2011 - heat pipe photovoltaic-thermal (pvt) hybrid system and its performance evaluation

Energy and Buildings 43 (2011) 35583567

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Energy and Buildings

j our na l ho me p age: www.elsev ier .com

A heat d sevaluat

Shuang-Y -Hua Key Laborato inistrb College of Pow

a r t i c l

Article history:Received 17 MReceived in re15 SeptemberAccepted 18 S

Keywords:Heat pipePhotovoltaic/tThermalelectrical conversionExergy efciencyPerformance evaluationTheoretical analysis

rmal maincells hermipe totranst (Nnvereleva

rate, packing factor of solar cell and heat loss coefcient has been carried out on the basis of the rstand second laws of thermodynamics. Results show that the overall thermal, electrical and exergy ef-ciencies of the heat pipe PV/T hybrid system corresponding to 63.65%, 8.45% and 10.26%, respectivelycan be achieved under the operating conditions presented in this paper. The varying range of operatingtemperature for solar cell on the absorber plate is less than 2.5 C. The heat pipe PV/T hybrid system is

1. Introdu

With thbuilding intconsidered has the potethe urban eelectrical enseparated Pthe effectivsystem [2]. of the demathe use of c

The maimany PV/T waste heattions. Rece[48] availaresults, one

CorresponChongqing 40

E-mail add

0378-7788/$ doi:10.1016/j.viable and exhibits the potential and competitiveness over the other conventional BIPV/T systems. 2011 Elsevier B.V. All rights reserved.

ction

e development of energy-saving building technology,egrated photovoltaic/thermal (BIPV/T) system has beenas an attractive technology for building integration andntial to become a major source of renewable energy innvironment [1]. BIPV/T system produces thermal andergy, which has higher overall output than that of twoV and solar thermal systems and potentially reducese system costs in comparison with the stand-alone PVBesides, the merit of a PV/T system lies in the reductionnds on physical space and the equipment cost throughommon frames and brackets [3].n part of a BIPVT system is PV/T collector. Up to date,systems (collectors) have been designed to remove the

and used as a source of energy for building applica-ntly, there are many rigorous review articles such asble that study the systems or market. From the review

can conclude that a signicant amount of research and

ding author at: College of Power Engineering, Chongqing University,0044, China. Tel.: +86 013657693789; fax: +86 23 65102473.ress: [email protected] (S.-Y. Wu).

development work on the PV/T technology has been conducted inthe last more than 30 years with a gradual increase in the levelof activities. Performance of hybrid PV/T systems has been studiedboth experimentally and numerically using either steady state ordynamic models. Nayak and Tiwari [9] predicted the performanceof a PV/T collector integrated with a greenhouse by means of energyand exergy analysis and made an attempt to validate the developedthermal model with experimental values for a typical day for clearday conditions. Dubey et al. [10] derived the performance analyticalexpressions for N hybrid photovoltaic/thermal (PV/T) air collectorsconnected in series. And the detailed performance evaluation ofenergy, exergy and electrical energy by varying the number of col-lectors and air velocity considering four weather conditions andve different cities of India has been carried out by consideringtwo different cases. Sarhaddi et al. [11] gave a detailed energy andexergy analysis to calculate the thermal and electrical parameters,exergy components and exergy efciency of a typical PV/T air col-lector, and improved the thermal model and electrical model of aPV/T air collector. In addition, a modied equation for the exergyefciency of a PV/T air collector was obtained in terms of designand climatic parameters. Corbin and Zhai [12] developed an exper-imentally validated computational uid dynamics (CFD) model fora novel BIPV/T collector. Besides, they have investigated the effectof active heat recovery by a liquid cooled heat absorber on the

see front matter 2011 Elsevier B.V. All rights reserved.enbuild.2011.09.017pipe photovoltaic/thermal (PV/T) hybriion

ing Wua,b,, Qiao-Ling Zhanga,b, Lan Xiaoa,b, Fengry of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Mer Engineering, Chongqing University, Chongqing 400044, China

e i n f o

ay 2011vised form

2011eptember 2011

hermal (PV/T) system

a b s t r a c t

Building-integrated photovoltaic/thenology for building integration. The the non-uniform cooling of solar PV veniently, a heat pipe photovoltaic/tdescribed by selecting a wick heat pA theoretical model in terms of heat effectivenessnumber of transfer unidict the overall thermalelectrical coparametric investigation by varying r/ locate /enbui ld

ystem and its performance

a Guoa,b

y of Education, Chongqing 400044, China

(BIPV/T) system has been considered as an attractive tech- part of a BIPV/T system is PV/T collector. In order to solveand control the operating temperature of solar PV cells con-al (PV/T) hybrid system (collector) has been proposed and

absorb isothermally the excessive heat from solar PV cells.fer process analysis in PV module panel and introducing theTU) method in heat exchanger design was developed to pre-sion performances of the heat pipe PV/T system. A detailednt parameters, i.e., inlet water temperature, water mass ow

S.-Y. Wu et al. / Energy and Buildings 43 (2011) 35583567 3559

Nomenclature

Ac heat exchange area between heated uid and the

AcellAcollCpD ExsolExthGIoLeLcN NTUNu Pr Re rcS TaTbTcellThpTiT0TsunTrefUcULW

Greek sym pvtcelleref

t

performancbetween PV

There armany otherrative collecuid ow, sformed a setypes of PVguration a

For the ewith rows opart of systally ows bheat by concooling (hecooling (heing the owof PV panel

the complexity of the internal heat transfer (there is heat con-duction, convection and radiation heat transfer) in PV/T systems,the temperature of solar PV panel should not be uniform, i.e. thetemperature of solar PV panel increases along the uid owing

on, levorabhiles, it

heat For o

andr, it tpe. Sf solsionr PV pipeg wh

dynaeat-.erencondenser section of heat pipe, m2

solar cell surface area, m2

PV panel area, m2

constant pressure specic heat capacity, J kg1 K1

heat pipe diameter, mexergy of heat radiation, Wthermal exergy, Wmass ow rate, kg/ssolar intensity, W/mlength of heat pipe evaporator section, mlength of heat pipe condenser section, mrow number of solar cellnumber of heat transfer unitNusselt numberPrandtl numberReynolds numberpacking factorabsorbed solar energy intensity, W/m

directiis unfameanwPV cellsons, apaper.manceanotheheat piature oconverof solaa heat freezintem. Aof the hstudies

Diff

ambient temperature, Cwall temperature of PV panel region, Csolar cell temperature, Cworking uid temperature of heat pipe, Cheated uid inlet temperature, Cheated uid outlet temperature, Csun temperature, Kreference operating temperature, Cheat convection coefcient, W m2 K1

overall heat loss coefcient, W m2 K1

pitch distance between the heat pipes, m

bolsabsorptivityabsorber plate thickness, mthermal conductivity, W m1 K1

transmissivity of glass cover; local time, hheat transfer effectivenessexergy efciencyefciency of solar cell photovoltaic transformationelectrical efciencycell efciency at the reference operating tempera-ture Trefthermal efciency

e of a BIPV/T collector and established the correlations performance and heat recovery.e alternative approaches in PV/T integration. Amongs, there can be selections among air, water or evapo-tors, at-plate or concentrator types, natural or forcedtandalone or building-integrated features, etc., whichries of the conventional PV/T systems. In general, two/T system have been considered, i.e. tube-in-plate con-nd parallel plate conguration [4].xisting PV/T systems, a cavity created by a solar PV panelf PV module on it and a glass cover is one of an importantem components. The cooling (heated) medium gener-eneath the solar PV panel and absorbs the excessivevection. Either air or water is usually selected as theated) medium. However, it should be noted that theated) medium absorbs heat from solar PV panels dur-

process, which may cause the temperature variation. Due to the distinctive feature of solar radiation and

rows and hsections inwith heat ping same dintroducedtransfer moestablishedparametersbe discussemation on system.

2. System

A wick its principlethe design (7#), glass space. All srectangulartor section material (3coated arouthe coolingof the wickradial ns pipe adiabasections, arals (8#). Thcooling (heows into/o(heated) uuid inlet/o

The wickThe solar incover, glassmodules anabsorb somon the otheheat loss bPV panel is to the high PV panel anading to non-uniform cooling of solar PV cells, whichle of photoelectric conversion efciency enhancement;, owing to the inhomogeneity of the temperature of solaris inconvenient for temperature control. For these rea-

pipe PV/T hybrid system has been put forward in thisne thing, it can make full use of the isothermal perfor-

adjustable operating temperature of the heat pipe; forakes advantage of efcient heat transfer performance ofuch a PV/T hybrid system not only ensures the temper-ar PV panel uniform thus improving the photoelectric

performance, but also makes the operating temperaturecells adjustable. Recently, Pei et al. [13] have designed

PV/T system that can be used in cold regions withouten compared with the traditional water-type PV/T sys-mic model was developed to predict the performancespipe PV/T system through simulation and experimental

t from the heat pipes stalled between the PV moduleaving different diameters of evaporator and condenser

[13], in this paper, a heat pipe PV/T hybrid systemipe arranged beneath the PV module rows and hav-

iameters of evaporator and condenser sections will be. Meantime, unlike the method employed in [13], a heatdel for performance evaluation of PV/T system will be

through theoretical analysis. Also, impact of relevant on the thermalelectrical conversion performance willd in detail. The present work contributes further infor-the innovation and performance evaluation of BIPV/T

descriptions

heat pipe PV/T system is proposed in this paper, and diagram is shown in Fig. 1. The main information onand construction is summarized here. The glass coverside seal (6#) and solar PV panel (2#) form a closedolar PV modules (1#) are laid on the solar PV panel in

arrangement; below which the wick heat pipe evapora-is closely attached using excellent thermal conductivity#). Insulation materials in evaporator section (5#) arend the wick heat pipe (4#) to minimize heat loss. If

(heated) medium is gas such as air, the outer surface heat pipe condenser section can be equipped with(11#) for heat transfer enhancement. The wick heattic section is set between the evaporator and condenseround which is also furnished with insulation materi-e wick heat pipe condenser section is arranged in theated) uid channel (12#). The cooling (heated) uidut of the cooling (heated) uid channel through coolingid inlet/outlet header (13#, 10#) and cooling (heated)utlet pipe (14#, 9#).

heat pipe PV/T system works in the following manner.sulation enters into the closed space composed by glass

side seal and solar PV panel, and heat up the solar PVd the solar PV panel. On the one hand, solar PV modulese of the solar energy and transform it into electricity;r hand, the solar PV panel is heated along with somey the way of convection and radiation. Once the solarheated, most of the energy is transferred by conductionthermal conductivity material which connects the solard wick heat pipe evaporator section, and then the wall

3560 S.-Y. Wu et al. / Energy and Buildings 43 (2011) 35583567

Fig. 1. The sch(1) Solar PV mheat pipe; (5) cover; (8) insupipe; (10) cooluid channel; inlet pipe.

of wick healiquid medithe wall of moves towaout the evathe evaporatributed wimean time,uid channabsorbing ttion by forc(heated) ucertain tem

3. Theoret

3.1. Theore

The calcshown in Fof an absorbackside ofand a thermsurface areanamed as pintensity is is S (withou

empe

sorpel, e wiwickith lld. TFig. 3. T

is abPV panthe casof the tions wmanifoeme of wick heat pipe photovoltaicthermal (PVT) hybrid system.odules; (2) solar PV panel; (3) thermal conductivity material; (4) wickinsulation material in evaporator section; (6) glass side seal; (7) glasslation material in adiabatic section; (9) cooling (heated) uid outleting (heated) uid outlet header; (11) radial ns; (12) cooling (heated)(13) cooling (heated) uid inlet header; and (14) cooling (heated) uid

t pipe evaporator section. Inside the wick heat pipe, theum is vaporized by the intense heat transferred fromevaporator section by convection. The generated vaporrd the wick heat pipe condenser section, where it givesporation latent heat. The resulting liquid is returned totor passively by gravity and/or capillary forces in dis-ck, and re-absorbs heat for repeating evaporation. In the

the cooling (heated) uid ows into the cooling (heated)el through cooling (heated) uid inlet header and pipe,he heat released from the wick heat pipe condenser sec-ed convection, and nally ows out through the coolingid outlet header and pipe when the outow reaches aperature.

ical model and its derivation

tical model

ulation model of a heat pipe PV/T hybrid system isig. 2. N row of solar cells are attached to top surfaceber plate with thickness , forming the PV panel. The

the PV panel is soldered with N row of wick heat pipesal insulation layer is added underneath. Acell is solar cell

and the ratio of cell area to PV panel area, which is alsoacking factor, is rc. The ambient temperature is Ta. SolarIo, while the solar energy intensity absorbed by PV panelt glass cover: S = Io; with glass cover: S = Io(), where

pipe diameper, and thepanel are atemperaturAN BN is arespectivelsolved. TheTcell,2, Tcell,3well conneTcell,2 Tb2,

As showthe condencrosswise mcondenser the secondcollector is

3.2. Theore

In orderPV panel asmade:

The syste Because tthe templigible.

Considerithe tempeof heat pi

There is apanel andlling ma

As describthe PV paFig. 2. The calculation model of heat pipe PV/T system.

rature variation of heated uid in the condenser section of heat pipe.

tivity of solar cell and is assumed to be equal to that of is transmissivity of glass cover. This study will discussth glass cover). The evaporator sections with length Le

heat pipes are welded to PV panel. The condenser sec-ength Lc of the wick heat pipes are immersed in a coolinghe pitch distance between the heat pipes is W, the heatter is D. The PV panel and heat pipe are made of cop-

thermal conductivity is . The left and right sides of PVdiabatic walls, which contain point B0 and A0. The walle of each PV panel region A1 B1, A2 B2, A3 B3, . . .. . .,ssumed to be uniform, which are Tb1, Tb2, Tb3, . . .. . ., TbN,y. All these temperatures are unknown and require to be

temperature of each row of solar cell, which are Tcell,1,, . . .. . . and Tcell,N, is also uniform. If the solar cells arected to the PV panel, the assumption that Tcell,1 Tb1,

Tcell,3 Tb3, . . .. . . and Tcell,N TbN is reasonable.n in Fig. 3, the heated uid ows in succession throughser sections from the 1st heat pipe to the Nth one in aanner. The heated uid outlet temperature of the rst

section equals to the heated uid inlet temperature of

one, and so on. The heated uid inlet temperature ofTi, which is a known quantity.

tical derivation

to write the energy balance equation for each region of shown in Fig. 2, the following assumptions have been

m is in quasi-steady-state condition.he thickness of PV panel is much less than the width,erature variation along the thickness of PV panel is neg-

ng the uniformity of heat pipe operating temperature,rature gradient of the PV panel along the axial directionpe is negligible.

neglected thermal conduction resistance between PV heat pipe wall due to a good thermal conductivity ofterials.ed in [14], the overall heat loss coefcient UL betweennel and the ambient is assumed to be constant.


The PV pais neglectadiabatic.

In view the regionssimilar to tsolar cell su

3.2.1. The rThe heat

considered n with widwith width of PV panel

The net

Qnet = qnetdwhere qnet iloss coefci

Accordintransfer dirthe elemen

Qx + Qnet =Based on

d2T

dx2+ S U

The gene

T = C0,1 exp

where C0,1The bou

dT

dx

x=0

= 0

Therefore

C0,1 = C0,2

where H = WSubstitu

T = ch(mxch(mH/

The heacontains po

QA1 = L

where F is tgular prol

3.2.2. The region B1 A2With the heated uid ows in succession through the condenser

of the 1st heat pipe to the Nth one, the temperature gradually goesup. Accordingly, the working uid temperature of heat pipe rises

m Th, B3 e heasiderm ofthe s

at xnts o

Tb1

,2 =

heat

L

the o B1 hat c

L

mL

The r gain

Ace

usef

GCp

ere Gser

cont hea

elec

ce

Acell,w ofotoveren

ener

QA1

n theFig. 4. The element control volume in solar PV panel.

nel is well insulated and the heat loss from insulationed. In the meantime, both end sides of the PV panel are

of the above assumptions, the heat transfer process in B0 A1, B1 A2, B2 A3, . . .. . ., BN A0 of PV panel ishe heat conduction problem of a n. In addition, therface area Acell is regarded as DLe for simplicitys sake.

egion B0 A1 transfer process in the region B0 A1 of PV panel can beas one-dimensional steady-state heat conduction of ath of (W D)/2. As shown in Fig. 4, a differential elementof dx is taken to analyze the energy balance. The length

along the axial direction of heat pipe is set to be 1.input heat rate from the solar irradiation Qnet is

x = [S UL(T Ta)]dx (1)s the net input heat ux; UL is the PV panel overall heatent.g to heat transfer analysis of B0 A1 region, the heatection is parallel to +x axes, thus the energy balance oft control volume in B0 A1 region is

Qx+dx (2)

the Fouriers law of heat conduction, Eq. (2) becomes

L(T Ta)

= 0 (3)

ral solution of Eq. (3) is:

(mx) + C0,2 exp (mx) +S

UL+ Ta (4)

and C0,2 are integration constants, m =

UL/.ndary conditions (the point B0 is located at x = 0) are:

, Tx=(WD)/2 = Tb1 (5)

= Tb1 (S/UL + Ta)2ch(mH/2)

(6)

D = (1 rc)W.ting Eq. (6) into (4), Eq. (4) becomes:

)2)

[Tb1

(S

UL+ Ta

)]+ S

UL+ Ta (7)

up, froB2 A3ner, thbe conprobletion is locatedconsta

C1,1 =

C1

Theis:

QB1 =

On regionplane t

QA2 =

=

3.2.3. The

QA1B1 =The

Qhp1 =wh

condenuid atthe rs

Theis [15]

Ecell,1 =whererst rocell phthe ref

Thecell isQA1 +

The(1)t ow rate, which enters into the vertical plane thatint A1 by conduction is:

edT

dx

x=H/2

= 12

HLeF[S UL(Tb1 Ta)] (8)

he standard n efciency for straight ns with rectan-e, and obtained from F = th(mH/2)

mH/2 .

2HLeF[S

+ mLe(

+ Acell,1S

Eq. (16) p1 to Thpn. Heat ow directions of the regions B1 A2, A4, . . .. . ., BN1 AN are reverse to +x axes. In like man-t transfer process in the region B1 A2 of PV panel caned as one dimension steady-state thermal conduction

a n with width of (W D). Thermal conduction equa-ame as Eq. (3), the boundary conditions (the point B1 is

= 0) are x = 0, T = Tb1; x = W D, T = Tb2. The integrationf Eq. (4) are

C1,2 (

S

UL+ Ta

);

[Tb1 (S/UL + Ta)] exp (mH)2sh(mH)

[Tb2 (S/UL + Ta)]2sh(mH)

(9)

ow rate into the vertical plane that contains point B1

edT

dx

x=0

= mLe(

Tb1 2C1,2 S

UL Ta

)(10)

ther hand, according to temperature distribution in theA2 of PV panel, the heat ow rate out of the verticalontains point A2 is

edT

dx

x=WD

e[C1,1 exp (mH) C1,2 exp (mH)] (11)

egion A1 B1 of the rst row of solar celled solar energy in the region A1 B1 of solar cell is:

ll,1[S UL(Tb1 Ta)] (12)ul energy obtained by the rst heat pipe is:

(T01 Ti) (13) is mass ow rate of heated uid owing through theof heat pipe; Cp is the specic heat capacity of heatedstant pressure; T01 is heated uid outlet temperature oft pipe.tricity energy transformed by the rst row of solar cell

ll,1Acell,1S = Acell,1Io()ref[1 T (Tcell,1 Tref)] (14)

1 is the rst row of solar cell surface areas; Tcell,1 is the solar cell temperature; cell,1 is the efciency of solaroltaic transformation; and ref is the cell efciency atce operating temperature Tref.gy balance in the region A1 B1 of the rst row of solar

B1 +QB1 = Qhp1 + Ecell,1 (15)

following equation can be obtained,

UL(Tb1 Ta)] + Acell,1[S UL(Tb1 Ta)]

Tb1 2C1,2 S

UL Ta

)= GCP(T01 Ti)

ref[1 T (Tcell,1 Tref)] (16)

contains unknown temperature Tb1, Tb2, T01.


3.2.4. The region An Bn of the nth (n = 2, 3, 4, . . .. . ., N 1) rowof solar cell

For the region An Bn of the nth (n = 2, 3, 4, . . .. . ., N 1) row ofsolar cell, the heat transfer process of each region is the same. Likethe analysis

mLe

(Tbn

= GCP(T0n Cn1,2 e

where

C(n1),1 = T

Cn1,2 =[T

Cn,2 =[Tbn

n (2, 3, It should

perature ofpanel; Tb(n+T0(n-1) is heis heated contains un

3.2.5. The rSince th

of solar cellsolar cell exfor brevitysboundary c

Tx=0 = TbN

Thereforare:

CN,1 =TbN1 +

The heapoint BN is:

QBN = L

The enerow of solarQBN + QAN

The usef

QhpN = GCpCombini

mLe

(2CN

= GCp(T0N CN1,2 eIt is obvi

TbN, T0(N1)

3.2.6. The relation T0n with TbnTake the rst heat pipe for an example, the heat transfer effec-

tiveness 1 and the number of heat transfer unit NTUc1 are denedas

ex

Uc,01e co26Re

uidm th

i + [ Tc,01ser t heaient e of le phore, E

i + [ the n

0(n1

ex

assuUc,0n

= m Eq

i + Tb2 +

Ti(1 + . . .

n (ordinqs. (1

unknainedre Tb

A1 we cipe T/T sy

Cp(T0IoA

Acoll elec

Nn=1IoA

reovenentt esshouhe amis no of the region A1 B1, we also have

2Cn,2 S

UL Ta

)+ Acell,n[S UL(Tbn Ta)]

T0(n1)) + mLe[Cn1,1 exp (mH)xp (mH)] + Acell,nSref[1 T (Tcell,n Tref)] (17)

b(n1) C(n1),2 (

S

UL+ Ta

)(17a)

b(n1) (S/UL + Ta)] exp (mH)2sh(mH)

[Tbn (S/UL + Ta)]2sh(mH)

(17b)

(S/UL + Ta)] exp (mH)2sh(mH)

[Tb(n+1) (S/UL + Ta)]2sh(mH)

(17c)

4, 5, . . . . . . , N 1). be noted that Tb(n1) is the region An1 Bn1 tem-

PV panel; Tbn is the region An Bn temperature of PV1) is the region An+1 Bn+1 temperature of PV panel;ated uid inlet temperature of the nth heat pipe; T0nuid outlet temperature of the nth heat pipe. Eq. (17)known temperature Tb(n1), Tbn, Tb(n+1), T0(n1), T0n.

egion AN BN of the Nth row of solar celle analysis method in the region AN BN of the Nth row

is almost the same as region A1 B1 of the rst row ofcept for different boundary conditions, thus neglected

sake. The right side surface of PV panel is adiabatic. Theonditions (the point BN is located at x = 0) are:

;dT

dx

x=(WD)/2

= 0 (18)

e, the integration constants of Eq. (4) general solution

(S/UL + Ta) exp (mH)

; CN,2 = TbN CN,1 (

S

UL+ Ta

)(19)

t ow rate enters into the vertical plane that contains

edT

dx

x=0

= mLe(CN,1 CN,2) (20)

rgy balance equation for the region AN BN of the Nth cell is:

BN =QAN + QhpN + Ecell,N (21)

ul energy gained by the Nth heat pipe is:

(T0N T0(N1)) (22)ng Eqs. (20)(22) leads to:

,1 TbN +S

UL+ Ta

)+ Acell,N[S UL(TbN Ta)]

T0(N1)) + mLe[CN1,1 exp (mH)xp (mH)] + Acell,NSref[1 T (Tcell,N Tref)] (23)ous that Eq. (23) contains unknown temperature Tb(N1),and T0N.

1 = 1

whereand thNu = 0.heated

Fro

T01 = Twherecondenthe rscoefcferencof singTheref

T01 = TFor

T0n = TAgain,

n = 1

It isUc,01 =

1 = 2Fro

T01 = TT02 =

T0n =

whereAcc

that Etain Nbe obtperaturegionwhile, heat pthe PV

t =G

whereThe

e =

Mocompoare notypes sunit, tworld p (NTUc1); NTUc1 =Ac1Uc,01

GCP(24)

is heat convection coefcient between heated uidndenser section of heat pipe, it can be obtained from0.6Pr1/3 [16]; Ac1 is the heat exchange area between

and the condenser section of heat pipe.e denition 1 = (T01 Ti)/(Tc,01 Ti), we have1 exp (NTUc1)](Tc,01 Ti) (25)is the working uid temperature of the rst heat pipesection and equal to the working uid temperature oft pipe Thp1. Considering that phase change heat transferof heat pipe is rather high, and the temperature dif-phase change heat transfer is much smaller than thatase convection heat transfer, namely, Tc,01 = Thp1 Tb1.q. (25) may be rearranged in the following form:

1 exp (NTUc1)](Tb1 Ti) (26)th heat pipe (n = 2, 3, 4, . . ., N),

) + [1 exp (NTUcn)](Tbn T0(n1)) (27)

p (NTUcn); NTUcn =AcnUc,0n

GCP(28)

med that each heat pipe is the same, namely Acn = Ac1,, we have

3 = 4 = . . . = n = (29). (26) to (29), the following equations are obtained:

(Tb1 Ti) = Tb1 + (1 )Ti (30) (1 )Tb1 + (1 )2Ti (31)

)n + (1 )n1Tb1 + (1 )n2Tb2 + (1 )Tb(n1) + Tbn (32)2, 3, 4, . . . . . . , N).g to the analysis of the relation T0n with Tbn, it is shown6), (17) and (23) consist of N equations which con-own quantities. Obviously, closed form solutions can

from these equations. Namely, we can gain the tem-1 (Tcell,1), Tb2 (Tcell,2), Tb3 (Tcell,3), . . .. . ., TbN (Tcell,N) of

B1, A2 B2, A3 B3,. . .. . ., AN BN of PV panel. Mean-an nd out the heated uid outlet temperature of each01, T02, T03, . . .. . ., T0N. Further, the thermal efciency ofstem t can be calculated as

N Ti)coll

(33)

is area of PV panel, Acoll = NWLe.trical efciency of PV/T system e can be expressed as

Ecell,n

coll=N

n=1cell,nSAcell,nIoAcoll

=N

n=1(cell,nrc) (34)

r, the energy of a PV/T system consists of two majors namely electrical energy and thermal energy whichentially the same in nature, even if these two energyld be of the same quantity and measured by the sameount of work transformed from them to the outsidet the same, taking the fact that work is a process of


energy transfer during which the energy does not degrade [17].Thermal energy (low grade) cannot produce work until a tem-perature difference exists between a heat source and a heat sink,whereas electrical energy (high grade) can completely transforminto work law approahybrid enerthe second evaluation

In evaluaexergy analation have Based on thresult that tefciency, i

Exsol =(1

where the sThe ther

hybrid syst

Exth = GCp[

Thus, thpressure dr

pvt =Exth +

4. Validati

In orderof the expea heat pipebetween thformance issolar collecPV/T hybridpresented mhas the samas an objectconditions, formance arcalculated rpercentageequation [2

RMS =

where n is tXcal,i denote

Fig. 5 sthe experiG = 0.0458 kthe calculatperature arespectivelylet temperasolar intensis observedand experimthermal efminor relat

Accordinfound in th

he comparison between the theoretical and experimental values of thermalance for heat pipe at plate solar collector in [20] at G = 0.0458 kg/s.

outlet temperature. This indicates that the theoreticald proposed in this paper is effective, and can be used in theance evaluation of heat pipe PV/T hybrid system.

ults and discussion

his study, the following parameters have been chosen forar cells: ref = 0.12, T = 0.0045 C1, Tref = 25 C. Besides, theration parameters of heat pipe PV/T system are taken as fol-he heat pipe was made of copper with total length of 0.92 mter diameter D of 0.122 m. The length of evaporator section.75 m and the length of condenser section Lc is 0.1 m. Theistance between the heat pipes W is 0.135 m. The glass coveras sized in 0.76 m 1.9 m 0.004 m, of which the transmit-

is 0.9. The PV panel of 1.89 m 0.75 m was made of copperas coated with anodic alumina spectral selective absorp-aterial of which the absorptivity is 0.94. The condenser

of heat pipe was immersed in the heated uid channel 0.288 m 0.1 m. The heated uid, namely water orderlyver the condenser section of the heat pipe in a crosswiser. Initial solar cell temperature distributions were assumedpanel, then the GaussSeidel iteration method was adoptede the above mentioned N equations, and the calculation

are described as follows. 7 shows hourly variations of ambient temperature Ta, solaron intensity Io and the outlet water temperature T0N for5 kg/s, rc = 0.9 and Ti = 37 C. It can be seen that the outletirrespective of the environment [3]. Hence, the rstch may not be comprehensive in the assessment of thegy performance. At this end, the exergy efciency fromlaw perspective offers a qualitative and standardizedof the hybrid performance.ting the performance of solar energy system using theysis, different methods to determine the exergy of radi-been put forward in a period of around 20 years [18].e analysis of heat engine, Jeter [19] has come to thehe exergy of heat radiation is determined by the Carnot.e.

TaTsun

)IoAcoll (35)

un temperature Tsun is typically regarded as 6000 K [8].mal exergy gained by the water ow through PV/Tem is evaluated by

T0N Ti Ta ln(

T0NTi

)](36)

e exergy efciency of PV/T hybrid system neglectingop exergy loss is determined asN

n=1Ecell,nExsol

(37)

on of theoretical model

to validate the present model and in view of the lackrimental data of heat pipe PV/T hybrid system, taking

at plate solar collector for an example, a comparisone theoretical and experimental results of thermal per-

given. It is worth noting that, the heat pipe at platetor has no solar cells in comparison with the heat pipe

system, and solar cell-related terms disappear in theodel. Herein, a heat pipe at plate solar collector whiche structure and operation parameters as [20] is selected

(the number of heat pipe is 14). Under certain weatherthe theoretical and experimental results of thermal per-e demonstrated in Figs. 5 and 6. In order to compare theesults with the experimental values, a root mean square

deviation (RMS) has been evaluated by the following1,22].

[100 (Xexp,i Xcal,i)/Xexp,i]2n

(38)

he number of the experiments implemented; Xexp,i and the experimental and calculated values, respectively.hows the theoretical water outlet temperatures VSmental values in [20] when the water ow rateg/s. As can be seen, there is a good agreement betweened and experimental values of the water outlet tem-nd thermal efciency with RMS = 0.24% and 4.33%,. Identically, Fig. 6 compares the theoretical water out-ture with the experimental values in [20] at anotherity when the water ow rate G = 0.0125 kg/s. Again, it

that there is a fair agreement between the calculatedental values of water outlet temperature and collectorciency with RMS = 0.64% and 3.89%, respectively, i.e.,ive deviation exists between the two.g to the above analysis, good agreements have beene theoretical and experimental results, especially the

Fig. 5. Tperform

water methoperform

5. Res

In tthe solcongulows: Tand ouLe is 0pitch dplate wtance and wtion msectionof 1.9 mows omannefor PV to solvresults

Fig.radiatiG = 0.0


Fig. 6. The comperformance f

water tempmum of 40.

Fig. 8 githe solar ceFig. 7, whewith increatime of 10:0row numbe48.0449.7the varying

Fig. 7. Hourlyoutlet water te

Fig. 8. The variation of solar cell temperature with row number at different localtimes.

indicates that the heat pipe cooling can make the temperature ofsolar cells on the absorber plate uniform. In addition, the solar celltemperature reaches a minimum at 15:00 and a maximum at 11:00.These obse

on in. 9 aon s

efes wtempr, it creargy es frradiatiFigs

ture Tiexergyincreaswater Furthecies dethe exeincreasparison between the theoretical and experimental values of thermalor heat pipe at plate solar collector in [20] at G = 0.0125 kg/s.

erature varies from a minimum of 38.85 C to a maxi-36 C at 15:00 and 11:00, respectively.ves the variation of solar cell temperature Tcell withll row number N at the weather conditions shown inre it is seen that the solar cell temperature increasessing solar cell row number. Also, during the local015:00, the variations of solar cell temperature withr are 49.6251.53 C, 51.2053.35 C, 50.7052.77 C,2 C, 47.2648.82 C and 44.8246.01 C. That is to say,

range of solar cell temperature is less than 2.5 C, which

variations of ambient temperature, solar radiation intensity and themperature at G = 0.05 kg/s, rc = 0.9 and Ti = 37 C.

between 8.1tively, whicof solar cellas expected63.3%, 56.1be becausetemperaturever, with of thermal increases awhich will system. In vof 8.439.2inlet water

The effeTcell, the th

Fig. 9. The vawater temperrvations are attributed to the hourly variation of solartensity.nd 10 demonstrate the effects of inlet water tempera-olar cell temperature Tcell, the thermal, electrical andciencies. It is evident that the solar cell temperatureith the increase of inlet water temperature and the inleterature has a great effect on solar cell temperature.

is to be noted that the thermal and electrical efcien-se with increasing the inlet water temperature, whileefciency increases. When the inlet water temperatureom 33 C, 37 C to 41 C, the electrical efciency ranges6 and 8.45%, 8.05 and 8.33%, and 7.92 and 8.21%, respec-h is due to the fact that the photovoltaic transformation

decreases on account of solar cell temperature increases. Also, the thermal efciency ranges between 59.1 and

and 59.2%, and 50.8 and 55.8%, respectively. This might of the fact that the increasing rate of the outlet watere is less than that of the inlet water temperature. How-the increment of inlet water temperature, the gradeenergy rises and the thermal exergy gained by waterlthough the heat quantity gained by water decreases,improve the overall exergy efciency of PV/T hybridiew of this, the overall exergy efciency is of the order0%, 9.119.78% and 9.6710.26%, respectively, when the

temperature varies from 33 C, 37 C to 41 C.cts of water mass ow rate G on solar cell temperatureermal, electrical and exergy efciencies are illustratedriation of solar cell temperature with row number at different inletatures.


Fig. 10. Hourllocal time at d

in Figs. 11 cell temperexpected. T53.49 C, 48ing to the wrespectivelyelectrical erate increasand 8.158heat removcell decreas

Fig. 11. The vamass ow ratey variations of the thermal, electrical and exergy efciencies with theifferent inlet water temperatures.

and 12. They indicate that there is a decrease in solarature with increase of the water mass ow rate ashe solar cell temperature ranges between 51.15 and.04 and 49.72 C, and 46.31 and 47.63 C correspond-ater mass ow rate of 0.03 kg/s, 0.05 kg/s and 0.07 kg/s,. In this case too, one can observe that the thermal andfciencies become higher when the water mass owes. The electrical efciency is 7.868.23%, 8.058.33%.39%, respectively. This is due to the fact that theal from solar cell is more and temperature of solares when the water mass ow rate increases. On the

riation of solar cell temperature with row number at different waters.


other hand58.461.7%to obtain hithat the incthe outlet woutlet watemass ow rto the incremal energythe overall output incris 9.069.66the inuencefciencies

Figs. 13Tcell, the thcell row nutors rc. Appthe solar cethe solar ce48.1249.9ing factor with the vathat the eledecreases wvaries from7.127.37%ciency is 5y variations of the thermal, electrical and exergy efciencies with theifferent water mass ow rates.

, the thermal efciency is 51.954.8%, 56.159.2% and, respectively. The increasing water mass ow rate tendsgher thermal efciency. This can be attributed to the factreasing water mass ow rate results in the reduction ofater temperature. However, the decreasing rate of ther temperature is lower than the increasing rate of waterate; hence more heat is absorbed by water which leadsase in thermal efciency. Although the grade of ther-

goes down as the increasing of water mass ow rate,exergy efciency which combines the effect of electricaleasing still rises, namely, the overall exergy efciency%, 9.119.78% and 9.159.86%, respectively. Obviously,e of water mass ow rate on the thermal and electrical

is greater than that on the overall exergy efciency. and 14 represent the plots of solar cell temperatureermal, electrical and exergy efciencies against solarmber N and the local time for different packing fac-arently, by increasing packing factor from 0.7 to 0.9,ll temperature decreases. For different packing factor,ll temperature varies in the range of 48.2250.10 C,4 C and 48.0449.72 C, respectively, showing the pack-has very small effect on the solar cell temperatureriation of less than 2 C. From Fig. 14, it can be seenctrical efciency increases and the thermal efciencyith increasing packing factor. When the packing factor

0.7, 0.8 to 0.9, the electrical efciency is 6.226.45%, and 8.058.33% respectively. Again, the thermal ef-7.560.6%, 56.859.9% and 56.159.2%, respectively.


Fig. 13. The variation of solar cell temperature with row number at different packingfactors.

Clearly, a signicant increase in the system electrical efciencyis noticed with the same increase of the packing factor. This isdue to the fact that the net thermal energy available to the sys-tem decreases on account of the decreased area exposed to theincident solar radiation. At the same time, the outlet water temper-ature decreases with increasing packing factor as expected. Thus,the lower water temperature is responsible for the decreased ther-mal exergy gain. On the other hand, the increasing rate of electricaloutput is greater than the decreasing rate of thermal exergy, onecan observe that the overall exergy efciency becomes higher for


Fig. 15. The variation of solar cell temperature with row number at different heatloss coefcients.

increased packing factor. The packing factor varying from 0.7, 0.8to 0.9 is corresponding to the order of the overall exergy efciencyas 7.177.88%, 8.128.82% and 9.119.78%, respectively.

From Fig. 15, it is clear that the solar cell temperature Tcellis lower when the heat loss coefcient UL increases as expected.The solar cell temperature varies in the range of 48.8850.78 C,48.2349.95 C and 47.6449.21 C with respect to the heat losscoefcient as 6 W/m2 K, 8 W/m2 K and 10 W/m2 K, respectively.Accordingly, the electrical efciency is 7.998.30%, 8.048.32%and 8.078.35%, whereas the thermal efciency is 61.2963.65%,57.2460.20% and 53.5557.10%, respectively, as shown in Fig. 16,y variations of the thermal, electrical and exergy efciencies with theifferent packing factors.

Fig. 16. Hourllocal time at dy variations of the thermal, electrical and exergy efciencies with theifferent heat loss coefcients.


which indicates that larger heat loss coefcient is benecial to theelectrical output and disadvantageous to the improvement of ther-mal performance. However, it is also important to note that there isonly a small increase in the electrical efciency for increasing heatloss coefcient. While one can observe that the heat loss coefcienthas a relatively great effect on the thermal efciency. As a result,it can be concluded that the variation of overall exergy efciencyis mainly determined by that of thermal exergy gained by water.When the heat loss coefcient increases, the heat gained by waterbecomes less and the grade of thermal energy declines simulta-neously. It follows that the thermal exergy gained by water is onthe decrease, which will lead to the decrease of the overall exergyefciency. And this is actually the truth, because when the heatloss coefcient varies from 6 W/m2 K, 8 W/m2 K to 10 W/m2 K, theoverall exergy efciency obtained from Fig. 16 becomes from 9.13to 9.87%, 9.12 to 9.80% and 9.11 to 9.74%, respectively. Comparedwith the effects of the heat loss coefcient on the thermal and elec-trical efciefound.

6. Conclus

In this The proposfull use of temperaturcompetitiveconversion ically invesexergy efcand exergy up to 63.65operating tthan 2.5 C.

The relaefcienciesparametersshows that improved bwater tempcient in theand increasand heat lothe hybrid sing factor oefciency oinlet watersignicantlyof water mexergy efcefciency idecrease of

Acknowledgments

This work is supported by National Natural Science Foundationof China (Project No. 51076171). The authors also wish to thankthe support from Natural Science Foundation Project of CQ CSTC(CSTC, 2010BB6062) and Project No. CDJXS 10141147 supportedby Fundamental Research Funds for the Central Universities.

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PV/T system. Also, decreasing inlet water temperatureing water mass ow rate, packing factor of solar cellss coefcient would increase the electrical efciency ofystem. The varying inlet water temperature and pack-f solar cell have distinct effect on the overall exergyf the heat pipe PV/T hybrid system, namely, a higher

temperature and packing factor of solar cell lead to higher system exergy efciency, while smaller effectsass ow rate and heat loss coefcient on the overalliency have been obtained, although the overall exergyncreases as the increase of water mass ow rate and

heat loss coefcient of system.

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A heat pipe photovoltaic/thermal (PV/T) hybrid system and its performance evaluation1 Introduction2 System descriptions3 Theoretical model and its derivation3.1 Theoretical model3.2 Theoretical derivation3.2.1 The region B0A13.2.2 The region B1A23.2.3 The region A1B1 of the first row of solar cell3.2.4 The region AnBn of the nth (n=2, 3, 4, , N1) row of solar cell3.2.5 The region ANBN of the Nth row of solar cell3.2.6 The relation T0n with Tbn

4 Validation of theoretical model5 Results and discussion6 ConclusionsAcknowledgmentsReferences

2011 - heat pipe photovoltaic-thermal (pvt) hybrid system and its performance evaluation

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