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Analytical expression of temperature dependent electrical efficiency of N-PVT water collectors connected in series
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ScienceDirect Solar Energy 114 (2015) 61–76 www.elsevier.com/locate/solener
Analytical expression of temperature dependent electrical efficiency of N-PVT water collectors connected in series Shyam a,⇑, G.N. Tiwari a, I.M. Al-Helal b b
a Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India Department of Agricultural Engineering, College of Food & Agricultural Sciences, King Saud University, P.O. Box 2460, Riyadh 11451, Saudi Arabia
Received 1 December 2013; received in revised form 9 January 2015; accepted 21 January 2015
Communicated by: Associate Editor Brian Norton
Abstract In the present study the series combination of N PVT water collectors, partially covered with photovoltaic module, in two different configurations namely case A: Photovoltaic module at lower portion; case B: Photovoltaic module at upper portion, have been analyzed. Analytical expressions for instantaneous thermal efficiency and temperature dependent electrical efficiency have been derived. The performances of both configurations have been compared on thermal efficiency basis and temperature dependent electrical efficiency basis. It has been concluded that at moderate mass flow rate, for large number of PVT water collectors connected in series both cases give nearly same results. Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Solar thermal; PVT water collector; Thermal efficiency; Temperature dependent electrical efficiency
1. Introduction The need of clean energy for the better environment compels, to use the renewable energy resources as much as possible. The conventional solar thermal technologies harness only the thermal energy. The photovoltaic (PV) systems convert the incident solar radiation into the electrical energy but the thermal energy absorbed has been wasted. To maximize the energy gain, the conventional solar thermal systems were integrated with the photovoltaic cells/module and the photovoltaic thermal (PVT) systems got more interest in the solar thermal research area. PVT systems utilize the thermal energy in addition to the electrical energy generated from the solar cells due to the radiation absorbed from the sun. The concept of PVT systems was given in late 70s by Kern and Russel (1978) and ⇑ Corresponding author. Tel.: +91 7838959195; fax +91 11 26591251.
E-mail address: [email protected] ( Shyam). http://dx.doi.org/10.1016/j.solener.2015.01.026 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.
Florschuetz (1979). Since then a large number of theoretical research as well as experimental research have been carried out by large number of researchers considering air in single pass and double pass flow pattern (Hendrie, 1980; Chandra et al., 1983; Bhargava et al., 1991; Sopian et al., 1995; Garg and Adhikari, 1997; Hegazy, 2000; Tiwari and Sodha, 2006, 2007) or water (Bergene and Lovvik, 1995; Garg and Agarwal, 1995; Chow, 2003; Chow et al., 2006) as the heat transfer fluid. Further the researches have been extended to optimize the design parameters and for improving the performance of PVT collectors on thermal energy basis and electrical energy basis; different configurations namely unglazed, single glazed and double glazed, PVT collectors have been analyzed. (Cox and Raghuraman, 1985; Garg et al., 1991, 1994; Huang et al., 2001; Zondag et al., 2002; Wei et al., 2006; Tripanagnostopoulos, 2007; Tripanagnostopoulos et al., 2007). Joshi and Tiwari (2007) studied the energy and exergy efficiencies of PVT air collectors. Zondag (2008)
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Nomenclature absorptivity of the solar cell mass flow rate of water ðkg=sÞ transmissivity of the glass specific heat of water (J/kgK) packing fraction of module length of PVT water collector covered by module ðmÞ gc solar cell efficiency Lc length of PVT water collect or covered by glazing ðmÞ gm = sg gc b PV module efficiency W width of PVT water collector ðmÞ FF fill factor Am ¼ WLm area of the module ðm2 Þ q density of water Ac ¼ WLc area of the glazing ðm2 Þ Lg thickness of glass cover (m) IðtÞ solar intensity ðW=m2 Þ Kg thermal conductivity of glass (W/m K) Ta ambient temperature (°C) Li thickness of insulation (m) Tc cell temperature (°C) Ki thermal conductivity of insulation (W/m K) Tp temperature of absorption plate (°C) Lp thickness of absorption plate (m) T fi inlet water temperature (°C) Kp thermal conductivity of absorption plate (W/ m K) Tf temperature of water (°C) T fom water temperature up to the portion covered by PV module (°C) ac m_ f sg Cf b Lm
extensively reviewed the flat plate collectors and discussed important key points regarding water collectors and air collectors. Hepbasli (2008) gave a review on exergetic analysis and assessment of renewable energy resources. Dubey and Tiwari (2009) experimentally validated the theoretical model for partially covered N PVT water collectors connected in series (covered by semitransparent PV module at the lower portion). Joshi et al. (2009) compared the PVT air collectors fully covered by opaque Photovoltaic (PV) module and semitransparent PV module and concluded that semitransparent PV module gives better performance. Dubey and Tiwari (2009) derived the analytical expression of electrical efficiency for fully covered PVT air collector and evaluated the performance for composite climatic conditions of New Delhi, India. Ibrahim et al. (2011) discussed the recent advances in flat plate PVT collectors. Dupeyrat et al. (2014) studied the thermal and electrical performance of a solar hot water system and showed that the PVT system gave more exergy saving than the conventional solar thermal systems. Amrizal et al. (2013) developed and validated the dynamical model for PVT
T foc T foN h0i ho hi U tc;a U tc;p hpf U tp;a U L:m U L;c PF 1 PF 2 PF 3 F0
water temperature up to the portion covered by glazing (°C) outlet water temperature at the end of the Nth PVT water collector (°C) heat transfer coefficient from bottom of PVT water collector to the ambient (W/m2 K) heat transfer coefficient from top of PVT water collector to the ambient (W/m2 K) heat transfer coefficient for space between the glazing and absorption plate (W/m2 K) over all heat transfer coefficient from cell to the ambient from top surface (W/m2 K) overall heat transfer coefficient from cell to the absorption plate (W/m2 K) heat transfer coefficient from blackened plate to the water (W/m2 K) overall heat transfer coefficient from absorption plate to the ambient (W/m2 K) overall heat transfer coefficient for module, from module to ambient (W/m2 K) overall heat transfer coefficient from glazing to ambient (W/m2 K) penalty factor due to the glass covers of module penalty factor due to the absorption plate below the module penalty factor due to the absorption plate for the portion covered by glazing collector efficiency factor
water collector in outdoor conditions and found that results were in good agreement with the results obtained from the steady state characterization. Recently Tian and Zhao (2013) reviewed different types of solar collectors and found that the PVT solar collector shows the best performance among the non concentrating solar collectors. 2. PVT water collector description In the present study a series combination of N number of PVT water collectors (Flat plate, tube in plate) partially covered by semitransparent photovoltaic (PV) module has been considered in two different configurations namely Case A: when the lower portion (inlet) of PVT water collector has been covered by the PV module and Case B: when the upper portion (outlet) of PVT water collector has been covered by the PV module. The comparison for these particular cases has been done to observe the effect on the performance of the collectors due to the different positions of the PV modules on the collector assembly. The top view of case A and case B has been shown in Figs. 1a and 1b. The
Shyam et al. / Solar Energy 114 (2015) 61–76
63
Glazing Water out
Water in PV module Insulated connecting pipes
Fig. 1a. Arrangement of PVT water collectors (module at lower portion) connected in series.
PV module Water out
Water in
Glazing Insulated connecting pipes
Fig. 1b. Arrangement of PVT water collectors (module at upper portion) connected in series.
Glazing PV module
Glazing
Solar cell Tfi
Solar cell Tfo,m
Tfi
Absorption plate Tfo,m
PV module
Absorption plate
Tfo
Air gap
Tfo
Air gap Water out
Water in
Water out
Water in
Insulation Insulation
Cut section of metallic tubes
Fig. 2a. Side view of flow pattern in PVT water collector (module at lower portion).
outlet of the first PVT water collector has been connected to the inlet of the second PVT water collector and further the outlet of the second PVT water collector has been connected to the inlet of the third PVT water collector and so on. The side view and front view of the flow patterns of the water inside the PVT water collectors have been shown in Figs. 2a, 2b and 2c. The extended view for a single tube below the absorber plate and the thermal energy flow diagram for water inside the tube has been shown in
Cut section of metallic tubes
Fig. 2b. Side view of flow pattern in PVT water collector (module at upper portion).
Glazing integrated with PV module Absorption plate Air gap
Water in
Metallic tubes
Insulation
Water out
Fig. 2c. Front view of flow pattern in PVT water collector.
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Shyam et al. / Solar Energy 114 (2015) 61–76
from Eq. (1) one can get,
Glazing integrated with PV module
Solar radiations
Tc ¼
Air gap
ðasÞ1;eff IðtÞ þ U tc;a T a þ U tc;p T p U tc;a þ U tc;p
*Assumed
Metallic tube
Insulation
terms have been given in appendix.
3.1.2. Energy balance for blackened absorber plate below the PV module
Absorber plate
Thermal energy gain from solar radiation
ap ð1 bÞs2g IðtÞWdx þ U tc;p ðT c T p ÞWdx ¼ F 0 hpf ðT p T f ÞWdx þ U tp;a ðT p T a ÞWdx
Thermal energy gain from left side of tube
Water inside tube
Thermal energy gain from right side of tube
ð3Þ
from Eqs. (2) and (3) one can get, Tp ¼
½ðasÞ2;eff þ PF 1 ðasÞ1;eff IðtÞ þ U L2 T a þ hpf T f ðU L2 þ hpf Þ
ð4Þ
The rate of thermal energy gain by the water below the absorber plate will be given by,
Total thermal energy gain by the water
Fig. 2d. Extended view of single tube below absorber plate and thermal energy flow diagram for water inside tube.
Fig. 2d. For better understanding of heat transfer and energy flow at different parts of the PVT water collector the thermal resistance diagram and the thermal energy diagram have been given in Figs. 3a and 3b for the portion covered by the PV module at XX’. Similarly for the portion covered with the glazing the thermal resistance diagram and thermal energy diagram at XX0 0 have been shown in Figs. 3c and 3d. The design parameters used in the numerical computation have been given in Table 1. The solar radiation and ambient temperature data have been taken from Indian meteorological department (IMD) Pune, India for clear sky day of New Delhi, India climatic condition in the month of January. The blackened absorption plate receives thermal energy from the direct radiation from non packing area of the semitransparent PV module and glazing in addition to the heat transferred by convection from the back surface of the solar cells of PV module. The water flowing in tubes get heated by the thermal energy transferred from absorbing plate to the water. 3. Thermal modeling 3.1. Lower portion of the PVT water collector covered by PV module (Case A) The energy balance equations have been written for quasi steady state one dimensional heat conduction and neglecting the ohmic losses. 3.1.1. Energy balance for solar cell of semitransparent PV module ac sg bIðtÞWdx ¼ U tc;a ðT c T a ÞWdx þ U tc;p ðT c T p ÞWdx þ gc sg bIðtÞWdx
ð2Þ
ð1Þ
m_ f C f
dT f dx ¼ F 0 hpf ðT p T f ÞWdx dx
ð5Þ
F0 is the collector efficiency factor calculated by following Duffie and Beckman (1991) and Tiwari (2004). Following Dubey and Tiwari (2009), for N identical PVT water collector the outlet water temperature at the end of the Nth PVT water collector is given by ðAF R ðasÞÞ1 1 K Nk T foN ¼ IðtÞ 1 Kk m_ f C f ðAF R U L Þ1 1 K Nk þ ð6Þ T a þ K Nk T fi 1 Kk m_ f C f The analytical expression for the temperature dependent electrical efficiency of solar cells of Nth PVT water collector has been derived using following relation, gcN ¼ g0 ½1 b0 ðT cN T 0 Þ
ðEvans;1981; Schott;1985Þ ð7Þ
where g0 is the efficiency at standard test condition i.e., at I(t) = 1000 W/m2 and T0 = 25 °C and T cN is the average solar cell temperature of Nth PVT water collector. To find out T cN one needs average plate temperature of Nth PVT water collector T pN and average water temperature of Nth PVT water collector T fN . The average water temperature below the portion covered by PV module, for Nth PVT water collector can be found as, T fN ¼
T fomN þ T foN 1 2
ð8Þ
where TfomN and TfoN1 are the temperature at the end of the PV module of the Nth PVT water collector and temperature at the end of the (N1)th PVT water collector. For N identical PVT water collectors the temperature at the end of the portion covered by PV module of the Nth PVT water collector can be found by as follows
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1 K Nk 1 IðtÞ T fomN ¼ ðAF R ðasÞÞm1 þ K m ðAF R ðasÞÞ1 m_ f C f 1 Kk 1 K kN 1 Ta þ ðAF R U L Þm1 þ K m ðAF R U L Þ1 m_ f C f 1 Kk þ K m K Nk 1 T fi From Eqs. (2), (4), (6), (8) and (9) one can get 1 ðU tc;a þ U tc;p Þ
o
ðasÞ1;eff þ
n U tc;p ðasÞ2;eff 0 U L2 þ F hpf
U tc;p F 0 hpf ðAF R ðasÞÞm1 0 2m_ f C f ðU L2 þ F hpf Þ 1 K Nk 1 þð1 þ K m ÞðAF R ðasÞÞ1 IðtÞ 1 Kk U tc;p U L2 þ U tc;a þ U L2 þ F 0 hpf þPF 1 tðasÞ1;eff
The rate of useful electrical energy gain from N identical PVT water collectors has been calculated by the following formula N X ð13Þ Q_ uel;N ¼ Am IðtÞ gmN 1
ð9Þ
T cN ¼
65
þ
U tc;p F 0 hpf ðAF R U L Þm1 2m_ f C f ðU L2 þ F 0 hpf Þ 1 K kN 1 þð1 þ K m ÞðAF R U L Þ1 Ta 1 Kk U tc;p F 0 hpf N 1 ð1 þ K m ÞK k þ T fi 2ðU L2 þ F 0 hpf Þ
þ
ð10Þ
Following Mishra and Tiwari (2013) the power required to pump the fluid is 0.8 W for a head of 1.2 m and 75% pump efficiency. The electrical output from the PVT collectors is of the order of kWh, hence the pumping power has been neglected in the present study. The rate of useful thermal energy gain from N identical PVT water collectors has been calculated using the following relation Q_ uth;N ¼ m_ f C f ðT foN T fi Þ
ð14Þ
on putting the value of T foN from Eq. (6) into Eq. (14) one can get, h i Q_ uth;N ¼ N ðAc þ Am Þ ðasÞeff ;N IðtÞ U L;N ðT fi T a Þ ð15Þ The instantaneous thermal efficiency of Nth PVT water collector is given as following ðT fi T a Þ Q_ uth;N ¼ ðasÞeff ;N U L;N gith;N ¼ ð16Þ IðtÞ N ðAc þ Am ÞIðtÞ 3.2. Upper portion of the PVT water collector covered by PV module (Case B) In this case the glazing was at the inlet of the PVT water collector and the PV module was at the far end
From Eqs. (7) and (10) one can get,
3 n o 3 33 U tc;p F 0 hpf U tc;p ac sg bþ U L2 þF ðasÞ þPF a s b Þ þ 0h 0h 1 c g 2;eff _ 2 C ðU þF m pf f f pf L2 6 7 77 6 66 97 8 7 n o 6 7 77 6 66 7 6 7 77 6 66 > > = 7IðtÞ 7 < PF 2 ðasÞ2;eff þPF 2 PF 1 ac sg b Am F Rm þð1þK m Þ 6 77 6 66 7 6 7 77 6 66 n oo N 1 5 6 7 77 6 1 64>n 1K A F U > c Rc L;c k 6 7 77 6 6 ; : Ac F Rc ðasÞc;eff þ ½PF 2 ðasÞ2;eff þPF 2 PF 1 ac sg bAm F Rm 1 m_ f Cf g0 61b0 6U tc;a þU tc;p 6 1K k 7 T 0 77 6 7 77 6 6 h n N 1 oi 6 7 77 6 6 1K k U tc;p F 0 hpf U tc;p U L2 6 7 77 6 6 þ U tc;a þ U L2 þF 0 hpf þ 2m_ f Cf ðU L2 þF 0 hpf Þ ðAF R U L Þm1 þð1þK m ÞðAF R U L Þ1 1K k Ta 6 7 77 6 6 4 5 55 4 4 h i 0 U F hpf ð1þK m Þ N 1 þ tc;p K T fi pf 0 k 2ðU L2 þF h Þ h h n N1 oii gcN ¼ 1K k U tc;p F 0 hpf U tc;p A F U L;c g0 b0 IðtÞ 1 ðU tc;a þU tc;p Þ sg bþ U L2 þF 0 hpf PF 1 sg bþ 2m_ f cf ðU L2 þF 0 hpf Þ PF 2 PF 1 sg bAm F Rm 1þð1þK m Þ 1 c m_ Rc 1K k f Cf 2
2
22
ð11Þ
Finally the temperature dependent electrical efficiency of PV module of Nth PVT water collector will be gmN ¼ sg bgcN
ð12Þ
from the inlet of the PVT water collector. The temperature at the end of the portion covered with glazing can be given as following (Duffie and Beckman, 1991; Tiwari, 2004),
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Shyam et al. / Solar Energy 114 (2015) 61–76
T foc1
0 ðasÞc;eff IðtÞ F Ac U L;c ¼ þ T a 1 exp U L;c m_ f C f 0 F Ac U L;c þ T fi exp m_ f C f
ð17Þ
Again using Eqs. (1), (3) and (5) with the boundary conditions at x ¼ 0; T f ¼ T foc1 and at x ¼ Lm ; T f ¼ T fo1 and following the same procedure as in Case A, the outlet temperature at the end of the Nth PVT water collector can be found as follows, T foN ¼
ðAF R ðasÞÞ1 1 K Nk ðAF R U L Þ1 1 K Nk IðtÞ þ T a þ K Nk T fi 1 Kk 1 Kk m_ f C f m_ f C f ð18Þ
One can obtain the temperature at the end of the portion covered by glazing the Nth PVT water collector for N identical PVT water collectors as follows
ðasÞ1;eff þ
From Eqs. (7) and (21), one can obtain the temperature dependent electrical efficiency of solar cells of Nth PVT water collector as following,
22
3 n o 3 33 U tc;p F 0 hpf U tc;p ac sg b þ U L2 þF ðasÞ þ PF a s b þ 0h 0 1 c g 2;eff 2m_ f C f ðU L2 þF hpf Þ pf 6 7 77 6 66 8 97 8 9 7 6 7 77 6 66 7 6 7 77 6 66 < = 7IðtÞ < ½PF 2 ðasÞ2;eff þ PF 2 PF 1 ac sg bAm F Rm = N1 þ 1K N K 1K 6 7 77 6 66 ð Þ ð Þ c k k 5 6 7 77 6 6 4 ðAF R ðasÞÞc1 þ 1K k 6 7 77 6 1 6 : ; : þðasÞc;eff Ac F Rc 1 Am Fm_ RmCU L;m ; 7 6 7 6 6 f f g0 61 b0 6U tc;a þU tc;p 6 T 07 7 77
7 6 7 7 6 6 K c ð1K N1 Þþð1K Nk Þ U tc;p F 0 h 6 7 77 6 6 U U k T 7 6 7 7 6 6 þ U tc;a þ U L2tc;pþhFL20 þ 2m_ f Cf ðU L2 þFpf 0 hpf Þ ðAF R U L Þc1 þ ðAF R U L Þ1 a 1K k pf 6 7 77 6 6 5 4 5 5 4 4 h i U F 0 hpf ðK c þK k Þ N 1 þ tc;p K T 0 fi k 2ðU L2 þF hpf Þ h h ii ¼ 1 Þþð1K N Þ K ð1K N U tc;p F 0 hpf U tc;p g0 b0 IðtÞ k k 1 ðU tc;a þU tc;p Þ sg b þ U L2 þF 0 hpf PF 1 sg b þ 2m_ f Cf ðU L2 þF 0 hpf Þ PF 2 PF 1 sg bAm F Rm c 1K k 2
gcN
1 ðU tc;a þ U tc;p Þ
U tc;p fðasÞ2;eff U L2 þ F 0 hpf U tc;p F 0 hpf ðAF R ðasÞÞc1 þPF 1 ðasÞ1;eff g þ 0 2m_ f C f ðU L2 þ F hpf Þ K c ð1 K kN 1 Þ þ ð1 K Nk Þ IðtÞ þðAF R ðasÞÞ1 1 Kk U tc;p U L2 þ U tc;a þ U L2 þ F 0 hpf U tc;p F 0 hpf þ ðAF R U L Þc1 0 2m_ f C f ðU L2 þ F hpf Þ K c ð1 K kN 1 Þ þ ð1 K Nk Þ þðAF R U L Þ1 Ta 1 Kk U tc;p F 0 hpf N 1 ðK þ þ K ÞK T fi ð21Þ c k k 2ðU L2 þ F 0 hpf Þ
T cN ¼
2
ð22Þ 1 K kN 1 IðtÞ T focN ¼ ðAF R ðasÞÞc1 þ K c ðAF R ðasÞÞ1 1 Kk m_ f C f N 1 1 Kk Ta þ ðAF R U L Þc1 þ K c ðAF R U L Þ1 1 Kk m_ f C f þ K c K Nk 1 T fi ð19Þ The average water temperature below the portion covered by PV module, for Nth PVT water collector in this case has been determined by using following relation, T fN ¼
T focN þ T foN 2
ð20Þ
where T focN and T foN are the temperature at the end of the glazing and the temperature at the end of the Nth PVT water collector respectively. From Eqs. (2), (4), (18), (19) and (20) one can get,
The temperature dependent electrical efficiency of PV module of Nth PVT water collector has been obtained using Eq. (12) by putting the value of gcN for Case B from Eq. (22). The rate of useful electrical energy gain has been computed by Eq. (13) but the value of gmN was taken for Case B. The rate of useful thermal energy gain and instantaneous thermal efficiency of Nth PVT water collector have been calculated with the help of Eqs. (15) and (16) but the value of T foN has been taken for case B from Eq. (18).
3.3. Limiting cases Case1: when all the PVT water collectors connected in series were fully covered by PV module (Ac = 0); Case2: when all the water collectors connected in series were fully covered by glazing only (Am = 0). The thermal and
Shyam et al. / Solar Energy 114 (2015) 61–76
electrical efficiencies for the limiting cases have been obtained by putting Ac = 0 or Am = 0 respectively. 3.3.1. Case1: PVT water collectors fully covered by PV module (Ac = 0)
gcN
ciency have been plotted against ðT m T a Þ=IðtÞ. T m has been taken as the average temperature of inlet water temperature and outlet water temperature of PVT water collector.
3 n o 3 33 U tc;p F 0 hpf U tc;p ac sg b þ U L2 þF ðasÞ þ PF a s b þ 0h 0h Þ 1 c g 2;eff _ 2 C ðU þF m pf f f pf L2 7 6 77 6 6 6 o h N1 io 5IðtÞ 7 6 7 77 6 6 4 nn 1K m 6 7 77 6 6 PF 2 ðasÞ2;eff þ PF 2 PF 1 ac sg b Am F Rm 1 þ ð1 þ K m Þ 1K m 6 7 77 6 1 6 7 6 7 6 6 g0 61 b0 6U tc;a þU tc;p 6 h n h N1 ioi 7 T 0 7 77 0h U F U U 1K tc;p pf m 7 6 7 7 6 6 þ U tc;a þ tc;p 0 L2 þ Am F Rm U L;m 1 þ ð1 þ K m Þ 1K m Ta 7 U L2 þF hpf 2m_ f C f ðU L2 þF 0 hpf Þ 6 77 6 6 5 4 5 5 4 4 h i U F 0 hpf ð1þK m Þ N 1 þ tc;p K T 0 fi m 2ðU L2 þF hpf Þ h h h iii ¼ N1 U tc;p F 0 hpf U tc;p g0 b0 IðtÞ m 1 ðU tc;a þU tc;p Þ sg b þ U L2 þF 0 hpf PF 1 sg b þ 2m_ f Cf ðU L2 þF 0 hpf Þ PF 2 PF 1 sg bAm F Rm 1 þ ð1 þ K m Þð1K Þ 1K m 2
2
2
67
2
h i A F U L;m where K m ¼ 1 m m_ Rm C f f ðT fi T a Þ Q_ uth;N ¼ ðasÞeff ;N U L;N gith;N ¼ ð24Þ IðtÞ NAm IðtÞ " # PF 2 ðasÞm;eff F Rm 1 ð1 K k;A ÞN ðasÞeff ;N ¼ ; N K k;A " # N F Rm U L;m 1 ð1 K k;A Þ Am F Rm U L;m ; K k;A ¼ U L;N ¼ N K k;A m_ f C f
3.3.2. Case 2: Water collectors fully covered by glazing (Am = 0) ðT fi T a Þ Q_ uth;N ¼ ðasÞeff ;N U L;N gith;N ¼ ð25Þ IðtÞ NAc IðtÞ " # F Rc ðasÞc;eff 1 ð1 K k;A ÞN ðasÞeff ;N ¼ ; N K k;A " # F Rc U L;c 1 ð1 K k;A ÞN Ac F Rc U Lc ; K k;A ¼ U L;N ¼ m_ f C f N K k;A For both the cases the expressions of instantaneous thermal efficiency were similar to the Hottel–Whiller–Bliss (HWB) equation. 4. Characteristics equation Performance of different PVT systems can be compared on the basis of instantaneous thermal efficiency and electrical efficiency. To compare case A and case B the instantaneous thermal efficiency and electrical effi-
ð23Þ
5. Methodology In order to develop the characteristics equation for the PVT water collectors under study, following methodology has been adopted. Step 1: The data of solar radiation on a horizontal surface provided by IMD, Pune, India has been calculated for inclined surface at 30° using MATLAB 2010a. Step 2: Corresponding to above data of solar radiation and ambient temperature the outlet water temperature, solar cell temperature, electrical efficiency of solar cell and instantaneous thermal efficiency of PVT water collector have been computed using MATLAB 2010a from Eqs. (6), (10), (11) and (16) respectively for case A. the same parameters for case B have been computed by using Eqs. (18), (21), (22) and (16) respectively.
6. Results and discussion The hourly variations of solar radiation and ambient temperature have been shown in Fig. 4 for a typical day in the month of January for New Delhi climatic condition for which the numerical computations have been done. Figs. 5a and 5b shows the variation of maximum outlet temperature, T foN ;max with number of PVT water collectors for both the cases i.e., case A and case B at mass flow rates 0.01 kg/s and 0.08 kg/s respectively. From these figures one can observe that as the number of PVT water collector increases the T foN ;max increases. At 0.01 kg/s mass flow rate, the increment in the T foN ;max were 56.4 °C (case A) and 51.8 °C (case B) for the increment of number of collectors from one to five, but for further increment of number of
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Shyam et al. / Solar Energy 114 (2015) 61–76
Fig. 3a. Thermal resistance diagram for the portion covered with PV module at XX0 .
collector from six to ten the increment in the T foN ;max were 15.8 °C (case A) and 14.8 °C (case B). At 0.08 kg/s mass flow rate, the increment in the T foN ;max were 11.7 °C (case A) and 11.6 °C (case B) for the increment of number of collectors from one to five, but for further increment of number of collector from six to ten the increment in the T foN ;max were 10.0 °C (case A) and 9.9 °C (case B). In case A the
increment in the T foN ;max has been higher compared to case B, it has been due to the fact that in case A, the PV module was at the inlet of PVT water collector hence PVT water collector receives less direct solar radiation at the lower portion i.e., only from the non packing area of the PV module unlike the case B where PVT water collector receives less direct solar radiation at the outlet.
Shyam et al. / Solar Energy 114 (2015) 61–76
69
Fig. 3b. Thermal energy diagram for the portion covered with PV module at XX0 .
The variation of T foN ;max with mass flow rate for five PVT water collectors connected in series has been given in Fig. 5c for case A and case B. It has been observed that as the mass flow rate increases the outlet water temperature decreases for both the cases. One can clearly observe that T foN ;max for case A has been significantly higher than T foN ;max for case B at very low mass flow rate but at higher mass flow rate the difference between T foN ;max of case A and case B decreases and at very high mass flow rate the outlet water temperature were nearly same for both the cases of
PVT water collectors. It has been due to the fact that at very high mass flow rate the contact time for heat to be transferred from tubes to the flowing water was very small. The variation of maximum solar cell temperatures T cN ;max and temperature dependent electrical efficiencies with number of collectors for both cases at mass flow rates 0.01 kg/s and 0.08 kg/s have been shown in Figs. 6a and 6b. It can be inferred from the figures that for both the cases, as the number of collectors increase the T cN ;max increases and the temperature dependent electrical efficiency
70
Shyam et al. / Solar Energy 114 (2015) 61–76
Fig. 3c. Thermal resistance diagram for the portion covered with glass cover at X0X0 0.
decreases as expected due to the hindrance effect at higher temperature. Also one can observe that T cN ;max was higher for case B, because the PV module was at the outlet of the PVT water collector and receives thermal energy from the hot water below the absorber plate in addition to the energy absorbed from solar radiation. Fig. 6c shows the variation of T cN ;max and temperature dependent electrical efficiency with mass flow rate. At higher mass flow rate the thermal energy from solar cell transferred rapidly to the flowing water, resulting lower values of solar cell temperature and better electrical efficiency. For five number of PVT water collectors connected in series the temperature dependent electrical efficiency increases from 11.42% to 11.75% for case A and 10.93% to 11.62% for case B when the mass flow rate increased from 0.01 kg/s to 0.08 kg/s.
The hourly variation of outlet water temperature at 0.04 kg/s mass flow rate and for five PVT water collectors connected in series for case A and case B has been shown in Fig. 7a. As the solar intensity and ambient temperature increases with time the outlet water temperature also increases in forenoon and decreases after around 2 pm in afternoon due to decrease in solar intensity and ambient temperature. The outlet water temperature in case A has higher value in comparison to case B as explained earlier. Fig. 7b shows the hourly variation of solar cell temperature and temperature dependent electrical efficiency for five number of PVT water collectors connected in series and mass flow rate 0.04 kg/s for case A and case B. The solar cell temperature in case A has smaller values compared to case B, therefore the temperature dependent electrical efficiency for case A has higher values as expected. At
Shyam et al. / Solar Energy 114 (2015) 61–76
71
Fig. 3d. Thermal energy diagram for the portion covered with glass cover at X0X0 0. Table 1 Values of design parameters used in numerical computations.
I(t)
Ta
1200
18 16
1000
14
800
12 10
600
8
400
Ta (0C)
H ¼ 1:7 m Am ¼ 0:605 m2 Ac ¼ 1:395 m2 h0i ¼ 5:8 W=m2 K hi ¼ 5:7 W=m2 K ho ¼ 9:5 W=m2 K U tc;p ¼ 5:58 W=m2 K hpf ¼ 100 W=m2 K U tc;a ¼ 9:20 W=m2 K PF 1 ¼ 0:378 PF 2 ¼ 0:924 U tp;a ¼ 4:74 W=m2 K U L:m ¼ 7:58 W=m2 K PF c ¼ 0:955 U L;c ¼ 4:52 W=m2 K Inclination = 30° Spacing between tubes = 0.125 m
I(t) (W/m2)
ac ¼ 0:9 sg ¼ 0:95 b ¼ 0:89 g0 ¼ 0:15 FF ¼ 0:8 ap ¼ 0:80 Lg ¼ 0:003 m K g ¼ 0:816 W=mK Li ¼ 0:1 m K i ¼ 0:166 W=mK Lp ¼ 0:002 m K p ¼ 64 W=mK cf ¼ 4179 J=kg K q ¼ 1000 kg=m3 b0 = 0.0045/°C F 0 ¼ 0:968 Tube diameter = 0.0125 m
6 4
200
2
0 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00
0
Time (Hour) Fig. 4. Hourly variation of solar radiation and ambient temperature for a typical day in the month of January.
Shyam et al. / Solar Energy 114 (2015) 61–76 Case A
Case B
Case A
m f = 0.01 kg/s
120
99
100
89
TcN,max (0C)
80 60 40
Case B
Case B 0.11 0.105
79
0.1
69 0.095
59
0.09
49
20
39
0 1
2
3
4
5
6
7
8
9
0.085 1
10
2
3
Fig. 5a. Variation of outlet temperature of Nth PVT water collectors with number of collectors connected in series at mass flow rate 0.01 kg/s.
Case A
45
Case B
4
5
6
7
8
9
10
Number of collectors
Number of collectors
Fig. 6a. Variation of solar cell temperature and temperature dependent electrical efficiency of Nth PVT water collectors with number of collectors connected in series at mass flow rate 0.01 kg/s.
Case A
m f = 0.08 kg/s
40
69
35
64
Case B Case A m f = 0.08 kg/s
Case B 0.11 0.109 0.108
25 20 15
59
0.107
54
0.106 0.105
49
10
0.104
5
44
0
39
1
2
3
4
5
6
7
8
9
10
0.103 0.102 1
2
Fig. 5b. Variation of outlet temperature of Nth PVT water collectors with number of collectors connected in series at mass flow rate 0.08 kg/s.
Case A
Case B
80
Case A
60
TcN,max (0 C)
TfoN,max (0C)
70
40 30 20 10 0 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100
m f (kg/s) Fig. 5c. Variation of outlet water temperature with mass flow rate of water for five PVT water collectors connected in series.
a mass flow rate of 0.04 kg/s and for ten PVT water collectors connected in series the maximum outlet water temperature T foN ;max were 62.0 °C and 61.1 °C for case A and case B respectively; and the solar cell temperature T cN ;max were 72.1 °C and 73.7 °C respectively for case A and case B. If the number of collectors further increased the difference in the outlet temperature and solar cell temperature for case A and case B reduces and have nearly same values.
4
5
6
7
8
9
10
Fig. 6b. Variation of solar cell temperature and temperature dependent electrical efficiency of Nth PVT water collectors with number of collectors connected in series at mass flow rate 0.08 kg/s.
Number of collectors= 05
50
3
Number of collectors
Number of collectors
90
ηmN
30
TcN,max (0C)
TfoN,max (0C)
Case A
m f = 0.01 kg/s
Case B
Case A
Case B
Number of collectors = 05 59 57 55 53 51 49 47 45 43 41 39 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100
0.12 0.118 0.116 0.114 0.112
ηmN
TfoN,max (0C)
140
ηmN
72
0.11 0.108 0.106 0.104
m f (kg/s) Fig. 6c. Variation of solar cell temperature and temperature dependent electrical efficiency with mass flow rate for five PVT water collectors connected in series.
The instantaneous thermal efficiency and temperature dependent electrical efficiencies have been shown in Figs. 8a and 8b for case A and case B respectively at 0.04 kg/s mass flow rate for five PVT collectors connected in series. One can observe from the figures that as the temperature increases the instantaneous thermal efficiency decreases with ðT m T a Þ=IðtÞ due to increase in losses.
Shyam et al. / Solar Energy 114 (2015) 61–76 m f = 0.04 kg/s, N=05
0.495 0.485
35
0.48
ηithN
30 25 20
0.25 0.2 0.15
0.455 0.45 0.016
0
0.1 0.018
08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00
ηith Case B 0.485
ηm Case B
m f = 0.04 kg/s, N=05
0.135
ηithN = 0.574 - 5.667[(Tm - Ta)/I(t)]
0.44
0.48
0.13
0.475
ηmN = 0.109 - 0.358[(Tm - Ta)/I(t)]
0.39
0.47
0.34
0.465
0.29
0.46
0.24
0.12 0.115
ηithN
0.125
0.455
0.11
0.45
0.105
0.445
0.1
Fig. 7b. Hourly variation of solar cell temperature and temperature dependent electrical efficiency at mass flow rate 0.04 kg/s for five PVT water collectors connected in series.
The instantaneous thermal efficiencies decrease from 49.0% to 45.5% (case A) and 48.2% to 44.6% (case B). The instantaneous thermal efficiencies for case A and case B have been shown in Fig. 8c for comparison purpose. One can observe from figure that case A has better performance compared to case B on thermal energy point of view. The temperature dependent electrical efficiency decreases marginally with ðT m T a Þ=IðtÞ. The maximum and minimum values of temperature dependent electrical efficiencies were 10.8% and 10.6% respectively for case A; whereas for case B these values were 10.4% and 10.2%. The temperature dependent electrical efficiencies for case A have higher values compared to case A which infer that case A has better performance compared to case B on electrical energy point of view. The characteristics equations have been obtained for instantaneous thermal efficiency and temperature dependent electrical efficiency for five PVT water collectors and at 0.04 kg/s mass flow rate for both the cases namely case A and case B. These equations were similar to Hottel– Whiller–Bliss (HWB) equations. For case A:
0.19 0.14 0.09
0.44 0.016
0.018
0.02
0.022
(Tm -Ta )/I(t) (0C-m2/W) Fig. 8b. Characteristics curves for thermal and electrical efficiencies for case B.
ηith Case A 0.49
ηith Case B
m f = 0.04 kg/s, N=05
Case A, ηithN = 0.583 - 5.612[(Tm - Ta)/I(t)] Case B, ηithN = 0.574 - 5.667[(Tm - Ta)/I(t)]
0.48
ηithN
50 45 40 35 30 25 20 15 10 5 0 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 Time (Hour)
0.022
Fig. 8a. Characteristics curves for thermal and electrical efficiencies for case A.
Case B
ηmN
Case B Case A m f = 0.04 kg/s, N=05
0.02
(Tm -Ta )/I(t) (0C-m2/W)
Time (Hour)
Case A
0.35
0.47
5
Fig. 7a. Hourly variation of outlet water temperature at mass flow rate 0.04 kg/s for five PVT water collectors connected in series.
0.4
0.3
0.46
10
0.45
0.475 0.465
15
TcN (0C)
ηm Case A m f = 0.04 kg/s, N=05
ηithN = 0.583 -5.612[(Tm - Ta)/I(t)] ηmN = 0.111 - 0.250[(Tm - Ta)/I(t)]
0.49
40
TfoN (0C)
ηith Case A
ηmN
Case B
ηmN
Case A 45
73
0.47 0.46 0.45 0.44 0.016
0.018
0.02
0.022
(Tm -Ta )/I(t) (0C-m2/W) Fig. 8c. Characteristics curves for thermal efficiencies for case A and case B.
For case B: githN ¼ 0:574 5:667½ðT m T a Þ=IðtÞ; gmN ¼ 0:109 0:358½ðT m T a Þ=IðtÞ: For 0.04 kg/s mass flow rate and ten PVT collectors connected in series, For case A:
githN ¼ 0:583 5:612½ðT m T a Þ=IðtÞ;
githN ¼ 0:539 5:996½ðT m T a Þ=IðtÞ
gmN ¼ 0:111 0:250½ðT m T a Þ=IðtÞ:
gmN ¼ 0:105 0:289½ðT m T a Þ=IðtÞ
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Shyam et al. / Solar Energy 114 (2015) 61–76
For case B: githN ¼ 0:529 6:048½ðT m T a Þ=IðtÞ gmN ¼ 0:104 0:296½ðT m T a Þ=IðtÞ From above equation one can see that the gain factor for case A (0.583 and 0.111) was higher compared to case B (0.574 and 0.109) for instantaneous thermal efficiency as well as for temperature dependent electrical efficiency whereas the loss coefficients for case A (5.612 and 0.250) were smaller compared to case B (5.667 and 0.358). But as the number of PVT water collectors increases to ten, the difference between the gain factors for instantaneous thermal efficiency for both cases (case A – 0.539, case B – 0.529); and the difference between gain factors for temperature dependent electrical efficiency decreases for both cases (case A – 0.105, case B – 0.104). Similarly the difference between the loss coefficients for instantaneous thermal efficiency (case A – 5.996, case B – 6.048) and for temperature dependent electrical efficiency (case A – 0.289, case B – 0.296) decreases. Therefore one can conclude that as the number of PVT water collectors connected in series increased the performance of both cases approaches closer to each other.
Appendix A A.1. Different terms used in numerical computation for case A U tc;a ¼
1 Lg þ h0 K g
1
;
U tc;p ¼
The present model has been studied for the climatic conditions of New Delhi, India for two different configurations. On the basis of present study following conclusion have been drawn: (i) At lower mass flow rate (0.01 kg/s) the outlet water temperature of PVT water collector connected in series, approaches to a constant value for less number of PVT water collector (07 collectors); but at higher mass flow (0.02 kg/s) rate the saturation to constant outlet water temperature has been reached for more number of PVT water collectors (10 collectors) for both cases. (ii) For a given number of PVT water collectors connected in series the outlet water temperature decreases with increasing mass flow rate and approaches to a constant value after 0.04 kg/s mass flow rate for both cases of present study. (iii) At moderate mass flow rate (nearly equal to or more than 0.03 kg/s), for very large number of water collectors connected in series the outlet water temperature and solar cell temperature were nearly same for both cases in present case; which infers that for large number of collectors connected in series, it is immaterial whether the PVT water collector is covered by PV module on lower portion or the upper portion.
1 ;
h0 ¼ 5:7 þ 3:8V; V ¼ 1 m=s;hi ¼ 5:7 W=m2 K; U tp;a ¼
1 1 þ U tc;a U tc;p
1
þ
Li 1 1 þ þ K i h0i hpf
1 ;
hi ¼ 2:8 þ 3V 0 ; V 0 ¼ 1 m=s: U tc;p U tc;a ; U L2 ¼ U L1 þ U tp;a ; U tc;p þ U tc;a hpf U L2 hpf U tp;a ¼ 0 ; U L;c ¼ 0 : F hpf þ U L2 F hpf þ U tp;a
U L1 ¼ U L;m
U tc;p hpf ; PF 2 ¼ 0 ; U tc;p þ U tc;a F hpf þ U L2 hpf : PF c ¼ 0 F hpf þ U tp;a
PF 1 ¼
ðasÞ1;eff ¼ ðac sg b gc sg bÞ; 7. Conclusions
1 Lg þ hi K g
ðasÞ2;eff ¼ ap ð1 bÞs2g :
ðasÞm;eff ¼ ½ðasÞ2;eff þ PF 1 ðasÞ1;eff ;
ðasÞc;eff ¼ PF c ap sg :
Am ¼ WLm is the area of PV module. Ac ¼ WLc is the area of the portion of the PVT water collector covered by glazing only. Ac F Rc U L;c : ðAF R ðasÞÞ1 ¼ Ac F Rc ðasÞc;eff þ PF 2 ðasÞm;eff Am F Rm 1 m_ f C f
Ac F Rc U L;c ðAF R U L Þ1 ¼ Ac F Rc U L;c þ Am F Rm U L;m 1 ; m_ f C f ðAF R U L Þ1 Kk ¼ 1 : m_ f C f F 0 Ac U L;c m_ f C f Ac F Rc ¼ 1 expð Þ ; U L;c m_ f C f 0 F Am U L;m m_ f C f Am F Rm ¼ 1 exp : U L;m m_ f C f ðAF R ðasÞÞm1 ¼ PF 2 ðasÞm;eff Am F Rm ; ðAF R U L Þm1 Am F Rm U L;m ¼ Am F Rm U L;m ; K m ¼ 1 : m_ f C f " # ðAF R ðasÞÞ1 1 ð1 K k;A ÞN ðasÞeff ;N ¼ ; ðAc þ Am Þ NK k;A " # N ðAF R U L Þ1 1 ð1 K k;A Þ ðAF R U L Þ1 ; K k;A ¼ : U L;N ¼ ðAc þ Am Þ NK k;A m_ f C f
Shyam et al. / Solar Energy 114 (2015) 61–76
A.2. Different terms used in numerical computation for Case B U tc;a ¼
1 Lg þ h0 K g
1
;
U tc;p ¼
1 Lg þ hi K g
1 ;
h0 ¼ 5:7 þ 3:8V; V ¼ 1 m=s; hi ¼ 5:7 W=m2 K; 1 1 1 1 Li 1 1 U tp;a ¼ þ þ þ þ ; U tc;a U tc;p K i h0i hpf h0i ¼ 2:8 þ 3V 0 ; V 0 ¼ 1 m=s: U tc;p U tc;a ; U L2 ¼ U L1 þ U tp;a ; U tc;p þ U tc;a hpf U L2 hpf U tp;a ¼ 0 ; U L;c ¼ 0 : F hpf þ U L2 F hpf þ U tp;a
U L1 ¼ U L;m
PF 1 ¼
U tc;p hpf ; PF 2 ¼ 0 ; U tc;p þ U tc;a F hpf þ U L2
PF c ¼
hpf : F 0 hpf þ U tp;a
ðasÞ1;eff ¼ ðac sg b gc sg bÞ; ðasÞ2;eff ¼ ap ð1 bÞs2g : ðasÞm;eff ¼ ½ðasÞ2;eff þ PF 1 ðasÞ1;eff ; ðasÞc;eff ¼ PF c ap sg : Am ¼ WLm is the area of PV module. Ac ¼ WLc is the area of the portion of the PVT water collector covered by glazing only. Am F Rm U L;m : ðAF R ðasÞÞ1 ¼ Am F Rm PF 2 ðasÞm;eff þ ðasÞc;eff Ac F Rc 1 m_ f C f
ðAF R U L Þ1 ¼ Am F Rm U L;m þ Ac F Rc U L;c
Am F Rm U L;m 1 m_ f C f
;
ðAF R U L Þ1 Kk ¼ 1 : m_ f C f ðAF R ðasÞÞc1 ¼ ðasÞc;eff Ac F Rc ; ðAF R U L Þc1 Ac F Rc U L;c ¼ Ac F Rc U L;c and K c ¼ 1 : m_ f C f " # N ðAF R ðasÞÞ1 1 ð1 K k;A Þ ðasÞeff ;N ¼ ; ðAc þ Am Þ NK k;A " # ðAF R U L Þ1 1 ð1 K k;A ÞN ðAF R U L Þ1 U L;N ¼ : ; K k;A ¼ ðAc þ Am Þ NK k;A m_ f C f References Amrizal, N., Chemisana, D., Rosell, J.I., 2013. Hybrid photovoltaic– thermal solar collectors dynamic modeling. Appl. Energy 101, 797– 807. Bergene, T., Lovvik, O.M., 1995. Model calculation on a flat-plate solar heat collector with integrated solar cells. Sol. Energy 55 (6), 453–462. Bhargava, A.K., Garg, H.P., Agarwal, R.K., 1991. Study of a hybrid solar system solar air heater combined with solar cells. Energy Convers. Mgmt 31, 471–479.
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ScienceDirect Solar Energy 114 (2015) 61–76 www.elsevier.com/locate/solener
Analytical expression of temperature dependent electrical efficiency of N-PVT water collectors connected in series Shyam a,⇑, G.N. Tiwari a, I.M. Al-Helal b b
a Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India Department of Agricultural Engineering, College of Food & Agricultural Sciences, King Saud University, P.O. Box 2460, Riyadh 11451, Saudi Arabia
Received 1 December 2013; received in revised form 9 January 2015; accepted 21 January 2015
Communicated by: Associate Editor Brian Norton
Abstract In the present study the series combination of N PVT water collectors, partially covered with photovoltaic module, in two different configurations namely case A: Photovoltaic module at lower portion; case B: Photovoltaic module at upper portion, have been analyzed. Analytical expressions for instantaneous thermal efficiency and temperature dependent electrical efficiency have been derived. The performances of both configurations have been compared on thermal efficiency basis and temperature dependent electrical efficiency basis. It has been concluded that at moderate mass flow rate, for large number of PVT water collectors connected in series both cases give nearly same results. Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Solar thermal; PVT water collector; Thermal efficiency; Temperature dependent electrical efficiency
1. Introduction The need of clean energy for the better environment compels, to use the renewable energy resources as much as possible. The conventional solar thermal technologies harness only the thermal energy. The photovoltaic (PV) systems convert the incident solar radiation into the electrical energy but the thermal energy absorbed has been wasted. To maximize the energy gain, the conventional solar thermal systems were integrated with the photovoltaic cells/module and the photovoltaic thermal (PVT) systems got more interest in the solar thermal research area. PVT systems utilize the thermal energy in addition to the electrical energy generated from the solar cells due to the radiation absorbed from the sun. The concept of PVT systems was given in late 70s by Kern and Russel (1978) and ⇑ Corresponding author. Tel.: +91 7838959195; fax +91 11 26591251.
E-mail address: [email protected] ( Shyam). http://dx.doi.org/10.1016/j.solener.2015.01.026 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.
Florschuetz (1979). Since then a large number of theoretical research as well as experimental research have been carried out by large number of researchers considering air in single pass and double pass flow pattern (Hendrie, 1980; Chandra et al., 1983; Bhargava et al., 1991; Sopian et al., 1995; Garg and Adhikari, 1997; Hegazy, 2000; Tiwari and Sodha, 2006, 2007) or water (Bergene and Lovvik, 1995; Garg and Agarwal, 1995; Chow, 2003; Chow et al., 2006) as the heat transfer fluid. Further the researches have been extended to optimize the design parameters and for improving the performance of PVT collectors on thermal energy basis and electrical energy basis; different configurations namely unglazed, single glazed and double glazed, PVT collectors have been analyzed. (Cox and Raghuraman, 1985; Garg et al., 1991, 1994; Huang et al., 2001; Zondag et al., 2002; Wei et al., 2006; Tripanagnostopoulos, 2007; Tripanagnostopoulos et al., 2007). Joshi and Tiwari (2007) studied the energy and exergy efficiencies of PVT air collectors. Zondag (2008)
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Nomenclature absorptivity of the solar cell mass flow rate of water ðkg=sÞ transmissivity of the glass specific heat of water (J/kgK) packing fraction of module length of PVT water collector covered by module ðmÞ gc solar cell efficiency Lc length of PVT water collect or covered by glazing ðmÞ gm = sg gc b PV module efficiency W width of PVT water collector ðmÞ FF fill factor Am ¼ WLm area of the module ðm2 Þ q density of water Ac ¼ WLc area of the glazing ðm2 Þ Lg thickness of glass cover (m) IðtÞ solar intensity ðW=m2 Þ Kg thermal conductivity of glass (W/m K) Ta ambient temperature (°C) Li thickness of insulation (m) Tc cell temperature (°C) Ki thermal conductivity of insulation (W/m K) Tp temperature of absorption plate (°C) Lp thickness of absorption plate (m) T fi inlet water temperature (°C) Kp thermal conductivity of absorption plate (W/ m K) Tf temperature of water (°C) T fom water temperature up to the portion covered by PV module (°C) ac m_ f sg Cf b Lm
extensively reviewed the flat plate collectors and discussed important key points regarding water collectors and air collectors. Hepbasli (2008) gave a review on exergetic analysis and assessment of renewable energy resources. Dubey and Tiwari (2009) experimentally validated the theoretical model for partially covered N PVT water collectors connected in series (covered by semitransparent PV module at the lower portion). Joshi et al. (2009) compared the PVT air collectors fully covered by opaque Photovoltaic (PV) module and semitransparent PV module and concluded that semitransparent PV module gives better performance. Dubey and Tiwari (2009) derived the analytical expression of electrical efficiency for fully covered PVT air collector and evaluated the performance for composite climatic conditions of New Delhi, India. Ibrahim et al. (2011) discussed the recent advances in flat plate PVT collectors. Dupeyrat et al. (2014) studied the thermal and electrical performance of a solar hot water system and showed that the PVT system gave more exergy saving than the conventional solar thermal systems. Amrizal et al. (2013) developed and validated the dynamical model for PVT
T foc T foN h0i ho hi U tc;a U tc;p hpf U tp;a U L:m U L;c PF 1 PF 2 PF 3 F0
water temperature up to the portion covered by glazing (°C) outlet water temperature at the end of the Nth PVT water collector (°C) heat transfer coefficient from bottom of PVT water collector to the ambient (W/m2 K) heat transfer coefficient from top of PVT water collector to the ambient (W/m2 K) heat transfer coefficient for space between the glazing and absorption plate (W/m2 K) over all heat transfer coefficient from cell to the ambient from top surface (W/m2 K) overall heat transfer coefficient from cell to the absorption plate (W/m2 K) heat transfer coefficient from blackened plate to the water (W/m2 K) overall heat transfer coefficient from absorption plate to the ambient (W/m2 K) overall heat transfer coefficient for module, from module to ambient (W/m2 K) overall heat transfer coefficient from glazing to ambient (W/m2 K) penalty factor due to the glass covers of module penalty factor due to the absorption plate below the module penalty factor due to the absorption plate for the portion covered by glazing collector efficiency factor
water collector in outdoor conditions and found that results were in good agreement with the results obtained from the steady state characterization. Recently Tian and Zhao (2013) reviewed different types of solar collectors and found that the PVT solar collector shows the best performance among the non concentrating solar collectors. 2. PVT water collector description In the present study a series combination of N number of PVT water collectors (Flat plate, tube in plate) partially covered by semitransparent photovoltaic (PV) module has been considered in two different configurations namely Case A: when the lower portion (inlet) of PVT water collector has been covered by the PV module and Case B: when the upper portion (outlet) of PVT water collector has been covered by the PV module. The comparison for these particular cases has been done to observe the effect on the performance of the collectors due to the different positions of the PV modules on the collector assembly. The top view of case A and case B has been shown in Figs. 1a and 1b. The
Shyam et al. / Solar Energy 114 (2015) 61–76
63
Glazing Water out
Water in PV module Insulated connecting pipes
Fig. 1a. Arrangement of PVT water collectors (module at lower portion) connected in series.
PV module Water out
Water in
Glazing Insulated connecting pipes
Fig. 1b. Arrangement of PVT water collectors (module at upper portion) connected in series.
Glazing PV module
Glazing
Solar cell Tfi
Solar cell Tfo,m
Tfi
Absorption plate Tfo,m
PV module
Absorption plate
Tfo
Air gap
Tfo
Air gap Water out
Water in
Water out
Water in
Insulation Insulation
Cut section of metallic tubes
Fig. 2a. Side view of flow pattern in PVT water collector (module at lower portion).
outlet of the first PVT water collector has been connected to the inlet of the second PVT water collector and further the outlet of the second PVT water collector has been connected to the inlet of the third PVT water collector and so on. The side view and front view of the flow patterns of the water inside the PVT water collectors have been shown in Figs. 2a, 2b and 2c. The extended view for a single tube below the absorber plate and the thermal energy flow diagram for water inside the tube has been shown in
Cut section of metallic tubes
Fig. 2b. Side view of flow pattern in PVT water collector (module at upper portion).
Glazing integrated with PV module Absorption plate Air gap
Water in
Metallic tubes
Insulation
Water out
Fig. 2c. Front view of flow pattern in PVT water collector.
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from Eq. (1) one can get,
Glazing integrated with PV module
Solar radiations
Tc ¼
Air gap
ðasÞ1;eff IðtÞ þ U tc;a T a þ U tc;p T p U tc;a þ U tc;p
*Assumed
Metallic tube
Insulation
terms have been given in appendix.
3.1.2. Energy balance for blackened absorber plate below the PV module
Absorber plate
Thermal energy gain from solar radiation
ap ð1 bÞs2g IðtÞWdx þ U tc;p ðT c T p ÞWdx ¼ F 0 hpf ðT p T f ÞWdx þ U tp;a ðT p T a ÞWdx
Thermal energy gain from left side of tube
Water inside tube
Thermal energy gain from right side of tube
ð3Þ
from Eqs. (2) and (3) one can get, Tp ¼
½ðasÞ2;eff þ PF 1 ðasÞ1;eff IðtÞ þ U L2 T a þ hpf T f ðU L2 þ hpf Þ
ð4Þ
The rate of thermal energy gain by the water below the absorber plate will be given by,
Total thermal energy gain by the water
Fig. 2d. Extended view of single tube below absorber plate and thermal energy flow diagram for water inside tube.
Fig. 2d. For better understanding of heat transfer and energy flow at different parts of the PVT water collector the thermal resistance diagram and the thermal energy diagram have been given in Figs. 3a and 3b for the portion covered by the PV module at XX’. Similarly for the portion covered with the glazing the thermal resistance diagram and thermal energy diagram at XX0 0 have been shown in Figs. 3c and 3d. The design parameters used in the numerical computation have been given in Table 1. The solar radiation and ambient temperature data have been taken from Indian meteorological department (IMD) Pune, India for clear sky day of New Delhi, India climatic condition in the month of January. The blackened absorption plate receives thermal energy from the direct radiation from non packing area of the semitransparent PV module and glazing in addition to the heat transferred by convection from the back surface of the solar cells of PV module. The water flowing in tubes get heated by the thermal energy transferred from absorbing plate to the water. 3. Thermal modeling 3.1. Lower portion of the PVT water collector covered by PV module (Case A) The energy balance equations have been written for quasi steady state one dimensional heat conduction and neglecting the ohmic losses. 3.1.1. Energy balance for solar cell of semitransparent PV module ac sg bIðtÞWdx ¼ U tc;a ðT c T a ÞWdx þ U tc;p ðT c T p ÞWdx þ gc sg bIðtÞWdx
ð2Þ
ð1Þ
m_ f C f
dT f dx ¼ F 0 hpf ðT p T f ÞWdx dx
ð5Þ
F0 is the collector efficiency factor calculated by following Duffie and Beckman (1991) and Tiwari (2004). Following Dubey and Tiwari (2009), for N identical PVT water collector the outlet water temperature at the end of the Nth PVT water collector is given by ðAF R ðasÞÞ1 1 K Nk T foN ¼ IðtÞ 1 Kk m_ f C f ðAF R U L Þ1 1 K Nk þ ð6Þ T a þ K Nk T fi 1 Kk m_ f C f The analytical expression for the temperature dependent electrical efficiency of solar cells of Nth PVT water collector has been derived using following relation, gcN ¼ g0 ½1 b0 ðT cN T 0 Þ
ðEvans;1981; Schott;1985Þ ð7Þ
where g0 is the efficiency at standard test condition i.e., at I(t) = 1000 W/m2 and T0 = 25 °C and T cN is the average solar cell temperature of Nth PVT water collector. To find out T cN one needs average plate temperature of Nth PVT water collector T pN and average water temperature of Nth PVT water collector T fN . The average water temperature below the portion covered by PV module, for Nth PVT water collector can be found as, T fN ¼
T fomN þ T foN 1 2
ð8Þ
where TfomN and TfoN1 are the temperature at the end of the PV module of the Nth PVT water collector and temperature at the end of the (N1)th PVT water collector. For N identical PVT water collectors the temperature at the end of the portion covered by PV module of the Nth PVT water collector can be found by as follows
Shyam et al. / Solar Energy 114 (2015) 61–76
1 K Nk 1 IðtÞ T fomN ¼ ðAF R ðasÞÞm1 þ K m ðAF R ðasÞÞ1 m_ f C f 1 Kk 1 K kN 1 Ta þ ðAF R U L Þm1 þ K m ðAF R U L Þ1 m_ f C f 1 Kk þ K m K Nk 1 T fi From Eqs. (2), (4), (6), (8) and (9) one can get 1 ðU tc;a þ U tc;p Þ
o
ðasÞ1;eff þ
n U tc;p ðasÞ2;eff 0 U L2 þ F hpf
U tc;p F 0 hpf ðAF R ðasÞÞm1 0 2m_ f C f ðU L2 þ F hpf Þ 1 K Nk 1 þð1 þ K m ÞðAF R ðasÞÞ1 IðtÞ 1 Kk U tc;p U L2 þ U tc;a þ U L2 þ F 0 hpf þPF 1 tðasÞ1;eff
The rate of useful electrical energy gain from N identical PVT water collectors has been calculated by the following formula N X ð13Þ Q_ uel;N ¼ Am IðtÞ gmN 1
ð9Þ
T cN ¼
65
þ
U tc;p F 0 hpf ðAF R U L Þm1 2m_ f C f ðU L2 þ F 0 hpf Þ 1 K kN 1 þð1 þ K m ÞðAF R U L Þ1 Ta 1 Kk U tc;p F 0 hpf N 1 ð1 þ K m ÞK k þ T fi 2ðU L2 þ F 0 hpf Þ
þ
ð10Þ
Following Mishra and Tiwari (2013) the power required to pump the fluid is 0.8 W for a head of 1.2 m and 75% pump efficiency. The electrical output from the PVT collectors is of the order of kWh, hence the pumping power has been neglected in the present study. The rate of useful thermal energy gain from N identical PVT water collectors has been calculated using the following relation Q_ uth;N ¼ m_ f C f ðT foN T fi Þ
ð14Þ
on putting the value of T foN from Eq. (6) into Eq. (14) one can get, h i Q_ uth;N ¼ N ðAc þ Am Þ ðasÞeff ;N IðtÞ U L;N ðT fi T a Þ ð15Þ The instantaneous thermal efficiency of Nth PVT water collector is given as following ðT fi T a Þ Q_ uth;N ¼ ðasÞeff ;N U L;N gith;N ¼ ð16Þ IðtÞ N ðAc þ Am ÞIðtÞ 3.2. Upper portion of the PVT water collector covered by PV module (Case B) In this case the glazing was at the inlet of the PVT water collector and the PV module was at the far end
From Eqs. (7) and (10) one can get,
3 n o 3 33 U tc;p F 0 hpf U tc;p ac sg bþ U L2 þF ðasÞ þPF a s b Þ þ 0h 0h 1 c g 2;eff _ 2 C ðU þF m pf f f pf L2 6 7 77 6 66 97 8 7 n o 6 7 77 6 66 7 6 7 77 6 66 > > = 7IðtÞ 7 < PF 2 ðasÞ2;eff þPF 2 PF 1 ac sg b Am F Rm þð1þK m Þ 6 77 6 66 7 6 7 77 6 66 n oo N 1 5 6 7 77 6 1 64>n 1K A F U > c Rc L;c k 6 7 77 6 6 ; : Ac F Rc ðasÞc;eff þ ½PF 2 ðasÞ2;eff þPF 2 PF 1 ac sg bAm F Rm 1 m_ f Cf g0 61b0 6U tc;a þU tc;p 6 1K k 7 T 0 77 6 7 77 6 6 h n N 1 oi 6 7 77 6 6 1K k U tc;p F 0 hpf U tc;p U L2 6 7 77 6 6 þ U tc;a þ U L2 þF 0 hpf þ 2m_ f Cf ðU L2 þF 0 hpf Þ ðAF R U L Þm1 þð1þK m ÞðAF R U L Þ1 1K k Ta 6 7 77 6 6 4 5 55 4 4 h i 0 U F hpf ð1þK m Þ N 1 þ tc;p K T fi pf 0 k 2ðU L2 þF h Þ h h n N1 oii gcN ¼ 1K k U tc;p F 0 hpf U tc;p A F U L;c g0 b0 IðtÞ 1 ðU tc;a þU tc;p Þ sg bþ U L2 þF 0 hpf PF 1 sg bþ 2m_ f cf ðU L2 þF 0 hpf Þ PF 2 PF 1 sg bAm F Rm 1þð1þK m Þ 1 c m_ Rc 1K k f Cf 2
2
22
ð11Þ
Finally the temperature dependent electrical efficiency of PV module of Nth PVT water collector will be gmN ¼ sg bgcN
ð12Þ
from the inlet of the PVT water collector. The temperature at the end of the portion covered with glazing can be given as following (Duffie and Beckman, 1991; Tiwari, 2004),
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Shyam et al. / Solar Energy 114 (2015) 61–76
T foc1
0 ðasÞc;eff IðtÞ F Ac U L;c ¼ þ T a 1 exp U L;c m_ f C f 0 F Ac U L;c þ T fi exp m_ f C f
ð17Þ
Again using Eqs. (1), (3) and (5) with the boundary conditions at x ¼ 0; T f ¼ T foc1 and at x ¼ Lm ; T f ¼ T fo1 and following the same procedure as in Case A, the outlet temperature at the end of the Nth PVT water collector can be found as follows, T foN ¼
ðAF R ðasÞÞ1 1 K Nk ðAF R U L Þ1 1 K Nk IðtÞ þ T a þ K Nk T fi 1 Kk 1 Kk m_ f C f m_ f C f ð18Þ
One can obtain the temperature at the end of the portion covered by glazing the Nth PVT water collector for N identical PVT water collectors as follows
ðasÞ1;eff þ
From Eqs. (7) and (21), one can obtain the temperature dependent electrical efficiency of solar cells of Nth PVT water collector as following,
22
3 n o 3 33 U tc;p F 0 hpf U tc;p ac sg b þ U L2 þF ðasÞ þ PF a s b þ 0h 0 1 c g 2;eff 2m_ f C f ðU L2 þF hpf Þ pf 6 7 77 6 66 8 97 8 9 7 6 7 77 6 66 7 6 7 77 6 66 < = 7IðtÞ < ½PF 2 ðasÞ2;eff þ PF 2 PF 1 ac sg bAm F Rm = N1 þ 1K N K 1K 6 7 77 6 66 ð Þ ð Þ c k k 5 6 7 77 6 6 4 ðAF R ðasÞÞc1 þ 1K k 6 7 77 6 1 6 : ; : þðasÞc;eff Ac F Rc 1 Am Fm_ RmCU L;m ; 7 6 7 6 6 f f g0 61 b0 6U tc;a þU tc;p 6 T 07 7 77
7 6 7 7 6 6 K c ð1K N1 Þþð1K Nk Þ U tc;p F 0 h 6 7 77 6 6 U U k T 7 6 7 7 6 6 þ U tc;a þ U L2tc;pþhFL20 þ 2m_ f Cf ðU L2 þFpf 0 hpf Þ ðAF R U L Þc1 þ ðAF R U L Þ1 a 1K k pf 6 7 77 6 6 5 4 5 5 4 4 h i U F 0 hpf ðK c þK k Þ N 1 þ tc;p K T 0 fi k 2ðU L2 þF hpf Þ h h ii ¼ 1 Þþð1K N Þ K ð1K N U tc;p F 0 hpf U tc;p g0 b0 IðtÞ k k 1 ðU tc;a þU tc;p Þ sg b þ U L2 þF 0 hpf PF 1 sg b þ 2m_ f Cf ðU L2 þF 0 hpf Þ PF 2 PF 1 sg bAm F Rm c 1K k 2
gcN
1 ðU tc;a þ U tc;p Þ
U tc;p fðasÞ2;eff U L2 þ F 0 hpf U tc;p F 0 hpf ðAF R ðasÞÞc1 þPF 1 ðasÞ1;eff g þ 0 2m_ f C f ðU L2 þ F hpf Þ K c ð1 K kN 1 Þ þ ð1 K Nk Þ IðtÞ þðAF R ðasÞÞ1 1 Kk U tc;p U L2 þ U tc;a þ U L2 þ F 0 hpf U tc;p F 0 hpf þ ðAF R U L Þc1 0 2m_ f C f ðU L2 þ F hpf Þ K c ð1 K kN 1 Þ þ ð1 K Nk Þ þðAF R U L Þ1 Ta 1 Kk U tc;p F 0 hpf N 1 ðK þ þ K ÞK T fi ð21Þ c k k 2ðU L2 þ F 0 hpf Þ
T cN ¼
2
ð22Þ 1 K kN 1 IðtÞ T focN ¼ ðAF R ðasÞÞc1 þ K c ðAF R ðasÞÞ1 1 Kk m_ f C f N 1 1 Kk Ta þ ðAF R U L Þc1 þ K c ðAF R U L Þ1 1 Kk m_ f C f þ K c K Nk 1 T fi ð19Þ The average water temperature below the portion covered by PV module, for Nth PVT water collector in this case has been determined by using following relation, T fN ¼
T focN þ T foN 2
ð20Þ
where T focN and T foN are the temperature at the end of the glazing and the temperature at the end of the Nth PVT water collector respectively. From Eqs. (2), (4), (18), (19) and (20) one can get,
The temperature dependent electrical efficiency of PV module of Nth PVT water collector has been obtained using Eq. (12) by putting the value of gcN for Case B from Eq. (22). The rate of useful electrical energy gain has been computed by Eq. (13) but the value of gmN was taken for Case B. The rate of useful thermal energy gain and instantaneous thermal efficiency of Nth PVT water collector have been calculated with the help of Eqs. (15) and (16) but the value of T foN has been taken for case B from Eq. (18).
3.3. Limiting cases Case1: when all the PVT water collectors connected in series were fully covered by PV module (Ac = 0); Case2: when all the water collectors connected in series were fully covered by glazing only (Am = 0). The thermal and
Shyam et al. / Solar Energy 114 (2015) 61–76
electrical efficiencies for the limiting cases have been obtained by putting Ac = 0 or Am = 0 respectively. 3.3.1. Case1: PVT water collectors fully covered by PV module (Ac = 0)
gcN
ciency have been plotted against ðT m T a Þ=IðtÞ. T m has been taken as the average temperature of inlet water temperature and outlet water temperature of PVT water collector.
3 n o 3 33 U tc;p F 0 hpf U tc;p ac sg b þ U L2 þF ðasÞ þ PF a s b þ 0h 0h Þ 1 c g 2;eff _ 2 C ðU þF m pf f f pf L2 7 6 77 6 6 6 o h N1 io 5IðtÞ 7 6 7 77 6 6 4 nn 1K m 6 7 77 6 6 PF 2 ðasÞ2;eff þ PF 2 PF 1 ac sg b Am F Rm 1 þ ð1 þ K m Þ 1K m 6 7 77 6 1 6 7 6 7 6 6 g0 61 b0 6U tc;a þU tc;p 6 h n h N1 ioi 7 T 0 7 77 0h U F U U 1K tc;p pf m 7 6 7 7 6 6 þ U tc;a þ tc;p 0 L2 þ Am F Rm U L;m 1 þ ð1 þ K m Þ 1K m Ta 7 U L2 þF hpf 2m_ f C f ðU L2 þF 0 hpf Þ 6 77 6 6 5 4 5 5 4 4 h i U F 0 hpf ð1þK m Þ N 1 þ tc;p K T 0 fi m 2ðU L2 þF hpf Þ h h h iii ¼ N1 U tc;p F 0 hpf U tc;p g0 b0 IðtÞ m 1 ðU tc;a þU tc;p Þ sg b þ U L2 þF 0 hpf PF 1 sg b þ 2m_ f Cf ðU L2 þF 0 hpf Þ PF 2 PF 1 sg bAm F Rm 1 þ ð1 þ K m Þð1K Þ 1K m 2
2
2
67
2
h i A F U L;m where K m ¼ 1 m m_ Rm C f f ðT fi T a Þ Q_ uth;N ¼ ðasÞeff ;N U L;N gith;N ¼ ð24Þ IðtÞ NAm IðtÞ " # PF 2 ðasÞm;eff F Rm 1 ð1 K k;A ÞN ðasÞeff ;N ¼ ; N K k;A " # N F Rm U L;m 1 ð1 K k;A Þ Am F Rm U L;m ; K k;A ¼ U L;N ¼ N K k;A m_ f C f
3.3.2. Case 2: Water collectors fully covered by glazing (Am = 0) ðT fi T a Þ Q_ uth;N ¼ ðasÞeff ;N U L;N gith;N ¼ ð25Þ IðtÞ NAc IðtÞ " # F Rc ðasÞc;eff 1 ð1 K k;A ÞN ðasÞeff ;N ¼ ; N K k;A " # F Rc U L;c 1 ð1 K k;A ÞN Ac F Rc U Lc ; K k;A ¼ U L;N ¼ m_ f C f N K k;A For both the cases the expressions of instantaneous thermal efficiency were similar to the Hottel–Whiller–Bliss (HWB) equation. 4. Characteristics equation Performance of different PVT systems can be compared on the basis of instantaneous thermal efficiency and electrical efficiency. To compare case A and case B the instantaneous thermal efficiency and electrical effi-
ð23Þ
5. Methodology In order to develop the characteristics equation for the PVT water collectors under study, following methodology has been adopted. Step 1: The data of solar radiation on a horizontal surface provided by IMD, Pune, India has been calculated for inclined surface at 30° using MATLAB 2010a. Step 2: Corresponding to above data of solar radiation and ambient temperature the outlet water temperature, solar cell temperature, electrical efficiency of solar cell and instantaneous thermal efficiency of PVT water collector have been computed using MATLAB 2010a from Eqs. (6), (10), (11) and (16) respectively for case A. the same parameters for case B have been computed by using Eqs. (18), (21), (22) and (16) respectively.
6. Results and discussion The hourly variations of solar radiation and ambient temperature have been shown in Fig. 4 for a typical day in the month of January for New Delhi climatic condition for which the numerical computations have been done. Figs. 5a and 5b shows the variation of maximum outlet temperature, T foN ;max with number of PVT water collectors for both the cases i.e., case A and case B at mass flow rates 0.01 kg/s and 0.08 kg/s respectively. From these figures one can observe that as the number of PVT water collector increases the T foN ;max increases. At 0.01 kg/s mass flow rate, the increment in the T foN ;max were 56.4 °C (case A) and 51.8 °C (case B) for the increment of number of collectors from one to five, but for further increment of number of
68
Shyam et al. / Solar Energy 114 (2015) 61–76
Fig. 3a. Thermal resistance diagram for the portion covered with PV module at XX0 .
collector from six to ten the increment in the T foN ;max were 15.8 °C (case A) and 14.8 °C (case B). At 0.08 kg/s mass flow rate, the increment in the T foN ;max were 11.7 °C (case A) and 11.6 °C (case B) for the increment of number of collectors from one to five, but for further increment of number of collector from six to ten the increment in the T foN ;max were 10.0 °C (case A) and 9.9 °C (case B). In case A the
increment in the T foN ;max has been higher compared to case B, it has been due to the fact that in case A, the PV module was at the inlet of PVT water collector hence PVT water collector receives less direct solar radiation at the lower portion i.e., only from the non packing area of the PV module unlike the case B where PVT water collector receives less direct solar radiation at the outlet.
Shyam et al. / Solar Energy 114 (2015) 61–76
69
Fig. 3b. Thermal energy diagram for the portion covered with PV module at XX0 .
The variation of T foN ;max with mass flow rate for five PVT water collectors connected in series has been given in Fig. 5c for case A and case B. It has been observed that as the mass flow rate increases the outlet water temperature decreases for both the cases. One can clearly observe that T foN ;max for case A has been significantly higher than T foN ;max for case B at very low mass flow rate but at higher mass flow rate the difference between T foN ;max of case A and case B decreases and at very high mass flow rate the outlet water temperature were nearly same for both the cases of
PVT water collectors. It has been due to the fact that at very high mass flow rate the contact time for heat to be transferred from tubes to the flowing water was very small. The variation of maximum solar cell temperatures T cN ;max and temperature dependent electrical efficiencies with number of collectors for both cases at mass flow rates 0.01 kg/s and 0.08 kg/s have been shown in Figs. 6a and 6b. It can be inferred from the figures that for both the cases, as the number of collectors increase the T cN ;max increases and the temperature dependent electrical efficiency
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Shyam et al. / Solar Energy 114 (2015) 61–76
Fig. 3c. Thermal resistance diagram for the portion covered with glass cover at X0X0 0.
decreases as expected due to the hindrance effect at higher temperature. Also one can observe that T cN ;max was higher for case B, because the PV module was at the outlet of the PVT water collector and receives thermal energy from the hot water below the absorber plate in addition to the energy absorbed from solar radiation. Fig. 6c shows the variation of T cN ;max and temperature dependent electrical efficiency with mass flow rate. At higher mass flow rate the thermal energy from solar cell transferred rapidly to the flowing water, resulting lower values of solar cell temperature and better electrical efficiency. For five number of PVT water collectors connected in series the temperature dependent electrical efficiency increases from 11.42% to 11.75% for case A and 10.93% to 11.62% for case B when the mass flow rate increased from 0.01 kg/s to 0.08 kg/s.
The hourly variation of outlet water temperature at 0.04 kg/s mass flow rate and for five PVT water collectors connected in series for case A and case B has been shown in Fig. 7a. As the solar intensity and ambient temperature increases with time the outlet water temperature also increases in forenoon and decreases after around 2 pm in afternoon due to decrease in solar intensity and ambient temperature. The outlet water temperature in case A has higher value in comparison to case B as explained earlier. Fig. 7b shows the hourly variation of solar cell temperature and temperature dependent electrical efficiency for five number of PVT water collectors connected in series and mass flow rate 0.04 kg/s for case A and case B. The solar cell temperature in case A has smaller values compared to case B, therefore the temperature dependent electrical efficiency for case A has higher values as expected. At
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71
Fig. 3d. Thermal energy diagram for the portion covered with glass cover at X0X0 0. Table 1 Values of design parameters used in numerical computations.
I(t)
Ta
1200
18 16
1000
14
800
12 10
600
8
400
Ta (0C)
H ¼ 1:7 m Am ¼ 0:605 m2 Ac ¼ 1:395 m2 h0i ¼ 5:8 W=m2 K hi ¼ 5:7 W=m2 K ho ¼ 9:5 W=m2 K U tc;p ¼ 5:58 W=m2 K hpf ¼ 100 W=m2 K U tc;a ¼ 9:20 W=m2 K PF 1 ¼ 0:378 PF 2 ¼ 0:924 U tp;a ¼ 4:74 W=m2 K U L:m ¼ 7:58 W=m2 K PF c ¼ 0:955 U L;c ¼ 4:52 W=m2 K Inclination = 30° Spacing between tubes = 0.125 m
I(t) (W/m2)
ac ¼ 0:9 sg ¼ 0:95 b ¼ 0:89 g0 ¼ 0:15 FF ¼ 0:8 ap ¼ 0:80 Lg ¼ 0:003 m K g ¼ 0:816 W=mK Li ¼ 0:1 m K i ¼ 0:166 W=mK Lp ¼ 0:002 m K p ¼ 64 W=mK cf ¼ 4179 J=kg K q ¼ 1000 kg=m3 b0 = 0.0045/°C F 0 ¼ 0:968 Tube diameter = 0.0125 m
6 4
200
2
0 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00
0
Time (Hour) Fig. 4. Hourly variation of solar radiation and ambient temperature for a typical day in the month of January.
Shyam et al. / Solar Energy 114 (2015) 61–76 Case A
Case B
Case A
m f = 0.01 kg/s
120
99
100
89
TcN,max (0C)
80 60 40
Case B
Case B 0.11 0.105
79
0.1
69 0.095
59
0.09
49
20
39
0 1
2
3
4
5
6
7
8
9
0.085 1
10
2
3
Fig. 5a. Variation of outlet temperature of Nth PVT water collectors with number of collectors connected in series at mass flow rate 0.01 kg/s.
Case A
45
Case B
4
5
6
7
8
9
10
Number of collectors
Number of collectors
Fig. 6a. Variation of solar cell temperature and temperature dependent electrical efficiency of Nth PVT water collectors with number of collectors connected in series at mass flow rate 0.01 kg/s.
Case A
m f = 0.08 kg/s
40
69
35
64
Case B Case A m f = 0.08 kg/s
Case B 0.11 0.109 0.108
25 20 15
59
0.107
54
0.106 0.105
49
10
0.104
5
44
0
39
1
2
3
4
5
6
7
8
9
10
0.103 0.102 1
2
Fig. 5b. Variation of outlet temperature of Nth PVT water collectors with number of collectors connected in series at mass flow rate 0.08 kg/s.
Case A
Case B
80
Case A
60
TcN,max (0 C)
TfoN,max (0C)
70
40 30 20 10 0 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100
m f (kg/s) Fig. 5c. Variation of outlet water temperature with mass flow rate of water for five PVT water collectors connected in series.
a mass flow rate of 0.04 kg/s and for ten PVT water collectors connected in series the maximum outlet water temperature T foN ;max were 62.0 °C and 61.1 °C for case A and case B respectively; and the solar cell temperature T cN ;max were 72.1 °C and 73.7 °C respectively for case A and case B. If the number of collectors further increased the difference in the outlet temperature and solar cell temperature for case A and case B reduces and have nearly same values.
4
5
6
7
8
9
10
Fig. 6b. Variation of solar cell temperature and temperature dependent electrical efficiency of Nth PVT water collectors with number of collectors connected in series at mass flow rate 0.08 kg/s.
Number of collectors= 05
50
3
Number of collectors
Number of collectors
90
ηmN
30
TcN,max (0C)
TfoN,max (0C)
Case A
m f = 0.01 kg/s
Case B
Case A
Case B
Number of collectors = 05 59 57 55 53 51 49 47 45 43 41 39 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100
0.12 0.118 0.116 0.114 0.112
ηmN
TfoN,max (0C)
140
ηmN
72
0.11 0.108 0.106 0.104
m f (kg/s) Fig. 6c. Variation of solar cell temperature and temperature dependent electrical efficiency with mass flow rate for five PVT water collectors connected in series.
The instantaneous thermal efficiency and temperature dependent electrical efficiencies have been shown in Figs. 8a and 8b for case A and case B respectively at 0.04 kg/s mass flow rate for five PVT collectors connected in series. One can observe from the figures that as the temperature increases the instantaneous thermal efficiency decreases with ðT m T a Þ=IðtÞ due to increase in losses.
Shyam et al. / Solar Energy 114 (2015) 61–76 m f = 0.04 kg/s, N=05
0.495 0.485
35
0.48
ηithN
30 25 20
0.25 0.2 0.15
0.455 0.45 0.016
0
0.1 0.018
08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00
ηith Case B 0.485
ηm Case B
m f = 0.04 kg/s, N=05
0.135
ηithN = 0.574 - 5.667[(Tm - Ta)/I(t)]
0.44
0.48
0.13
0.475
ηmN = 0.109 - 0.358[(Tm - Ta)/I(t)]
0.39
0.47
0.34
0.465
0.29
0.46
0.24
0.12 0.115
ηithN
0.125
0.455
0.11
0.45
0.105
0.445
0.1
Fig. 7b. Hourly variation of solar cell temperature and temperature dependent electrical efficiency at mass flow rate 0.04 kg/s for five PVT water collectors connected in series.
The instantaneous thermal efficiencies decrease from 49.0% to 45.5% (case A) and 48.2% to 44.6% (case B). The instantaneous thermal efficiencies for case A and case B have been shown in Fig. 8c for comparison purpose. One can observe from figure that case A has better performance compared to case B on thermal energy point of view. The temperature dependent electrical efficiency decreases marginally with ðT m T a Þ=IðtÞ. The maximum and minimum values of temperature dependent electrical efficiencies were 10.8% and 10.6% respectively for case A; whereas for case B these values were 10.4% and 10.2%. The temperature dependent electrical efficiencies for case A have higher values compared to case A which infer that case A has better performance compared to case B on electrical energy point of view. The characteristics equations have been obtained for instantaneous thermal efficiency and temperature dependent electrical efficiency for five PVT water collectors and at 0.04 kg/s mass flow rate for both the cases namely case A and case B. These equations were similar to Hottel– Whiller–Bliss (HWB) equations. For case A:
0.19 0.14 0.09
0.44 0.016
0.018
0.02
0.022
(Tm -Ta )/I(t) (0C-m2/W) Fig. 8b. Characteristics curves for thermal and electrical efficiencies for case B.
ηith Case A 0.49
ηith Case B
m f = 0.04 kg/s, N=05
Case A, ηithN = 0.583 - 5.612[(Tm - Ta)/I(t)] Case B, ηithN = 0.574 - 5.667[(Tm - Ta)/I(t)]
0.48
ηithN
50 45 40 35 30 25 20 15 10 5 0 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 Time (Hour)
0.022
Fig. 8a. Characteristics curves for thermal and electrical efficiencies for case A.
Case B
ηmN
Case B Case A m f = 0.04 kg/s, N=05
0.02
(Tm -Ta )/I(t) (0C-m2/W)
Time (Hour)
Case A
0.35
0.47
5
Fig. 7a. Hourly variation of outlet water temperature at mass flow rate 0.04 kg/s for five PVT water collectors connected in series.
0.4
0.3
0.46
10
0.45
0.475 0.465
15
TcN (0C)
ηm Case A m f = 0.04 kg/s, N=05
ηithN = 0.583 -5.612[(Tm - Ta)/I(t)] ηmN = 0.111 - 0.250[(Tm - Ta)/I(t)]
0.49
40
TfoN (0C)
ηith Case A
ηmN
Case B
ηmN
Case A 45
73
0.47 0.46 0.45 0.44 0.016
0.018
0.02
0.022
(Tm -Ta )/I(t) (0C-m2/W) Fig. 8c. Characteristics curves for thermal efficiencies for case A and case B.
For case B: githN ¼ 0:574 5:667½ðT m T a Þ=IðtÞ; gmN ¼ 0:109 0:358½ðT m T a Þ=IðtÞ: For 0.04 kg/s mass flow rate and ten PVT collectors connected in series, For case A:
githN ¼ 0:583 5:612½ðT m T a Þ=IðtÞ;
githN ¼ 0:539 5:996½ðT m T a Þ=IðtÞ
gmN ¼ 0:111 0:250½ðT m T a Þ=IðtÞ:
gmN ¼ 0:105 0:289½ðT m T a Þ=IðtÞ
74
Shyam et al. / Solar Energy 114 (2015) 61–76
For case B: githN ¼ 0:529 6:048½ðT m T a Þ=IðtÞ gmN ¼ 0:104 0:296½ðT m T a Þ=IðtÞ From above equation one can see that the gain factor for case A (0.583 and 0.111) was higher compared to case B (0.574 and 0.109) for instantaneous thermal efficiency as well as for temperature dependent electrical efficiency whereas the loss coefficients for case A (5.612 and 0.250) were smaller compared to case B (5.667 and 0.358). But as the number of PVT water collectors increases to ten, the difference between the gain factors for instantaneous thermal efficiency for both cases (case A – 0.539, case B – 0.529); and the difference between gain factors for temperature dependent electrical efficiency decreases for both cases (case A – 0.105, case B – 0.104). Similarly the difference between the loss coefficients for instantaneous thermal efficiency (case A – 5.996, case B – 6.048) and for temperature dependent electrical efficiency (case A – 0.289, case B – 0.296) decreases. Therefore one can conclude that as the number of PVT water collectors connected in series increased the performance of both cases approaches closer to each other.
Appendix A A.1. Different terms used in numerical computation for case A U tc;a ¼
1 Lg þ h0 K g
1
;
U tc;p ¼
The present model has been studied for the climatic conditions of New Delhi, India for two different configurations. On the basis of present study following conclusion have been drawn: (i) At lower mass flow rate (0.01 kg/s) the outlet water temperature of PVT water collector connected in series, approaches to a constant value for less number of PVT water collector (07 collectors); but at higher mass flow (0.02 kg/s) rate the saturation to constant outlet water temperature has been reached for more number of PVT water collectors (10 collectors) for both cases. (ii) For a given number of PVT water collectors connected in series the outlet water temperature decreases with increasing mass flow rate and approaches to a constant value after 0.04 kg/s mass flow rate for both cases of present study. (iii) At moderate mass flow rate (nearly equal to or more than 0.03 kg/s), for very large number of water collectors connected in series the outlet water temperature and solar cell temperature were nearly same for both cases in present case; which infers that for large number of collectors connected in series, it is immaterial whether the PVT water collector is covered by PV module on lower portion or the upper portion.
1 ;
h0 ¼ 5:7 þ 3:8V; V ¼ 1 m=s;hi ¼ 5:7 W=m2 K; U tp;a ¼
1 1 þ U tc;a U tc;p
1
þ
Li 1 1 þ þ K i h0i hpf
1 ;
hi ¼ 2:8 þ 3V 0 ; V 0 ¼ 1 m=s: U tc;p U tc;a ; U L2 ¼ U L1 þ U tp;a ; U tc;p þ U tc;a hpf U L2 hpf U tp;a ¼ 0 ; U L;c ¼ 0 : F hpf þ U L2 F hpf þ U tp;a
U L1 ¼ U L;m
U tc;p hpf ; PF 2 ¼ 0 ; U tc;p þ U tc;a F hpf þ U L2 hpf : PF c ¼ 0 F hpf þ U tp;a
PF 1 ¼
ðasÞ1;eff ¼ ðac sg b gc sg bÞ; 7. Conclusions
1 Lg þ hi K g
ðasÞ2;eff ¼ ap ð1 bÞs2g :
ðasÞm;eff ¼ ½ðasÞ2;eff þ PF 1 ðasÞ1;eff ;
ðasÞc;eff ¼ PF c ap sg :
Am ¼ WLm is the area of PV module. Ac ¼ WLc is the area of the portion of the PVT water collector covered by glazing only. Ac F Rc U L;c : ðAF R ðasÞÞ1 ¼ Ac F Rc ðasÞc;eff þ PF 2 ðasÞm;eff Am F Rm 1 m_ f C f
Ac F Rc U L;c ðAF R U L Þ1 ¼ Ac F Rc U L;c þ Am F Rm U L;m 1 ; m_ f C f ðAF R U L Þ1 Kk ¼ 1 : m_ f C f F 0 Ac U L;c m_ f C f Ac F Rc ¼ 1 expð Þ ; U L;c m_ f C f 0 F Am U L;m m_ f C f Am F Rm ¼ 1 exp : U L;m m_ f C f ðAF R ðasÞÞm1 ¼ PF 2 ðasÞm;eff Am F Rm ; ðAF R U L Þm1 Am F Rm U L;m ¼ Am F Rm U L;m ; K m ¼ 1 : m_ f C f " # ðAF R ðasÞÞ1 1 ð1 K k;A ÞN ðasÞeff ;N ¼ ; ðAc þ Am Þ NK k;A " # N ðAF R U L Þ1 1 ð1 K k;A Þ ðAF R U L Þ1 ; K k;A ¼ : U L;N ¼ ðAc þ Am Þ NK k;A m_ f C f
Shyam et al. / Solar Energy 114 (2015) 61–76
A.2. Different terms used in numerical computation for Case B U tc;a ¼
1 Lg þ h0 K g
1
;
U tc;p ¼
1 Lg þ hi K g
1 ;
h0 ¼ 5:7 þ 3:8V; V ¼ 1 m=s; hi ¼ 5:7 W=m2 K; 1 1 1 1 Li 1 1 U tp;a ¼ þ þ þ þ ; U tc;a U tc;p K i h0i hpf h0i ¼ 2:8 þ 3V 0 ; V 0 ¼ 1 m=s: U tc;p U tc;a ; U L2 ¼ U L1 þ U tp;a ; U tc;p þ U tc;a hpf U L2 hpf U tp;a ¼ 0 ; U L;c ¼ 0 : F hpf þ U L2 F hpf þ U tp;a
U L1 ¼ U L;m
PF 1 ¼
U tc;p hpf ; PF 2 ¼ 0 ; U tc;p þ U tc;a F hpf þ U L2
PF c ¼
hpf : F 0 hpf þ U tp;a
ðasÞ1;eff ¼ ðac sg b gc sg bÞ; ðasÞ2;eff ¼ ap ð1 bÞs2g : ðasÞm;eff ¼ ½ðasÞ2;eff þ PF 1 ðasÞ1;eff ; ðasÞc;eff ¼ PF c ap sg : Am ¼ WLm is the area of PV module. Ac ¼ WLc is the area of the portion of the PVT water collector covered by glazing only. Am F Rm U L;m : ðAF R ðasÞÞ1 ¼ Am F Rm PF 2 ðasÞm;eff þ ðasÞc;eff Ac F Rc 1 m_ f C f
ðAF R U L Þ1 ¼ Am F Rm U L;m þ Ac F Rc U L;c
Am F Rm U L;m 1 m_ f C f
;
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