Numerical studies on thermal and electrical performance of a fully wetted absorber PVT collector with PCM as a storage medium

Renewable Energy 109 (2017) 168e187

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Numerical studies on thermal and electrical performance of a fully wetted absorber PVT collector with PCM as a storage medium
ne
zo a, **, Ste
phanie Giroux–Julien b Ankita Gaur a, *, Christophe Me 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: Received 15 September 2016 Received in revised form 21 January 2017 Accepted 28 January 2017 Available online 4 February 2017

A detailed mathematical models is developed for a fully wetted absorber photovoltaic thermal (PVT) collector with and without phase change material (PCM) under its absorber channel. Thermal and electrical investigations were carried out using PCM OM37 for typical winter and summer days in Lyon, France. The system is analyzed under energy and exergy performances. PCM incorporation in a water PVT 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, provides better electrical and thermal stabilities to the system. Overall thermal energy and overall exergy of PVT system for a winter day as well as for a typical summer day, are found to be strongly in favor of adding PCM. The effects of mass of PCM on module temperature, outlet water temperature, and PV 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.

Keywords: PV modules Photovoltaic thermal system Mass of PCM Exergy

1. Introduction There is an urgent need of development of renewable energy sources due to rapid growing demand of energy. In our modern society, inadequate supply of conventional energy sources is a critical challenge. Emission of carbon di oxide and other pollution from the fossil fuels is another a major issue as it is causing climate change [1]. Solar energy is one of the fastest growing sources of renewable energy. There are numerous foremost directions for solar technology growth such as Photovoltaic (PV) panel which directly convert the solar energy into electrical energy. It is a most mature technology but unfortunately typically power of PV module decreases with 0.2e0.5%/
C increase of temperature [2]. Therefore to maximize the performance of PV module its temperature regulation is strongly needed which is usually done by cooling the PV module via

* Corresponding author. ** Corresponding author. E-mail address: [email protected] (A. Gaur). http://dx.doi.org/10.1016/j.renene.2017.01.062 0960-1481/© 2017 Elsevier Ltd. All rights reserved.

some cooling techniques like air cooling and water cooling. An increment in electrical yield by water flow on the front of the PV modules based on crystalline and multi crystalline Si, has been observed before [3,4]. The extracted surplus heat of PV module can be used to fulfil the need of thermal energy for industrial and residential sectors. Such system is known as photovoltaic thermal (PVT) technology: a single unit that can increase the efficiency of PV module by using solar thermal system. In 1978 the first design and performance of a PVT collector was presented, where water and air were used as a cooling fluid [5]. Since then a significant amount of theoretical and experimental research on PVT systems has been carried out [6e15]. A theoretical analysis via use of modified hotel whillier model was presented by Florschuetz [16]. Further Lalovic et al. conducted a theoretical analysis on PVT water collector and suggested that such system can be useful as pre heater for domestic 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. He et al. [20]. carried out a research on PVT system in which natural convection was used to circulate the cold water. They found the

A. Gaur et al. / Renewable Energy 109 (2017) 168e187

thermal efficiency lesser than a conventional thermosyphon solar water heater but the energy saving efficiency was found to be greater. The same hybrid system was dynamically modelled by Chow et al. [21]. They suggested that the performance of the system can be enhanced by insertion of PV cells on the lower portion of collector. Kalogirou and Tripanagnostopoulos [22] stated that PVT is economically feasible for industrial applications in a Mediterranean environment. Assoa et al. [23] presented a steady-state two-dimensional thermal model for PVT collector based on sheet-and-tube concept whereas the experimental study was carried out by Zondag et al. [24]. Dupeyyrat et al. [25] performed an experiment on PVT collector to enhance its performance. They found the global efficiency of PVT collector more than 87%. Touafek et al. [26] studied the PVT system and PV module separately and found the thermal system cause improvement in efficiency of PV collector. Shyam et al. [27,28] investigated the N-PVT water collectors connected in series and validated their thermal model with experimental studies. They found the collector partially covered by semitransparent PV module at inlet of PVT water collector gives better result compared to that covered by PV module at outlet of the collector. However they have concluded that both configuration give similar results for large number of collectors connected in series. An experimental study was carried out by Jin et al. [29] on water type glazed and unglazed PV thermal collector. They concluded that the unglazed PVT collector results in lower thermal efficiency and higher thermal efficiency as compared to the glazed PVT collector. Further Jin et al. [30] performed an experiment on unglazed liquid PVT collector with a sheet and tube type of absorber and other with fully wetted absorber type. They observed that the PVT collector with fully wetted absorber are more efficient. Solar water heating system is a superior technology that has been widely realized for domestic and industrial applications. Though, still research is being carried out on unglazed PVT water collectors to improve its performance in both senses i.e. electrical and thermal. Recently some of the important studies have been done on the use of phase change materials with PVT systems for minimizing the temperature of PV module [31e38]. PCM can store a high latent heat due to phase change occurs and having a melting point suitable for the application. Therefore in PVT water collector PCM can regulate the temperature of PV module by absorbing the heat on melting and can extend the duration of water heating as well by releasing heat on freezing. Rabin et al. [39] studied a solar collector storage system using salt hydrate eutectic mixture as PCM. They developed a mathematical model for charging process by considering the negligible natural convection. Chaabane et al. [40] presented a numerical study of an integrated collector storage solar water heater with two different PCM (myristic acid and RT-42 graphite) and three radii of this PCM layer. They found that the highest water temperature corresponds to the lowest radius. Bouadila et al. [41] performed an experiment on an integrated solar latent storage collector with two PCM-filled cavities incorporating below the absorber. The results showed that the paraffin increased the performance of the solar collector at night. This paper aims to understand the effect of integration of OM 37 as a phase change material on the electrical and thermal performance of an unglazed fully wetted type absorber PVT water collector. For that purpose theoretical models have been developed and solved numerically for PVT water collector with incorporation of PCM under the absorber channel, for charging and discharging approach. The results have also been compared with collector without PCM. The numerical calculations have been done for a typical day of winter (20 Feb) and summer (8July) of Lyon, France.

169

For incidence of the maximum solar radiation, the PV module in northern hemisphere are placed south oriented, having inclination with horizontal surface equal to the latitude of the system's station [42,43]. Since the present study is carried out for climatic conditions of Lyon which is located at 45.7600
N, 4.8400
E in France therefore PV module is considered to be south oriented and inclined at an angle of 45
to the horizontal. A thin layer of PCM below the water tubes of a water collector will store a substantial quantity of heat within PCM during sunshine and at the night duration, solidification cause the discharging of stored heat that will keep the water warm even at night too. 2. Thermal analysis A schematic diagram of the anticipated fully wetted absorber type unglazed PVT water collector with PCM is depicted in Fig. 1. The present fully wetted absorber type PVT collector set up consists of a frameless mono-crystalline semitransparent PV panel rated at 110 W, having efficiency 18% under standard test conditions (STC). The photovoltaic parameters of the PVT system at STC are shown in Table 1. The detailed structure of fully wetted absorber type PVT collector with PCM is presented in Fig. 2(a). PV modules used in present PVT collector considered to be semitransparent as higher efficiency is obtained using semitransparent or bi glass PV modules due to the solar radiation incident on non packing area of PV module is transmitted through the glass however absorbed by the blackened plate [44,45]. Hence heat is convected to the water from back PV cells as well as from top surface of the blackened plate. The area of the PVT collector is 2 m2 which is connected with an insulated water tank of capacity 100 L. A DC pump of the capacity 24 W was used to force the flow of water which is operated by the PV module itself. In order to maximize the heat transfer area fully wetted channel approach of collector has been used that reduce the thermal resistance between water and collector fluid by allowing rectangular shape channel for water flow [46]. There is no absorber sheet in fully wetted absorber collector as PV module itself makes one face of channel. The heat is transferred from back surface of PV module to the flowing water. In fully wetted absorber type PVT water collector, a good thermal transfer improves the useful thermal output and reduces the temperature difference between the PV cells and the fluid (water) results better cooling effect and electrical efficiency of PV module. The PVT collectors are considered to be made up of black painted copper rectangular channel attached to each other and covered with PV absorber as shown in Fig. 2. These collectors are thermally protected with 50 mm glass wool insulation. The bottom and sides of the PVT collector are perfectly insulated. A space is formed between the insulation and absorber plate where PCM is filled via PVC pipe that could be better for the volume dissemination at the time of PCM melting. A bio-based Phase Change Material (PCM) OM37 was used which is an organic material having large amount of heat energy stored in the form of latent heat. It can be absorbed or released when the materials change state from solid to liquid or liquid to solid. Ingredients of OM 37 are from 100% bio based raw materials which are non hazardous, biodegradable and non toxicis usually the most available and cheaper phase change material therefore in the present study OM 37 has been used. The properties of OM37 is also given in Table 1 [47]. The PV panel converts visible and ultraviolet parts of the solar spectrum into electricity but infrared part of spectrum and excess heat of PV module are absorbed by the fully wetted absorber. That excess heat is convectively transferred to the flowing water in channel. The blackened absorber plate or channel absorbs solar

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

Table 1 Design parameters of PVT collector and used for the computation. PV module Specific heat, Cpv Thermal conductivity, kpv Emissivity, epv PV module efficiency at STC Packing factor Apv

apv ab

Solar cell temperature coefficient Absorber channel density Absorber thermal conductivity, Kp Absorber thermal thickness, Lp Cw m_ w OM 37 melting point Tm Kpcm,s Kpcm,l Cpcm,l Cpcm,s Lpcm Density of pcm (solid) Density of pcm (liquid) Insulation Thickness, Lin Insulation conductivity,Kin Storage tank capacity Ctank DC pump power

900 (J/kg K) 140 (W/m K) 0.93 18% 0.89 2m2 (1  2) 0.89 0.9 0.405 K-1 2702 (kg/m3) 310 (W/m K) 0.0012 m 4190 J/KgK 0.04 kg/s 37
C 0.5 w/mK 0.44 w/m K 1.76 kJ kg/K 2.27 kJ kg/K 211 kJ/kg 960 kg/m3 862 kg/m3 0.05 m 0.030 (W/m K) 100 L 24 W

system. Thermal network for charging and discharging mode of present fully wetted absorber type PVT water collector with PCM and without PCM have been shown in Fig. 3(a)e(c) respectively. 3. Thermal model To write the energy balance equations for the components of fully wetted type absorber PVT water collector with integration of PCM, the following assumptions have been considered;  The heat capacitance of front and back glass of PV module, absorber channel and insulating material are negligible as compared to water and PCM.  The glass is considered purely transparent.  The rate of water flow is assumed to be constant,  The ohmic losses and side losses in PV modules are negligible.  There is a good contact of PCM with absorber channel.  The temperature gradient through the thickness of PCM is considered negligible and only an uniform average temperature Tpcm, during the melting and solidification processes is considered.

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 convection (indirect gain). A fraction of thermal energy is transferred by convection to the water and rest is transmitted to the PCM via conduction. When the temperature of wetted absorber channel becomes higher than that of the PCM heat is stored as a sensible heat until its melting point arrives. In the mean time PCM starts melting and when entire melting of the PCM is finished, heat will be stored in the melted PCM as a sensible heat. When solar radiation decreases, the PVT collector component starts to cool down, the melted PCM releases heat to the absorber channel and hence to water until the PCM gets solidified. Therefore PCM supplies heat to the water during the time of low intensity solar radiation as well as during the night. Thus the thermal efficiency of unglazed PVT collector is enhanced as water gets heated from the excess heat of PV module and from PCM, also it can produce the hot water even at night time. The heat from PV module is dissipated by the water and PCM as well. Therefore along with thermal efficiency improvement, it is also an attempt to enhance the electrical efficiency of PVT

The energy balance equations for components of PVT collector during sunshine hours can be written as follows:  PV module:

mpv Cpv

   dTpv h ¼ apv tg IðtÞ  ht;pvw Tpv  Tw  hr;pvsky Tpv dt       Tsky  ht;pva Tpv  Ta  ht;pvb Tpv  Tb i  hpv IðtÞ bApv (1)

In this equation, left hand side term indicates the energy stored in PV module whereas on right hand side first term corresponds to the rate of absorbed solar radiation received by the PV module and the second term represents the overall heat 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 radiative and convective overall heat losses from PV module to the sky and ambient through front glass respectively and the fifth term is convective heat loss to the blackened absorber plate whereas last term indicates electrical energy produced by PV module. In Eq. (1) ht;pvw is convective heat transfer coefficient from cells of PV module to water through back glass of module.

"

ht;pvw

Lbg ¼ þ hc;pvw Kbg 1

Kw Nu De

  Nu ¼ 8:235 11:893a þ3:76a2 5:814a3 þ5:361a4 2a5

#1

Convective heat transfer coefficient hc;pvw has been calculated using empirical relation for forced convective heat transfer [48] as:

hc;pvw ¼

For fully developed laminar flow in rectangular channels with constant heat flux condition (present case) the Nusselt number (Nu) has been calculated using correlation suggested by Kays and Crawford [49] as:

(2) where, a is the aspect ratio [¼channel height(b)/channel width(a)] For non circular channel equivalent diameter can be calculated as

De ¼ 4

ab 2ða þ bÞ

The rest heat transfer coefficients using in Eq. (1) have been calculated as:

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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.

" ht;pvsky ¼

1 hr;pvsky

þ

Lg Kg

"

# ht;pva ¼

1

hc;pva

hr;pvsky is calculated as [40]:



hr;pvsky ¼εpv sApv Tpv þTsky





þ

Lg Kg

#

Tsky is calculated using relation given by Swinbank [50] as;

Tsky ¼ 0:0522Ta1:5

2 2 Tpv and þTsky

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).







hpv ¼ h0 1  b0 Tpv  T0 :

(3)

 Fully wetted absorber channel:

  ab ð1  þ ht;pvb Tpv  Tb bAb   ¼ hc;bw ðTb  Tw ÞAb þ hc;bpcm Tb  Tpcm Ab

bÞt2g IðtÞAb

(4)

Here, first term of right hand side corresponds to the energy absorbed by the blackened absorber plate via non packing area of module and second term is overall heat gain form PV cells through back glass whereas the left hand side indicates the heat transfer from the blackened absorber to the water via convection and to PCM via conduction respectively.

Heat transfer coefficients from absorber channel to water has 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  Water inside the fully wetted absorber channel: Referring to Fig. 2(b) in which an incremental area of collector is taken b dx, where b is width of the collector and dx is an incremental length along the collector. The heat gain transferred to the water as it moves from x to x þ dx be given by: :

;

Q ¼ mw Cw dTw here dTw is the change in water temperature for an incremental length dx. The heat gain per unit area transferred to the water at a ;

;

distance x from the inlet of collector is given by qw ¼ mwbCw

dTw : dx

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A. Gaur et al. / Renewable Energy 109 (2017) 168e187

Therefore The energy balance for the rate of thermal energy gain for cross sectional area bdx by water inside the absorber channel can be written as:

  ; dTw dx ht;pv/w Tpv  Tw bdx þ hc;b/w ðTb  Tw Þbdx ¼ mw Cw dx (5) The terms of left hand side are the overall heat transfer to 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 absorber channel on integration the Tw from x ¼ 0 to x ¼ L one can get the average water temperature.  Phase change material (PCM):

where M ¼ mpcm Cs;pcm for Tpcm < Tm M ¼ mpcm Lpcm for Tpcm ¼ Tm M ¼ mpcm Cl;pcm for Tpcm > Tm The single term on the left side of Eq. (6) is the heat gain to the PCM from absorber channel and the first term on the right hand side is thermal energy stored in PCM whereas the second term corresponds to the overall heat loss from PCM to the ambient through insulation. Overall heat transfer coefficient Ut,pcm is determined as:

Ut;pcm/a

L 1 ¼ in þ Kin hi

(7) Eqs. (1), (5) and (6) are solved analytically by using the method of separation of variables and following expressions have been obtained for the temperatures of PV module (Tpv), water (Tw) and PCM (Tpcm) respectively:

Tw ¼

 f1 ðtÞ  1  ea1 t þ Tpv0 ea1 t a1  f2 ðtÞ  1  ea2 t þ Tw0 ea2 t a2

Tpcm ¼

 f3 ðtÞ  1  ea4 t þ Tpcm0 ea3 t a3

(i) For Tpcm ¼ Tm þ VT

    mpcm Lpcm ¼ Ut;pcma Tpcm  Ta Ab þ hc;pcmb Tpcm  Tb Ab (11a) (ii) For Tpcm sTm

    dTpcm ¼ Ut;pcm/a Tpcm  Ta Ab þ hc;pcm/p Tpcm  Tb Ab dt (11b)

where M ¼ mpcm Cl;pcm for Tpcm > Tm M ¼ mpcm Cs;pcm for Tpcm < Tm In Eqs. (11a) and (11b) the heat is stored in PCM as a latent heat and thermal energy respectively which would be equal to the overall heat loss to the ambient through insulation and convective heat transfer to the absorber channel. The heat transfer coefficient between the melted PCM and absorber channel is augmented by free convection and the following relation [52] has been used to estimate the Nusselet number for heat transfer coefficient. Rayleigh number (Ra ¼ Gr*Pr)

Nu ¼ 0:133Ra0:326 0:0686

t2 g ab ð1  bÞIðtÞ þ hc;bw Tw þ hcd;bpcm Tpcm þ ht:pvb bTpv hc;bw þ hcd;bpcm þ ht:pvb b

Tpv ¼

 PCM



1

From Eq. (4)) Tb is obtained as:

Tb ¼

The energy balance equation for components of PVT collector with PCM during off sunshine can be written as follows:

M

    dTpcm þ Ut;pcma Tpcm  Ta Ab hcd;bpcm Tb  Tpcm Ab ¼ M dt (6)



3.2. PVT collector with PCM (discharging mode)

l Drm

0:068

where Ra, Drm and l are the Rayleigh number, thickness of the PCM and length of the absorber respectively. Heat transfer from phase change material to water has been considered through blackened metallic absorber channel/plate. The overall heat transfer coefficient from phase change material to the water will be equivalent heat transfer of conductive heat transfer coefficient of blackened absorber plate and convective heat transfer from that plate to water.  Fully wetted absorbing channel:

   hc;pcmb Tpcm  Tb bdx ¼ hc;bw ðTb  Tw Þbdx þ hc;bpv Tb   Tpv bdx (12)

(8)

(9)

(10)

where f1 ðtÞ; f2 ðtÞ and f3 ðtÞ are the average values off1 ðtÞ; f2 ðtÞ, andf3 ðtÞ, which are functions of solar radiation, ambient temperature, sky temperature and heat transfer coefficients at time interval dt and can be considered as constants. Tpv0 ; Tw0 and Tpcm0 are the 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 given in Appendix I.

Now in discharging mode the heat source will be the PCM. Here in above equation, the term of right hand side is the convective heat gain to the absorber channel from PCM and the left members are the convective heat transfer from absorber channel to the water and PV module respectively.  For PV module:

    dTpv þ ht;pv/sky Tpv  Tsky Apv ht;bpv Tb  Tpv Apv ¼ mpv Cpv dt   þ ht;pv/a Tpv  Ta Apv (13) During discharging, a convective heat transfer from absorber channel to the PV module via water takes place and some of the

A. Gaur et al. / Renewable Energy 109 (2017) 168e187

heat is stored by the PV module and rest is lost to the sky and ambient via radiation and convection respectively. From Eq. (12) the expression for Tb can be obtained as:

Tb ¼

hc;pcmb Tpcm þ hc;b/w Tw þ ht;pvb Tpv b hc;pcmb þ hc;bw þ bht;pvb

(14)

Further by using method of separation of variables Eqs. (11) and (13) are solved analytically as:

Tpcm

 f ðtÞ  1  ea5 t þ Tpcm0 ea4 t ¼ 4 a4

Tpv ¼

 f5 ðtÞ  1  ea5 t þ Tpv0 ea5t a5

Mw Cw

175

  dTtan k ¼ ðUAÞw/a Ta  Tw;tan k dt

(20)

The solutions of Eqs. (19) and (20) were obtained as given below Eqs. (21) and (22) respectively:

Tw;tan k ¼

 f6 ðtÞ  1  ea6 t þ Tw;tan 0 ea6t a6

(21)

  Tw;tan k2 ¼ Ta 1  ea7t þ Tw;tan 0 ea7t

(15) The expressions for f5 ðtÞ, a6 and a7 are given in Appendix I.

(16)

The expressions forf4 ðtÞ f5 ðtÞ, a4 and a5 are given in Appendix I.

3.5. Overall electrical and thermal energy The daily electrical energy in KWh of a PVT collector was obtained as:

Eel;daily ¼

N1 h bA t IðtÞ X pv g pv

1000

i¼1

;

(22)

3.3. PVT collector without PCM The energy balance equations for PV module and water will be similar as Eqs. (1) and (5) but for absorber channel heat loss through insulation to the ambient would be from absorber channel only. It can be written as follows:





ab ð1  bÞt2g IðtÞAb þ ht;pvb Tpv  Tb bAb ¼ hc;bw ðTb  Tw ÞAb þ Ut;ba ðTb  Ta ÞAb

0

Lin 1 þ Kin hi

(23)

Qth ¼ Qw;tan k ¼ Mw Cw ðTw0  Twi Þ (17)

where

"

Qel ¼ Eel;daily  Pw Pw is power consumption by DC pump from PV module. Heat gain for water in storage tank was calculated as:

 Wetted absorber channel:

Ut;b/a ¼

N1 is the number of sun shine hours per day. Net daily electrical energy for present system was calculated as:

#1

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 temperature difference would be the difference of consecutive water temperature in tank only. The overall thermal energy was calculated as [53],

Qoverall;thermal ¼ Qth þ From Eq. (17) the expression for Tb can be written as:

Tb ¼

t2 g ab ð1  bÞIðtÞ þ hc;bw Tw þ hcd;bpcm Tpcm þ h1 bTpv hc;bw þ hcd;bpcm þ h1

(18) The same methodology has also been adopted to solve the Equations for PVT water collector without PCM.

The energy balance for the storage tank during the day can be written as follows: 

Qel  Pw

gm

;

(25)

where gm is the conversion efficiency of thermal power plant which depends upon quality of coal (gm ¼ 0.38 for good quality of coal). To convert the thermal efficiency into equivalent electrical energy the Carnot efficiency factor [54] was used.



Ta þ 273 ; Qoverall;exergy ¼ Qel;daily þ Qth 1  Two þ 273

(26)

where Ta and Two are ambient and water outlet temperature respectively. The daily electrical and thermal efficiencies of the present system were calculated using the following relations:

3.4. Water storage tank

mw Cw ðTwo  Twi Þ ¼ Mw Cw

(24)

  dTw;tan k þ ðUAÞw/a Tw;tan k  Ta dt (19)

There is no forced mode in PVT collector without PCM during the night time, In such case the energy balance for tank water can be written as:

P

hel;daily ¼

Qel

24hours

P

Apvt b

IðtÞ

(27)

24 hours

P

hth;daily ¼

Qth

24hours

Apvt

P

24 hours

IðtÞ

(28)

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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 formula [55,56]. Hence beam and diffuse radiations on the PVT collector 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 components with and without PCM. For both the cases Mathcad15 program 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 considered to be inlet water temperature (Twi) for next hour. Fig. 4 shows a detailed flowchart entailing the various steps to solve the mathematical 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 collector 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 corresponds 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 achieved, 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 due to the admirable heat transfer from the PV module to the water through the contact area of entire PV module as back surface of PV module itself forms one side of channel and water remains in the direct touch of PV module resulting very low temperature difference. Therefore the Tw of the fully wetted PVT collector is quite close to Tpv under the effectual convective heat transfer. However, a slight increment is observed in Tb. Since the absorber plate receives thermal energy from PV cells (indirect gain) as well as via non packing area of PV module (I(t) is transmitted through glass, direct

Fig. 4. Flow chart for the analysis of present PVT system.

gain) results into a increment in its temperature. The channel water is also in direct contact with absorber. Fig. 6(a) and (b) also represent variation of PV module efficiency with time, where it decreased and then increased with time. The minimum efficiencies of PV modules for a typical winter and summer days are observed as 15.7% at ~12:00 h and 14.2% at 13:00 h respectively. This variation in module efficiencies can be understood by variation in module temperatures which are maximum at ~12 h on winter day and at ~13 h on summer day. It is because of the reduction in band gap energy with rise of cell operating temperature. The reduction in

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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 which affects the cell voltage significantly. The reduction in cell voltage with rise in operating temperature is due to the rapid increase in reverse saturation current I0 (Voc ¼ KT/q  log Isc/I0).

5.2.2. With PCM From Fig. 6, it is clearly seen that water gets heated during sunshine hours only. There is a fast drop in temperature of storage water in tank overnight and in sunshine hours Tm is quite high causing lower electrical efficiency. Further to enhance the overnight production of hot water and hpv with reduced Tm, the same system is studied using PCM OM 37 beneath on the collector. Fig. 7(a) and (b) shows the hourly variations of Tpv, Tpcm,Two, Tb, Tw,tank and hpv for a winter (Fig. 7(a)) and summer (Fig. 7(b)) days. The maximum values of Tpv, Tw, Tb, and Tw,tank were obtained at ~12:00 h for winter as 46.78
C, 46.84
C, 46.89
C and 40.43
C and at ~13:00 h for summer day as 53.86
C, 53.58
C, 53.34
C and 49.45
C respectively. Here, as the solar intensity increases, Tpcm increases due to the heat transfer from blackened absorber via conduction. It can be seen that the PCM started to melt after 11 h on a typical winter day and after 9 h on a summer day from the beginning of PVT collector exposure to solar radiation. Afterwards, Tpcm remains almost constant from its temperatures of 43.9
C at~12 h in winter 41.23
C at~10 h on summer day till it melts completely then after sunset it decreases slowly in the discharging process of the heat stored within the PCM. The time requisite for PCM in entire charging or discharging depends on its thermal conductivity. PCM material 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 processes in energy systems [58]. This is also a challenge for biobased PCMs. An extensive research in that area is being carried out to enhance the thermal conductivity of existing PCM by adding particles with high thermal conductivity. Thermally conductive additives such as expanded graphite, aluminum, copper and aluminum nitride have been investigated that improve the overall

thermal conductivity of PCM with faster heat transfer [59]. Few Another approaches of macroscopic-capsules and microencapsulation to reduce the adverse effect of thermal conductivity 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 neutral for both the phase change material and the heat transfer fluids is used. However micro-encapsulation is a quite new method in which the PCM is encapsulated in a small shell of polymer materials with a diameter of micrometers (at the moment for paraffin's only) results a large heat-exchange surface. Using containment can also increase the surface area by reducing the distance from the external heat source to the center of the PCM. therefore the heat has to travel less distance which can increase the rate of heat transfer. One can observe from Figs. 6 and 7 that during night due to decreased ambient temperature with time the water temperature in tank (Tw,tank) without PCM decreases faster than that of (Tw,tank) with PCM. For night PCM will act as a heat source for water and decrease its temperature very slowly. In charging mode (during sunshine hours) the outlet temperatures are much higher than the inlet temperature whereas during discharging mode there is no remarkable temperature difference between inlet and outlet water temperature as water is receiving heat energy from PCM only but is worth to note the fact that, at ~5 h in the morning of winter and summer typical days, the outlet Two and Tw,tank were found to be 34.78
C, 31.67
C and 34.89
C, 33.15
C respectively, whereas for without PCM the Tw,tank at ~5 h were 14.98
C for winter and 27.75
C for summer (Figs. 6 and 7). Hence hot water can be obtained in early morning when it is really needed to take shower or other uses.

5.2.3. Comparison of electrical efficiencies of PVT system with and without PCM Fig. 8 compares the PV module efficiencies of fully wetted absorber PVT collector with and without PCM at different time intervals. For a typical day of summer daily average electrical efficiency of PV modules of PVT collector with PCM and without PCM were found to be 16.30% and 15.40% respectively whereas for

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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 improvement in efficiency with PCM can be understood as the heat capacity of PCM is high. It stores excess heat of PV module via

absorber plate resulting reduced module temperature and improved electrical efficiency. A maximum reduction of module temperature with PCM for summer at12 h and at 13 h for winter

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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 improvement of electrical efficiency point of view, use of PCM is quite effective.

5.2.4. Optimization of mpcm(kg) for the present PVT system Fig. 9 shows the effect of varying mass of PCM for 10 kg (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 temperature (Two) temperature and PCM temperature (Tpcm). It can be seen that during the day time in sunshine hours when mass of PCM increases from 10 Kg to 30 Kg the outlet temperature decreased whereas during the night time it increased with increased mass of PCM. The reason behind this is that during the day time PCM remains in charging mode and acts as a heat sink for PV

module and absorber plate. Therefore as the mass of PCM increases up to a certain amount the heat capacity of PCM increases and it can store more amount of heat during the day time resulting lower outlet temperature whereas in off sunshine, during night it acts as a heat source and release more heat to the water with increase mass but it was also observed that after an optimal mass and thickness of 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.

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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 30 kg which can be attributed as the PCM is completely in liquid state and the activation of the latent heat is not allowed. It is

interesting to see that after 30 kg of PCM if we increase more mass then temperatures are found to be lesser than that of temperatures 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).

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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 thermal flow cannot pass through it perfectly and PCM will act as a semi infinite material resulting less energy storage. It was observed that, as the PCM mass increased, temperature of PCM decreased which is quite obvious because of the increased time taken by the PCM to attain its melting temperature. Heat required to melt the PCM must be equal to the product of its mass (mpcm) and latent heat (L) i.e. H ¼ mpcm* Lpcm. Hence for excellent performance of 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. 5.2.5. Effect of different mpcm on Tpv and hpv Fig. 10 shows the effect of mass of PCM on Tpv and hpv It is clearly seen from figure that hpv increases with increase of PCM mass and Tpv decreases. The reason behind this is the increased mass of PCM increases its heat capacity that can store more amount of heat resulting reduced Tpv and higher hpv. For present system melting point of PCM OM 37 is 37
C which has been found suitable for winter (Feb) and summer (July) of climatic condition of Lyon France. It was observed that during the summer it attains melting temperature very quickly, though it was found to be good for summer as well but it could be a problem for very high ambient temperature and solar radiation. In such case the PCM will be melted completely very rapidly and latent heat would not be allowed. In such case heat can be stored as a sensible heat only. Also the module temperature can reach very high resulting lower electrical efficiency. This possibility of deterioration in the performance of present PVT collector can be minimized if it is operated at relatively lower temperatures, which can be achieved by increasing the mass flow rate during the summer to compensate for increased ambient temperature and solar radiation. 5.3. Effect of mass flow rate (kg/s) of water on Tpv and hpv Fig. 11 shows the variations Tpv of and hpv with mass flow rate of

;

water mw . The module temperature was observed to decrease with ;

increment in mw causing higher electrical efficiency of PV module. ;

This is all because of more heat dissipation on increment of mw . For very low

; mw

of 0.0005 kg/sec the hpv and Tpv were found to be ;

58.02
C and 15.1%, whereas for very high mw of 0.075 kg/s the hpv and Tpv were found to be 25.29
C and 18% respectively. There is no benefit in increasing the mass flow rate beyond 0.04 kg/s. 5.4. Thermal and electrical energy performances of the system 5.4.1. Daily thermal energy and overall energy Fig. 12 compares the hourly thermal power of present PVT collector with PCM and without PCM for winter and summer day. It was observed that during the day time PVT collector without PCM exhibited higher thermal energy due to high solar radiation and ambient temperature but in evening solar radiation is low and in night PVT collector with PCM exhibited higher thermal energy. The daily thermal energy and overall thermal energy from PVT collector with PCM and without PCM for a winter (Feb) day were found to be 8.74 kWh, 13.18 kWh and 5.32 kWh, 9.26 kWh respectively whereas for summer day (July) the thermal energy and overall thermal energy were found to be 9.21 kWh and 14.14 kWh for PVT with PCM and 6.499 kWh and 11.79 kWh for without PCM. The overall thermal energy was observed higher in summer. As expected the length of the day in summer, when solar radiation is available is higher than that of the month of winter (Feb). On the other hand the thermal efficiency was also calculated using Eq. (27) for the fully wetted PVT with PCM and it was found to be 84.01% for winter day (Feb) and 59.66% for summer day(July). The reason behind higher thermal efficiency in winter can be attributed as the total length of solar radiation (power input) is lesser than that of the summer. Thermal energy with PCM was observed higher for both summer and winter day. It is obvious because system with PCM produce thermal energy efficiently during the night as well.

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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 winter day and 43.73% for summer day. 5.4.2. Daily electrical energy and overall exergy Fig. 13 shows the hourly variations of electrical power of PVT collector with and without PCM, for the winter and summer days. It is clear from the figure that for both winter and summer PVT collector with PCM exhibited higher electrical energy as compared to without PCM which correspond to higher electrical efficiency with PCM than that of without PCM what is discussed above in detail. The daily electrical energy and overall exergy for PVT collector with PCM and without PCM were found to be 2.05, 2.675 kWh and 1.95 kWh, 2.65 kWh respectively for summer and 1.52 kWh, 2.35 kWh and 1.50 kWh, 1.98 kWh respectively for winter. Hence it is clearly seen that for both months overall exergy was also observed higher in summer compared to the winter correspond to the higher number of sunshine hours in summer than that of winter. 5.5. Characteristics curves for the present PVT system 5.5.1. For thermal efficiencies Thermal efficiencies of the present PVT water collector with PCM and without PCM were conventionally calculated as a function of the reduced temperature Twi  Ta =IðtÞ , where Twi and Ta are the PVT collector's inlet water temperature and the ambient temperature respectively and I(t) is the incident solar radiation. Thermal efficiency can be represented as

hth ¼ h0th a1



Twi  Ta IðtÞ



where h0th is the thermal efficiency at zero reduced temperature or thermal gain factor and a1 is the thermal heat loss coefficient.

Fig. 14 shows the variation of thermal efficiencies as a function of Twi  Ta =IðtÞ for PVT collector with and without PCM on the typical days of winter (20 Feb) and summer (8 July). These characteristics curves are similar to the Hottel-Whiller-Bliss equations of a flat plat collector [2,7]. The efficiencies for both the conditions (with and without PCM) are observed to decrease with increment in reduced temperatureTwi  Ta =IðtÞ. This variations in efficiencies with reduced temperature are also similar for the months of Feb and July however their gain factors or thermal efficiencies at zero reduced temperature (h0th ) and loss coefficients (a1 ) are different for each case. It can be seen from Fig. 13 that the thermal efficiencies at zero reduced temperature or gain factor for PVT collector with PCM (Feb ¼ 0.46, July ¼ 0.66) was slightly lesser than that of without PCM (Feb ¼ 0.47, July ¼ 0.70), that can be attributed to higher module temperature (Tm) resulting elevated water temperature, However for both the months, the loss coefficient for PVT with PCM (Feb ¼ 2.33, July ¼ 11.01) were observed lesser compared to PVT collector without PCM (Feb ¼ 5.10, July ¼ 12.08). Hence, incorporation of PCM reduces the heat losses and provides better thermal stability to the system. 5.5.2. For electrical efficiencies The electrical efficiencies of the PVT collector with and without PCM for both months, under the outdoor condition are shown in Fig. 15. The electrical efficiency can be represented as hel¼ hoel a2 ðTwi  Ta =IðtÞÞ., here hoel . ielectrical efficiency of collector at zero reduced temperature or electrical gain factor and a2 is the electrical loss coefficient. These characteristics curves are also similar to the Hottel-Whiller-Bliss equations of a flat plat collector. It can be observed from the figure that the electrical gain factors 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) compared to without PCM (Feb ¼ 0.19, July ¼ 0.17) (Feb ¼ 1.05, July ¼ 0.44) respectively. It is because of the absorption of excess

A. Gaur et al. / Renewable Energy 109 (2017) 168e187

and 1.95 kWh,2.65 kWh respectively for summer and 1.52 kWh, 2.35 kWh and 1.50 kWh, 1.98 kWh respectively for winter. ;  mpcm and mw have significant effect on Tpcm,Tpv, Tw and hpv.

heat of PV module by PCM due to latent heat absorption mechanism resulting higher electrical efficiency with minimized electrical losses. 6. Conclusions An unglazed Fully wetted type absorber PVT collector with PCM integrated beneath the absorber plate and without PCM has been investigated by developing thermal model for temperatures of different component of system and electrical efficiencies under winter and summer climatic conditions of Lyon, France. On the basis of present studies the following conclusions are drawn.

185

The present study is limited to numerical analysis of performance of fully wetted absorber channel PVT collector with PCM for specified solar radiation and ambient temperature. The same can be extended to experimental investigations for validation of the present model. Also thermal conductivity enhancement, CO2 mitigations and life cycle cost analysis can be performed.

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 next day.

The unknown parameters used in the various equations are given below:

h f1 ðtÞ ¼

a1 ¼

i

apv tg IðtÞ þ ht;pvw Tw þ hr;pvsky Tsky þ ht;pva Ta þ ht;pvb Tb  hpv IðtÞ bApv mpv Cpv

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

ht;pv/w Tpv bdx þ hc;b/w Tb bdx f2 ðtÞ ¼ mw cw 

 Ut;pcm/a Ta þ hc;pcm/p Tb Ab f3 ðtÞ ¼ mpcm Cpcm  f4 ðtÞ ¼ Apcm

f5 ðtÞ ¼

hc;pcmb Tb þ Ut;pcma Ta

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

mpcm Cpcm

 a4 ¼ Apcm

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

f6 ðtÞ ¼

mw Cw ðTwo  Twi Þ þ ðUAÞw/a Ta Mw Cw

a6 ¼

a5 ¼

hc;pcmb þ Ut;pcma



mpcm Cpcm ht;bpv þ ht;pv/sky þ ht;pv/a Apv

ðUAÞw/a Ta Mw Cw

mpv Cpv

a6 ¼ a6

 PV module in PVT system with PCM exhibit lower module temperature than that of without PCM leading to higher electrical efficiency. A maximum reduction of module temperature with PCM for summer at 12 h and at 13 h for winter day was observed up to ~16.04
C and ~5
C respectively.  For a typical day of summer daily average electrical efficiency of PV modules of PVT collector with PCM and without PCM were found to be 16.30% and 15.40% respectively whereas for winter it has been found to be 16.87% and 16.5% respectively.  The daily thermal energy and overall thermal energy from PVT collector with PCM and without PCM for a winter (Feb) day were found to be 8.74 kWh, 13.18 kWh and 5.32 kWh, 9.26 kWh respectively whereas for summer day (July) the thermal energy and overall thermal energy were found to be 9.21 kWh and 14.14 kWh for PVT with PCM and 6.499 kWh and 11.79 kWh for without PCM.  The daily electrical energy and overall exergy for PVT collector with PCM and without PCM were found to be 2.05, 2.675 kWh

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Nomenclature A: area (m2) b: width of PV module (m) c: cell C: specific heat (J kg1 K1) h: heat transfer coefficient (W m2 K1) IðtÞ: incident solar radiation (W m2) K: thermal conductivity (W m1 K1) L: thickness (m) M: mass (kg) m_ f : mass flow rate of fluid (kg s1) Re : Reynolds number (dimensionless)
T: temperature ( C) U: overall heat transfer coefficient (W m2 K1) V: velocity (m s1) Tfg: front glass temperature Tbg: back glass temperature Tw: water temperature Tb: absorber temperature Greek symbols

a: absorptivity (dimensionless) b: packing factor (dimensionless) r: density (kg m3) n: kinematic viscosity (m2 s1) h: efficiency (dimensionless) Subscripts a: ambient air b: absorber channel l: liquid

A. Gaur et al. / Renewable Energy 109 (2017) 168e187 m: melting point s: solid w: water w0: outgoing water win: inlet water pv: Photovoltaic module

pcm: Phase change material i: Insulation fg: front glass bg: back glass cod: conduction

187