Performance evaluation of inverted absorber photovoltaic thermal compound parabolic concentrator (PVT-CPC): Constant flow rate mode

Applied Energy 167 (2016) 70–79

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Performance evaluation of inverted absorber photovoltaic thermal compound parabolic concentrator (PVT-CPC): Constant flow rate mode Deepali Atheaya a,⇑, Arvind Tiwari b, G.N. Tiwari a, I.M. Al-Helal c a

Centre for Energy Studies, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India BAG Energy Research Society, Varanasi, India c Department of Agricultural Engineering, College of Food & Agricultural Sciences, King Saud Univ., P.O. Box 2460, Riyadh 11451, Saudi Arabia b

h i g h l i g h t s
Thermal modelling of inverted absorber PVT-CPC collector system is developed.
An analytical expression for the module efficiency of the above system is derived.
An energy and exergy analysis has also been carried out.

a r t i c l e

i n f o

Article history: Received 16 June 2015 Received in revised form 13 January 2016 Accepted 14 January 2016

Keywords: Inverted absorber Compound parabolic concentrator Characteristic equation

a b s t r a c t In this paper, a new design of a glazed and an unglazed inverted absorber partially covered photovoltaic thermal compound parabolic concentrator (PVT-CPC) water collector has been proposed. The performance of proposed systems has been compared with partially covered inclined and horizontal PVT-CPC water collector systems for constant mass flow rate mode. Analytical expressions for the outlet fluid temperature (Tfo1) and electrical efficiency of the proposed systems have been derived and presented. Based on the analytical thermal model, a software program has been developed in MATLAB 2010a to determine the outlet fluid temperature, electrical efficiency, thermal energy, electrical energy and overall exergy efficiency of the systems. The results showed that the glazed inverted absorber partially covered PVT-CPC water collector system exhibited higher values of instantaneous thermal efficiency. Further, the glazed inverted absorber partially covered PVT-CPC system is more suitable for higher thermal energy. However, the partially covered inclined PVT-CPC water collector is more favourable for electrical energy requirements. Further, the inverted absorber partially covered PVT-CPC system is cost effective. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The PVT-CPC technologies are being developed globally to achieve enhanced thermal and electrical outputs. Brogen et al. [1] have suggested that in this way, the system can be made more efficient. A lot of research has been done on the reverse flat plate collectors [2–4]. The performance of a single and double absorber reverse flat plate collector were determined by Goel et al. [5]. It was found that the thermal performance of double absorber reverse flat plate absorber was the best. Norton et al. [6] have proposed first time and investigated the performance of curved

⇑ Corresponding author. Tel.: +91 9910446852; fax: +91 11 26591251. E-mail address: [email protected] (D. Atheaya). http://dx.doi.org/10.1016/j.apenergy.2016.01.023 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

inverted–vee absorber compound parabolic solar energy collectors. Based on the concept proposed by Norton et al. [6], a parametric study of reverse flat plate cabinet dryer was done by Goyal and Tiwari [7] and it was found that it gave better performance as compared to a flat plate normal cabinet dryer. Such work was extended for inverted absorber asymmetric CPC solar still which was designed by Tiwari et al. [8]. An experimental validation for an inverse absorber solar still (IASS) was carried out by Dev et al. [9] at Muscat, Oman. It was concluded that higher yields were obtained by using IASS. This was due to the minimum thermal losses in IASS. A comparative study of inverted absorber asymmetric (IACPC) with symmetric tubular (TACPC) absorber compound parabolic concentrating solar collectors was done by Kothdiwala et al. [10]. It was found that the solar collector efficiency of an IACPC was much more than TACPC.

D. Atheaya et al. / Applied Energy 167 (2016) 70–79

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Nomenclature A Aa Aam Aac Ar Arm Arc b bo cf dx F0 FR h Lrm Lrc Lr PF 1 PF 2 PF c It Ib Ibb C _f m U t;ca U t;cp U t;pa

area (m2) total aperture area (m2) (Aa = Aam + Aac) aperture area over PV module (m2) aperture area over glazed portion (m2) total receiver area (m2) receiver area covered by PV module (m2) receiver area covered by glass (m2) breadth of receiver (m) breadth of aperture area (glass) (m) specific heat of fluid (J/kg K) elemental length (m) flat plate collector efficiency factor flow rate factor, dimensionless heat transfer coefficient, W/m2 K length of receiver covered by PV module (m) length of receiver covered by glass (m) total length of the aperture area (m) penalty factor, first dimensionless penalty factor, second dimensionless penalty factor, third dimensionless total radiation, (W/m2) beam Radiation, (W/m2) beam radiation at an angle b, (W/m2) conductance (W/m2 K) mass flow rate of water in (kg/s) overall heat transfer coefficient from solar cell to ambient through glass cover (W/m2 K) overall heat transfer coefficient from solar cell to absorber plate (W/m2 K) overall heat transfer coefficient from absorber plate to ambient (W/m2 K)

Chow et al. [11] carried out energy and exergy analysis of photovoltaic thermal (PVT) collector with and without glass cover. It was found that if the thermal energy requirement was more than a glazed PVT system was found to be more feasible. However, if we require higher PV cell efficiency than the unglazed system has been observed to be more viable. Kong et al. [12] fabricated a low concentrated photovoltaic thermal hybrid system. The concentrator was made by using fresnel lens and two flat mirrors. The photovoltaic modules of 18 solar cells were pasted on the Aluminium receiver. The results showed that on a clear day the electrical and thermal efficiencies were 10% and 56% respectively. Li et al. [13] presented a performance study of solar cell arrays based on trough concentrating photovoltaic thermal systems. It was observed that GaAs (Gallium Arsenide) cells showed superior performance as compared to single, poly crystalline Si cells and super cells. Dupeyrat et al. [14] investigated a single glazed flat plate photovoltaic thermal hybrid water collector. They reported that the standard PV panel showed higher thermal efficiency and lower electrical efficiency due to glazing. Calise et al. [15] conducted the energy and exergy analysis of parabolic trough photovoltaic thermal solar collectors. They concluded that thermal and electrical efficiencies improved manifolds when the beam radiation was high. Bahaidarah et al. [16] compared the flat PV string system with the PV-CPC system. They reported that the power output of PV-CPC system was more than that obtained from the flat PV. The power output for PV-CPC system with cooling was found to be 39% higher and without cooling 23% higher than the flat PV system. Recently, Abu-Bakar et al. [17] presented a rotationally asymmetrical compound parabolic concentrator (RACPC). It was found that when this system was coupled with a concentrating

U L1 Q th

go

bo T Tfo1

overall heat transfer coefficient from blackened surface to ambient (W/m2 K) available thermal energy (W) efficiency at standard test condition (It = 1000 W/m2, T o = 25 °C) temperature coefficient of efficiency (K1) temperature (K) outlet fluid temperature at the end of glazed inverted absorber PVT-CPC system (K)

Greek letters a absorptivity b packing factor q reflectivity s transmittivity gi instantaneous thermal efficiency ðasÞeff product of effective absorptivity and transmittivity g thermal efficiency Subscripts a ambient c solar cell o outlet eff effective f fluid fi inlet fluid fo1 outlet fluid g glass m module p plate

photovoltaic system, the electrical output of the system was considerably increased. This research paper mainly focuses on the performance study of a glazed and unglazed inverted absorber partially covered PVT-CPC water collector system and it has been compared with the partially covered inclined PVT-CPC and partially covered horizontal PVT-CPC water collector systems. This analysis has not been carried out by any one so far. Thus, we have proposed a novel design of an inverted integrated PVT-CPC water collector system to increase the thermal and electrical performance. The proposed system has the following novelty as compared to partially covered PVT-CPC system: (i) there is a direct heat gain from the top and also indirect heat gain from the bottom and (ii) there is an also reduced bottom heat loss due to absorber facing downwards. 2. Proposed systems description Following four configurations of the proposed system are investigated: 2.1. Case (i) Glazed inverted absorber partially covered PVT-CPC water collector (a new proposed concept) The cut sectional front view of a glazed inverted absorber partially covered PVT-CPC water collector system is illustrated in Fig. 1a. The beam radiation falls on the reflector 1 of compound parabolic concentrator (CPC) and approaches the bottom surface of CPC and it again gets reflected from the reflector 2 and reaches the horizontal inverted absorber surface of the system. The

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Fig. 1a. Cut sectional front view of a glazed inverted absorber partially covered PVT-CPC water collector system.

inverted absorber consists of two portions namely lower and upper portions. The lower portion of the absorber is covered with semitransparent PV module and upper portion is covered with glass cover (Fig. 1b). The water is made to flow in the metallic tubes present above the inverted blackened absorber of the glazed inverted absorber PVT-CPC water collector system. The top surface of the tube in plate system is covered with glass. There is a direct gain of beam radiation to blackened absorber by transmission through non packing factor area of the PV module and indirect gain by convection from back of solar cells of semitransparent PV module to blackened absorber. After blackened absorber is heated then there is transfer of thermal energy from blackened surface to flowing water and hence the water is heated and moves in upward direction due to low density (Fig. 1c). The hot water available at outlet of PVT collector becomes the inlet of glazed portion. The hot inverted absorber surface is facing downwards so convection losses are suppressed. Hence the downward heat losses are reduced significantly in the proposed system as a result of which the system gives better performance.

Fig. 1b. Cut sectional side view at semitransparent section(x–x0 ) of a glazed inverted absorber partially covered PVT-CPC water collector system.

Fig. 1c. Cut sectional side view at a glazed section(y–y0 ) of glazed inverted absorber partially covered PVT-CPC water collector system.

D. Atheaya et al. / Applied Energy 167 (2016) 70–79

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2.2. Case (ii) Unglazed inverted absorber partially covered PVT-CPC water collector system (new concept)

2.4. Case (iv) Partially covered horizontal PVT-CPC water collector system (See Fig. 4a and 4b)

In the present case an insulating layer of a given thickness has been used at the top surface to reduce the overall heat transfer coefficient. The cut sectional front view of an unglazed inverted absorber PVT-CPC water collector system is shown in Fig. 2.

The beam radiation falls horizontally on the system (Fig. 4c) unlike case (iii). The climatic data is taken for the month of January, New Delhi (India), from India Metrological Department (IMD), Pune (India) for numerical computation for all cases mentioned above.

2.3. Case (iii) Partially covered inclined PVT-CPC water collector system, Atheaya et al. [18]. (See Figs. 3a and 3b) The beam radiation falls on the aperture surface and gets reflected from the reflector towards the PV module. The absorber plate is half covered with PV module and the remaining part is glazed. The electricity is produced from the PV module and the thermal energy gained is used for heating water which flows beneath. The outlet fluid of PV module portion becomes the inlet fluid to the glazed absorber system. Tfo1 is the outlet fluid temperature that exits from the overall system. Here the beam radiation is incident on an inclined surface at an angle of 30°. This has been done due to the fact that New Delhi (India) is located at latitude of (28° 360 000 ) 30° approximately.

3. Thermal modelling Following assumptions were considered to write the energy balance equations for the analysis of the present systems:
The PVT-CPC systems are in quasi steady state.
In the PV module, the ohmic losses between solar cells are negligible.
The heat capacity of glass cover and solar cell materials in the PV module are neglected.

Fig. 2. Cut sectional front view of an unglazed inverted absorber partially covered PVT-CPC water collector system.

Tfi

Fig. 3b. Front view of partially covered inclined PVT-CPC water collector system.

Solar cells

reflectors

Glass

Lrm

Lrc

Tfo1

Fig. 3a. Top view of partially covered inclined PVT-CPC water collector system.

Fig. 4a. Cut sectional side view of horizontal partially covered PVT-CPC water collector system.

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D. Atheaya et al. / Applied Energy 167 (2016) 70–79

(c) For flowing fluid below the receiver/absorber

_ f cf m

dT f dx dx

¼ F 0 hpf ðT p  T f Þbdx

½the rate of heat carried by flowing fluid above the absorber plate

ð3Þ

½the rate of thermal energy transferred from plate to fluid

From Eqs. (1) and (2) we can get an analytical expression for the solar cell (T c ) and absorber plate (T p ) temperatures as follows:

Tc ¼

Tp ¼

ðasÞ1b;eff Ibb þ U t;ca T a þ U t;cp T p ðU t;ca þ U t;cp Þ

ð4Þ

asIt þ ðasÞ2b;eff Ibb þ PF 1 ðasÞ1b;eff Ibb þ ðU t;pa þ U L1 ÞT a þ F 0 hpf T f ðU tpa þ U L1 þ F 0 hpf Þ ð5Þ

Fig. 4b. Cut sectional front view at y–y0 of horizontal partially covered PVT-CPC water collector system.

Further, Eqs. (3)–(5), are solved to get the expression of fluid  temperature, T f 1 with initial conditions T f x¼0 ¼ T f 1 as follows:

2

Tf 1 ¼ 4

n o PF 2 asIt þ ðasÞmb;eff Ibb

U l;m  0  F U l;m bx þ T fi exp _ f cf m

3   0  F U l;m bx þ T a 5 1  exp _ f cf m

ð6Þ

By using above equation, the average fluid temperature can be obtained as follows:

Tf 1 ¼ or,

1 Lrm

Z

Lrm

ð7Þ

T f 1 dx; 0

n o3 " #    PF 2 asIt þ ðasÞmb;eff Ibb  F_ rm F rm F rm 4 5 1  0 þ T a 1  0 þ T fi 0 ¼ U l;m F F F 2

Tf 1

ð8Þ Fig. 4c. Cut sectional front view at x–x0 of horizontal partially covered PVT-CPC water collector system.


The temperature is uniform across the PV module and glass cover.

The temperature dependent solar cell efficiency (gc ) expression as given by Evans [19] and Schott [20] is as follows:






gc ¼ go 1  bo ðT c  T o Þ

ð9Þ

By substituting values of (T f 1 ) from Eq. (8) in Eqs. (5) and (4), 3.1. The energy balance equations of each section of the glazed inverted absorber partially covered PVT-CPC water collector system [case (i)] are given below Lower portion of the glazed inverted partially covered PVT-CPC water collector system. (a) For semi-transparent photovoltaic (PV) module (Fig. 1a)






qq0 ac s2g bc Ibb Aam ¼ U t;ca ðT c  T a Þ þ U t;cp ðT c  T p Þ Arm þ qq0 gm Ibb Aam ½the rate of solar radiation received by PV module

½the rate of thermal energy loss from PV module to ambient and the thermal energy transferred from solar cell to plate

½the rate of electrical energy produced by PV module

ð1Þ (b) For blackened tube in plate type receiver/absorber

½asIt  U t;pa ðT p  T a ÞArm þ qq0 ap s3g ð1  bc ÞIbb Aa m þ U t;cp ðT c  T p ÞArm ½the rate of thermal energy received from top glazing to absorber plate

½the rate of thermal energy available to the absorber plate through CPC

½the rate of thermal energy loss from solar cell to absorber plate

value of (T c ) is evaluated and thus by further substituting average solar cell temperature expression in Eq. (9), the analytical expression of temperature dependent solar cell efficiency is developed and it is given as follows:

2

3 33 qq0 ac s2g bðAam =Arm Þ 6 7 77 6 6 6 7 77 6 6 6 7 77 U t;cp fðasÞ2b;eff þPF 1 qq0 ac s2g bc ðAam =Arm Þg 6 6 Ibb 6 þ 7 77 0 6 6 ðU L2 þF hpf Þ 7 77 6 ðUt;ca þUt;cp Þ 6 6 6 7 77 6 6   6 7 7 6 6 0 2 57 4 0 PF 2 fqq ac sg bc ðAam =Arm Þg
6 77 6 F rm þF  PF 2 1  6 77 6 0 U l;m F 6 77 6 6 77 go 6 1  b o6 77 6 6 77 6 U asIt þ 6 þ ðUt;ca þUt;cp 77 6 0 ÞðU þF h Þ t;cp L2 pf 6 77 6 6 77 6 h i 6 77 6 U t;cp U L2 0 Ta F rm 6 77 6 6 ðUt;ca þUt;cp Þ U t;ca þ ðUL2 þF 0 hpf Þ þ F  PF 2 ½1  F 0  þ 77 6 6 77 6 4 55 4 F 0 PF 2 T fi
F rm  þ ðUt;ca þUt;cp Þ F 0  T o h gc ¼
i g b b qq0 s ðA =Arm ÞIbb U t;cp PF 1 F 00 PF 2 PF 2 F rm 1 þ þ 1  1  o o cðUt;cagþUam 0 0 Þ U ðU þF h Þ F t;cp 2

2

L2

¼ F 0 hpf ðT p  T f ÞArm

pf

lm

ð10Þ

½the rate of thermal energy transferred from plate to the fluid

ð2Þ

The expression of the outlet fluid temperature at the end of PV module is given as

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D. Atheaya et al. / Applied Energy 167 (2016) 70–79

n

o

2 3   0  PF 2 asIt þ ðasÞmb;eff Ibb F U l;m Arm 4 T fo ¼ þ T a 5 1  exp _ f cf U l;m m  0  F U l;m Arm þ T fi exp _ f cf m

3.3. Exergy analysis Following Bejan [21] and Hepbasli [22], we can evaluate the useful exergy delivered by the working fluid (E_ xc ) in ‘W’ as follows

ð11Þ The energy balance of conventional CPC collector and flowing fluid for the glazed inverted absorber PVT-CPC water collector system can be written as follows:

½asIt  U t;pa ðT p  T a ÞArc þ qq0 ap s2g Ibb Aac ¼ F 0 hpf ðT p  T f ÞArc

E_ el ¼ gm Ib qAam

ð18Þ

"

ð13Þ

In the above Eq. (19), Ta is the surrounding temperature (Kelvin) and Ts is the sun temperature (6000 K). For glazed inverted absorber partially covered PVT-CPC water collector system [case (i)]

thermal energy transferred from glazed plate to fluid

The solutions of the above Eqs. (12) and (13) is given as follows:



4 # 4 Ta 1 Ta þ ¼ ½Aa Ib þ Ar It  1  3 Ts 3 Ts

Overall exergy efficiency ¼ gm þ

ðT fo1 ¼ T f at x ¼ Lrc Þ o 2 n 3   0  PF c asIt þ ðasÞcb;eff Ibb F U l;c Arc 4 : þ T a 5 1  exp _ f cf U l;c m  0  F U l;c Arc ð15Þ þ T 0fi exp _ f cf m

3.4. Energy analysis

2 T fo1 ¼ 4

n o PF c asIt þ ðasÞcb;eff Ibb U l;c 

þ

PF 2 fasIt þðasÞcb;eff Ibb g

 exp

U l;m

 0  F U l;c Arc _ f cf m

3 þ Ta5

þ Ta

h

  F rc U l;c Arc _ f cf m

F rm U l;m Arm _ f cf m

i

h n 0 oi _ cf m F U l;n Arm where F rm ¼ U fArm 1  exp _ m c f f h n 0 oil;n F U q;c Arc 1  exp _ c m

þ T fi exp

F 0 U l;m Arm _ f cf m

o

ð16Þ and

_ c m

F rc ¼ U q;cf Afrc

f f

3.2. Unglazed inverted absorber partially covered PVT-CPC water collector system
 Here, ‘‘ asIt  U t;pa ðT p  T a Þ Arc ” term becomes zero as instead of glazing the top surface is insulated.

ð21Þ

E_ xc Aa Exi

ð22Þ

The thermal energy available from PVT-CPC system for four cases is calculated in Watt (W) as follows:

_ f cf ðT fo1  T fi Þ Q th ¼ m

ð23Þ

The electrical energy generated by the PV modules in Watt (W) for [case (i)] and [case (ii)] is calculated from following equation:

E_ el1;2 ¼ gm Ibb qq0 Aam

ð24Þ

Further, the electrical energy generated by the PV modules in Watt (W) of [case (iii)] and [case (iv)] is calculated by Eq. (25) as follows:

E_ el ¼ gm Ibb qAam n

E_ xc E0xi

The overall exergy efficiency for the [case (ii)], [case (iii)] and [case (iv)] are given as below:

Hence the outlet fluid temperature at the end of glazed inverted absorber partially covered PVT-CPC collector (T fo1 ) is given by

The outlet fluid temperature, T fo at the end of PV module will become the inlet fluid temperature of the glazed absorber portion (T 0fi ¼ T fo ). Therefore, the expression for the outlet fluid temperature at the end of glazed inverted absorber partially covered PVT-CPC water collector system is given as follows:

ð20Þ

The overall exergy efficiency for the [case (i)] is given as below:

Overall exergy efficiency ¼ gm þ

ð14Þ

ð19Þ

"

E0xi

o 2 n 3   0  PF c asIt þ ðasÞcb;eff Ibb F U l;c bx 4 Tf ¼ þ T a 5 1  exp _ f cf U l;c m  0  F U l;c bx þ T 0fi exp _ f cf m



4 # 4 Ta 1 Ta þ 3 Ts 3 Ts

Exi ¼ Ib 1 

½the rate of thermal energy transferred from plate to fluid

½the rate of thermal energy received by the absorber plate through CPC

dT f dx ¼ F 0 hpf ðT p  T f Þbdx dx ½the rate of

½the rate of heat carried by flowing fluid above the absorber plate

The exergy extracted by the PV module (E_ el ) in W is evaluated as

ð12Þ

(e) Flowing fluid

_ f cf m

ð17Þ

To determine the performances of four cases, the exergy of solar radiation is calculated (Patela [23] and Szargut [24]) as follows:

(d) Absorber plate

½the rate of thermal energy received from top glazing to absorber plate

ðT þ 273Þ _ f cf ðT fo  T fi Þ  E_ f cf ðT a þ 273Þ ln fo E_ xc ¼ m ðT fi þ 273Þ

ð25Þ

4. Results and discussion Fig. 5 illustrates the hourly variation of beam radiation (Ib ), beam radiation at an angle of 30° (Ibb ) and total radiation (It ) for the typical month of January. The various design parameters of all the cases are given in Tables 1–3. The hourly variation of outlet fluid temperature (Tfo1) for four cases has been shown in Fig. 6. For glazed inverted absorber partially covered PVT-CPC system [case (i)], the outlet fluid temperature has been observed to be maximum as more solar radiation is received on the absorber plate. It can be justified with the fact that the total radiation reaching to the absorber plate is the sum of total radiation (It ) reaching absorber plate directly through the glass cover and beam radiation (Ib ) getting reflected from different surfaces and reaching finally at the bottom of the absorber plate. This results in substantially

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D. Atheaya et al. / Applied Energy 167 (2016) 70–79 1000

Table 2 Various design parameters of an unglazed inverted absorber partially covered PVTCPC system [case (ii)].

Solar Radiation, W/m 2

900 800

Parameters

Values

700

Aa ; Aam ; Aac Arc ; Arm ; Ar Lrm ; Lrc bo ; b F0 Inclination angle F rc ; F rm

2 m2, 1 m2, 1 m2 0.5 m2, 0.5 m2, 1 m2 1 m, 1 m 1 m, 0.5 m 0.9680 30° 0.9147, 0.9149 1000 kg/m3 0.816 W/m K, 0.166 W/m K, 64 W/m K 0.003 m, 0.100 m, 0.002 m 0.7224, 1.0168, 1.0167 100 W/m2 K 5.7 W/m2 K, 5.8 W/m2 K, 9.5 W/m2 K 0.84, 0.84 0.9, 0.8 4179 J/kg K, 2.8 W/m2 K 1.54 W/m2 K, 1.58 W/m2 K, 0.8834 W/m2 K 1.57 W/m2 K, 2.45 W/m2 K 2.14 W/m2 K, 5.58 W/m2 K 1.55 W/m2 K 0.89, 0.95 0.15, 0.0045 °C 0.0025 kg/s

600 500 400 300

Beam radiation, I b o Beam radiation at an angle 30, I bβ Total Radiation, I t

200 100 0

08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time, hours Fig. 5. Hourly variation of beam radiation, beam radiation at an angle 30° and total radiation.

Table 1 Various design parameters of a glazed inverted absorber partially covered PVT-CPC system [case (i)]. Parameters

Values

Aa ; Aam ; Aac Arc ; Arm ; Ar Lrm ; Lrc bo ; b F0 Inclination angle F rc ; F rm

2 m2, 1 m2, 1 m2 0.5 m2, 0.5 m2, 1 m2 1 m, 1 m 1 m, 0.5 m 0.9680 30° 0.9147, 0.9149 1000 kg/m3 0.816 W/m K, 0.166 W/m K, 64 W/m K 0.003 m, 0.100 m, 0.002 m 0.7240, 0.9818, 0.9968 100 W/m2 K 5.7 W/m2 K, 5.8 W/m2 K, 9.5 W/m2 K 0.84, 0.84 0.9, 0.8 4179 J/kg K, 2.8 J/kg K 1.54 W/m2 K, 5.05 W/m2 K, 3.50 W/m2 K 4.96 W/m2 K 2.12 W/m2 K, 5.58 W/m2 K, 3.51 W/m2 K 0.89, 0.95 0.15, 0.0045 °C 0.0025 kg/s

r

Kg ; Ki; Kp Lg ; Li ; Lp PF 1 ; PF 2 ; PF c hpf hi ; hi1 ; ho q; q0 ac ; ap cf ; C U L1 ; U L2 ; U l;c U l;m U t;ca ; U t;cp ,U t;pa bc ; sg go ; bo _f m

higher thermal energy and outlet fluid temperature. Hence, in the unglazed inverted absorber partially covered PVT-CPC system [case (ii)], the outlet fluid temperature has been reported to be less than that of [case (i)]. Further, in [case (iv)], the outlet fluid temperature has been found to be less than [case (iii)] since the available beam radiation was less in case (iv) as system was kept horizontal and in case (iii), the system was kept inclined at an angle of 30°. Fig. 7 shows the variation in electrical efficiency with time. It can be seen from the figure that an electrical efficiency obtained is maximum in case (iv) followed by case (iii) and case (ii). Also, from Eq. (9), we have observed that, the electrical efficiency decreases with increase of solar cell temperature. In a glazed inverted absorber PVT-CPC water collector system because of high solar intensity as mentioned earlier, the temperature of PV module was also increased which lead to a drop in electrical efficiency. The characteristic equations for four cases have been developed as follows:

r

Kg ; Ki; Kp Lg ; Li ; Lp PF 1 ; PF 2 ; PF c hpf hi ; hi1 ; ho q; q0 ac ; ap cf ; C U L1 ; U l;c ; U i;t U l;m ; U l;n U t;ca ; U t;cp U t;pa bc ; sg go ; bo _f m

Table 3 Various design parameters of Partially covered PVT-CPC water collector system [case (iii)] and Partially covered horizontal PVT-CPC water collector system [case (iv)]. Parameters

Values

Aa ; Aam ; Aac Arc Arm Ar Lrm ; Lrc bo ; b F 0 ; F rc ; F rm Kg ; Ki; Kp

2 m2, 1 m2, 1 m2 0.5 m2, 0.5 m2, 1 m2 1 m, 1 m 1 m, 0.5 m 0.9680, 0.8693, 0.8110 0.816 W/m K, 0.166 W/m K, 64 W/m K 0.003 m, 0.100 m, 0.002 m 0.3782, 0.9512, 0.9842 100 W/m2 K, 0.84 5.7 W/m2 K, 5.8 W/m2 K, 9.5 W/ m2 K 30°

Lg ; Li ; Lp PF 1 ; PF 2 ; PF c hpf ; q hi ; ho b (only for Partially covered PVT – CPC system) ac ; ap cf U L1 ; U l;c U l;m ; U t;pa U t;ca ; U t;cp sg ; bc go ; bo ; m_ f

0.9, 0.8 4179 J/kg K 3.47 W/m2 K, 4.7 W/m2 K 7.87 W/m2 K, 4.8 W/m2 K 9.17 W/m2 K, 5.58 W/m2 K 0.95,0.89 0.15, 0.0045 °C 0.0025 kg/s

(1) For [case (i)] glazed inverted absorber partially covered PVTCPC water collector system

gi;th

" # Tm  Ta ¼ 0:67  4:12 I0eff

ð26Þ

(2) For [case (ii)] unglazed inverted absorber partially covered PVT-CPC water collector system " #

gi;th ¼ 0:50  2:81

Tm  Ta I0eff

ð27Þ

(3) For [case (iii)] partially covered inclined PVT-CPC water collector system " #

gi;th ¼ 0:4898  3:72

Tm  Ta I0eff

ð28Þ

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D. Atheaya et al. / Applied Energy 167 (2016) 70–79

Instantaneous thermal efficiency η i,th , in fraction

140

Outlet fluid temperature Tfo1,oC

120 100 80 60 40 20 0

case(i)Glazed inverted absorber partially covered PVT-CPC system case(ii)Unglazed inverted absorber partially covered PVT-CPC system case(iii)Partially covered inclined PVT-CPC system case(iv)Partially covered horizontal PVT-CPC system

08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Electrical efficiency ηm , percentage

0.4

0.3 case(i) Glazed inverted absorber partially covered PVT-CPC system case(ii) Unglazed inverted absorber partially covered PVT-CPC system case(iii)Partially covered inclined PVT-CPC system case(iv)Partially covered horizontal PVT-CPC system 0.02

Fig. 6. Hourly variation of an outlet fluid temperature (Tfo1) for case (i) glazed inverted absorber partially covered PVT-CPC system, case (ii) unglazed inverted absorber partially covered PVT-CPC system case (iii) partially covered inclined PVTCPC system and case (iv) partially covered horizontal PVT-CPC system.

14

0.5

0.2

Time, hours

15

0.6

case(i) Glazed inverted absorber partially covered PVT-CPC system case(ii) Unglazed inverted absorber partially covered PVT-CPC system case(iii)Partially covered inclined PVT-CPC system case(iv)Partially covered horizontal PVT-CPC system

0.03

0.04

0.05

(Tm-Ta)/(I'eff), oCm2/W Fig. 8. Thermal characteristic curve for case (i) glazed inverted absorber partially covered PVT-CPC system, case (ii) unglazed inverted absorber partially covered PVT-CPC system case (iii) partially covered inclined PVT-CPC system and case (iv) partially covered horizontal PVT-CPC system.

Table 4 Values of gain factor and loss term for instantaneous thermal efficiency for different cases.

13 12

Cases

Description of system studied

Gain factor

Loss term

11

Case (i)

Glazed inverted absorber partially covered PVT-CPC water collector system Unglazed inverted absorber PVT-CPC water collector system Partially covered PVT-CPC water collector system Partially covered horizontal PVT-CPC water collector system

0.67

4.21

0.50

2.81

0.48

3.72

0.44

2.74

10

Case (ii)

9

Case (iii)

8

Case (iv)

7 6 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time, hours Fig. 7. Variation in electrical efficiency with time for case (i) glazed inverted absorber partially covered PVT-CPC system, case (ii) unglazed inverted absorber partially covered PVT-CPC system case (iii) partially covered inclined PVT-CPC system and case (iv) partially covered horizontal PVT-CPC system.

(4) For [case (iv)] partially covered horizontal PVT-CPC water collector system

gi;th

" # Tm  Ta ¼ 0:4492  2:74 I0eff

ð29Þ

The thermal characteristic curves of all four cases are also shown in Fig. 8. The gain factor and loss term for an instantaneous efficiency for different cases are given in Table 4. Table 5 shows the comparison of cost per kW h (Rs/kW h) for (i) an inverted absorber partially covered PVT-CPC system and (ii) a partially covered PVT-CPC system. The computation has been made by using the annualized uniform cost (Unacost) method, Tiwari [25] by considering initial investment, different interest rate (i = 10%, 15%, 20%) and life of the system (n = 10, 15, 20 years). The salvage value has been considered at 10% of initial investment and maintenance cost has been neglected due to the small system. From Table 5 it can be seen that for any given interest rate and system life an inverted absorber partially covered PVT-CPC system has been cost effective. Fig. 9 shows the variation in overall exergy efficiency with time for cases (i), (ii), (iii) and (iv). The overall exergy efficiency has been calculated by using Eqs. (21) and (22). It was concluded that the

Table 5 Uniform Cost per kW h (Rs/kW h) estimation for different interest rates (i = 10%, 15%, 20%) and different life of the system. System

Capital cost (P) Rs

Life of the system in years (n)

Uniform cost per kW h (Rs/kW h) i = 4%

i = 8%

i = 12%

Inverted absorber partially covered PVT-CPC system

13,500

10 15 20

2.03 1.50 1.24

2.51 2.00 1.76

3.03 2.55 2.34

Partially covered PVT-CPC system

10,500

10 15 20

2.68 2.02 1.67

3.31 2.69 2.37

3.93 2.90 3.15

overall exergy efficiency for glazed inverted absorber partially covered PVT-CPC water collector system was higher due to increase in the amount of thermal energy. From Fig. 9, it can be observed that the overall exergy efficiency for the remaining cases ie. (ii) (iii) and (iv) shows a decreasing trend (the influence of electrical energy is comparatively more than that of thermal energy). However, the overall exergy depends upon the total effect of the electrical efficiency and the exergy efficiency of thermal energy. The maximum thermal energy generation occurs in the case of glazed inverted absorber PVT-CPC water collector system [case (i)] as shown in Fig. 10 as expected due to more solar radiation available. The lower thermal energy was observed in the [case (ii)] as compared with case (i). However, it is much more than cases (iii) and (iv) as expected.

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D. Atheaya et al. / Applied Energy 167 (2016) 70–79

Overall Exergy efficiency, in fraction

0.16

6. Recommendation Following recommendations have been made:

0.15

0.14

case(i) Glazed inverted absorber partially covered PVT-CPC system case(ii) Unglazed inverted absorber partially covered PVT-CPC system case(iii)Partially covered inclined PVT-CPC system case(iv)Partially covered horizontal PVT-CPC system

0.13


The present study must be carried out for N-Inverted absorber PVT-CPC system connected in series by using different fluids in order to effectively utilise preheating for large scale cooking system and power generation.
Experimental validations should be carried out for novel design of the proposed system.

0.12

Appendix A

0.11 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00

Time, hours Fig. 9. Variation of overall exergy efficiency with time for case (i) glazed inverted absorber partially covered PVT-CPC system, case (ii) glazed inverted absorber partially covered PVT-CPC system case (iii) partially covered inclined PVT-CPC system and case (iv) partially covered horizontal PVT-CPC system.

8

hi ¼ 2:8 þ 3V; V ¼ 1 m=s; ho ¼ 5:7 þ 3:8V ðasÞ1b;eff ¼ qq0 ðac s2g bc  gm ÞAam =Arm  1  1 Lg 1 Lg 1 Lg 1 U t;ca ¼ þ þ þ ; U t;cp ¼ þ K g C K g ho K g hi U t;cp U t;ca  U t;cp PF 1 ¼ ; U L1 ¼ U t;ca þ U t;cp U t;ca þ U t;cp

4

ðasÞ2b;eff ¼ qq0 ap s3g ð1  bc ÞAam =Arm  1 1 Lg 1 U t;pa ¼ þ þ ; U t;pa þ U L1 ¼ U L2 hi K g ho hpf hpf U L2 PF 2 ¼ ; U l;m ¼ ðU L2 þ F 0 hpf Þ ðU L2 þ F 0 hpf Þ

3

ðasÞmb;eff ¼ ðasÞ2b;eff þ PF 1 ðasÞ1b;eff

7 6

Daily Energy, kWh

The design parameters of the glazed inverted absorber partially covered PVT-CPC water collector system [case (ii)] are given as follows:

Thermal Energy Electrical Energy

5

qq0 ap s2g Aac =Arc ¼ ðasÞcb;eff

2

0

hpf hpf  U t;pa ; U l;c ¼ 0 ðF 0 hpf þ U t;pa Þ ðF hpf þ U t;pa Þ Aa ¼  It ; I0eff ¼ Ieff þ Ib Ar

PF c ¼

1

case(i)

case(ii)

case(iii)

case(iv)

Ieff

Fig. 10. Daily energy (thermal and electrical) in kW h for various cases.

References 5. Conclusions Based on the present studies, the following conclusions have been drawn: (1) The outlet water temperature and overall exergy efficiency has been found to be higher for the glazed inverted absorber PVT-CPC water collector system [case (i)]. (2) It has been found that electrical efficiency for the glazed system [(case i)] was minimum as compared to the remaining cases [case (ii–iv)] due to higher operating temperature in [case (i)]. (3) It has been concluded that in terms of availability of thermal energy, the glazed inverted absorber partially covered PVTCPC system is better than the remaining systems as explained earlier. (4) On the basis of developed characteristic curves for four cases, it has been concluded that the instantaneous thermal efficiency was significantly higher for the glazed inverted absorber partially covered PVT-CPC system [case (i)]. (5) The uniform cost (Rs/kW h) for an inverted absorber partially covered PVT-CPC system has been found to be lower than the partially covered PVT-CPC system.

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