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Building and Environment 41 (2006) 843–850

www.elsevier.com/locate/buildenv

Thermal modeling for greenhouse heating by usingthermal curtain and an earth–air heat exchanger

Ashish Shukla, G.N. Tiwari�, M.S. Sodha

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

Received 4 April 2005; accepted 18 April 2005

Abstract

In this paper, a thermal model for heating of greenhouse by using different combinations of inner thermal curtain, an earth–air

heat exchanger, and geothermal heating has been developed. The analysis incorporates the study of thermal performance of three-

zone greenhouse. The calculations have been made for a typical production greenhouse in southern part of Argentina; available

climatic data has been used. The thermal performance of a greenhouse having thermal curtain and an earth–air heat exchanger has

been compared with a greenhouse having thermal curtain and geothermal energy. It is seen that the fluctuations in temperature in

the vicinity of plants are comparable in the two cases. From the results, it is seen that an earth–air heat exchanger might prove an

alternative source for heating of greenhouse when geothermal energy is not available. It has also been observed that, the increase in

temperature of zone I is more for the greenhouse with geothermal than the greenhouse with an earth–air heat exchanger.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Earth–air heat exchanger; Geothermal energy; Thermal curtain

1. Introduction

Heating of greenhouses is one of the most importantactivities during winter season and it is an essentialrequirement for proper growth and development ofwinter growing crops [1]. Greenhouse heating can beobtained by active or passive methods of heating. Foractive heating in comparison to ground collector, warmwater and an earth–air heat exchanger the groundgeothermal water is a better option. Thermal heating ofgreenhouses using the active method has been investi-gated by many researchers [2–5]. The study of green-house heating by the passive method [6–8] has also beenmade by many scientists. The passive heating may berealized through water storage, rock bed storage,presence of north wall, mulching, phase changingmaterial, movable insulation and thermal curtain.

e front matter r 2005 Elsevier Ltd. All rights reserved.

ildenv.2005.04.014

ing author. Tel.: +9111 2659 1258;

9 2208.

ess: gntiwari@ces.iitd.ernet.in (G.N. Tiwari).

Among passive heating modes a thermal curtain orthermal screen is one of the most practical andappropriate means for reducing the energy consumptionin greenhouses [9,10].

Night curtain or thermal screen are drawn inside oroutside the greenhouse in nighttime during winterperiod to reduce heat losses to the ambient environment.The curtain helps in retaining thermal energy near theplants and prevents the radiative heat losses to the coldnight sky air in maintaining good heat distributioninside the greenhouse [11]. A theoretical model forestimating the energy conserving potential of a nightcurtain in greenhouse has been given by Chandra andAlbright [12]. Arinze et al. [13] have studied the effectsof movable internal curtain placed in between theglazing of double-layered structure. Basically the curtainprovides additional thermal energy resistance thatreduces the overall rate of heat transfer to thesurroundings. An external curtain is placed betweenthe greenhouse canopy and the surrounding atmospherewhereas an internal curtain is placed between the crop

ARTICLE IN PRESS

Nomenclature

A area (m2)Ca specific heat of air (J/kg �C)CP specific heat of plant (J/kg �C)FP fraction of incoming solar radiation falling

on plants (dimensionless)FR heat removal factor of an earth–air heat

exchangerhg1 convective heat transfer heat coefficient from

floor of greenhouse to air in zone I (W/m2 �C)h12 convective heat transfer heat coefficient from

air in zone I to zone II (W/m2 �C)h23 convective heat transfer heat coefficient from

air in zone II to zone III (W/m2 �C)h3a convective heat transfer heat coefficient from

air in zone III to ambient air (W/m2 �C)ht convective heat transfer coefficient from

flowing hot water to zone I (W/m2 �C)hp convective and evaporative heat transfer

coefficient from plant mass to zone I (W/m2 �C)

hg1 heat transfer coefficient from ground tolarger depth of ground (W/m2 �C)

AiI i solar radiation falling on different surfaces ofgreenhouse cover (W/m2)

MP total mass of plant (kg)_ma mass flow rate of air (kg/s)

ma mass of air in zone I (kg)_Qu useful energy obtained from an earth–air heat

exchanger or geothermal energy (W)T temperature (�C)To temperature inside ground (�C)Tw temperature of hot water from geothermal

source (�C)

X predicted valuesY experimental values

Greek symbols

a absorptivity (dimensionless)t1 transmissivity of thermal blanket (dimension-

less)t2 transmissivity of thermal curtain (dimension-

less)t3 transmissivity of greenhouse cover (dimen-

sionless)1 infinity (at larger depth)

Subscripts

1 zone I in the greenhouse2 zone II in the greenhouse3 zone III in the greenhousea ambiente east wall of greenhouseexp experimentalg ground of greenhousei different walls and roofs of greenhousen north wall of greenhouseP plantpred predictedr roomR roofsw south wall of greenhouset plastic tubeer east roofwr west roofww west wall

A. Shukla et al. / Building and Environment 41 (2006) 843–850844

and structural cover of greenhouse. However thethermal internal curtain is preferred to the externalthermal curtain as the latter is exposed to outsideweather causing early deterioration. Experimental re-sults of Bailey [9], Roberts et al. [14] and analyticalstudies of Seginer and Albright Louis [11], Chandra andAlbright [12] indicate the usefulness of the thermalcurtain for energy conservation.

The use of thermal curtain reduces the losses butwe also need to heat the greenhouse for proper growthof plants, because the thermal condition of theground influences the availability and utilization ofmineral elements, seed germination and rooting systemof plants. Several scientists [15–17] have reportedutilization of geothermal energy for heating of green-houses. As geothermal energy is not available every-where, energy stored in earth has also proved to bedesirable option for greenhouse heating. The passive

heating technique in which heat is given to thegreenhouses from the earth has become popularnowadays. Stable temperature of earth at the largerdepths is an attraction for researchers to use earthfor passive heating; this temperature of earth is equalto the mean annual solar temperature of any place.The conditioning of air by an earth–air heat ex-changer has been studied by several scientists [18–20].Heating of greenhouse using an earth–air heat exchan-ger has been studied [21–23] and it is seen that the use ofan earth–air heat exchanger is very effective in heatingof greenhouse.

In this paper, an attempt has been made to develop animproved model, given by Ghoshal and Tiwari [24], byincorporating the side losses through walls of each zone.Further, the relative performance of thermal curtain,geothermal heating and an earth–air heat exchanger hasalso been studied.

ARTICLE IN PRESSA. Shukla et al. / Building and Environment 41 (2006) 843–850 845

2. System description

The schematic diagram of an even span greenhouse insouthern part of Argentina (32.2�S latitude and 64.3�Wlongitude) has been shown in Fig. 1a. The greenhousehas been divided into three zones:

(i)

Sola

r ra

diat

ion

(W/m

2 )

(a)

(b)

Fig.

and (

typic

Zone I: space between the ground and thermalblanket.

(ii)

Zone II: space between the thermal blanket andceiling (thermal curtain).

(iii)

Zone III: space between the ceiling (thermalcurtain) and roof.

Various wood sticks at appropriate places give thesupport for thermal blanket over the ground. Fourtemperature sensors for zones I–III, and ambienttemperature have been placed as shown in Fig. 1a.The transparent single polyethylene sheet has been usedfor construction of roof and walls of greenhouse,whereas thermal curtain made of 50-mm transparentpolyethylene sheets has been used inside east and westwall. The greenhouse has orientation of east–west

0

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (Hour)

Total solar radiation

Diffuse solar

Ground

7.0

1.0

2.40

1.30

E

N

W

S

Ta

Sun

0.2

T3Zone III

Zone II

Thermal blanketCloth peg T2

Sticks

Double wall

[Thermal curtain]

Ceiling[Thermal curtain]

T1Zone I

1. (a) Schematic diagram of the greenhouse (Barral et al. 1999)

b) hourly variation of total radiation and diffuse radiation for a

al day of February in southern part of Argentina.

direction. The room air of zone I has been heated by:

(i)

Geothermal heating: The tubes, made of black lowdensity polyethylene film of 250-mm thick and160mm diameter have been placed on the groundof greenhouse. The hot water available from thegeothermal sources is allowed through the tubes.There is heat transfer from hot water in tube to zoneI of greenhouse.or

(ii)

An earth–air heat exchanger (EAHE): The PVCpipes having diameter of 0.06m and length of 78mhas been buried at depth of 1.5m. In this case air ofzone I is allowed through the buried pipes forextracting the thermal energy from ground. Then thehot air is fed into zone I.

The thermal blanket is light and transparent and it isonly moved when horticultural work is necessary. Afterits movement, it can be slide back almost effortlesslyalong the supporting wire. It remains permanently overthe plants all through out the winter period. A roof ventin the east direction has also been provided to overcomeoverheating as shown in Fig. 1a. The design parametersfor the proposed greenhouse have been given in Table 1.

3. Basic principle

The solar radiation, after transmission through the roofand the ceiling is absorbed by the plant and the ground ofgreenhouse. The thermal energy available in the plant andthe ground is transferred to room air by respiration,convection and radiation. The ceiling and the roofreduces the heat loss through the roof due to reducedvalues of heat transfer coefficient during day and night.Further, a thermal blanket is used over the plants toretain the temperature near the plants. Due to the thermalblanket, there is again reduction in top loss coefficientthrough the roof. In harsh cold climatic conditions thethermal blankets and curtains are not able to create adesirable temperature inside greenhouse. To enhance theroom air temperature of zone I geothermal energy or anearth–air heat exchanger are used. Since the east and westwalls are double glazed, little heat loss occurs throughwalls; however this has been taken into account.

4. Thermal modeling

Following assumptions have been made in writingenergy balance for different zones of greenhouse:

(i)

The greenhouse is in a quasi-steady-state condition. (ii) Radiative heat exchange between walls, roofs and

plant mass is neglected.

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Table 1

Input parameters used for computation

Parameter Values

Ae 36m2

Ag 105m2

An 20.8m2

As 20.8m2

As1 30.0m2

As2 42.0m2

Aer 54.6m2

Awr 55.9m2

Aww 36.0m2

CP 4190 J/kg �C

FP 0.3

h12 2.8W/m2 �C

h23 2.8W/m2 �C

h3a 9.5W/m2 �C

hg1 2.8W/m2 �C

hg1 0.52W/m2 �C

ht 65.31W/m2 �C

hP 27.35W/m2 �C

MP 190 kg

ag 0.4

aP 0.5

t1 0.95

t2 0.95

t3 0.8

A. Shukla et al. / Building and Environment 41 (2006) 843–850846

(iii)

Specific heat of plants in the greenhouse has beentaken to be the same as that of water.

(iv)

Relative humidity inside the greenhouse does notvary with height.

T1 ¼ðAIÞeffA þ F1ðAIÞeffG þ ðUAÞa�1Ta þ ðUAÞ1�aTa þ hPTPAP þ FR _macaTo þ h1aTaAs1

ðUAÞ1�a þ ðUAÞa�1 þ APhP þ FR _maca þ h1aAs1, (6)

(v)

Heat capacity of air inside the greenhouse isneglected.

Energy balance of the three zone greenhouse may beexpressed as follows:

For zone I

For plant mass:

ðaPÞðFPÞðt3Þðt2Þðt1ÞX6i¼1

AiI i

( )

¼ hPðTP � T1ÞAP þMPCPdTP

dt, ð1Þ

For ground:

ðagÞð1� FPÞðt3Þðt2Þðt1ÞX6i¼1

AiI i

( )

¼ hg1ðTg � T1ÞAg þ hg1ðTg � T1ÞAg, ð2Þ

For greenhouse air:

ð1� agÞð1� FPÞðt3Þðt2Þðt1ÞX6i¼1

AiI i

( )

þ hg1ðTg � T1ÞAg þ hPðTP � T1ÞAP þ _Qu

¼ h12ðT1 � T2ÞAg þ h1aðT1 � TaÞAs1, ð3Þ

where _Qu ¼ h5ATðTW � T1Þ thermal heating bygeothermal energy and _Qu ¼ FR _macaðTo � T1Þ heatingby an earth–air heat exchanger.

The hourly variation of the beam and diffuseradiation needed for theoretical validation of the datahas been shown in Fig. 1b. The total radiation ðI iÞ on ithcomponent of greenhouse has been evaluated by usingLiu and Zordan formula [25].

During off-sunshine hours

X6i¼1

ðAiI iÞ ¼ 0.

The energy balance for zones II and III may beexpressed as,

For zone II

h12ðT1 � T2ÞAg ¼ h23ðT2 � T3ÞAg þ h2aðT2 � TaÞAs2,

(4)

For zone III

h23ðT2 � T3ÞAg ¼ h3aðT3 � TaÞAR. (5)

With the help of Eqs. (2), (4) and (5), an expression forT1 from Eq. (3) can be written as:

where

ðaPÞðFPÞðt3Þðt2Þðt1ÞX6i¼1

AiI i

( )¼ ðAIÞeffP,

ðagÞð1� FPÞðt3Þðt2Þðt1ÞX6i¼1

AiI i

( )¼ ðAIÞeffG,

ð1� agÞð1� FPÞðt3Þðt2Þðt1ÞX6i¼1

AiI i

( )¼ ðAIÞeffA,

ðUAÞ1�a ¼h12AgððUAÞ2�a þ h2aAs2Þ

ðUAÞ2�a þ h2aAs2 þ h12Ag,

ðUAÞa�1 ¼h12ðUAÞ2�aAg

Agh12 þ ðUAÞ2�a

,

ðUAÞ2�a ¼h2ah3aARAg

Agh23 þ ARh3a

ARTICLE IN PRESSA. Shukla et al. / Building and Environment 41 (2006) 843–850 847

and

F1 ¼hg1

hg1 þ hg1.

After substituting the expression of T1 from Eq. (6) inEq. (1), the following first-order differential equation isobtained:dTP

dtþ aTP ¼ BðtÞ, (7)

where

BðtÞ ¼ZðAIÞeffP þ hPAPfF 1ðAIÞeffG þ ðAIÞeffA þ ðUAÞ1�aTa þ ðUAÞa�1Ta þ FR _macaTo þ h1aTaAs1g

ZMPCP,

Z ¼ ðUAÞ1�a þ ðUAÞa�1 þ APhP þ FR _maca þ h1aAs1

and

a ¼hPAP

ZMPCPððUAÞ1�a þ ðUAÞa�1 þ FR _maca þ h1aAs1Þ.

Assuming the solar intensity and ambient as well asgreenhouse air temperature uniform for 0� t timeinterval, the solution of Eq. (7) can be written as

TP ¼B̄ðtÞ

að1� e�atÞ þ TP0e

�at, (8)

where B̄ðtÞ is the average of BðtÞ for 0� t time intervaland TP0 is the initial plant temperature. Plant tempera-ture has been computed from Eq. (8) by using the designparameters of Table 1 and climatic data of Fig. 1b.Knowing the TP, the air temperatures of zones I, II, andIII have been evaluated by using Eqs. (6), (4) and (5) forfollowing cases:

(i)

without geothermal heating and an earth–air heatexchanger;

(ii)

with geothermal heating only; (iii) with an earth–air heat exchanger only.

4.1. Heating potential

Heating potential in zone I of the greenhouse isobtained from the equation:

Qh ¼X

macaðT1 � TaÞDt. (9)

4.2. Thermal load leveling

As the fluctuation of air temperature in the vicinity ofplants plays a vital role for their growth and develop-ment, these fluctuations in temperature have beenquantified by a factor called thermal load leveling(TLL) and is expressed mathematically as

TLL ¼T r;max � T r;min

T r;max þ T r;min. (10)

4.3. Statistical analysis

(i) Coefficient of correlation (r0)The coefficient of correlation can be evaluated from

the following expression:

r0 ¼NP

xi yi �PðxiÞ

PðyiÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

NP

x2i �

Pxi

� �2q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNP

y2i �

Pyi

� �2q . (11)

(ii) Root mean square of percent deviation (e)The closeness of predicted values and experimental

data can be presented in terms of root mean square ofpercent deviation. The expression used for this purposeis as follows:

e ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPðeiÞ

2

n

s; ei ¼

Xpred � X exp

Xpred. (12)

5. Results and discussion

In order to validate the present model, design andclimatic parameter of experimental greenhouse as givenby Barral et al. [10] have been used to compute room airtemperature of zones I and II, respectively. The resultshave been shown in Fig. 2.

Experimental results have also been given in the samefigure with coefficient of correlation (r0) and root meansquare of percent deviation (e) in Fig. 2. It is seen thatfor significance level of 0.3, the confidence level forpredicted temperatures in zones I and II are coming86% and 83%, respectively. It can be inferred that thereis fair agreement between theoretical and experimentalobservations.

The results for hourly variation of temperatureof zones I–III for different cases have been shown inFig. 3.

For comparison the hourly values of ambientair temperature has also been shown in the samefigure. It is clear from Fig. 3a that room air tem-perature in zone I is significantly higher in com-parison with temperature of zones II and III due tominimum heat loss from top as well as sides of zone I.In this case no additional heating of zone I has beencarried out.

Effect of geothermal heating during off-sunshinehours on temperature in zone I has been shown in

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0369

1215182124273033

19 20 21 22 23 24 1 2 3 4 5 6Time (Hour)

Tem

pera

ture

(°C

)

Predicted temperature in zone IPredicted temperature in zone IIExperimental temperature in zone IExperimental temperature in zone II

zone I, r’ = 0.81, e = 9.7 %zone II, r’ = 0.87, e = 10.2 %

Fig. 2. Hourly variation of predicted and experimental values of

temperature in greenhouse for southern part of Argentina.

Fig. 3. Hourly variation of temperature in three-zone greenhouse: (a)

without any heating; (b) with geothermal heating and (c) with an

earth–air heat exchanger for a typical day of February in southern part

of Argentina.

0

5

10

15

20

25

30

Without any heating With geothermal heating With an earth-air heatexchanger

Dai

ly H

eatin

g Po

tent

ial (

MJ)

Fig. 4. Variation of heating potential in first zone of three-zone

greenhouse for Argentina.

A. Shukla et al. / Building and Environment 41 (2006) 843–850848

Fig. 3b. There is a sharp increase of about 5.5 �C inroom air temperature during off-sunshine hours asexpected.

Effect of an EAHE on temperature of zone I,as shown in Fig. 3c, indicates that there is sharpdecrease in maximum temperature of zone I duringsunshine hours and marginal increase during off-sunshine hours as expected. It may be due to the factthat an EAHE acts as sink during sunshine hours andsource during off-sunshine hours. Thus, one canconclude that an EAHE cannot be economical forArgentina as shown in Fig. 4 in terms of heatingpotential (Eq. (9)).

Thermal load leveling has been calculated in zone Iof greenhouse for three cases namely greenhousewithout any heating, greenhouse with geothermalheating and greenhouse with an EAHE. It can beseen from Fig. 5, that value of TLL is maximum forgreenhouse without any heating, almost same forgreenhouse heating by geothermal energy and anEAHE.

Similar computations were carried out for coldclimatic conditions of Srinagar (34.09 �N latitude and74.83 �W longitude), India and the monthly heatingpotentials have been shown in Fig. 6 for differentmonths of the year.

It can be observed that the heating potential ismaximum during summer period as expected. It isimportant to note that an EAHE can be economical forthe places without any other source of heating namelygeothermal.

Effect of length and flow rate on heating potential fora typical day in February has been shown in Fig. 7. Thisindicates that the 20m length is optimum for theassumed design parameters. The heating potentialdecreases as mass flow rate increases. This can beexpected on the basis that the thermal loss at highermass flow rate.

ARTICLE IN PRESS

0

0.1

0.2

0.3

0.4

0.5

0.6

Without any heating With geothermal heating With an earth air heatexchanger heating

The

rmal

load

leve

ling

Fig. 5. Variation of TLL in zone I of greenhouse for a typical day of

February in southern part of Argentina.

0

100

200

300

400

500

600

700

800

900

Jan Feb March April May June July Aug Sep Oct Nov Dec

Month of year

Hea

ting

Pote

ntia

l (M

J)

Fig. 6. Monthly heating potential in first zone of greenhouse for 15

February 2004 in Srinagar, India.

15

16

17

18

19

20

10 20 30 40 50 60Length (m)

Hea

ting

Pote

ntia

l (M

J)

10

12

14

16

18

20

0.04 0.16 0.36 0.65 1.02 1.47Mass flow rate (kg/s)

Hea

ting

Pote

ntia

l (M

J)

(a)

(b)

Fig. 7. Variation of heating potential for 15 February 2004 with: (a)

length of pipe and (b) mass flow rate in first zone of three-zone

greenhouse in Srinagar, India.

A. Shukla et al. / Building and Environment 41 (2006) 843–850 849

6. Conclusions

On the basis of present study, the following conclu-sions can be made:

(i) Use of an earth–air heat exchanger is a viableoption in those where geothermal energy is notavailable.

(ii) Use of auxiliary geothermal heating is moreeffective for protecting winter growing plants againstchilled winter than an earth–air heat exchanger.

(iii) Desired temperature of air surrounding the plantscan be maintained by incorporating thermal curtain,blanket just above the plants and an earth–air heatexchanger (or geothermal heating) during cold winterperiod.

(iv) Fluctuations in temperature of air in zone arehigher in absence of any heating system and least in caseof greenhouse heating with geothermal energy.

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