Thermal performance of a greenhouse with a phase change material north wall

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Energy and Buildings

jo u r n al h om epa g e :w w w . e l s e v i e r . c o m / l o c a t e / e n b u i l d

Thermal performance of a greenhouse with a phase change material north wall

F. Berroug

, E.K. Lakhal

, M. El Omari

, M. Faraji

, H. El Qarnia

aLaboratoired’Automatiquedel’EnvironnementetProcédésdeTransfert,UniversitéCadiAyyad,FacultédesSciencesSemlalia,DépartementdePhysique,AffiliéauCNRST,URAC28, Marrakech,Morocco

bLaboratoiredePhysiquedesMatériaux,Microélectronique,AutomatiqueetThermique,DépartementdePhysiques,FacultédesSciencesAinChock,UniversitéHassanII,Casablanca, Morocco

cLaboratoiredeMécaniquedesFluidesetEnergétiques,UniversitéCadiAyyad,FacultédesSciencesSemlalia,DépartementdePhysique,Marrakech,Morocco

a r t i c l e i n f o

Articlehistory:

Received8June2011

Receivedinrevisedform10July2011 Accepted19July2011

Keywords:

PCM

Greenhouseheating Northwall Numericalanalysis

a b s t r a c t

Solarenergyisconsideredoneofthemostprospectivesourcesofrenewableenergyforgreenhouse heatingincoldperiodforMediterraneanclimate.Inthispaper,thethermalperformanceofanorth wallmadewithphasechangematerial(PCM)asastoragemediumineast–westorientedgreenhouseis analyzedanddiscussed.CaCl2·6H2OwasusedasaPCM.Anumericalthermalmodeltakenintoaccount thedifferentcomponentsofthegreenhouse(cover,plants,insideairandnorthwallPCM)andbased onthegreenhouseheatandmassbalance,hasbeendevelopedtoinvestigatetheimpactofthePCMon greenhousetemperatureandhumidity.CalculationsweredonefortypicaldecadeclimateofJanuaryin Marrakesh(31.62^◦N,8.03^◦W).Resultsshowsthatwithanequivalentto32.4kgofPCMpersquaremeter ofthegreenhousegroundsurfacearea,temperatureofplantsandinsideairwerefoundtobe6–12^◦C moreatnighttimeinwinterperiodwithlessfluctuations.Relativehumiditywasfoundtobeonaverage 10–15%loweratnighttime.

©2011ElsevierB.V.Allrightsreserved.

1. Introduction

Duetothehighcostofenergy,theuseofalternativeheating systemisimportantforagreenhousetoprovideoptimuminside conditionsduringwintermonths.Thebasicstrategyofgreenhouse passiveheatingsystemistoreducetheheatlossesandatthesame timetotransferexcessheatfrominsidethegreenhouseduringthe daytoheatstorage.Thisheatisusedduringthenighttosatisfythe heatingneedsofthegreenhouse.Severaltypesofpassivesolarsys- temsandtechniqueshavebeenproposedandusedby[1–3].The mostimportantexistinggreenhouseheatingsystemsare:water storage,rockbedstorage,mulching,movableinsulationandther- malcurtain,groundaircollectorandnorthwallstorageisalsoused forraisingthegreenhouseairtemperature.Forgreenhouselocated innorthernhemisphere,east–westorientationisthemostsuitable, itfavoritesamaximumofsolarradiationsinwinterandaminimum ofsolarradiationsinsummer.Foreast–westorientedgreenhouse, amaximumsolarradiationfallonthesouthwallduringwinter monthsandleavesthegreenhousethroughnorthwall.Tiwari[4]

hassuggestedatermcalled‘solarfractionfornorthwall’toquan- tifythislossthroughnorthwall.Thevalueofsolarfractionwillbe moreduringwintermonthsbecauseofthelawaltitudeangleofthe

∗Correspondingauthor.

E-mailaddress:f.berroug@ucam.ac.ma(F.Berroug).

sunandhencetheheatlosseswillbemore.Thereforeseveralworks intheliteraturerevealsthattheuseofnorthwallsforabsorption orreflectanceofsolarradiationscanraisethegreenhouseairtem- peratureandreducetheheatingneedsofthegreenhouse.Working withtheconceptofsolarfractionradiationonthenorthwall,water wasstoredinblacksteelbarrelsplacedinthenorthsidetoraise theinsideairtemperatureingreenhousesituatedatFlagstaff,USA (35.12^◦N,111.39^◦W)inwhichvegetablesweregrown[5].Thesys- temabsorbstheincidentsolarradiationsduringtheday.Duringthe night,thestoredheatisreturnedtothegreenhousebyconvection andradiation.Althoughthecostofthesesystemswaslowbutthe watercontainersoccupiedvaluablegroundspace.Inanotherappli- cationofnorthwall,somereflectivematerialcanbepaintedonthe northwalltoreflectsolarradiationstowardstheplantsandfloor.In onesuchstudy,northwallwasconstructedhavingreflectivesur- faceina50m²glasshouse[6].Ahighreflectivewhitecoating(93%) wasdoneonplywoodtoreflectthebeamradiationtowardsthe greenhouseplantsandfloor.Itwasobservedthatthegreenhouse required14%lesserenergyforheatingduringwintermonthsas comparedtoaconventionalgreenhouse.Guptaetal.[7]replaced northwallbyaninclinedsurfacetomaximizethesolarradiationon floorofthegreenhouse.Ithasbeenfoundthataninclinedreflective surfaceismoresuitableforutilizingsolarradiationstransmitting outthroughnorthwall.Withaconventionalgreenhousesolardryer of24m² groundarea(east–westorientation)andusinginclined reflective north wall covered with aluminized reflector sheet, 0378-7788/$–seefrontmatter©2011ElsevierB.V.Allrightsreserved.

doi:10.1016/j.enbuild.2011.07.020

Nomenclature

Ap plantssurface(m²)

Ag groundareaofthegreenhouse(m²) Ac coversurface(m²)

Aw northwallsurface(m²)

A_i ithinclinedsurfaceofgreenhouse(m²) ca specificheatofair(Jkg⁻¹K⁻¹)

cp specificheatofPCM(Jkg⁻¹K⁻¹) ea outsidewatervaporpressure(kPa) e_i insidewatervaporpressure(kPa)

e(T) saturated water vaporpressure attemperature T (kPa)

Fwc geometricalshapebetweenthewallandthecover h^rc,w heat transfer coefficient due to long wave radi-

ation between the cover and the wall radiation (Wm⁻²K⁻¹)

h^c_w,i convective heat transfer coefficient between the insideairandthewall(Wm⁻²K⁻¹)

I_b beamradiationonahorizontalsurfaceatanyinstant (Wm⁻²)

I_d diffuse radiation on a horizontal surface at any instant(Wm⁻²)

I_i totalincidentsolarradiationfluxonithinclinedSur- faceatanyinstant(Wm⁻²)

k thermalconductivityofthePCM(Wm⁻¹K⁻¹) Ka thermalconductivityoftheair(Wm⁻¹K⁻¹) Lc characteristiclengthofthecover(m) LAI leafareaindex

l_f characteristiclengthoftheleafplants(m) Lw lengthofthewall(m)

L thickofthewall(m) N leakagerate(h⁻¹) Nu Nusseltnumber

Qc totalsolarradiationincidentonthecover(Wm⁻²) Q_p totalsolarradiationincidentontheplants(Wm⁻²) Qw totalsolarradiationincidentonthewall(Wm⁻²) r reflectioncoefficientoftheground(≈0.2)

St total solarradiationfalling ontheGreenhouseat eachwallandroof(Wm⁻²)

T walltemperature(^◦C)

Tw interiorfacewalltemperature(^◦C) Tm meltingtemperatureofthePCM(^◦C) T_i insideairtemperatureofthegreenhouse(^◦C) Ta outsideairtemperature(^◦C)

T_c covertemperature(^◦C) Tp plantstemperature(^◦C) Va outsidewindspeed(m/s) V greenhouseairvolume(m³) Greeksymbols

˛sc,sc,sc absorptivity,reflectivityandtransmissivityofthe covertosolarradiation

˛sw,sw absorptivity,reflectivityofthewalltosolarradia- tion

˛sp,sp absorptivity,reflectivityoftheplantstosolarradia- tion

Stefan–Boltzmanconstant(5.67×10⁻⁸Wm⁻²K⁻⁴) psychometricconstant(≈0.0667kPaK⁻¹)

PCMdensity(kgm⁻³) a airdensity(kgm⁻³)

εp emission coefficient for thermal radiation of the plants

εc emission coefficient for thermal radiation of the cover

εw emissioncoefficientforthermalradiationofthewall Subscripts

c cover

p plants

i insideair

w wall

EW eastwall NW northwall SW sudwall SR sudroof NR northroof WW westwall

productreceivedthereflectedbeamradiation(whichotherwise leavesthroughthenorthwall)inadditiontothedirecttotalsolar radiationavailableonthehorizontalsurfacewhichincreasethe insideairandcroptemperature[8].Inclinationangleofthereflec- tivenorthwallcanbeoptimizedforagivenwidthandheightofa greenhouse,butitisalsofoundthataninclinedreflectingsurface cannotreducelossesofsolarradiationtozero[7].Manystudieson sensiblethermalstorageonmassivenorthwallwerereported.The conceptofopaquenorthwalliscommonlyemployedforeast–west orientedgreenhouseinnorthernhemisphere.Northwallisthere- foreinsulatedexternallyandpaintedblackinternallyforthermal storage.Duringthedaytime,incidentsolarradiationsimpingeon thewallandraiseitsthermalstorage.Thisstoredenergyisreleased duringthenightforthermalheatinginsidethegreenhouse.The northwallofa30m²glasscoveredgreenhousewasusedforheat- ingandstorageofthermalenergy[5].Thegreenhousewassituated inChateauroux(46.85^◦N,1.72^◦E),Franceinwhichtomatoeswere grown.Theeastandwestsideswereinsulatedandanorthwall of60cmthicknesswasconstructed.Thesystemwasabletomeet 82% annualheating needsof thegreenhouse.In anotherappli- cation,northwallwasconstructedwithstonesinsidea 350m² glasshousesituatedatAtalia,usedforvegetablegrowing[9].The greenhousewasable tomaintain1–2^◦C higher inside airtem- peraturethantheminimumoutdoorairtemperature.Thenorth wallofa20m² polyethylene(PE)coveredgreenhouseswascon- structedwith60cmwideconcreteblocks[5].Thewallwasused asa heatstorageunit duringdayandsupplied heatduringthe nightbyconvectionandradiation.Thesegreenhouseswerepro- motedforraisingvegetablesunderextremeclimaticconditions.

Thegreenhousesweremaintainedat15–20^◦Cduringthewinter conditionswhenoutsideairtemperaturewaslessthan10^◦C.The impactofnorthstoragewallwasstudiedontheinsideairtem- peraturesofthreegreenhousesmeasuring100m²PEcovered,at Athens(37.90^◦N,23.70^◦E),Greece,2000m²PEcoveredatAthens, Greeceand1000m² glasscoveredatChania,Greece[10].These systemssatisfiedabout35–50%heatingneedsofthegreenhouses.

Inthisworksthermal energywasstoredinthewallassensible heat,theperformanceofthewallisaffectedbythethicknessand mediaused for heat storage.However, theoptimum structural thicknessofthewallattaint60cminseveralworks[5].Fangand Li[11] foundthat theoptimum thickness of thewallfor solar passiveheated buildingattain 45cm. Thesensible storage wall requiredhighvolumeandtemperaturedifference.Thelatentther- malstoragehasmanyadvantagesoverthesensibleone:highheat capacity,lessvolume,lowstoragetemperature,thermalenergyis storedandreleasedatanalmostconstanttemperature.Thereare alargenumbersofPCMsthatmeltandsolidifyatawiderangeof

temperatures,makingthemattractiveinanumberofapplications, especiallyingreenhouse.Organicandinorganiccompoundsarethe twomostcommongroups ofPCMs.MostorganicPCMssuchas paraffinwaxesarechemicallystableandnon-corrosives,arecom- patiblewithmostbuildingmaterials,haveahighlatentheatper unitweightandarerecyclable.Theirdisadvantagesarelowther- malconductivity,highchangesin volumeduring phasechange andflammability.Inorganiccompoundssuchassalthydrateshave much higher latentheat per unit volume, higher thermal con- ductivity,arenonflammableandlowerincostincomparisonto organiccompounds; theyarecorrosivetomostmetals andsuf- ferfromdecompositionandsupercooling,whichcanaffecttheir phasechangeproperties.Nucleatingandthickeningagentscanbe addedtoinorganicPCMstominimizesupercoolinganddecompo- sition.Useofphasechangematerialcapsulesassembledasapacked bedisoneoftheimportantmethodsthathavebeenproposedto achievetheobjectiveofhighstoragedensitywithhigherefficiency [12].ThemostfrequentlyusedPCMingreenhouseareCaCl2·6H2O, Na₂SO₄·10H₂Oandparaffin.KernandAldrich[13]usedCaCl₂·6H₂O asaPCMinaerosolcanstoinvestigateheatstoragepossibilitiesina 36m²groundareagreenhousecoveredwithfiberglass.Theyfound thatphasechangestoragesystemcanprovidea desirablealter- nativetorockstorage.InanexperimentalstudybyBoulardand Baille[14],CaCl2·6H2Owasutilizedinagreenhousewith176m² groundareas,doublepolycarbonate-coverandforcedventilation, CaCl₂·6H₂O(2970kg)waspackedincontainersandplacedalong thenorthwall.ThePCMcouldprovide30%nightheatingneeds duringthewinterperiod.Ozturketal.[15]performedanexper- imentalevaluationofenergyandexergyefficiencyofaseasonal latentheatstoragesystemforgreenhouseheatingusingparaffin waxasaPCMina180m²greenhousegroundareas.Thesystem consistsoffiveunits:(1)flatplatesolaraircollectors(asheatcol- lectionunit27m²),(2)latentheatstorageunit(6000kgofparaffin wax),(3)experimentalgreenhouse,(4)heattransferunitand(5) dataacquisitionunit.Itwasobservedthattheaveragenetenergy efficiencyofthearrangementwas40.4%.Inthisstudywepurpose theinclusionofphasechangematerialinnorthwallofthegreen- houseandanalyzetheimpactofPCMnorthwall(PCMNW)on thermal performanceof agreenhouse.Thissystemwasalready usedinbuildingbySharmaetal.[16]andhecanreducebothcool- ingandheatingdemands.Bourdeau[17]testedtwopassivestorage collectorwallsusingCaCl₂·6H₂O(meltingpoint29^◦C)asaphase changematerial,heconcludedthatan8.1cmPCMwallhasslightly betterthermalperformancethana40cmthickmasonrywall.

2. Mathematicalmodel 2.1. PCMnorthwall

Thenorthwallofthegreenhouseisinsulatedexternallyand internallyreceivedafractionoftotalsolarradiationtransmittedto thegreenhouseandhasaradiativeandconvectiveheatexchange withthecomponentsofthegreenhouse.

Followingassumptionsweremade:

•PCMishomogeneousandisotropic.

•Themodeofheattransferisconductiononly,theconvectionis neglected(encapsulatedPCM).

•Heattransferisone-dimensional.

Usinganenthalpymethod,theenergyequationinthewallreads as:

cp∂T

∂t = ∂

∂x

k∂T

∂x

−Hm∂f

∂t (1)

Fig.1.Energybalanceofgreenhousecomponents.

Thelasttermtakesintoaccountthelatentenergyassociatedwith phasechangewhentheyoccur.ThelatentheatofmeltingisHm, frepresentstheliquidfractionofmeltanditisgivenby:

f =0 if T>Tm

0<f<1 if T=Tm

(2)

TmisthemeltingtemperatureofthePCM.

Boundaryconditionsinthewallare:

•x=0,interiorsurfaceofthePCMwall(facingthegreenhouseas showninFig.1:

Qw^s +Q_i,w^c +Qp,w^r +Qc,w^r =Qw^cond (3) whereQw^s (Wm⁻²)isthesolarradiationabsorbedbythePCM wall; Q_i,w^c (Wm⁻²)is the convective heat transfer from the insideairtothewall;Qp,w^r (Wm⁻²)andQc,w^r (Wm⁻²)arethe netthermalradiationbetweenthewallandrespectivelythecover andtheplants;Qw^cond (Wm⁻²)istheconductifheattransfer throughthePCMwall.Eq.(3)canbewrittenas:

˛swQw+h^c_i,wAw

Ag

(Ti−Tw)+h^rp,wAw

Ag

(Tp−Tw)

+h^rc,wAw

Ag

(Tc−Tw)=−k∂T

∂x

x=0

Aw

Ag

(4) Althefluxesofheatareexpressedperm²ofgroundareaofthe greenhouse.

•x=L,exteriorsurfaceofthewall:

∂T

∂x

x=L

= 0 (5)

Thermo-physicalpropertiesofthePCMareevaluatedas:

km=fkl+(1−f)ks, (cp)_m=f(cp)_l+(1−f)(cp)_s (6) For selectingthePCMforthenorthwall, thefollowing desir- able’s properties ofcalcium chloridehexahydrate weretaken intoaccount:highlatentfusionperunitmass,chemicalstabil- ity,meltinginthedesiredoperatingtemperaturerange,small

volumechangeduringphasetransition,availabilityinlargequan- titiesand low price. The north wallwas filled with 777.6kg of calcium chloride hexahydrate, corresponding to32.4kg of PCM/m²ofthegreenhousegroundsurface.

2.2. Greenhousecomponents

Tomathematicallydescribethethermalbehaviorofthegreen- house,threecomponentsthatplayimportantrolesinthethermal balance:thecover,theinsideairandtheplantsareanalyzed(Fig.1).

Thefollowingassumptionsaremade:

-Relativehumidityand temperatureofinside airare supposed uniforms.

-Heatcapacityoftheenclosedairandthecoverareneglected.

- Climatedatearehourlyinvariable.

- Noradiantheatisabsorbedbytheground,whichisfullycovered byvegetation:heatandhumidityexchangedbetweentheground andtheinsideairisneglected.

-Nocondensationwithinthegreenhouse.

-Thereisnowater-stresssituationintheplants.

2.2.1. Greenhousecover

Theenergybalanceofthecoverisgivenby:

Qc^s+Qa,c^c +Qi,c^c +Qsky,c^r +Qp,c^r +Qw,c^r =0 (7) whereQc^s (Wm⁻²)isthesolarradiationabsorbedbythecover;

Qa,c^c (Wm⁻²)andQ_i,c^c (Wm⁻²)aretheconvectiveheattransfer betweenthecoverandrespectivelytheoutsideandinsideairofthe greenhouse.Q_sky,c^r (Wm⁻²), Qp,c^r (Wm⁻²)and Qw,c^r (Wm⁻²) arethenetthermalradiationbetweenthecoverandrespectively thesky,theplantsandthePCMNW.Eq.(7)canbewrittenas:

˛scQc+h^ca,cAc

Ag

(Ta−Tc)+h^c_i,cAc

Ag

(Ti−Tc)+h^r_sky,cAc

Ag

(Tsky−Tc) +h^rp,cAp

Ag

(Tp−Tc)+h^rw,cAw

Ag

(Tw−Tc)=0 (8) whereT_sky istheskytemperature(^◦C)whichwascalculatedby Swinbank[18]:

Tsky=0.0552×(Ta+273.16)^1.5−273.16 (9)

2.2.2. Greenhouseplants

Theenergybalanceoftheplantssurfaceinsteadystatecondi- tionsis:

Qp^s+Qc,p^r +Qw,p^r =Q_p,i^c +Q_p,i^l (10) whereQp^s (Wm⁻²)isthesolarradiationabsorbedbytheplants;

Qc,p^r (Wm⁻²)andQw,p^r (Wm⁻²)arethenetthermal radiation betweentheplantsandrespectivelythecoverandthePCMNW;

Q_p,i^c (Wm⁻²)isthesensibleheattransferbetweentheplantsand theinsideairofgreenhouse;Q_p,i^l (Wm⁻²)isthelatentheattrans- ferbetweentheplantsandtheinsideairofgreenhouse.Eq.(10) canbewrittenas:

˛spQp+h^rc,pAc

Ag

(Tc−Tp)+h^rw,pAw

Ag

(Tw−Tp)

=aca LAITp−Ti

ra +aca×LAI

[e^∗(Tp)−ei]

ra+rs (11) Thesaturatedwatervaporpressuree*(Tp)atthetemperatureofthe plantsiscommonlycalculatedbythefollowingempiricalformula

relatingaccuratelysaturatedwatervaporpressuretotemperature forthetemperaturerangebetween0and60^◦C[19]:

e^∗(Tp)=0.6108exp

Tp+237.3

(12) Theaerodynamicresistancera(s/m)oftheplantsisdeducedfrom thecharacteristicofairflowinthegreenhouseandtheleaflength.

ItisexpressedbyHaxaire[20]as:

ra=lfaca

Nu Ka

(13) Thestomatalresistancer_s(s/m)oftheplantsisderivedfromasim- pleempiricalrelationship[21]withglobalradiation(inthefirst approximation,thethermalandhumiditydependencesofgreen- houseplantstranspirationwereneglected):

rs=200×[1+exp(0.05(50−QP))] (14) 2.2.3. Insideair

2.2.3.1. Sensible heat. The sensible heat balance of the air is describedbythefollowingequation:

Q_p,i^c +Q_c,i^c +Q_w,i^c +Q_a,i^c =0 (15) whereQ_p,i^c ,Q_c,i^c andQ_w,i^c aretheconvectiveheattransferbetween theinsideairandrespectivelytheplants,thecoverandthePCM wall.Q_a,i^c representthesensibleheattransferbetweentheinside airandtheoutsideairduetoleakageorventilation.Eq.(15)canbe writtenas:

h^cp,i

Ap

Ag

(Tp−Ti)+h^cc,i

Ac

Ag

(Tc−Ti)+h^cw,i

Aw

Ag

(Tw−Ti)

+h^c_a,i(Ta−Ti)=0 (16) where h^c_a,i is thesensible heat transfer coefficientbetweenthe insideairandtheoutsideair,calculatedusingtheformulaofFuchs etal.[22]:

h^c_a,i=aca×N×V 3600×Ag

(17) whereNistheleakagerateexpressedinnumber ofairvolume renewalsperhour(h⁻¹).Inthisstudy,weusedtherelationship betweenNandVafoundedexperimentallybymeansofthetracer gastechniqueforalowcostplasticgreenhouseinaMediterranean area,thisexpressionisgivenbyBailleatal.[23]:

N=0.29×Va+0.76 (18)

2.2.3.2. Latentheat. Innon-condensationconditions(i.e.transpi- rationistheonlysourceofwatervapor)thelatentheatbalanceof thegreenhouseairisdescribedbythefollowingequation:

Q_p,i^l =Q_i,a^l (19)

whereQ_p,i^l (Wm⁻²)isthelatentheattransferbetweentheplants andtheinsideair;Q_a,i^l (Wm⁻²)representthelatentheattrans- ferbetweentheinside airandtheoutsideairduetoleakageor ventilation.Eq.(19)canbewrittenas:

aca×LAI

[e^∗(Tp)−ei] ra+rs = h^c_i,a

(ei−ea) (20)

2.2.4. Solarradiationscomputations

Totalsolarradiationavailableonthegreenhousecoveriscom- putedforeachwallandroofofthegreenhouseusingLuiandJordan formula[24]forinclinedsurface:

St=

i

AiIi (21)

with I_i=

Ib+

Id

+r

(Ib+Id) (22)

whereiisEW,WW,NW,SW,SR,NR.

isthezenithangleofsunonaninclinedsurface;histhealti- tudeangleofsunwithvertical;ˇistheslopeofthesurfacewith horizontal.

TotalsolarfractionFis theratiooftotal solarradiationloss fromthegreenhousetototalsolarradiationtransmittedinsidethe greenhouse[4].ThevalueofFwillbemoreduringwintermonths becauseofthelowaltitudeangleofthesunandhencethelosses willbemore.Amodelhasbeendevelopedtocalculate“totalsolar fraction”,whichquantifiesthelossesofalltransmittedsolarradi- ationcominginsidethegreenhouse.Theselossestakeplacefrom northwall/roof,andeast/westwallforeast–westorientedgreen- house.ThefractionfallingonthenorthwallF_nisthemostimportant comparedtotheotherface[4],whichmotivethisstudyandgives theideaofstoringthisenergyinaMCPNW.

Solarradiationstransmittedintothegreenhouseareassumed tobereflectedmultiplybetweenthegreenhouseplants,coverand PCMNW.Howeverthetotalsolarradiationsincidentsonplants, coverandPCMnorthwallaregivenapproximatelyby[25]:

Qp=scSt[(1−F)(1+scsp)+sc(F−Fn)+wFn] (23) Qc=scSt (1−F)(1+spsc)+(F−FNW)(1+spsc)+ 1

sc

(24)

Qw=FnscSt (25)

2.2.5. Convectiveheattransfercoefficients

Empiricalequationsthatwereusedtocalculatetheconvective coefficientsare[26]:

h^ca,c=0.95+6.76Va^0.49 with Va≤6.3m/s (26) h^ci,c= NuKa

Lc , h^ci,p=NuKa

lf , h^ci,w=NuKa

Lw

(27) CorrelationdevelopedbyMonteith[27]andCampbell[28]based ontheconvectionregimeandthetypeofairflowinsidethegreen- houseareusedforthecomputationoftheNusseltnumber.

2.2.6. Radiativeheattransfercoefficients

Theradiativeheattransfercoefficientsaregivenby:

h^r_sky,c=εc(T_sky² +Tc²)(Tsky+Tc) (28)

h^rp,c=(Tp²+Tc²)(Tp+Tc)

εp−1+Ap

Ac

εc −1

(29)

h^rw,c=(Tw²+Tc²)(Tw+Tc) 1 Fwc + 1

εw−1+Aw

Ac

εc −1

(30)

h^rw,p=(Tw²+Tp²)(Tw+Tp)

εw−1+Aw

Ap

(31) Thegeometricalshapefactorsarecalculatedusingformulain[29].

2.2.7. Numericalcomputationandusedparameters

Theobtainedequations arenon linearbecausetheradiative transfercoefficientcanappearwiththeterm(T_i+T_j)(T_i²+T_j²)in theradiativecomponentand theconvectivetransfercoefficient appearwiththeterm|T_i−T_j|^ain theconvectivecomponent.To

Table1

Parametersusedforthecomputation.

Parameters Values

Greenhouse

V(m³) 57.6

Ag(m²) 4×6

Plants

LAI 3

lf(m) 0.03

εsp 0.3

sp 0.7

εp 1

Ap LAI×Ag

Cover

sp 0.9

sp 0.05

˛sc 0.05

εc 0.5

Ac(m²) 59.07

PCM(CaCl2·6H2O)[30]

Tm(^◦C) 29

kl,ks(Wm⁻¹K⁻¹) 0.539,1.088

1,s(kg/m³) 1560,1800

cp1,cps(Jkg⁻¹K⁻¹) 2130,1460

Hm(kJ/kg) 187.49

˛sw 0.9

sw 0.1

˛w 0.99

L(cm) 4

Aw(m) 1.8×6

Price($/kg) 2

Toxiceffect No

resolve this problemiteratively,theabove terms mustbe con- sidered constant within each time step. The new value of the obtained temperature T_i and T_j will be used to substitute the term(T_i+T_j)(T_i²+T_j²)bytheterm(T_i+T_j)(T²_i +T²_j)andtheterm

|T_i−T_j|^abytheterm|T_i−T_j|^a.Theprocesscontinuesuntilconver- gencereached.Notethat,theenergybalanceplantsequationwas notlinearizedbecauseofthepresenceoftheexponentialtermof saturatedwatervaporpressure.Itsnumericalsolutionisperformed byaniterativeNewton–Raphsonprocedure.Afinite-volumecode hasbeendeveloped inordertodeterminethetemperatureand theliquidfractioninthePCMwall.Inputsforthemodelinclude solarradiationsonhorizontalsurface(global,diffuse),outsideair temperature,relativehumidityandwindspeed.Parametersthat needtobespecifiedincludethegreenhouseconfiguration(cover materiel,dimensions),theplantscharacteristicsand thethermo physicalpropertiesofthePCMasgiveninTable1.

2.3. Validationofthenumericalmodel

Numericalcodewasvalidatedbycomparingitwiththeexperi- mentalresultsperformedbySethiandSharma[31].Experimental measurementsofplantsandinsideairtemperaturesperhourare madeinevenspangreenhousewithplasticcoverandintroducing thesameorientationanddimensionsasthatadoptedinthepresent model.Usingsimilarparametersofentranceadoptedintheexperi- enceof[31],Fig.2illustratesthehourlyvariationofthemeasured andcalculatedplantsandinsideairtemperature.Resultsshowa goodconcordancebetweenbothmodelswithdifferenceaverage of3%forthetemperatureofplantsand4%forthetemperatureof insideair.Thisallowsconcludingthatourmodelallowssimulating climaticparameterscorrectlyinsidethegreenhouse.

3. Resultsanddiscussions

Fig.3showsthetotalsolarradiationfallingonthegreenhouse for a typical climatedecade of January in Marrakesh (31.62^◦N,

Fig.2.Hourlyvariationofthepredictedandmeasuredplantsandinsideairtem- peratures.

8.03^◦W). The figure illustrates also the solar radiation fraction transmittedinthegreenhouseandincidentonthenorthwall.Fora conventionalgreenhouse(withoutPCMNW),thesefractionleaves thegreenhousebecauseofthehighsolarradiationstransmission ofaplasticcover.Alsothesefractiondependonthetimeoftheday, solaraltitudeangle,nthdayoftheyearandsolarazimuthangle [4].Sothisfractionishighinwintermonthsduetothelowalti- tudeangleofthesun.ForagreenhousewithPCMNWasamedium ofstorage,thisenergywillbestoredduringthedaytimeandwill bereleasedduringthenightforthermalheatinginsidethegreen- house.Alsotheisolationoftheexternalfaceofthenorthwallcan reducesignificantlyheatlossesthroughthecover.

Fig.4presentsthehourlyvariationoftheliquidfractionandthe northwalltemperaturefortheseconddayfromthetypicalclimate decadeofJanuaryinMarrakesh.Analysisforsuchfigureshowsthat liquidfractionincreaseduringthemorning(from9hto11h)due totheincreasingincidentsolarradiationsandthewalltempera- tureremainsoverlyunchanged,becausealltheenergytransmitted tothewalliscompletelyusedtomeltthePCMasa latentheat offusion.Aftertheseperiod(from11hto13h),walltemperature startincreasingduetotheactivationofthesensibleheatstorage

Fig.3.Hourlyvariationofthetotalincidentsolarradiationonthegreenhouseand onthenorthwallforatypicalclimatedecadeofJanuaryinMarrakesh.

Fig.4.Hourlyvariationoftheliquidfractionandthetemperatureofthenorthwall foratypicalclimatedayofJanuaryinMarrakesh.

andleadstoarapidmelting ofPCMandliquidfractionreaches 1at13h,butsolarradiationpersistsafter13h,whatleadstoan overheatingoftheliquidPCMlayer(Tw=54^◦Cat17h).After17h, solarradiationdisappears,outsideairtemperaturedecreaseand consequentlytheinsidegreenhousetemperaturedecrease.Heat transferchangesthedirectionfromthewall(hottermedium)to theinsidegreenhouse(coldmedium).LiquidPCMandwalllosses theirheatbutliquidfractionremainsunchanged(f=1)becausethe liquidPCMwassuperheated(sensibleheatstorage).Afterabout 20hliquidfractionbeginstodecrease(solidificationordischarg- ingperiod)and weremarksthat thewalltemperatureremains relativelyconstants(latentheatoffusion)untilthemorning(9h).

Itwasobservedthatduringthenight,walltemperaturenever fallsdown(27^◦C)whentheoutsideairtemperaturedropuntil5^◦C.

ThenorthwallincorporatingPCMplaystheroleofaheatsinkdur- ingthedayandaheatsourceduringthenight.Theenergystored duringthedayisreleasedatnight.Approximately,thesametrend wasobservedduringtheotherdaysofthetypicalclimatedecade ofJanuaryinMarrakesh(Fig.5)whichleadstoapassiveheatingof thegreenhouse.

Thehourlyvariationoftemperatureforoutsideair,plants,cover andinsideairofgreenhousewithandwithoutPCMNWforthe

Fig.5.Hourlyvariationoftheliquidfractionandthetemperatureofthenorthwall forthetypicaldecadeclimateofJanuaryinMarrakesh.

Fig.6.Hourlyvariationoftheoutsideairtemperature,plants,coverandinside airtemperaturewithandwithoutPCMNWforatypicalclimatedayofJanuaryin Marrakesh.

seconddayfromthetypicaldecadeclimateofJanuaryinMarrakesh havebeenpresentedinFig.5.Fromthefigure,foraconventional greenhouse(withoutPCMNW),itisseenthatduringtheday,the temperatureofplants,coverandinsideairarehigherthantheout- sideairtemperatureduetothesolarradiationsabsorbedbythe plantsand dissipateas sensibleheat andlatentheat insidethe greenhouse.Butduringthenightthepictureisinvertedandtheout- sideairiswarmerthantheinsidegreenhouseduetothenocturnal lossesofpolyethylenecoveredgreenhousebyleakage,convection andradiationduringwinterperiods[23].

ThediurnalvariationoftemperaturesforgreenhousewithPCM NWwasobservedtobe1–2^◦Chigherfrom9hto13h(Fig.6).This duetothefractionofsolarradiationsreflectedfromthenorthwall andincidentontheplants(w=0.1).Butfrom14to20h,there occurredmoredifferenceintemperature5–12^◦Cfor plantsand insideairand2–5^◦Cforcover.Thisremarkabletemperaturedif- ferenceisduetotheoverheatingofthePCMNWaswasmentioned above.Theincreasedtemperaturedifferencebetweenthewalland thegreenhousecomponents(plants,insideairandcover)creates animportantconvectiveandradiativeheattransfer.From21to9h, thenocturnalvariation oftemperatureforthegreenhousewith thePCMNWwere observedtobe3–8^◦Chigher forplants and insideair,and1–4^◦Cforcover.Thisperiodcorrespondstothedis- chargeprocessofthePCM(solidification)andasitwasmentioned above thewalltemperature remains approximately unchanged (Tm=29^◦C).Thewallcanbeconsideredasaheatsourceandthe heatistransferredtothegreenhousecomponents(plants,inside airandcover)byconvectionandradiation.Withtheuseofthe PCMNW,thegreenhouseairtemperaturewasmaintained3–4^◦C higherascomparedtooutsideairduringnighttime,thiscreatea healthyenvironmentofplantsduringwinterperiod.

Fig. 7 shows the effect of the PCM NW on relative humid- ity.Thegreenhouseairrelativehumiditywasmaintained10–14%

lower as compared to the relative humidity in conventional

Fig.7.Hourlyvariationoftheoutsideandtheinsiderelativehumidityforgreen- housewithandwithoutPCMNWfortypicalclimatedayofJanuaryinMarrakesh.

Fig.8.Performancesofthegreenhousecomponentswithdifferentthicknessesof PCMnorthwall.

greenhouse.ThePCMsystemisabletocreateapassivedehumidifi- cationprocessespeciallyatnighttimeduetotheincreaseininside airtemperature.

Fig.8showsthetimewisevariationoftheinsidegreenhouse airandwalltemperaturesandliquidfractionforvariousPCMNW thicknesses.Theperformancesofthegreenhousecomponentsfor thecolderandthehotterdayfromthetypicaldecadeclimateof JanuaryinMarrakesharepresentedinTable2.Forthecasewith 2cmofPCM,liquidfractiondecreasesto0.03(≈0)forthecolder nightinJanuaryasshowninTable2.Thisthicknessisconsidered notsafe,becauseitispracticaltodonotsolidifyallthePCMforthe verycoldperiods.Thetargetwashowtomaintainasustainable Table2

PerformancesofthegreenhousecomponentswithdifferentthicknessesofPCMNorthwall.

2cm 4cm 5cm

Coldday Warmday Coldday Warmday Coldday Warmday

NonemeltedPCM 3% 6% 50% 57% 64% 68%

Tw,max(day) 49^◦C 67^◦C 42^◦C 57^◦C 41.7^◦C 54^◦C

Ti,max(night) 12.33^◦C 11.11^◦C 12.4^◦C 11.25^◦C 12.4^◦C 11.33^◦C

Fig.9.Dailyvariationsofthermalloadleveling,TLL,forthetypicaldecadeclimateofJanuaryinMarrakesh.

heatsourceforthegreenhouse.Also,forthisvalueofthePCMNW thickness(2cm),itwasobservedthat,duringthehotterday,wall temperatureexceeds67^◦C,whatcandamagetheplantslocated nearthewall(Table2).FortheothervaluesofthePCMthickness, liquidfractionneverreaches0,thisleadtoestablishthewalltem- peraturetothevalueof(Tm=29^◦C)andthesameeffectofthePCM thicknessonthewalltemperaturewasobservedforthethreeother valuesofthePCMthickness.Forthehigherthicknesses(L>4cm), theliquidfractionvariesbetween1and0.68.Soonly32%ofthe dailyheatstoredinthewallwasusedand68%ofthePCMlayer seemstobenotnecessary.Thisleadtoconcludethatincorporating aNorthwallhaving4cmofPCMthicknessisthebestandpracti- calchoiceforheatinggreenhouselocatedinMarrakesh(31.62^◦N, 8.03^◦W).

TheperformanceofPCMNWasapassiveheatingsystemforthe greenhousehasbeenevaluatedintermsofthermalloadleveling, TLL,andheatingpotential,Q_h,usingthefollowingequations[32]:

⎧ ⎪

⎪ ⎪

⎨

⎪ ⎪

⎪ ⎩

TLL=Ti,max−Ti,min

Ti,max+Ti,min

Qh=

maca(Ti(t)−Ta(t))

(32)

Thermalloadleveling, TLL,is a ratioeven usedtoquantifythe fluctuationsof temperatureinside thegreenhouse.Thelessthe fluctuations,thebetteristheenvironmentfor plantsinsidethe greenhouse.Inwinter,TLLshouldhavelowervaluebyincorpo- ratingheatingmethodduetotheincreaseof(T_i,max+T_i,min)aswell

Fig.10.Dailyvariationsoftotalheatingpotential,Qh,forthetypicaldecadeclimateofJanuaryinMarrakesh.

asdecreaseof(T_i,max−T_i,min)ascomparedtoTLLwithoutheating arrangementfor optimalenvironment for growthand develop- ment of plants. The results for daily variation of thermal load leveling for greenhousewith and withoutPCM NW have been showninFig.9.ItcanbeseenthatthevalueofTLLismaximum for greenhousewithoutPCM NW and it isreduced on average about half for greenhousewith PCM NW. The lower values of thermal load leveling indicate the decrease in the fluctuations ofgreenhouseairandthereby,there occursanimprovementof desiredenvironmentforplantsinthegreenhouse.Similarly,the dailyvariationsoftotalheatingpotential,Q_h(Eq.(32))obtained fromPCMNWfortypicalclimatedecade(Marrakesh–January) werecalculatedandhavebeenshowninFig.10.Fromtheresults, it is seen that the heating potentials obtained in greenhouse withPCMNWwerehigherascompared togreenhousewithout PCMNW.

4. Conclusion

Foreast–westorientedgreenhouse,maximumsolarradiations fallsonthesouthwallduringwintermonthsandafractionofthis solarradiationsleavesthegreenhousethroughnorthwall.There- fore,aphasechangematerialnorthwallisproposedinthisstudy forabsorptionandreflectanceofsolarradiations.Duringtheday time,incidentsolarradiationsonthewallraiseitsthermalstorage.

Thisstoredenergyisrealizedtothegreenhousebyconvectionand radiation.Theperformanceofthesystemwasevaluatedintermsof thermalloadlevelingandpotentialheatingforatypicaldecadecli- mateofJanuaryinMarrakeshFromthepresentstudy,thefollowing conclusionscanbedrawn:

-Thereoccursa6–12^◦Criseofplantsandinsideairtemperature and4–5^◦Cforcovertemperatureatnighttimeduetotheuseof a4cmthickPCMNWasastoragemedium.

-Fluctuationoftemperatureforgreenhouseairislessinagreen- housewithPCMNW.

-Relativehumidityis10–15%lowerinagreenhousewithPCMNW.

-PCM Thickness of 4cm is practical and sufficient for heating greenhouselocatedinMarrakesh(31.62^◦N,8.03^◦W).

Acknowledgements

Thepresentworkwasaccomplishedwiththefinancialsupport oftheCNRSTaspartofProgramURAC,ConventionURAC28.

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