Analysis of PV/T flat plate water collectors connected in series

Available online at www.sciencedirect.com

www.elsevier.com/locate/solener

Solar Energy 83 (2009) 1485–1498

Analysis of PV/T flat plate water collectors connected in series

Swapnil Dubey *, G.N. Tiwari

Centre for Energy Studies, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India

Received 15 December 2008; received in revised form 3 April 2009; accepted 8 April 2009Available online 9 May 2009

Communicated by: Brian Norton

Abstract

Photovoltaic–thermal (PV/T) technology refers to the integration of a PV and a conventional solar thermal collector in a single pieceof equipment. In this paper we evaluate the performance of partially covered flat plate water collectors connected in series using theo-retical modeling. PV is used to run the DC motor, which circulates the water in a forced mode. Analytical expressions for N collectorsconnected in series are derived by using basic energy balance equations and computer based thermal models. This paper shows thedetailed analysis of thermal energy, exergy and electrical energy yield by varying the number of collectors by considering four weatherconditions (a, b, c and d type) for five different cities (New Delhi, Bangalore, Mumbai, Srinagar, and Jodhpur) of India. Annual thermaland electrical energy yield is also evaluated for four different series and parallel combination of collectors for comparison purpose con-sidering New Delhi conditions. This paper also gives the total carbon credit earned by the hybrid PV/T water heater investigated as pernorms of Kyoto Protocol for New Delhi climatic conditions. Cost analysis has also been carried out.

It is observed that the collectors partially covered by PV module combines the production of hot water and electricity generation andit is beneficial for the users whose primary requirement is hot water production and collectors fully covered by PV is beneficial for theusers whose primary requirement is electricity generation. We have also found that if this type of system is installed only in 10% of thetotal residential houses in Delhi then the total carbon credit earned by PV/T water heaters in terms of thermal energy is USD $144.5millions per annum and in terms of exergy is USD $14.3 millions per annum, respectively.� 2009 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic; Exergy; Thermal energy; Flat plate PV/T collectors; Carbon credit

1. Introduction

Several theoretical and experimental studies of PV/Tsystems are available in the literature. Kern and Russell(1978) have introduced the main concepts of these sys-tems with results for the cases that water or air is usedas heat removal fluid. The theoretical model of PV/Tsystems using conventional thermal collector techniquesand an extension of the Hottel–Whillier model for theanalysis of PV/T systems was introduced by Hendrie(1979) and Florschuetz (1979), respectively. Raghuraman(1981) presented numerical methods for predicting the

0038-092X/$ - see front matter � 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2009.04.002

* Corresponding author. Tel.: +91 9868929291; fax: +91 11 26591121.E-mail address: [email protected] (S. Dubey).

performances of liquid PV/T flat plate collectors. Lalovic(1986) proposed a novel transparent type of a-Si cell as alow cost improvement for hybrid systems. The rationalebehind the hybrid concept is that a solar cell convertssolar radiation to electrical energy with peak efficiencyin the range of 9–12%, depending on specific solar-celltype and the amount of heat removed by the water.More than 80% of the solar radiation falling on photo-voltaic (PV) cells is not converted into electricity, buteither reflected or converted into thermal energy. Thisleads to an increase in the PV cell’s working temperatureand consequently, a drop of electricity conversion effi-ciency. Zondag et al. (2002) have developed a model ofa hybrid PV/T water collector and performed experimen-tal studies of such systems for varying sizes.

mailto:[email protected]

Nomenclature

A area, m2

C specific heat (J/kg �C)_Ex exergy (W)F 0 flat plate collector efficiency factor, dimension-

lessFR flow rate factor, dimensionlessh heat transfer coefficient (W/m2 �C)P present cost of the system, RupeesPF1 penalty factor first due to the glass cover of PV

module, dimensionlessPF2 penalty factor second due to the absorber below

PV module, dimensionlessi interest rate (%)I(t) incident solar intensity (W/m2)K thermal conductivity (W/m K)_m rate of flow of water mass (kg/s)M mass of water (kg)N number of collectorsn life time of the system (years)n0 number of riser tubes_Qu rate of useful energy transfer (kW)R1 annual operation and maintenance cost (Ru-

pees)S salvage value (Rupees)T temperature (�C)Tw water temperature (�C)Ut c,a an overall heat transfer coefficient from solar

cell to ambient through glass cover (W/m2 �C)UL1 an overall heat transfer coefficient from blacken

surface to ambient (W/m2 �C)V air velocity (m/s)

W width of two tubes (m)€ conversion factor for energy of solar radiation

into exergy, dimensionlessgo efficiency at standard test condition

(I(t) = 1000 W/m2 and Tc = 25 �C), dimension-less

gc temperature dependent efficiency, dimensionless

Subscripts

a ambientsc solar cellc1 first collectorc2 second collectoreff effectivef fluidfi inlet fluidfo outgoing fluidg glassm modulep platew water

Greek

a absorbtivity(as)eff product of Effective absorbtivity and transmit-

tivityb packing factorgi an instantaneous thermal efficiencyg efficiency of solar cells transmittivity

1486 S. Dubey, G.N. Tiwari / Solar Energy 83 (2009) 1485–1498

The overall electrical efficiency of a PV module can beincreased by increasing the packing factor (PF) and byreducing the temperature of the PV module by withdraw-ing heat absorbed in the PV module, (Zondag et al. (2003)and Chow (2003)). Packing factor is the ratio of total areaof solar cells to the area of PV module. The fluid used toremove heat from the PV module may be either air orwater. A device containing a PV module where heatabsorbed in the PV module is withdrawn by a fluid isreferred as a PV/T collector.

For PV/T water heating systems, two types of PV/T col-lectors have been considered, namely with the followingconfigurations,

(a) The parallel plate configuration, Prakash (1994) andHuang et al. (2001), Tiwari and Sodha (2006a),Tiwari et al. (2006) and

(b) The tube-in-plate configuration, Zondag et al. (2002),Chow (2003, 2006), Huang et al. (2001) and Kalogi-rou (2001), Tiwari and Sodha (2006b).

Chow et al. (2006) concluded that the tube-in-plate absor-ber collector with single glazing is regarded as one of themost promising designs. He also concluded that the flat platecollector partial covered by PV module gives better thermaland electrical output from the PV/T water heating system.He has concluded his findings on the basis of indoor simula-tion. In order to decrease the PV cell’s working temperatureand consequently increase in the electricity conversion effi-ciency, PV/T collectors are introduced to simultaneouslygenerate electricity and thermal energy, (Ji et al., 2007).Robles-Ocampo et al. (2007) designed and made an originalwater-heating planar collector and a set of reflecting planes.They concluded that the estimated overall solar energy utili-zation efficiency for the system related to the direct radiationflux is of the order of 60%, with an electric efficiency of 16.4%.Recently, Zondag (2008) carried out a rigorous review onresearch work of a PV-thermal collectors and systems, car-ried out by various scientists till 2006. His review includesthe history and importance of photovoltaic hybrid systemand its application in various sectors. It also includes charac-

S. Dubey, G.N. Tiwari / Solar Energy 83 (2009) 1485–1498 1487

teristic equations, a study of design parameters, marketing,etc. Dubey and Tiwari (2008) developed a thermal modelof a PV integrated solar water heater and validated the exper-imental results.

The relations between energy and exergy, energy andsustainable development, energy policy making, exergyand the environment and exergy are reported by Dincer(2002) in detail.

Carbon Credit Trading (Emission Trading) is an admin-istrative approach used to control pollution by providingeconomic incentives for achieving reductions in the emis-sions of pollutants. A credit gives the owner the right toemit one ton of carbon dioxide. International treaties suchas the Kyoto Protocol set quotas on the amount of green-house gases countries can produce. Energy consumption ofa country is one of the indicators of its socio economicdevelopment. Per capita energy consumption in India isalso one of the lowest in the world. It is about 30% of thatin China, about 22% of that in Brazil, and about 3.18% ofthat in USA. With development the per capita energy con-sumption is likely to increase. For energy India depends onoil and gas imports, which account for over 65% of its con-sumption; it is likely to increase further considering theeconomic development, rise in standard of living of peopleand rising prices. Coal, which currently accounts for over60% of India’s electricity production, is the major sourceof emission of greenhouse gases and that of acid rains. Inthe business-as-usual scenario, India will exhaust its oilreserves in 22 years, its gas reserves in 30 years and its coalreserves in 80 years (Kalshian, 2006).

In this paper, the performance of N partially covered col-lectors connected in series are evaluated by considering thefour weather conditions for five different cities (New Delhi,Bangalore, Mumbai, Srinagar, and Jodhpur) of India.

These cities are classified under the five different climaticcondition of India. The four type of weather conditions aredefined as,

Type a: The ratio of daily diffuse to daily global radia-tion is less than or equal to 0.25 and sunshine hours greaterthen or equal to 9 h.

Type b: The ratio of daily diffuse to daily global radia-tion between 0.25 and 0.50 and sunshine hours between 7and 9 h.

Type c: The ratio of daily diffuse to daily global radia-tion between 0.50 and 0.75 and sunshine hours between 5and 7 h.

Type d: The ratio of daily diffuse to daily global radia-tion is greater than or equal to 0.75 and sunshine hours lessthen or equal to 5 h.

Data for different climates were obtained from IndianMetrological Department (IMD), Pune.

2. Thermal analysis

The cross sectional view of absorber tubes, PV coveredflat plate collector and collectors connected in series areshown in Fig. 1a. A tube has a diameter of 0.0125 m and

the distance between the tubes is 0.125 m. Fig. 1a showsthe streams of energy and exergy inflow, outflow anddestruction in the system. For the present study a conven-tional tube-in-plate type collector of area 2 m2 and storagetank having a capacity of 200 l has been considered. The col-lectors are partially covered by PV module (0.165 m2) andconnected in series (Fig. 1b). To increase the absorption ofsolar radiation the absorber plate of collector is blackenedby black paint of high absorbtivity and less emmisivity.

In order to write the energy balance equation of PV/Tsolar water collectors connected in series, the followingassumptions have been made:

� One dimensional heat conduction is good approxima-tion for the present study.� The heat capacity of PV/T collector has been neglected

in comparison with the heat capacity of water in thestorage tank.� There is no temperature stratification in the water of the

storage tank due to the forced mode of operation.� The system is in quasi-steady state.� The ohmic losses in the solar cell are negligible.

The energy balance equations for N water collectorsconnected in series are as follows:

2.1. Combinations of PV/T collectors connected in series/

parallel

Case A: All the collectors are partially covered by PVmodules and connected in series (present case; Fig. 1b).

Following Dubey and Tiwari (2008), the useful heat out-put from the N collectors connected in series can be given as,

_Qu;N ¼ N � Ac½ðasÞeff ;N IðtÞ � UL;NðT fi � T aÞ� ð1Þ

This expression is similar to the expression derived byDuffie and Beckman (1991) and Tiwari (2005) for glass cov-ered collectors connected in series. The detailed expressionfor partially covered collectors is given in the Appendix.

ðasÞeff ;N ¼ ðF RðasÞÞ11� ð1� KKÞN

NKK

" #and

UL;N ¼ ðF RULÞ11� ð1� KKÞN

NKK

" #ð2Þ

where KK ¼ ½ðA F RULÞ1_mf Cf

� and

ðAF RðasÞÞ1 ¼ AmF RmPF 2ðasÞm;eff 1� AcF RcU L;c

_mf Cf

� ��

þ AcF RcðasÞc;eff

ið3Þ

ðAF RU LÞ1 ¼ AmF RmU L;m 1� AcF RcUL;c

_mf Cf

� �þ AcF RcU L;c

� �ð4Þ

xin = I(t)

xthermal = carnot × Qu

xdest

Tfo1Tfo2

Tfi

Inlet Outlet

Cut section of a tube

Thermal Absorber

Air Gap

Thermal Insulation Metallic Frame

Glazing Surface Solar Cell

Inlet

Outlet

1st 3rd2rd Nth

Tfo, N

Tfi

Tfo, 3Tfo, 2Tfo, 1

Inlet

Outlet

1st 3rd2rd

Tfo

Tfi 4th 6th5th

Inlet

Outlet

1st 3rd2rd Nth

Tfo, N

Tfi

Tfo, 3Tfo, 2Tfo, 1

Inlet

Outlet

1st 3rd2rdTfi

Tfo

1st 3rd2rd

a

b

c

d

e

Fig. 1. (a) Cross sectional side view of a flat plate collector partially covered by PV. (b) Collectors partially covered by PV connected in series (presentcase). (c) Collectors fully covered by PV module and fully covered by glass cover are connected in series (PV-glass combination). (d) Collectors fullycovered by PV connected in series. (e) Series and parallel combination of collectors (two panels) fully covered by PV (mixed combination).


The rate of thermal energy available at the end of firstcollector is given as,

_Qu;1ðmþcÞ ¼ _mf Cf ðT fo1 � T fiÞ ð5Þ

From Eq. (1a) (given in the Appendix) and Eq. (5), theoutlet fluid temperature at the end of first collector can beevaluated as,

T fo1¼ðAF RðasÞÞ1

_mf CfIðtÞþðAF RU LÞ1

_mf CfT aþT fi 1�ðAF RULÞ1

_mf Cf

� �

Similarly, the outlet fluid temperature at the end of sec-ond collector can be evaluated as,

T fo2¼ðAF RðasÞÞ2

_mf CfIðtÞþðAF RULÞ2

_mf CfT aþT fi2 1�ðAF RULÞ2

_mf Cf

� �

As, Tfi2 = Tfo1,For a number of collectors connected in series, the outlet

temperature of the first collector will be the inlet for secondcollector, the outlet temperature of the second will be theinlet for the third collector and so on. Hence, for a system


of N collectors connected in series, the outlet fluid temper-ature (TfoN) from the Nth collector can be expressed in theterms of the inlet temperature of the first collector.

For N identical set of collectors connected in series, theoutlet fluid temperature at the end of Nth collector can bedefined as,

T fo N ¼ðA F RðasÞÞ1

_mf Cf

1� KNK

1� KK

� �IðtÞ

þ ðA F RULÞ1_mf Cf

1� KNK

1� KK

� �T a þ T fi KN

K ð6Þ

Case B: Identical set of collectors fully covered by PVmodule and fully covered by glass cover are connected inseries (PV-glass combination; Fig. 1c). The expression forthe outlet fluid temperature from mixed combination arederived as,

T fo N ¼ðasÞc;eff IðtÞ

U L;cþ T a

� �1� exp

F 0AcU L;c

_mf Cf

� ��

�1� exp � F 0AcUL;c

_mf Cf

� �n oNc

1� expF 0AcUL;c

_mf Cf

� �264

375

þPF 2ðasÞm;eff IðtÞ

UL;mþ T a

� ��

� 1� exp �N mF 0AmUL;m

_mf Cf

� ��

þT fi exp �NmF 0AmU L;m

_mf Cf

� ��exp � F 0AcU L;c

_mf Cf

� �� Nc

ð5aÞ

where Nc is the number of collectors covered by glass coverand Nm is the number of collectors covered by PV module.

The expression for the useful heat yield from mixedcombination are derived as,

_Qu;N ¼ _mf Cf

ðasÞc;eff IðtÞU L;c

þT a

� �1� exp �F 0AcU L;c

_mf Cf

� ��

�1� exp � F 0AcUL;c

_mf Cf

� �n oNc

1� expF 0AcUL;c

_mf Cf

� �264

375

þPF 2ðasÞm;eff IðtÞ

U L;mþT aþT fi

� �

� 1� exp �N mF 0AmUL;m

_mf Cf

� �� exp �F 0AcUL;c

_mf Cf

� �� Nc

ð5bÞ

Case C: All collectors fully covered by PV module andconnected in series (Fig. 1d).

The outlet fluid temperature (TfoN) for N collector isderived as,

T fo N ¼PF 2ðasÞm;eff IðtÞ

U L;mþ T a

� �1� exp �NmF 0AU L;m

_mf Cf

� ��

þ T fi exp �N mF 0AUL;m

_mf Cf

� �ð6aÞ

The useful heat output from N identical set of collectorsis derived as,

_Qu;N ¼ AmF Rm PF 2ðasÞm;eff

1� ð1� KKÞNm

Nm KK

" #IðtÞ

"

� U L;m1� ð1� KKÞNm

N m KK

" #ðT fi � T aÞ

#ð6bÞ

Case D: Series and parallel combination of N identicalsets of panels fully covered by PV (mixed combination;Fig. 1e).

The expression for outlet fluid temperature from mixedcombination is derived as,

T foNs ¼PF 2ðasÞm;eff IðtÞ

U L;mþT a

� �1� exp �NmF 0AmU L;m

Ns _mf Cf

� ��

�1� exp �NmF 0AmUL;m

Ns _mf Cf

� �n oNs

1� exp �NmF 0AmUL;m

Ns _mf Cf

� �264

375

þT fi exp �NmF 0AU L;m

N s _mf Cf

� �� Ns

ð7aÞ

Here Nm is number of collectors covered by PV modules(connected in parallel), and NS is number of identical set ofpanels (connected in series).

The useful heat output from N identical set of panels isderived as,

_Qu;Ns ¼NmAmF m

NSPF 2ðasÞm;eff

1� ð1� KKÞNs

NsKK

" #IðtÞ

"

� U L;m1� ð1� KKÞNs

N sKK

" #ðT fi � T aÞ

#ð7bÞ

For two sets of panel each having three collectors,KK = 0.0886 and FRm = 0.8404.

2.2. Energy balance equation for storage water tank

Following Dubey and Tiwari (2008), the rate of thermalenergy available at the outlet of Nth collector is fed intoinsulated storage tank, and then the energy balance ofthe whole system will be,

_Qu;N ¼ MwCwdT w

dtþ ðUAÞtkðT w � T aÞ ð8aÞ


The above equation can be solved by assuming Tfi = Tw

due to perfectly insulating connecting pipes. Here it isassumed that there is no withdrawal of hot water fromthe storage tank. Using Eq. (1) and (8a) the tank watertemperature can be obtained as,

dT w

dtþ aT w ¼ f ðtÞ ð8bÞ

In order to obtain an approximate solution of Eq. (8b), thefollowing assumptions have been made:

(a) The time interval Dt (0 < t < Dt) is small.(b) The function f(t) is constant, i.e. f(t) = f ðtÞ for the

time interval Dt.(c) a is constant during the time, interval Dt.

where, a ¼ ½AN UL;NþðUAÞtk �MwCw

and f ðtÞ ¼ ðasÞeff ;N AN IðtÞþ½AN UL;NþðUAÞtk �T a

MwCw

The solution of Eq. (8b) can be written as

T w ¼f ðtÞ

að1� e�atÞ þ T w0e�at ð9Þ

where, Two is the temperature of storage tank water at t = 0and f ðtÞ is the average value of f(t) for the time interval be-tween 0 and t.

2.3. Instantaneous thermal efficiency

An instantaneous thermal efficiency of N flat plate col-lector can be defined as,

gi ¼_Qu;N

N c � Ac � IðtÞ

or; gi ¼ ðasÞeff ;N � U L;NT fi � T a

IðtÞ ð10Þ

2.4. Thermal energy yield

The energy analysis is based on the first law of thermo-dynamics, and the expression for total thermal yield can bedefined as,

X_Qu;total ¼

X_Qu;thermal þ

P_Qu;electrical

0:38ð11Þ

Overall thermal output from a PV/T system = thermalenergy collected by the PV/T system + (electrical output/c�power).where, c�power is the electric power generation effi-ciency of a conventional power plant for India.

This is so because electrical energy is a high-gradeform of energy which is required for operation of DCmotor. This electrical energy has been converted toequivalent thermal by using electric power generationefficiency as 0.38 for a conventional power plant, (Huanget al., 2001).

2.5. Exergy yield

The exergy analysis is based on the second law of ther-modynamics, which includes accounting the total exergyinflow, exergy outflow and exergy destructed from thesystem.X

_Exin �X

_Exout ¼X

_Exdest

or;X

_Exin �Xð _Exthermal þ _ExelectricalÞ ¼

X_Exdest ð12Þ

where,

Exergy of radiation ¼ _Exin

¼ Ac � Nc � IðtÞ

� 1� 4

3� T a

T s

� �þ 1

3� T a

T s

� �4" #

;

ð13aÞ

Petela (2003)

Thermal exergy ¼ _Exthermal ¼ _Qu 1� T a þ 273

T fo þ 273

� �ð13bÞ

Electrical exergy ¼ _Exelectrical ¼ gc � Ac � Nc � IðtÞand overall energy ¼ _Exthermal þ _Exelectrical ð13cÞ

where, Ac is area of collector and Ts is the Sun temperaturein Kelvin.

2.6. Temperature dependent electrical energy yield

Following Dubey and Tiwari (2008) the energy balanceequation for solar cells of PV module (glass–glass) is givenas

acscbcIðtÞWdx ¼ ½Ut c;aðT c � T aÞ þ hc;pðT c � T pÞ�Wdx

þ scgobcIðtÞ � Wdx ð14aÞ

From Eq. (14a), the expression for cell temperature is

T c ¼ðasÞl;eff IðtÞ þ U tc;aT a þ hc;pT p

Utc;a þ hc;pð14bÞ

An expression for temperature dependent electrical effi-ciency of a PV module (Schott, 1985; Evans, 1981) is givenby,

gc ¼ g0½1� 0:0045ðT c � 25Þ� ð15Þ

For blackened absorber plate temperature below the PVmodule

apð1� bcÞs2gIðtÞ þ hc;pðT c � T pÞ ¼ hp;f ðT p � T f Þ ð16aÞ

From Eq. (16a), the expression for plate temperature is

T p ¼ðasÞ2;eff IðtÞ þ PF 1ðasÞ1;eff IðtÞ þ UL1T a þ hp;f T f

UL1 þ hp;f

ð16bÞ

The net electrical energy yield is defined as


_Qu; net electrical ¼ Power generated by PV modules

� Power consumed by pump ð17Þor; _Qu; net electrical ¼ gc � Ac � Nc � IðtÞ � P con; pump

where P con;pump ¼ 35 W ð18Þ

In addition to the above equations the relations used fordefining the design parameters (Table 1) and configurationof PV/T collectors connected in series are given in Appendix.

Table 1Design parameters of photovoltaic thermal (PV/T) collector and storagetank.

Parameters Values

ACollector 2 m2

APV 0.165 m2

AC 1.835 m2

Cf 4190 J/kg KD 0.0125 mF’ 0.968FRc 0.95FRm 0.96h 1000 W/m2

hc,p 5.7 W/m2

hp,f 100 W/m2

PF1 0.375PF2 0.965K 204 W/m K_m 0.06 kg/sMw 200 kgUL 6 W/m2

UL1 3.56 W/m2 KULC 6 W/m2

ULm 3.44 W/m2 KUt c,a 9.5 W/m2 KUtk 4.38 W/m2 KV 1 m/sW 0.125 mac 0.9sc 0.95bc 0.83gc 0.12ap 0.8sg 0.95

100

200

300

400

500

600

700

800

900

08:00 09:00 10:00 11:00 12:00 1

Time (Ho

So

lar

inte

nsi

ty, W

/m2

I(t)

Fig. 2. Hourly variation of solar intensity and ambient

3. Results and discussion

3.1. Electrical and thermal energy yield

The variation of solar intensity and ambient tempera-ture for a typical day in the summer month (April) isshown in Fig. 2. Considering case A, Eq. (6) has been com-puted using MATLAB 7.0 software for evaluating thehourly outlet water temperature by varying the numberof collectors from four to ten at constant mass flow rate( _m = 0.04 kg/s), for a typical day in the month of Aprilfor a given design and climatic parameters (Table 1). Theresults show that the outlet water temperature increasesfrom 60 to 86 �C at 1 p.m. as the number of collectorincreases from four to ten, as shown in Fig. 3. The hourlyvariation of ambient temperature is also shown in the samefigure. Similarly, Eqs. (1) and (13c) have been used for eval-uating the useful thermal and electrical energy yield. Theresult shows that the useful thermal energy yield increasesfrom 4.17 to 8.66 kWh and electrical energy yield increasesfrom 0.052 to 0.123 kWh as the number of collectorincreases from four to ten, variations are shown in Figs.4 and 5. And similarly, Eq. (10) has been used for evaluat-ing the instantaneous efficiency. The variation of instanta-neous efficiency with number of collectors is shown inFig. 6. The energy yield per unit area is 2.66 kWh. Hourlyvariation of temperature dependent electrical efficiency byvarying the number of collectors at constant flow rate( _m = 0.04 kg/s) is shown in Fig. 7. As the number of collec-tors increases cell temperature increases due to increase inwater temperature, hence, cell efficiency decreases (0.091–0.086).

Eq. (9) has been used for evaluating the tank water tem-perature. Hourly variation of tank water temperature byvarying the number of collectors at constant mass flow rate( _m = 0.01 kg/s) is shown in Fig. 8a. This figure shows thatthe tank water temperature increases from 69.6 to 95.4 �C,as the number of collector increases from two to ten, asexpected. However, the variation of tank water tempera-

3:00 14:00 15:00 16:00 17:00

urs)

15

20

25

30

35

40

Am

bie

nt

tem

per

atu

re, o

C

Ta

temperature of a typical day in the month of April.

25

35

45

55

65

75

85

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

Time (Hour)

Ou

tlet

tem

per

atu

re, o

C

N = 4

N = 6

N = 8

N = 10

Ta

Fig. 3. Hourly variation of fluid outlet temperature by varying the number of collectors at constant flow rate ( _m = 0.04 kg/s).

1

2

3

4

5

6

7

8

9

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

Time (Hour)

Th

erm

al e

ner

gy,

kW

h

N = 4

N = 6

N = 8

N = 10

Fig. 4. Hourly variation of thermal energy yield by varying the number of collectors at constant flow rate ( _m = 0.04 kg/s).

0.01

0.04

0.07

0.10

0.13

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

Time (Hour)

Ele

ctri

cal e

ner

gy,

kW

h

N = 4

N = 6

N = 8

N = 10

Fig. 5. Hourly variation of electrical energy yield by varying the number of collectors at constant flow rate ( _m = 0.04 kg/s).

0.4

0.45

0.5

0.55

0.6

0.65

0.002 0.003 0.004 0.005 0.006 0.007 0.008

(Tfi-Ta)/I(t)

Inst

ante

neo

us

effi

cien

cy

N = 4

N = 6

N = 8

N = 10

Fig. 6. Hourly variation of instantaneous efficiency v/s (Tfi�Ta)/I(t) by varying the number of collectors at constant flow rate ( _m = 0.04 kg/s).


0.080

0.085

0.090

0.095

0.100

0.105

0.110

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

Time (Hour)

Ele

ctri

cal e

ffic

ien

cy

N = 4

N = 6

N = 8

N = 10

Fig. 7. Hourly variation of temperature dependent electrical efficiency by varying the number of collectors at constant flow rate ( _m = 0.04 kg/s).

30

40

50

60

70

80

90

100

08:00 11:00 14:00 17:00 20:00 23:00 02:00 05:00

Time (Hours)

Tan

k w

ater

tem

per

atu

re, o

C

N = 2 N = 4 N = 6 N = 8 N = 10

At, m = 0.01 kg/sec �

30

40

50

60

70

80

90

100

08:00 11:00 14:00 17:00 20:00 23:00 02:00 05:00

Time (Hours)

Tan

k w

ater

tem

per

atu

re,

oC

m = 0.005 kg/s m = 0.01 kg/s m = 0.02 kg/s

m = 0.04 kg/s m = 0.06 kg/s m= 0.08 kg/s

At, N = 4

a

b

Fig. 8. (a) Hourly variation of tank water temperature by varying the number of collectors at constant flow rate ( _m = 0.01 kg/s). (b) Hourly variation oftank water temperature by varying the mass flow rate for four collectors (N = 4).


ture with mass flow rate for fixed number of collectors(N = 4) is shown in Fig. 8b. It increases from 71.5 to97.7 �C as the mass flow rate increases from 0.005 to0.08 kg/s.

Variation of temperature difference (DT, between inletand outlet) by varying the number of collectors (2–20) andmass flow rate (0.005–0.04 kg/s) is shown in Fig. 9a.Fig. 9a shows that for a given mass flow rate ( _m = 0.02 kg/s) the temperature difference increases (71.8–108 �C) as thenumber of collector increases (2–10) and then becomes con-stant. For a lower mass flow rate constant temperature differ-ence is obtained at less number of collectors. At higher mass

flow rate curve is moving towards constant temperature dif-ference and will be obtained at large number of collectors(more than 20). It also depends upon the area of the collec-tors. This curve is useful for designing a water heating systemfor a given capacity. Mass flow rate and number of collectorscan be fixed for a desired temperature difference. Fig. 9bshows the variation of useful heat yield by varying the massflow rate (0.01–0.1 kg/s) and number of collectors (2–6).Increase in mass flow rate will increase the heat yield andthen becomes constant.

Eqs. (11) and (12) have been used for calculating theoverall thermal energy and exergy yield. Hourly variation

10

30

50

70

90

110

130

2 4 6 8 10 12 16 20

No. of collectors

Tem

per

atu

re d

iffe

ren

ce,

ΔT

m = 0.005 kg/s

m = 0.01 kg/s

m = 0.02 kg/s

m = 0.04 kg/s

4.5

6.5

8.5

10.5

12.5

14.5

16.5

0.01 0.02 0.04 0.06 0.08 0.1

Mass flow rate, kg/sec

Use

ful

hea

t g

ain

, kW

h

N = 2

N = 4

N = 6

a

b

Fig. 9. (a) Variation of temperature difference (DT, between inlet and outlet) by varying the number of collectors and mass flow rate. (b) Variation ofuseful heat gain by varying the number of collectors and mass flow rate.

1

2

3

4

5

6

7

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

Time (Hour)

Ove

rall

ther

mal

en

erg

y,

kWh

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

Ove

rall

exer

gy,

kW

hThermal energy Exergy

Fig. 10. Hourly variation of overall thermal energy and exergy at constant flow rate and for four collectors (N = 6 and _m = 0.04 kg/s).


of overall thermal energy and exergy yield at constant flowrate and collectors (N = 6 and _m = 0.04 kg/s) are shown inFig. 10. Daily overall thermal energy and exergy yieldobtained are 43.3 and 4.26 kWh, respectively.

The monthly yield in thermal energy, exergy and electri-cal energy are evaluated by considering the six collectorsconnected in series and at constant mass flow rate of0.04 kg/s. The total yield is calculated by considering thefour types of weather conditions (a, b, c, and d type) of

New Delhi as shown in Fig. 11a. The total annual yieldfor thermal energy, electrical energy and exergy are12824.2, 211 and 1273.7 kWh, respectively, which is shownin same figure. Fig. 11b shows that the total yield (energy,exergy and electrical energy) is maximum in summermonths and minimum in winter months. The variationsin yield for a, b, c, and d type weather conditions for eachmonth depends upon the number of days belongs to thattype, for example, in January month, number of ‘a’ type

50

150

250

350

450

550

650

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

Month of Year

Th

erm

al e

ner

gy

yiel

d, k

Wh

Type a

Type b

Type c

Type d

Annual = 12824.2 kWh

0

2

4

6

8

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

Month of Year

Ele

ctri

cal

ener

gy

yiel

d, k

Wh

Type a

Type b

Type c

Type d

Annual = 211 kWh

0

10

20

30

40

50

60

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DECMonth of Year

Exe

rgy

yiel

d, k

Wh

Type a

Type b

Type c

Type d

Annual = 1273.7 kWh

a

b

c

Fig. 11. (a) Monthly variation of thermal energy yield by considering a, b, c, d type weather conditions for New Delhi. (b) Monthly variation of electricalenergy yield by considering a, b, c, d type weather conditions for New Delhi. (c) Monthly variation of exergy yield by considering a, b, c, d type weatherconditions for New Delhi.


days is minimum (3 days) and ‘b’ type days is maximum(11 days) . The variation in the percentage contributionfor obtaining the total annual thermal energy yield fromfour types of weather conditions a, b, c, and d are 16.8%,25.5%, 33.1% and 24.4%, respectively, for New Delhi con-dition. This variation is nearly the same for the energy,exergy and electrical energy yield. The annual yield by con-sidering the four types of weather conditions for five differ-ent cities of India (New Delhi, Bangalore, Mumbai,Srinagar, and Jodhpur) is shown in Fig. 12. The total max-imum annual yield is obtained for the Jodhpur city andminimum for the Srinagar city. The percentage variationbetween Jodhpur and Srinagar city is 25.1%. The annualyield for New Delhi, Mumbai and Bangalore are nearlysame. The percentage variation between New Delhi, Mum-bai and Bangalore with Srinagar are 12.4%, 14.8% and9.6%, respectively. Variation of annual thermal and electri-

cal energy yield for A, B, C, and D cases (Fig. 1b–e) con-sidering six collectors and _m = 0.04 kg/s for New Delhicondition is shown in Fig. 13. Results shows that case Ais better from thermal point of view and case D is betterfrom electrical point of view. Depending upon the users’requirement different series – parallel and PV-glass combi-nations can be made.

3.2. Cost analysis of different configurations of PV/T water

collectors

The annualized uniform cost analysis in terms of Rs./kWh for all the four cases of PV/T water collectors areas follows:

Present value of the system, Tiwari (2005)

0

2000

4000

6000

8000

10000

12000

14000

Case A Case B Case C Case D

An

nu

al t

her

mal

en

erg

y yi

eld

, kW

h

0

500

1000

1500

2000

2500

3000

An

nu

al e

lect

rica

l en

erg

y yi

eld

, kW

h

Thermal energy Electrical energy

Fig. 13. Variation of annual thermal energy and electrical energy yield for A, B, C and D cases considering six collectors and _m = 0.04 kg/s for New Delhicondition.

0

300

600

900

1200

1500

1800

New Delhi Jodhpur Mumbai Bangalore Srinagar

An

nu

al o

vera

ll ex

erg

y an

d

elec

tric

al e

ner

gy

yiel

d, k

Wh

10000

11000

12000

13000

14000

15000

An

nu

al o

vera

ll th

erm

al e

ner

gy

yiel

d, k

Wh

Exergy Electrical Energy Thermal Energy

Fig. 12. Annual yield in energy, exergy and electrical energy for five different cities of India considering a, b, c, d type weather conditions.

Table 2Cost of the different components of PV/T collector.

Components Amount (Rs.)

Flat plate collector with supportstructure and without glazing

12,000/-

PV module 18,400/- per m2

Toughened glass (0.04 m) 300/- per m2

Operation, maintenance and pumpreplacement cost (R1)

1500/- per year

Total number of collectors 6Life time of system (n) 30 yearsInterest rate (i) 10%


¼ P þ R1

ð1þ iÞn � 1

ið1þ iÞn� �

� S1

ð1þ iÞn� �

where P is present cost of the system (Rs.), i is interest rate(%), n is life time of the system (years), R1 is annual oper-ation and maintenance cost (Rs.) and S is salvage value(Rs.) and annualized uniform cost of the system (Unacost),Tiwari (2005)

¼ Present value� Capital recovery factor

¼ Present value� ið1þ iÞn

ð1þ iÞn � 1

� �

The cost of the different components of PV/T collectorhas been given in Table 2. The detailed results of energyyields (kWh), total cost (Rs.), salvage value (Rs.) and annu-alized uniform cost (Rs./kWh) for all the four cases aregiven in Table 3. Table shows that the configuration of caseA is economical (Rs. 0.84/kWh) when the primary require-ment of user is thermal energy yield and case D is econom-ical (Rs. 12.8/kWh) when the primary requirement of useris electrical energy yield.

3.3. Carbon credit earned by PV/T solar water heater for

New Delhi condition considering case A

(a) Thermal Energy (Fig. 11a)

Annual thermal energy yield per annum = 12824.2 kWhThe average carbon dioxide (CO2) equivalent intensity

for electricity generation from coal is approximately0.98 kg of CO2/kWh (Watt et al., 1998). However, 40% istransmission and distribution losses and 20% loss is dueto the inefficient electric equipments used.

Then, the total figure comes to be around = 0.982+ 0.4 + 0.2 = 1.58 kg of CO2/kWh.

The carbon dioxide emission reduction = 12824.2� 10�3 � 1.58 = 20.26 tons of CO2.

If carbon dioxide emission reduction is at present beingtraded at €21/tons (European Climate Exchange, 2008),then the carbon emission reduction by water heater comes

Table 3Energy yields (kWh), total cost (Rs.), salvage value (Rs.) and annualized uniform cost (Rs./kWh) for all the four cases.

Configurations Energy yields(kWh)

Total cost of the PV/T collectors (Rs.)

Salvagevalue(Rs.)

Presentvalue(Rs.)

Annualizeduniform cost(Rs.)

Annualizeduniform cost (Rs./kWh)

Thermal Electrical Thermal Electrical

Case A: All the collectors are partially covered byPV modules

12,824 211 93,516/- 1,08,432/- 1,01,431/- 10,752/- 0.84 50.9

Case B: Identical set of collectors fully covered byPV module and fully covered by glass cover

9712 1183 1,84,200/- 1,17,149/- 1,91,625/- 20,312/- 2.09 17.2

Case C: All collectors fully covered by PV module 6602 2206 2,29,800/- 1,27,056/- 2,99,657/- 31,763/- 4.18 14.4Case D: Series and parallel combination of PV

covered collectors6285 2470 2,29,800/- 1,27,056/- 2,99,657/- 31,763/- 5.05 12.8

Total = 3,002,166 Residence

Residence-cum-other use

Shop, Office

School, College, etc.

Hotel, Lodge, Guest House, etc.

Hospital, Dispensary, etc.

Factory, Workshop, Workshed, etc.

Place of worship

77.18%

2,316,996

22.82%

Fig. 14. Percentage variation of occupied census houses in Delhi. (Source:

Census of India 2001).


to = 20.26 � 21 � 63.5 = Rs. 27019.6 per annum (where€1 = Rs. 63.5: August 20, 2008) = USD $624.0 (whereUSD $1 = Rs. 43.3: August 20, 2008).

(b) Exergy (Fig. 11c)Annual exergy yield per annum = 1273.7 kWhThe carbon dioxide emission reduction = 1273.7

� 10�3 � 1.58 = 2.01 tons of CO2.If carbon dioxide emission reduction is at present being

traded at €21/tons (European Climate Exchange, 2008),then the carbon emission reduction by water heater comesto = 2.01 � 21 � 63.5 = Rs. 2683.5 per annum (where€1 = Rs. 63.5: August 20, 2008) = USD $61.9 (whereUSD $1 = Rs. 43.3: August 20, 2008).

The percentage variation of occupied census houses inDelhi (Anon, 2008) is shown in Fig. 14. The percentageof residence houses is 77.18% (2,316,996). If we assume thatPV/T hybrid water heaters are installed on only 10% of theresidential houses then the total carbon emission reductionby theses houses comes to = 624.0 � 2,31,700 = USD$144.5 millions per annum (in terms of thermal energy),and = 61.9 � 2,31,700 = USD $14.3 millions per annum(in terms of exergy).

4. Conclusions

In this paper, the flat plate collectors partially and fullycovered by PV module are considered. A detailed analysisof energy, exergy and electrical energy are presented and it

is concluded that the partially covered collectors (case A)are beneficial in terms of annualized uniform cost (Rs./kWh) if the primary requirement of user is thermal energyyield and fully covered collectors (case D) are beneficialwhen the primary requirement is electrical energy yield.This type of configurations is very useful in the urbanand rural areas, where the hot water and electricity arerequired simultaneously. The detailed analysis of annualyield obtained in terms of thermal energy, exergy and elec-trical energy for five different cities of India (New Delhi,Bangalore, Mumbai, Srinagar, and Jodhpur) shows thatthe Jodhpur is the best place for installing such types ofwater collectors.

PV/T solar water heater is also helpful for CO2 mitiga-tion and earning the carbon credits, it has found that, ifthis type of system is installed only at 10% of the total res-idential houses in Delhi then the total carbon credit earnedby PV/T water heater in terms of thermal energy is USD$144.5 millions per annum and in terms of exergy is USD$14.3 millions per annum, respectively.

Appendix. Following Dubey and Tiwari (2008), theuseful heat output of the first collector can be given as,

_Qu;m1 ¼ Am1F Rm1ðPF 2ðasÞm1;eff IðtÞ � U L;m1ðT fi � T aÞÞ

and _Qu;c1 ¼ Am1F Rc1ððasÞc1;eff IðtÞ � UL;c1ðT fo1 � T aÞÞ.Here, T fo1 ¼ T fi þ

_Qu;m1

_mf Cf, then

_Qu;1ðmþcÞ ¼ Am1F Rm1PF 2 asð Þm1;eff ð1�Ac1F Rc1UL;c1

_mf CfÞ

�

þAc1F Rc1ðasÞc1;eff

iIðtÞ

� Am1F Rm1U L;m1 1� Ac1F Rc1UL;c1

_mf Cf

� ��þ Ac1F Rc1UL;c1�ðT fi � T aÞ

_Qu;1ðmþcÞ ¼ ðAF RðasÞÞ1IðtÞ � ðA F RULÞ1ðT fi � T aÞ ð1aÞ

where, ðAF RðasÞÞ1 ¼ ½AmF RmPF 2ðasÞm;eff ð1�AcF RcUL;c

_mf CfÞþ

AcF Rc ðasÞc;eff �and ðAF RU LÞ1 ¼ ½AmF RmU L;mð1� AcF RcUL;c

_mf CfÞ þ AcF RcUL;c�

Similarly, the useful heat output of the second collectorcan be given as,


_Qu;2ðmþcÞ ¼ ðAF RðasÞÞ2IðtÞ � ðAF RULÞ2ðT fo1 � T aÞ ð1bÞ

Here, T fo1 ¼ T fi þ_Qu;1ðmþcÞ

_mf Cf

_Qu1;2 ¼ ðAF RðasÞÞ1 1� ðAF RU LÞ2_mf Cf

� �þ ðAF RðasÞÞ2

� �IðtÞ

� ðAF RU LÞ1 1� ðA F RULÞ2_mf Cf

� ��þ AF RU LÞ2 �

ðT fi � T aÞ ð1cÞ

The expression for N identical set of collectors con-nected in series is given in thermal modeling.

The flat plate collector efficiency is given by the ratio ofactual useful heat collection rate to the useful heat collec-tion rate when the collector absorbing plate is at local fluidtemperature.

F 0 ¼ 1W�ULpDh þ W

DþðW�DÞF

where, F ¼ tanh½mðW�DÞ�=2½mðW�DÞ�=2

and m ¼ffiffiffiffiffiULKd

qNow, the flow rate factor (FR) given by

F R ¼_mCf

AcUL1� exp �AcU LF 0

_mCf

� ��

In modeling equations, we use the following relationsfor defining the design parameters, which is shown in Table1.

ðasÞm;eff ¼ PF 1ðasÞ1;eff þ ðasÞ2;eff

Here,ðasÞ1;eff ¼ ðasc � gscÞbscsg and ðasÞ2;eff ¼ apð1� bscÞs2

g

The first penalty factors is due to the glass cover of PVmodule (PF1) and the second penalty factor is due to theabsorber below PV module (PF2) which are defined as,

PF 1 ¼hc;p

U t c;a þ hc;pand PF 2 ¼

hp;f

U L1 þ hp;f

U t c;a ¼ 5:7þ 3:8V ; UL1 ¼Ut c;a � hc;p

Ut c;a þ hc;p

U Lm ¼U L1 � hp;f

U L1 þ hp;f

hc;p ¼ 5:7þ 3:8V ; V ¼ 0 m=s

The values of h, hp,f, asc, ssc, bsc, gsc, ab and sg are takenfrom Duffie and Beckman (1991), Tiwari (2005) and Tiwariand Sodha (2006b).

References

Anon. Census of India-2001. 2008. (<http://www.censusindia.gov.in/Census_Data_2001/States_at_glance/State_Links/07_del.pdf>).

Chow, T.T., 2003. Performance analysis of photovoltaic-thermal collectorby explicit dynamic model. Solar Energy 75, 143–152.

Chow, T.T., He, W., Ji, J., 2006. Hybrid photovoltaic-thermosyphonwater heating system for residential application. Solar Energy 80, 298–306.

Dincer, I., 2002. The role of exergy in energy policy making. Energy Policy30, 137–149.

Dubey, S., Tiwari, G.N., 2008. Thermal modeling of a combined system ofphotovoltaic thermal (PV/T) solar water heater. Solar Energy 82, 602–612.

Duffie, J.A., Beckman, W.A., 1991. Solar Engineering of ThermalProcesses. John Wiley and Sons, New York.

Evans, D.L., 1981. Simplified method for predicting PV array output.Solar Energy 27, 555–560.

Florschuetz, L.W., 1979. Extension of the Hottel–Whillier model to theanalysis of combined photovoltaic/thermal flat plate collectors. SolarEnergy 22, 361–366.

Hendrie, S.D., 1979. Evaluation of combined photovoltaic/thermalcollectors. In: Proc. ISES Int. Congress, Atlanta, USA, vol. 3, 1865–1869.

Huang, B.J., Lin, T.H., Hung, W.C., Sun, F.S., 2001. Performanceevaluation of solar photovoltaic/thermal systems. Solar Energy 70 (5),443–448.

Ji, J., Lu, J.P., Chow, T.T., He, W., Pei, G., 2007. A sensitivity study of ahybrid photovoltaic/thermal water-heating system with natural circu-lation. Applied Energy 84, 222–237.

Kalogirou, S.A., 2001. Use of TRYNSYS for modeling and simulation ofa hybrid PV-thermal solar system for Cyprus. Renewable Energy 23,247–260.

Kalshian, R., 2006. Energy versus emissions: the big challenge of the newmillennium. By Info Change News and Features. (<www.infochange-india.org/agenda5_01.jsp>).

Kern Jr., E.C., Russell, M.C., 1978. Combined photovoltaic and thermalhybrid collector systems. In: Proc. 13th IEEE Photovoltaic Specialists,Washington DC, USA, 1153–1157.

Lalovic, B., 1986. A hybrid amorphous silicon photovoltaic and thermalsolar collector. Solar Cells 19, 131–138.

Petela, R., 2003. Exergy of undiluted thermal radiation. Solar Energy 86,241–247.

Prakash, J., 1994. Transient analysis of a photovoltaic-thermal solarcollector for co-generation of electricity and hot air/water. EnergyConversion and Management 35, 967–972.

Raghuraman, P., 1981. Analytical predictions of liquid and air photovol-taic/thermal flat plate collector performance. Journal of Solar EnergyEngineering 103, 291–298.

Robles-Ocampo, B., Ruız-Vasquez, E., Canseco-Sanchez, H., Cornejo-Meza, R.C., Tra paga-Martınez, G., Garcıa-Rodriguez, F.J., Gonza-lez-Hernandeze, J., Vorobiev, Y.V., 2007. Photovoltaic/thermal solarhybrid system with bifacial PV module and transparent plane collector.Solar Energy Materials and Solar Cells 91, 1966–1971.

Schott, T., 1985. Operational temperatures of PV modules. In: Proceed-ings of 6th PV Solar Energy Conference, 392–396.

Tiwari, G.N., 2005. Solar Energy: Fundamentals, Design, Modeling andApplications. Narosa Publishing House, New Delhi.

Tiwari, A., Sodha, M.S., 2006a. Performance evaluation of hybrid PV/thermal water/air heating system: a parametric study. RenewableEnergy 31 (15), 2460–2474.

Tiwari, A., Sodha, M.S., 2006b. Performance evaluation of solar PV/Tsystem: an experimental validation. Solar Energy 80 (7), 751–759.

Tiwari, A., Sodha, M.S., Chandra, A., Joshi, J.C., 2006. Performanceevaluation of photovoltaic thermal solar air collector for compositeclimate of India. Solar Energy Materials and Solar Cells 90 (2), 175–189.

Watt, M., Jhonson, A., Ellis, M., Quthred, N., 1998. Life cycle airemission from PV powered systems. Progress in Photovoltaic ResearchApplication 6 (2), 127–136.

Zondag, H.A., 2008. Flat-plate PV-Thermal collectors and systems areview. Renewable and Sustainable Energy Reviews 12 (4), 891–959.

Zondag, H.A., de Vries, D.W., van Helden, W.G.J., van Zolengen, R.J.C.,Steenhoven, A.A., 2002. The thermal and electrical yield of a PV-thermal collector. Solar Energy 72 (2), 113–128.

Zondag, H.A., de Vries, D.W., van Helden, W.G.J., van Zolengen, R.J.C.,Steenhoven, A.A., 2003. The yield of different combined PV-thermalcollector designs. Solar Energy 74 (3), 253–269.

http://www.censusindia.gov.in/Census_Data_2001/States_at_glance/State_Links/07_del.pdf

http://www.censusindia.gov.in/Census_Data_2001/States_at_glance/State_Links/07_del.pdf

http://www.infochangeindia.org/agenda5_01.jsp

http://www.infochangeindia.org/agenda5_01.jsp

Documents

Analysis of PV/T flat plate water collectors connected in series