCM was observed higher for
both summer and winter day. It is obvious because system with
Fig. 11 shows the variations Tpv of and hpv with mass flow rate of PCM produce thermal energy efficiently during the night as well.
184 A. Gaur et al. / Renewable Energy 109 (2017) 168e187

Fig. 15. The variation of electrical efficiencies of PVT collector with PCM and without PCM as a function of reduced temperature ðTwi  Ta =IðtÞÞ .

Thermal efficiencies without PCM were observed to be 52.34% for Fig. 14 shows the variation of thermal efficiencies as a function
winter day and 43.73% for summer day. of Twi  Ta =IðtÞ for PVT collector with and without PCM on the
typical days of winter (20 Feb) and summer (8 July). These char-
5.4.2. Daily electrical energy and overall exergy acteristics curves are similar to the Hottel-Whiller-Bliss equations
Fig. 13 shows the hourly variations of electrical power of PVT of a flat plat collector [2,7]. The efficiencies for both the conditions
collector with and without PCM, for the winter and summer days. It (with and without PCM) are observed to decrease with increment
is clear from the figure that for both winter and summer PVT col- in reduced temperatureTwi  Ta =IðtÞ. This variations in efficiencies
lector with PCM exhibited higher electrical energy as compared to with reduced temperature are also similar for the months of Feb
without PCM which correspond to higher electrical efficiency with and July however their gain factors or thermal efficiencies at zero
PCM than that of without PCM what is discussed above in detail. reduced temperature (h0th ) and loss coefficients (a1 ) are different
The daily electrical energy and overall exergy for PVT collector for each case. It can be seen from Fig. 13 that the thermal effi-
with PCM and without PCM were found to be 2.05, 2.675 kWh and ciencies at zero reduced temperature or gain factor for PVT collector
1.95 kWh, 2.65 kWh respectively for summer and 1.52 kWh, with PCM (Feb ¼ 0.46, July ¼ 0.66) was slightly lesser than that of
2.35 kWh and 1.50 kWh, 1.98 kWh respectively for winter. without PCM (Feb ¼ 0.47, July ¼ 0.70), that can be attributed to
Hence it is clearly seen that for both months overall exergy was higher module temperature (Tm) resulting elevated water tem-
also observed higher in summer compared to the winter corre- perature, However for both the months, the loss coefficient for PVT
spond to the higher number of sunshine hours in summer than that with PCM (Feb ¼ 2.33, July ¼ 11.01) were observed lesser
of winter. compared to PVT collector without PCM (Feb ¼ 5.10,
July ¼ 12.08). Hence, incorporation of PCM reduces the heat losses
5.5. Characteristics curves for the present PVT system and provides better thermal stability to the system.

5.5.1. For thermal efficiencies 5.5.2. For electrical efficiencies

Thermal efficiencies of the present PVT water collector with The electrical efficiencies of the PVT collector with and without
PCM and without PCM were conventionally calculated as a function PCM for both months, under the outdoor condition are shown in
of the reduced temperature Twi  Ta =IðtÞ , where Twi and Ta are the Fig. 15. The electrical efficiency can be represented as
PVT collector's inlet water temperature and the ambient tempera- hel¼ hoel a2 ðTwi  Ta =IðtÞÞ., here hoel . ielectrical efficiency of collec-
ture respectively and I(t) is the incident solar radiation. tor at zero reduced temperature or electrical gain factor and a2 is
Thermal efficiency can be represented as the electrical loss coefficient. These characteristics curves are also
similar to the Hottel-Whiller-Bliss equations of a flat plat collector.
Twi  Ta It can be observed from the figure that the electrical gain factors
hth ¼ h0th a1
IðtÞ with PCM (Feb ¼ 0.20, July ¼ 0.174) are observed to be higher with
lesser electrical loss coefficients (Feb ¼ 0.87, July ¼ 0.35)
where h0th is the thermal efficiency at zero reduced temperature or compared to without PCM (Feb ¼ 0.19, July ¼ 0.17) (Feb ¼ 1.05,
thermal gain factor and a1 is the thermal heat loss coefficient. July ¼ 0.44) respectively. It is because of the absorption of excess
 A. Gaur et al. / Renewable Energy 109 (2017) 168e187 185

heat of PV module by PCM due to latent heat absorption mecha- and 1.95 kWh,2.65 kWh respectively for summer and 1.52 kWh,
nism resulting higher electrical efficiency with minimized electrical 2.35 kWh and 1.50 kWh, 1.98 kWh respectively for winter.
;
losses.  mpcm and mw have significant effect on Tpcm,Tpv, Tw and hpv.

6. Conclusions The present study is limited to numerical analysis of perfor-

mance of fully wetted absorber channel PVT collector with PCM for
An unglazed Fully wetted type absorber PVT collector with PCM specified solar radiation and ambient temperature. The same can be
integrated beneath the absorber plate and without PCM has been extended to experimental investigations for validation of the pre-
investigated by developing thermal model for temperatures of sent model. Also thermal conductivity enhancement, CO2 mitiga-
different component of system and electrical efficiencies under tions and life cycle cost analysis can be performed.
winter and summer climatic conditions of Lyon, France. On the
basis of present studies the following conclusions are drawn.
Appendix I
 During the night PCM acts as a heat source for the collector
water and can provide the hot water until the early morning of The unknown parameters used in the various equations are
the next day. given below:

h i
apv tg IðtÞ þ ht;pvw Tw þ hr;pvsky Tsky þ ht;pva Ta þ ht;pvb Tb  hpv IðtÞ bApv
f1 ðtÞ ¼
mpv Cpv

h i
ht;pvw þ hr;pvsky þ ht;pva þ ht;pvb bApv
a1 ¼
mpv Cpv

 
ht;pv/w Tpv bdx þ hc;b/w Tb bdx ht;pv/w þ hc;b/w bdx
f2 ðtÞ ¼ a2 ¼
mw cw mw cw
   
Ut;pcm/a Ta þ hc;pcm/p Tb Ab Ut;pcm/a Ta þ hc;pcm/p Tb Ab
f3 ðtÞ ¼ a3 ¼
mpcm Cpcm mpcm Cpcm

   
hc;pcmb Tb þ Ut;pcma Ta hc;pcmb þ Ut;pcma
f4 ðtÞ ¼ Apcm a4 ¼ Apcm
mpcm Cpcm mpcm Cpcm

ht;bpv Tb þ ht;pv/sky Tsky þ ht;pv/a Ta Apv ht;bpv þ ht;pv/sky þ ht;pv/a Apv

f5 ðtÞ ¼ a5 ¼
mpv Cpv mpv Cpv


mw Cw ðTwo  Twi Þ þ ðUAÞw/a Ta ðUAÞw/a Ta
f6 ðtÞ ¼ a6 ¼ a6 ¼ a6
Mw Cw Mw Cw

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m: melting point pcm: Phase change material

s: solid i: Insulation
w: water fg: front glass
w0: outgoing water bg: back glass
win: inlet water cod: conduction
pv: Photovoltaic module