Transient analysis of a winter greenhouse integrated with solar still

Transient analysis of a winter greenhouse integrated with solar still

Energy Convers. Mgmt Vol. 27, No. 3, pp. 267-273, 1987 Printed in Great Britain. All rights reserved 0196-8904/87 $3.00 + 0.00 Copyright © 1987 Perga...

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Energy Convers. Mgmt Vol. 27, No. 3, pp. 267-273, 1987 Printed in Great Britain. All rights reserved

0196-8904/87 $3.00 + 0.00 Copyright © 1987 Pergamon Journals Ltd

T R A N S I E N T A N A L Y S I S OF A W I N T E R G R E E N H O U S E I N T E G R A T E D WITH SOLAR STILL Y. P. YADAVt and G. N. TIWARI:~ Centre of Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi 110 016, India

(Received 2 May 1986) Abstract--The present work deals with a simple transient analysis of a winter greenhouse integrated with a solar still. Explicit expressions for the temperatures of still cover, brine (basin-water), basin of the still/roof of the greenhouse, greenhouse air, plants and floor of the greenhouse have been developed so as to study the transient thermal performance of the system. The effect of several parameters, namely relative humidity, ventilation/infiltration, heat capacity of basin water and plants, etc. has been incorporated in the analysis. On the basis of numerical calculations, some interesting conclusions have been made. Greenhouse

Solar still

Transient analysis

NOMENCLATURE Ab = Ad = Ar = Ag = ,4 =

Ap = Ca = ht = h2 = h3 = h4 = h5 = h6 = hd = he~ = h~ = hf = hp = H. = Ht2 = Hw =

Area of basin o f still/roof of greenhouse (m 2) Area of door (m 2) Area of floor of greenhouse (m 2) Area of one of still covers (m 2) Area of wall o f greenhouse (m2); i = E, W, N, S where E, W, N, and S correspond to east, west, north and south walls, respectively Area of plants (m 2) Specific heat o f air (J kg -I °C - t ) Heat transfer coefficient from brine to glass cover (W m-2 oC -1 ) Heat transfer coefficient from glass to ambient (Wm 2°C-l) Heat transfer coefficient from basin to water (W m -2 °C - l ) Heat transfer coefficient from basin to greenhouse air (W m -2 °C -1) Heat transfer coefficient from basin to plants (Wm-I oc-I) Heat transfer coefficient from basin to floor of greenhouse (W m 2 °C- i ) Heat transfer coefficient from door to ambient (W m -2 °C - l ) Evaporative heat transfer coefficient from brine to glass cover (W m -2 °C-i ) Heat transfer coefficient from greenhouse air to ambient (W m 2 oC-~) Heat transfer coefficient from floor to greenhouse a i r ( W m 2oc ~) Heat transfer coefficient from plants to greenhouse air Solar intensity at first surface of inclined glass cover (W m -2) Solar intensity at second surface of inclined glass cover (W m -2) Solar intensity available at vertical wall o f greenhouse, where i = E, W, N, S ( W m -2)

~'Lecturer, Department of Physics, C.M. Science College, Darbhanga, Bihar. :~Assistant Professor in the Centre. Current address for correspondence: Department of Physics, The University of Papua New Guinea, P.O. Box 320, Papua New Guinea. E.C.M. 27/3 A


L = Latent heat of vaporization to m = Number of air changes due ventilation/infiltration thew = Mass of distillate from solar still (kg m -2) Mp = Heat capacity of plants (J ° C - t) Mw = Heat capacity of brine/basin water (J °C-~) p = Partial pressure of water vapour at temperature T (Pa) 3R H = Difference in absolute humidity in inside and outside air Ta = Ambient temperature (°C) Tb = Basin temperature of still (°C) Ts = Still cover temperature (°C) Tt = Floor temperature o f greenhouse (°C) Tp = Plant temperature (°C) TR = Air temperature inside greenhouse (°C) Tw = Brine temperature/water temperature of still (°C) T® = Ground temperature (°C) zt~ = Fraction of energy absorbed by first inclined still cover zl2 = Fraction of energy absorbed by second inclined still cover z 2 = Fraction of energy absorbed by brine/water o f still z3 = Fraction of energy absorbed by basin o f still z~ = Transmittivity of vertical wall, where i = E, W, N,S ~a = Absorptivity of air inside greenhouse ctf = Absorptivity of floor of greenhouse % = Absorptivity of plants y = Relative humidity

INTRODUCTION With the development of greenhouses and water c o n s e r v a t i o n t e c h n i q u e s in agriculture, it is p o s s i b l e to have small scale agricultural activity in places w h e r e only saline o r b r a c k i s h w a t e r is available. Solar distillation m a y , in m o s t cases, be able to p r o v i d e the r a t h e r m o d e s t d e m a n d for fresh water, c o n s i s t e n t with a clever choice o f c r o p s , a suitable t h e r m a l e n v i r o n m e n t p r o v i d e d by the g r e e n h o u s e a n d efficient water conservation technology. Thus, an integrated



design of greenhouse-cum-solar still presents an exciting possibility for support of small scale agriculture in places where only saline or brackish water is available. The part of solar radiation, essential for the growth of plants, may be provided by having part of the wall of glazing or transparent plastic material on the basis of the still, forming the roof of the greenhouse, made of transparent material. Thus, it is the desert climate, where fresh water is not easily available, which gave rise to the concept of a controlled environment greenhouse. Fresh water for irrigation purposes becomes a costly commodity when transported to these areas [1-3]. This problem is overcome in a greenhouse integrated with a solar still, as it provides the fresh water needed for the irrigation of plants grown within the greenhouse itself. Although several authors have studied in detail different aspects of solar distillation and thermal load levelling in buildings, little attention has been paid to the use of solar stills for controlling environment, along with distilled water production; the work has been restricted to greenhouses. Several greenhouses combined with solar stills are available in the literature. Two small greenhouses with solar stills incorporated in them were constructed by Qasim [4]. The difference between the first and second unit, from the design point of view, was that the top part of the second unit containing the solar still was completely sealed off from the greenhouse below. It was found that none of the plants in the first unit survived, while all the plants in the second unit survived. Tinant et al. [5] constructed a greenhouse to study the viability of several kinds of polyethylene sheets. The shortcoming of this design is that only one part of the still cover is exposed to solar radiation. Selcuk[6] has analysed the thermal performance of a greenhouse whose roof is covered with a solar still. The thermal analysis carried out by Selcuk [6, 7] is complex, and hence is difficult to use for optimization of certain parameters. Recently, Tiwari and Dhiman [8] have proposed a mathematical model of a greenhouse, based on periodic analysis, whose top surface is covered by a solar still. Their model is almost identical to the proposition of Sodha et al. [9] that a still can be placed on the roof of a building for producing distilled water and at the same time assisting in air conditioning the building. The mathematical model of Tiwari and Dhiman [8] regards the basin of the still as painted black and the base of the still is such that it does not allow passage of the visible solar radiation needed for growth of the plant. Further, they have taken into account the variation of ground temperature, which is not needful because the diurnal fluctuations of temperature at the surface of the earth are fully damped out in the first few centimeters from the surface, as suggested by Eckert and Drake[10] and Ramakrishna Rao et al. [l 1]. Moreover, this model deals only with the periodic thermal performance of the system. In actual

practice, due to watering of the plants, the system attains a transient behaviour which could not be accurately studied by the periodic analysis presented by Tiwari and Dhiman [8]. Keeping in view all these considerations, we have developed a transient analytical model of a winter greenhouse integrated with a solar still (Fig. 1). The base of the solar still, lodged in the upper part of the house, is made of a semi-transparent plastic which permits a sufficient amount of visible solar radiation to penetrate into the greenhouse, unlike Tiwari and Dhiman [8]. This helps plants growth due to improved photosynthetic activity. Both the inclined still covers intercept solar radiation, unlike Tiwari and Dhiman [8]. The still covers (semi-transparent plastic) are inclined so that the condensed water could trickle down along the collector-trough. The four walls of the system are also made of semi-transparent plastic, and a door on the north side has been provided for entrance/air changes. As the diurnal fluctuations of the temperatures at the surface of the earth are fully damped out within the first few centimeters from the surface, the ground temperature has been regarded as constant over short periods (such as a day). This concept helps in introducing an overall heat transfer coefficient for the heat transferred from the floor of the greenhouse to the ground and, in this way, enables one to get rid of solving the conductivity equations, as done by Tiwari and Dhiman [8]. Explicit expressions for the temperatures of still cover, brine, basin of the solar still, greenhouse air, plant and floor of the greenhouse have been developed, based on the transient analysis of the system. Various parameters, namely relative humidity, ventilation/infiltration, heat capacity of brine (basin water) etc., have also been incorporated in the analysis to investigate their effects on the performance of the system. In order to reduce the night heat losses through the walls of the proposed design, the walls were covered by movable insulation (say Tirpal) during off-sunshine hours. Numerical calculations have been made for the same sets of climatic and system parameters as done by Tiwari and Dhiman. On the basis of the numerical results, the following conclusions have been made: (i) A winter greenhouse integrated with a solar still reaches a quasi-steady state after 3-4 days of either plantation or watering of the plants; (ii) A significant effect on the inside air temperature was observed after watering the plants; (iii) An increase in yield of the still and inside air temperature was observed due to covering the walls by Tirpal during off-sunshine hours; and (iv) The fluctuation in the inside room air temperature is reduced by increasing the water mass in the basin, which reduces the yield of the still. ANALYSIS Figure l shows the schematic sketch of the green-



STILL-COVER~ ;'1 " e R , N E ( S T , L L - W A T E R ) - - - - BAS,N OF Sr,Lt




[:c_2~----2t,~---~-! Fig. 1. Schematic diagram of the greenhouse integrated with solar still.

house integrated with the solar still. The following Brine assumptions have been made while writing the energy z~Ag('ru Hi1 + "q2Hl2) + Abh3(Tb -- Tw) balance for the various components of the system: (1) The heat capacity of the transparent plastic is negli=Mdrw w d t + A b h l ( T w - T~). (2) gible, and there are no temperature gradients along its thickness and water depth; (2) The heat capacity of air inside the greenhouse is negligible; (3) The pot Basin o f the still~roof o f the house temperature is the same as that of the plants; (4) The surface area of both still covers is the same; (5) The ~3Ajql H. + Zl2Hl2) water mass in the basin of the still is constant; (6) = Abh3(Tb -- Tw) + A b h , ( T b - TR) There is no leakage in the still; (7) The area of the water surface and basin surface over which water + Abhs(Tb - Tp) + Abh6(Th -- Tr). (3) stands are the same; (8) The convective heat transfer coefficients are considered to be constant; and (9) Greenhouse air There is no temperature gradient along the wall u,(AiriHvi) thickness. The heat and mass transfer relationships in the + A b h , ( V b - TR) + Aphp(Tp -- TR) solar still have been written following Dunkle [3]. + A p h o { p ( T p ) - yp(TR)} + A r h r ( T f - TR) Now, the energy balances at the still cover, brine in the solar still, basin of the still, greenhouse air, plants = Aih~(T . - T~) + A d h d ( T , - L ) and floor of the house may be expressed, respectively, q- V0.k- VI(TR - Ta). (4) as follows: Plants (A ) Sunshine Hours

~p(A,¢,Hv,) + dTp

Still cover

= M p - - ~ - + Aphp(Tp - T . )

Ag(~u Hn + Zl2Hi2) + Abhl(Tw - T~) = agh2(Tg - T~).

Abhs(Tb - Tp)


+ h o A p { p ( T p ) - vp(TR)}.




Floor o f the greenhouse

a z = Abh4,

o~f(AiziHvi ) + Abh6(T b - Tf)

b E = - ( A b h 4 + Aphp + Afhf+ A i h i

: A f h f ( T f - TR) + A f h b ( T f - Too )


+ Adhd + V1 -- AohoTRl) ,


C2 = Afhf,


A i z i n v i = AE~'EHVE +

K 2 = --[~,(AiriHvi ) + Aph o T o + Apho{(R1 To + R2) -- TR2}

+ AN'~NHVN + A s z s n v s ,

Aihi= AEhE + Awhw + ANhN + Ashs,

"~- ( A i h i -~- A d h d =~- V 1)T, -

V o = mgaaLfR H


a 3 = Abh6,


b 3 = Afhf, V l = mM:(Ca +


C 3 = - ( A b h 6 + Afhf + Afhb) ,

The vapour pressure of water has been approximated linearly in the operating range of temperature as

p ( T ) = R l T + R 2.

K 3 = [otf(AiziHvi ) + Afh b T~]


(7) a2 b2 b3 bl

Equations (3), (4) and (6) may be put in the forms, respectively, al Tb + bl TR + Cl Tf= Kl,


a2 Tb + b2 TR + Cz Tf = K 2


a3 Tb + b3 Ta + C3 Tr = K3 .



(72 •

Upon rearrangement and simplification, equations (2), (5), (11), (12) and (13) yield



Now, equations (1), (8), (9) and (10) yield






Tg - (Abhl + Agh2) Tw

4 q-

"~l A g ('~II HI2 +

d - - t - + n 2 T w + 1 2 T ° = g ( t ) + B'



(Abhl + Agh2) Agh2 (Abhl + Agh2)



nl = ~_~[Abhl + Abh 3 w t_

(Abhl)2 Abhl + Agh2

(Ab h3)2(b2e3 - b3 e2!] KKI3 b l

Cl /

Tb= K 2 b 2 c 2 A, b3 C3 /






Abh3 lI = ~ [Abhs(b3c2- b2c3) + Aphp(b3Cl - bl c3)],


K 2 c2


f ( t ) = l~r--~IAg('CIIHll+'cI2HI2)

1(3 e 3 1

Abhl .cl


× r 2 4 Abhl + Agh2

Tf = a 2 b2 /(2 b3




+ ~-(b2e3+~

al = Abh3 + Abh4 + Abhs + Abh6, bl = - A b h 4 , Cl = - A b h 6 ,

K l = "c3Ag('CllHll + rI2HI2) + Abh3 Tw + Abh5 T0,




x {(bl c3 -- b3 el )~Xa-- (61 C2 -- 62 Cl )~Xf}

( AgAghlh2 Abh3 + ~-A~-4-A)2 + A X ( b l c 3 - b 3 c l ) ( A i h , + Adhd+ Vi) }T.],







[(bl Cz -- b~ cl )Afhb T~


-- lz) -4- x/(nl

-- (blC 3 - b3cl)V 0

0~± =

4- (blc3 -- b3cOAohoR2(1 -~,)],

C+ = n I ,4- ~:cn2,

D+ = A 4- a+B. The solution of equation (17) will be

/tbh5 Aoh o ,4- Abh 5 - - ~ -

X {Abhs(b2e 3 - b3e2),4, Aphp(bfc 3 - b3el) }

Tw+ ~ Tp = e c±,

+ ~ _ 2 ( 1 _ e c ± , ) + K + e c±,, (18) K+ being the constants to be determined with the help of the initial conditions

4- (a3cl -- a I c3)Aphp}], 1


Tw(t = 0) = Two

p 4---~'--[(1c3--h3Cl) Abh5 b


x oq - (bl c2 - b2cl )~f] Aph o

Tp(t = O) = Too.


[(a I C2 -- a2c I )ctf

,4- (a3e I --


K+ = T,~o + a+ Tp0.

Now, from equation (18),



q a , ( ~ . n . + rl2nl~) A X {Abhs(bzc3 ,4- Apho(a3c2

[~e c+, I S+(t) ec+tdt ot+ - o~ [_( do

+ ~+-+ D+ (1 -- e c+,) + K + e - "c+, t

-- b3c2)z 3

-- a2c3),.f3}


(Aihi4- Adhd + Vl) A




a I C3)}Ta


c ,




+ Apho {P(T o) - )'P(TR)} {AAh5 × --(blc3-b3q)q

(t)eC tdt



× {Abhs(blca - b3Cl) 4- Aphp(a3 C l



Aph o A [Abhs(a3cz- a2c3)

,4- ~



x [Abhs(b3c z - b2e3) - Aohp(a3e 2 - a2c3)], -~p[

- 12) 2 -4- 4nz12


S+ (t) = f ( t ) ,4- ~+ g(t)

Abh3 m2 = mo/~

l2 =



Aohp A





x(alcl4-a, c3)--l}] +e c ,

and B =~


f0 S ( t ) e c ' d t + ~ -D( 1 - e

+Ke -c ' } - ( ~ + + a

[{Aphp(al c2 - a2c,)


c ') (20)

Expressions (11), (20), (12), (13), (19) and (14) stand for the temperatures of glass cover, brine (water), basin of the still/roof of greenhouse, greenhouse air, plant and floor of the greenhouse, respectively.

- Abh5 (blCz - b2cl)}Arhb T~ - {Abhs(b I c3 - b3cl) 4- Aohp(a3cl -4- al c3)} Vo].

Expression for water distillate

Equations (14) and (15) may be expressed as

The heat transferred per unit area per unit time by evaporation from the water surface to the glass cover is expressed as

d dt (Tw + ~t+ Tp) + C+ (T. + ~t+ To) = S+ (t) 4- D + ,


Qow = h¢(Tw - Tg).








l o'-'

v 30 W n¢ I.< n¢ W n II.I


i \ ,,,


' 10 0





./ '\













/ \



1'0 g


I g




Fig. 2. Hourly variation of yield and temperature for 4 successive days. Hence, the mass transfer rate, i.e. the water distillate produced per unit time per unit basin area will be written as Qew rhew = - - . L

In this case, all expressions will be the same except the value of solar intensity will be zero and the numerical value of heat transfer coefficient from inside air to ambient air through the walls will change. It is due to the fact that, during this period, the walls were covered by Tirpal which reduces the heat losses and changes the values of heat transfer coefficients, Tiwari [12]. RESULTS AND DISCUSSION The relevant parameters used for numerical calculations are as follows (see Tiwari and D h i m a n [8]):

h i ( = h E = h N = h s = h w ) = 1 6 . 5 W m 2°C 1 (during day), h i = 2 W m - 2 oC I (during night), h d = 2 . 0 W m -2 o c - I ' h p = 1 5 . 0 W m 2°C-I, h i = 1 6 . 0 7 6 W m 2°C J, h3= 1 3 5 . 5 W m 2°C 1, C~ = 1006.0Jkg -l °C -j, h 4 = h s = h 6 = 5 . T W m 2°C-1 ' h2 = 40.88 W m -2 °C -1, h e w = 8 . 5 5 W m 2oC 1,

2711 = 2712 =


272= O, z3 = 0.7, Y=0.8


(B ) Off-Sunshine Hours

AN = 10.0m 2, Ap = 10.0m 2, h 0 = 0.013 hp,

m ~0~

z~(= 27E= 27w= ZN = 27s)= 0.8,

and Mw = 628,500 J °C 1 The values of solar radiation on the different walls and roof and of ambient air temperature can be obtained by using Tables 1 and 2 of Tiwari and Dhiman [8]. Climatic conditions are assumed to be constant for 4-5 days for calculation purposes. The variations of yield, water temperature, inside air and plant temperature with time for four successive days have been plotted in Fig. 2. It is clear from this figure that no yield was observed from the still for half of the first day, as well as a few hours early in the morning due to lower water temperature than that of the glass cover of the still. Also, the system reaches quasi-steady state conditions after 3-4 days. Other conclusions are as follows: (i) There is a decrease in inside room air temperature by 2-3°C after watering the plants early in the morning. This effect has been taken into account in the analysis by increasing the plant heat capacity and decreasing its water temperature at initial conditions; (ii) There is an increase in yield by 10-15% after covering the walls with Tripal; and (iii) The fluctuation in the inside room air temperature is also reduced for higher water mass in the basin.

Acknowledgement--Mr Y. P. Yadav extends his sincere thanks to University Grants Commission, India, for awarding him a teacher fellowship.


I. Research and Development Progress Report No. 489, Ot~ce of Saline Water, USDI, Washington (1969). 2. Technical Bulletin 169, Agricultural Experiment Station, The University of Arizona (1969). 3. R. V. Dunkle, International Developments in Heat Transfer, p. 895. University of Colorado (1961). 4. S. R. Qasim, J. envir. Sci. Hlth 13(8), 615 (1978). 5. D. Tinaut, G. Echaniz and F. Ramos, Optica pura appl. 11, 59 (1978).



6. M. K. Selcuk, A S M E A. Winter Meet. New York, Paper No. 70/WA 15063 (1970). 7. M. K. Selcuk, Trans. A S H R A E No. 2172 (1971). 8. G. N. Tiwari and N. K. Dhiman, Energy Convers. Mgmt. 25, 217-223 (1985). 9. M. S. Sodha, A. Kumar, A. Srivastava and G. N. Tiwari, Energy Convers. Mgmt 20, 191 (1980). 10. E. R. Eckert and R. D. Drake, Heat and Mass Transfer. Tata McGraw-Hill, New York (1974). 11. G. Ramakrishna Rao, R. V. Ramamohan and B. V. Ramana Rao, 1977 A. Arid Zone 165 (1977). 12. G. N. Tiwari, Int. J. sol. Energy 3, 19-24 (1984).