estimation of an efficiency factor for a greenhouse: a numerical and experimental study

E L S E V I E R Energy and Buildings 28 (1998) 241-250

EI IE| G'I' AHD

UILDII IG

Estimation of an efficiency factor for a greenhouse: a numerical and experimental study

G.N. Tiwari *, P.K. Sharma, R.K. Goyal, R.F. Sutar Centre for Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi-110 016, India

Received 25 May 1997; received in revised form 14 October 1997; accepted 8 November 1997

Abstract

An analytical expression for instantaneous thermal efficiency (7/i) of a greenhouse in terms of design and climatic parameters has been derived by considering the energy balance equations for different components of the greenhouse. The present analysis can be used for testing the suitability of greenhouses of different sizes and shapes for given climatic conditions. Numerical computations for determination of instantaneous thermal efficiency (~?i) and greenhouse efficiency factor (F') have been carried out for a typical greenhouse. Parametric studies have also been carried out to predict the performance of the system. Experimental validation has also been reported for a climatic condition of Delhi. It is observed that:

1. there is a fair agreement between theoretical and experimental observations, and 2. the instantaneous thermal efficiency (~7i) increases with increase of relative humidity (7) due to less evaporation as expected.

© 1998 Elsevier Science S.A. All rights reserved.

Keywords: Greenhouse; Solar energy; Off-season crop production and thermal efficiency

1. Introduction

Greenhouses are now available in various shapes and sizes, suitable for different climatic zones. A greenhouse in an expensive option for rural farmers in India. Selecting a greenhouse that will perform most efficiently depends on many factors. Essentially, a well designed greenhouse should be able to maintain a required environment inside a greenhouse enclosure for healthy growth of plants for maximum yield.

Mathematical models have been successfully developed for describing heat and mass transport processes in a greenhouse micro climate [ 1-4] . Energy balance equations have been used to construct a model which permits prediction of climatic conditions in a greenhouse based on outside weather conditions [5]. These models have not considered the effect of evaporative and conductive losses from plant components and the ground respectively which is important to predict the thermal performance of a greenhouse.

To facilitate the modelling procedure, a greenhouse is considered to be composed of a number of separate but interactive components. These are cover, floor, growing medium, air space and crop.

* Corresponding author. Tel.: +91 11 666979/5040; fax: +91 11 686 2037.

Crop productivity depends on the proper environment and more specifically on the thermal performance of the system. The performance can be predicted using a mathematical model with proper assumptions.

In the present study, the effect of evaporative and conductive losses from the plant and floor respectively is considered to predict the performance of a particular greenhouse in terms of various design and climatic parameters; namely greenhouse efficiency factor (F ' ) , overall total heat loss coefficient (Ueff) and effective reference temperature (T~ff). An instantaneous thermal efficiency similar to a flat plate solar collector has also been derived in terms of design and climatic parameters.

2. Description and working principle of a greenhouse

The greenhouse design considered for analysis is 6 m X 4 m with a centrally raised roof, as shown in Fig. l ( a ) . The minimum and maximum height of the greenhouse are 2 m and 3 m respectively. A door having dimensions of 0.94 m × 1.80 m is provided on one of the shorter sides. The covering of the greenhouse is a single layer of UV stabilized poly- ethylene sheet having a transmissivity of 0.7.

0378-7788/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PIIS0378-7788(97)00062-5

242 G.N. Tiwari et aL /Energy and Buildings 28 (1998) 241-250

Transparent ~ : ~ roof i2,.~,:~"

Radiation

Convection

Opaque WaLl Curlains

(=~) g l ( t ]

(b)

qra

Cc

m

I" Tea

Ta

~ ~cp

=Cp

Fig. 1. (a) Cross-sectional view of a greenhouse showing various energy gains/losses. (b) Thermal circuit diagram of a greenhouse showing various thermal resistances. (c) Photograph of the experimental greenhouse.

Inside the greenhouse, plants are kept in pots on the floor. These plants have a large amount of foliage with an area about four times that of the floor area.

Since the study is under simulated conditions, it is assumed that no radiative heat exchange takes place from the sides of the greenhouse. Hence, all the vertical walls are covered using an opaque curtain. The entire radiation from a solar simulator is allowed to pass through the roof only.

The radiation after reflection and absorption is transmitted inside the greenhouse. Part of the transmitted radiation is absorbed by the plant leaf and the rest is absorbed by the uncovered floor area. Part of the absorbed energy is utilized to raise the plant temperature and rest is convected and radi- ated to the greenhouse enclosure room air. Hence the room temperature is increased due to thermal energy received from the plant as well as from the floor area.

A part of thermal energy from the floor is lost to the ground by conduction. The loss/gain of thermal energy from the enclosure room air to ambient air depends on the temperature difference between the two. The various thermal losses in the proposed greenhouse through different components are shown in a thermal circuit diagram, Fig. 1 (b). A photograph of experimental greenhouse is shown in Fig. 1 (c).

3. Thermal analysis

3.1. A l b r i g h t m o d e l

Albright et al. [6] have shown that the following simple time dependent thermal model of a greenhouse could ade- quately represent its heat balance under unventilated conditions mostly required for winter green_house for heating purposes.

[ dTm'~ .+aSo-U( i-To)-CtT)- =0 where a=so la r energy utilization coefficient, fraction; H = heat flux from heater, W / m 2 K; So = solar radiation flux on a horizontal surface, W/m2; U = overall heat transfer coefficient, W / m ~ K; Ti = greenhouse temperature, K; To = ambient air temperature, K; C=hea t capacity, J/K; Tm= greenhouse floor temperature, K; R = additional heat loss term, W / m 2 K.

Albright et al. [6] has not incorporated the parameters as mentioned below, required for cooling in harsh summer climatic conditions. 1. effect of evaporation from the plant which is very signif-

icant parameter for cooling requirement 2. ground thermal losses 3. ventilation for reducing inside room air temperature (%) 4. relative humidity which is an another important parameter

for cooling/heating By incorporating the above mentioned parameters for cool-

ing requirements of a greenhouse, a new thermal model has been produced.

G.N. Tiwari et al./ Energy and Buildings 28 (1998) 241-250 243

3.2. Proposed model

In order to write energy balance equations for different components of the proposed greenhouse, the following assumption have been made: 1. Properties of plant mass considered equivalent to water

mass for all thermal analysis proposes due to high content of water in the plant.

2. The relative humidity inside the greenhouse does not vary with height due to wetted floor/watering channel.

3. Analysis is based on quasi-steady state conditions inside the greenhouse due to transient behavior for short time intervals (At).

4. No stratification in temperature of plant, greenhouse enclosure, and covers etc. due to the low operating temperature range.

5. Heat capacity of air inside greenhouse is neglected in comparison to heat capacity of plants due to the larger specific heat of water.

6. Ground heat loss from the floor to the ground has been considered in a steady state mode. Energy balance equations for different components of the

greenhouse (Fig. l (a) ), are as follows:

3.3. Greenhouse plants

dTp +[hpAp (Tp-T R) +hep (To--T R)] ap('rs)=Mp dt

(1)

The rate of solar flux absorbed by plant surface = the rate of thermal flux used to raise the temperature at the plant + the rate of thermal energy convected and evaporated from the plant to enclosed room.

3.4. Greenhouse floor

ag(1-ap)(~-s)=-k~x AG+hGAc (TIx=o-TR) x = 0

(2)

The rate of solar flux received by the floor surface = the rate of the thermal energy conducted into the ground at x = 0 + the rate of thermal energy transfered to the greenhouse enclosure due to convection and evaporation.

of room air + The rate of thermal energy convected out of greenhouse through each wall surface, roof and door.

[V I(TR-T a)]-[hp (Tp-T R) +hep (Tp-T R)]Ap

--AGhG (TI,,=o-TR) (3)

the rate of thermal energy carried away due to ventilation- the rate of thermal energy transfered by convection and evaporation from the plant to enclosed room-the rate of thermal energy transfered by convection and evaporation from the floor to greenhouse enclosure, where

h~p = 0.016hp[ P(TP °) - "/p(TR°) ] Tpo - TRo

without linearisation of p(T)

or,

[ RI(Tpo- ~/Tro) + R2( 1 - " / ) ] hep = 0.016hp Yp o _ Tro ;

with linearisation of p(T) = RIT + R2

and R1 and R2 can be obtained by linear regression analysis for a given operating temperature range which varies with climatic conditions.

S=AESE+AwSw+ANSN+AsSs+ARSR

V 1 -- 0.3 NV and Ma = 0 (assumption 5 ) The rate of thermal energy conducted in the ground can be

expressed as

-k~T I =hb (Tlx=o-T~) OX x=o

with

T I x ~ = T ~ = T a

The rate of evaporated mass can be evaluated by using the following expression:

Ii%= hep (Tp-TR) (3a) h

Eqs. ( 1 ) - (3) , after neglecting heat capacity of air, can be combined into the following form:

dTt' +aTp=f( t ) (4) dt

3.5. Greenhouse enclosed air

(1-ag)(1-ap)( ' r s )

dTR = M.---~- + [ h(t) (TR-T. ) +hDAD (TR-T. ) ]

The rate of solar flux received by the greenhouse enclosure = the rate of thermal energy used to raise the temperature

where

a= M~p[(hpAp+Aphep)( 1 - h p A P + A e h e r ] ] U, ].]

and

f(t) = M~p[(°rr)effS + (hpAp+Aph'p)(U2+Ub) T " + K K ] u ,

244 G.N. Tiwari et al./ Energy and Buildings 28 (1998) 241-250

Eq. (4) can be solved with following assumptions. • Integrating with limit 0 - t = A t (t--3600 s for present

study) • In i t i a l c o n d i t i o n Tp [ x = o = Tpo • f(t) can be considered as f(t) for At time interval. • most of heat transfer coefficients are constant for At time

interval. The solution of Eq. (4) is

f(t) Tp= ( 1 - e -a~) +Tpoe -at (5) a

After knowing the plant temperature Tp, the value of enclosed room air temperature TR Can be determined using the following expression,

TR---- [(h~'effI+%ff2)'rS+(U2+UbAG)Ta+HPG'Tp] (6) Ul

Here, it is important to mention that f(t) and 'a' depend on design and climatic parameters including cooling effects through U1, U2, KK and h,p. The decrease or increase in the plant temperature can be achieved with and without cooling effect for summer and winter conditions respectively. How- ever, the supplemental heat, if required, can be supplied by external sources and this effect can be incorporated in the left hand side of Eq. (3). It is only required for few days in harsh winter conditions of Delhi. In this way, the overall thermal efficiency can either be reduced or increased as per requirement.

Eqs. (5) and (6) can be used to determine the plant and enclosed room air temperature for a complete cycle (24 h) for a given climatic condition.

An instantaneous thermal efficiency of a greenhouse is the ratio of thermal energy used to raise temperature of the plant from Tpo to Tp to input energy and it is given by

Table 1 (a) Design parameters for a greenhouse without linearisation of p(T)

Serial. Design Expression for design Remarks No. parameters parameters

1. F' M e ( 1 - e - at) Greenhouse efficiency factor determines overall instantaneous thermal efficiency Eq. (5) U~ff.t

[ hTeffl + Tell2 ~ - - - - - 2. (aT)eft (O~pT) + [ ~t t ] ( ['ll'l(j )

3. Ua~ (hpA0 + hepAp) ( 1 - HPG/U,)

HH.Ta+ KK 4. Teff

U0ef

5. HH HPG (U2+Ub) /Uj 6. HPG hoA p + Aolae p 7. Ub Ac, h ~ / ( h b h c ) 8. U~ h(t) +AohD+ V~ + Ub + HPG 9. U2 h(t) + ADhD + VI

10. %e*, as( 1 - % ) r

11. ~'eef2 (1 - as) (1 - ap) ~"

(b) Design parameters for a greenhouse with linearisation

Serial Design parameters and their expression

No.

Determines the utility of solar radiation for controlled environment in the greenhouse

Strong function of various heat loss coefficients and surface areas

Generally it is equivalent to ambient, similar to characteristics curve for flat plate collector

1

2 3 4 5 6 7 8 9

10

(Or'/') eff = 0¥.'r + (h%m + %f~)HPGT/UI T~u = (HH Ta + K K - HPGVt /U0 /Uaf t HH = (U 2 "~- UbAg ) HPG/U~ KK = - HPGK/U~ - HoApR2( 1 - y) HPG = Ap(hp + hoyRi ) Ut = ~A~h~(t ) + AD" ht, + V~ + hpAp + hoAp "yR 1 @ UbAg U 2 = ~Aih i (t) + AD" hD + V l %m = ag ( 1 - ~ )

~efr2 = (1 - otg) (1 -Otp) K = - R2( 1 - y) hoAp

G.N. Tiwari et al. / Energy and Buildings 28 (1998) 241-250 245

Mp (Tp-Tpo)

= Mp(1-e -a t ) [(ot,r)eff~-Ueff(Tpo-Teff)] SU~fft

,F [ Teo- Teef ~-] =F )J (7)

where F' and ( O/'r)eff are the greenhouse efficiency factor and an effective absorptivity-transmittivity product for greenhouse respectively. The effective overall heat transfer coefficient from the plant to the effective outside temperature (T~ff) is given by U~ff.

An expression for F', (a~')eff, Ueff and T~ef are given in Table 1 with remarks.

Eq. (7) is similar to the characteristic equation of a flat plate collector (FPC) which is the equation of straight line between */i and (Tpo -T~f f ) / i . Eq. (7) has been derived for the first time for greenhouse applications which is only valid for lower heat capacity of the plants. In this case, the second term gives the loss factor = gradient = m = - F'U~ff i.e. the slope of the curve ( @ = tan- 1 m). For heating and cooling of greenhouse, this term should be minimum and maximum respectively which can not be derived from Albright model.

4. Numerical computations, results and discussion

In order to evaluate Eqs. (5 ) - (7 ) , the design parameters of Table l (a ) and (b) and Table 2(a) and (b) have been used. The results obtained for Tp, TR, Teff, Ueff, (C~'/')eff, 1"/i and F' have been shown in Figs. 2-8 and Table 3.

The derived heat balance equations have been used to prepare a computer program written in FORTRAN 77. The

inputs for the program are ambient temperature, the air exchanges @ 5 per minute in the summer climate, solar intensity (both averaged over one hour period), relative humidity inside the greenhouse and greenhouse design data viz. area of greenhouse, area of plant cover, mass of plant material, transitivity etc.

The output of the program provides the hourly average temperature of plants, temperature of greenhouse enclosure, and values of design parameters such as F', (Tpo-Teff)/S, and the instantaneous efficiency (r/i).

In order to verify the accuracy of the developed model, experimental validation was carried out for design parameters given in Table 2(a) and (b) for winter as well as summer climatic conditions of Delhi. The effect of cooling namely ventilation has been considered for summer condition only (rate of ventilation during peak sunshine hours has been taken as 6000 Kg°C/h). The measured values of solar intensity (S) and ambient temperature (Figs. 2 and 3) for both climatic conditions obtained during the experiment were used for computation purposes. The temperature of plant (Tp) and enclosed room air (TR) and instantaneous thermal efficiency (~i) have been calculated by using the Eqs. (5 ) - (7 ) . The plant temperature was measured by infrared thermometer. The obtained results for the plant temperature (Tp) and enclosed room air temperature (T~) for both climatic conditions (November, 1995-June, 1996) have been shown in the same Figs. 2 and 3 for comparison purposes. The difference between theoretical and experimental plant and the room air temperature found to vary from - 2.6°C to 4.5°C. It can therefore be observed that there is a fair agreement between theoretical and experimental results for both climatic conditions. Further, it is important to mention here that there is about 14°C increase in the enclosed room air temperature during the day time and it becomes equal to ambient temper-

Table 2

Symbol Value Symbol Value

(a) Constants used for the experimental study Ao 24.0 m 2 7 0.7 Aa 26.4 m 2 a v 0.55 Ao 1.70 m 2 ot~ 0.06 Ao 8.0 m 2 y 0.4 Mo 80.0 X 4190 J/°C lab 1.0 ho 5.7 W/m2°C hD 3.99 hp 5.7 W/m2°C v 0.0 t 3600 s Ca 1006.0

(b) Constants used in the present simulation (for Figs. 7 and 8) A~ 8.0 m 2 ~" 0.7 A R 11.314 m 2 o v 0.55 (Assumed due to green leaves) AD 1.0 m 2 O~G 0.06 (Takakura, [9] ) Ap 40.0 m 2 y 0.4---0.8

Mp 80.0 × 4190 J/°C hb 1.0 Ta 15 °C bD 3.99 Tpo 17°C 1~ 147.7 s(t) 500 W / m 2 lap 5.7 t 3600 s v 0.0

246 G.N. Tiwari et aL / Energy and BuiMings 28 (1998) 241-250

r~ 40 o

15

10

4o

~0 ~ 25 g, 2o

10 5 0

I?

f I | '

0 4 8 12 16 20 24 T i m e o f the d a y , h

(i) N o v . , g 5

I I F " i /

• 4

3

4 8 12 16 20 24 Time of the day,h

. r (p)

• Tr(e)

700 e ~ 35

600 "~ 30

500 ~, ~ 25

400 "~ ¢~ ~ 20

200 "q o ~' 10

,100 ~ 0

700 ~1~ 35

600 .~. 30

500 °r'> 25

300 ~ ~ 15 ~oo ~ 100 ~ 10

5

• Tr(P) e T&

I I I I

f 5

0 ' /J 0 0 ,~ 8 12 16 20 24

Time of the day,h

( i i ) D e c . , 9 5

"' r" , , , ' "1 600

- Lo?t 1 "oo

" 17 1~, - I ~ ° ° ~

_,5t t1 4::: 0 4 8 12 16 20 24

Time of the dey, h (iv) Feb.96

v T ( e )

5O0

500

200

1100

Fig. 2. Hourly variation of different temperatures namely, T o, TR, T, and solar intensity for January, 22.

oO 413

50

10

45 k;

o 40

2 0

I I % n I I '

0 4 8 2 16 20 24

T i m e of t h e D a y , h

(i) M a r c h , 9 6

70(3 o ''} 55

600 ~ ~- 30

400 .~

~oo 2

100

0

l I I 1 I "

0 # B 12 16 20 24

T i m e o f t h e D a y , h

(ii[) Ma y ,9 6 Tp(p)

• Tp(e)

t800 =E~ o° 45

600 ~ ~ 4 0

- 20o a & so

0 ~ ~ 25

• T ( p )

o T ( e )

i I I I I ' "

0 4 8 12 16 20 24

T i m e o f t h e D a y . h

(ii) A p r i l , 9 6

~ 0 4 6 12 16 20 04

T i m e of t h e D a y , h

( i v ) J u n e , 9 6 ,, T &

1000 =~

1800

600 "~ @

400

' 200

600 ~

500 ~-

400 .~

300

200 .~

100

0

Fig. 3. Hourly variation of different temperatures namely, Tp, TR, Ta and solar intensity for May, 22.


o,..,

25

20

15

10

h b

I I t I

4 8 12 16

Time of the Day (h)

i 40

3O

"~ 25 ~E

-

]' 20

I 10 20 24

Fig. 4. Hourly variation of different temperatures namely, T~tr, T~ and Uef f

for January, 22.

45 ~ 1000

4-0

t:-', 30

2 5 I r I t I

0 4 8 12 1 O 20 24

Time of t he Day (Ix)

800

00o S" ca

¢ ,400

200

Fig. 5. Hourly variation of different temperatures namely, T~ff, T, and U~ff for May, 22.

ature in off-sunshine hours. The temperature during off-sunshine hours can be further increased either by covering the north portion of greenhouse (Northern Hemisphere) or by providing the additional heat from other sources. From Fig. 3, it can also be seen that inside room air temperature is about 2-3°C higher than ambient temperature due to ventilation by forced convection. For both climatic conditions, the plant temperature was lower than enclosed room air temperature due to evaporation and transpiration from the plant leaves as expected. The room temperatures can be further brought down by using evaporative cooling even below the ambient temperature by about 3-5°C. The relative humidity is increased by misting arrangements.

The hourly variation of T~ff, U~ff of Table 1 (a) for both winter and summer climatic conditions have been shown in Figs. 4 and 5 respectively. It can be observed that T~rf is exactly same as T a for winter climatic condition (Fig. 4). It is due to the fact that no ventilation effect was considered in

winter. It can also be seen analytically in Table 1 (a). How- ever, T~ff is lower than T, in summer due to inclusion of ventilation effect (Fig. 5). From the same figures, one can conclude that the U~ff is lower during sunny hours and higher in off-sunshine hours in accordance with the results reported

v

VI

o

. i o

.o

.~.

m

o

m

(a) Heating

8

7

8

5

4

3

2

1

0 0.00

i i i

t i i

o.o~ o.o2 o.oa

qr~- T.n) / S

(b) Cooling 2.5

2 0

1.5

1.0

0.5 - 0 . 0 0 3

I I

I I - 0 . 0 0 2 -0 .001

0,04

0.000

(Tg-Tet f ) /S

Fig. 6. Instantaneous efficiency curve for (a) heating and (b) cooling without linearisation of the partial vapor pressure (p (T) ) .

0.80

L L

0

"6 0.75 LL

u

0.70 W

¢-

c

0.65 t .9

--f-- E f f i c iency

0.5

0.4 ~

W

0.3 E

e- l -

0.2 o

0

c O

0.1 E

0-60 L I t 1 I t I 0.0 0 t. 0-5 0.6 0.7 0.8

R e l a t i v e H u m i d i t y ( 't ')

Fig. 7. Effect of relative humidity on F' and thermal efficiency without linearisation of the partial vapor pressure (p (T) ) without linearisation of the partial vapor pressure (p (T) ) .

248 G.N. Tiwari et al. / Energy and Buildings 28 (1998) 241-250

0.70

0.6~ "lJ-

0 *6 0

u_ 0.66

c ._~ u

m 0.6 t.

o t- c

~ 0.62

0.60 10

F' 0.390

Efficiency '0.389 ~- >,, ~J

0.388

0-387

0.386 "6

o.385

0-38/, o

2 0 383

0.382

0,381

, , , ZnO.380 15 20 25 3~0 35

Plant area (sq. rn) Fig. 8. Effect of plant area on F ' and thermal efficiency without l inearisation

of the partial vapor pressure ( p ( T ) ) .

Table 3 Hourly variation of greenhouse efficiency factor ( F ' ) and (a~)eft

Time of the day Winter Summer

6.00 - - 0.0194 0.43 7.00 - - 0.00956 0.48 8.00 0.11 0.59 0.00772 0.51 9.00 0.13 0.567 0.00955 0.48

10.013 0.17 0.52 0.01 0.46

l 1.00 0,16 0.525 0,01 0.47 12,00 0.15 0.53 0,01 0.48

13.00 0.14 0.56 0.007 0.52 14.00 0.13 0.56 0.006 0.56

15.00 0.13 0.56 0.003 0.75 16.00 0.13 0.56 0.003 0.71

17.00 0.13 0.56 0.003 0.69 18.00 - - 0.003 0.70

19.00 - - 0.003 0.69

earlier. Further, the value of Uaf in summer is much higher the winter value due to ventilation effect.

The plot of Eq. (7) for both climatic condition has been shown in Fig. 6. It shows the characteristics curve ( ~7i. versus (Tpo-T~f0 /S ) ) for a greenhouse operating under winter climatic condition. The behavior of this curve is similar to the characteristics curve of a fiat plate collector (Fig. 6.17.2 of chapter 6 at page no. 307 of Duffle and Beckman, 1991). The characteristics curve of a greenhouse having non linear phenomena due to variation in the Uaf (Fig. 4) unlike fiat plate collector. However, the characteristics curve of the same greenhouse for summer climatic condition with cooling effect behaves just opposite to the characteristics curve of winter greenhouse as expected. It is due to the fact that Taf in summer is lower than ambient air temperature as mentioned earlier.

The hourly variation of F' and (otr)~ff for both climatic conditions have been given in Table 3. It is observed that there is a variation in F' and (c~')~ff for conditions. It is due to the temperature dependent evaporative heat loss from the plant to the enclosed room air.

It can be observed from Fig. 7 that the increase of relative humidity inside the greenhouse enclosure increases the efficiency of the greenhouse. More energy is, therefore available to the plant matter than it lost through the enclosure.

However, as the plant area increases, there is a marginal drop in efficiency. This drop, shown in Fig. 8, is quite insig- nificant compared to the 3-4°C increase in the enclosure temperature which is reflected in the decrease of the greenhouse efficiency factor F'.

Due to the generalized nature of certain data taken in this study, the estimates could be approximate. However, there is a definite trend which can be seen from the Figs. 7 and 8. The values of certain terms such as Teff and Greenhouse Efficiency Factor F', have been predicted as expected.

The values of TR and Tp predicted is less than the experimental because of the following reasons: 1. the theoretical results are for ideal condition, i.e. without

stratification in vertical position inside the greenhouse (one of the consumption).

2. in the real situation, there was stratification from the top of the plant to the canopy cover due to fact that there was always quick replacement of top air by the exhaust fan.

5. Conclusions

Based on numerical computations for indoor simulation of a garden greenhouse, the following conclusions have been drawn: 1. instantaneous thermal efficiency (r/i) of a greenhouse

increases with increase of relative humidity inside the enclosure,

2. instantaneous thermal efficiency (r/i) and greenhouse efficiency factor (F ' ) decrease insignificantly with an increase of plant area for a given heat capacity of the plant, and

3. there is a reasonable agreement between theoretical and experimental results for both climatic conditions.

6. Recommendat ion

The proposed model can be used for testing and standari- zation of a greenhouse of any design for any climatic conditions. The model which is very simple, has been found very effective in prediction of the plant and the room air temperatures.


7. Nomenclature

A area, m 2 AD area of door, m 2 Am greenhouse floor area, m 2 Ap area of foliage AR area of roof, m 2 Ca specific heat of air, J /Kg °C F' greenhouse efficiency factor hb heat transfer coefficient between floor and soil, W/

m 2 °C

hD heat transfer coefficient between room air and ambient air through door, W/m 2 °C

h~p evaporative heat transfer coefficient from the plant to enclosed room air, W / m 2 °C

hc heat transfer coefficient between floor and the air W / m 2 ° C

hp heat transfer coefficient between the plant and the enclosure air, W/m 2 °C

h(t) overall total heat transfer coefficient from inside room to ambient through walls, floor and canopy cover, W / m 2 °C

K thermal conductivity of soil, W/m°C L thickness,m Mp heat capacity of plants (mass of plants x specific

heat of plants), J/°C Ma heat capacity of enclosed air (mass of air x specific

heat), J/°C N number of air changes/h from the door ventilation p(T) partial vapor pressure at temperature T, N /m 2

(p(T) = RvT + R2; RI and R2 can be obtained by linear regression)

S(t) intensity of solar radiation (hourly average) at time t, W / m 2

T lx=o temperature of ground at x = 0 (floor), °C Ta ambient temperature, °C Tp plant temperature at time t, °C Tpo plant temperature at time t = 0, °C TR greenhouse enclosure room air temperature, °C t time, s V I rate of exchange due to ventilation, W/°C x position coordinate along depth inside ground, m V volume of the greenhouse, m3

Greek letters

% o~ G ap

A

T */i

absorptivity of green house floor absorptivity of greenhouse cover (canopy cover) absorptivity of plant transitivity of canopy cover latent heat of vaporization, J /Kg relative humidity instantaneous thermal efficiency

Suffix d dry soil

D door E east G floor m moist soil N north p plant R room S south W west

Acknowledgements

The work reported in this paper was partially supported by ICAR, Govt. of India, New Delhi.

Appendix

(a) Calculation of lab An overall bottom loss coefficient can be calculated by the

following formula

hb= + L---~ (A-l)

By substituting the above values in Eq. (A- l ) , hb = 1.5 W /m 2 °C.

(b) Calculation of h(t) An expression for h(t) is given by

h(t) = hE(t)AE + hw(t)Aw + hrq(t) Ar~ + hs(t)As + hR(t)AR

hE is the overall heat loss coefficient from enclosed room air to ambient through east wall transparent cover and can be expressed as

hE(t) ---- +

where hi and hE are internal and external heat loss coefficient and can be expressed as

hi =hp+h~p

and the external heat loss coefficient is as suggested by Duffle and Beckman [7] and Wong [8]

h2=5.7+3.8V

Similarly, other heat transfer coefficients for walls and roof can be evaluated.

(c) Calculation of ho The numerical value of hD can be calculated from the

following expression:

1 + LD

250 G.N. Tiwari et al. / Energy and Buildings 28 (1998) 241-250

(d) Calculation of lag The hG can be obtained as

hG.I~ Nu= =C(Ra) n (A-2)

K ,

where C = 0.54 and n = 1/4 for a hot surface facing upward, [91.

From above equation,

i hc = 0.54Ka_ (Ra) L

For an average enclosed room temperature (TR)----32°C and AT = 5°C, the following physical properties of moisture have been used.

Thermal conductivity = 0.623W/m°C

Raileigh number(Ra) =2.482213X10m.L 3 .AT

Average f loor dimension (I) = 3m

After substituting above parameters in Eq. (A-2), one gets, lag = 147.7 W / m 2 °C.

References

[ 1] F.I. Soribe, R.B. Curry, Simulation of lettuce growth in an air supported plastic greenhouse, J. Agric. Engg. Res. 18 (1973) 133- 140.

[2] P. Chandra, L.D. Albright, N.R. Scott, A time dependent analysis of greenhouse thermal environment, Trans. ASAE 24 (2) ( 1981 ) 442- 449.

[3] P. Chandra, J.K. Singh, A.K. Dogra, G. Majumdar, Solar energy collection potential of plastic greenhouse, Energy 4 (1989) 21-27.

[4] X. Yang, T.H. Short, R.D. Fox, W.L. Bauerle, Dynamic modelling of the micro climate of a greenhouse cucumber row crop, Part I, Theo- retical model. Trans. ASAE 33 (5) (1990) 1701-1709.

[5] M.J. Maher, T.O. Flaherty, An analysis of greenhouse climate, J. Agric. Engg. Res. 18 (1973) 197-203.

[6] L.D. Albright, I. Sieginer, L.S. Marsh, A. Oko, In situ thermal cali- beration of unventilated greenhouses, J. Agric. Engg. Res. 31 (1985) 265-281.

[7] J.A. Duffle, W.A. Beckman, Solar Engineering of Thermal Processes, 2nd edition, Wiley, New York, 1991.

[8] H.Y. Wong, 1977, Heat Transfer for Engineers, Longman, London. [9] T. Takakura, K.A. Jorden, L.L. Boyd, Dynamic simulation of plant

growth and environment in the greenhouse, Trans. ASAE 14 ( 1971 ) 964-971.

estimation of an efficiency factor for a greenhouse: a numerical and experimental study

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