INTRODUCTION
In recent years, the fish farming in greenhouse is gaining popularity
in the colder region of India. Usually, the water temperature of this
region drops below 15°C in the winter season. Temperature is a critical
water quality parameter in aquaculture. Because fish are ectothermic,
temperature affects their growth rate (Davis, 1961; Galtsoff, 1964). For
indoor rearing conditions, heater and chillers are commercially available
to do this, but for outdoor earthen pond, controlling the water temperature
is more difficult and expensive.
Greenhouse is suitable to enhance water temperature. Thermal modeling
of greenhouse in relation to heating and cooling have been experimented
in different climatic conditions and found effectively for crop production
and drying (Jain, 2002). Over the past few years, many researchers reported
fish or prawn culture in greenhouse (Ra`anan and Cohen, 1980/1981; Wood
and Ghannudi, 1985; Kumar et al., 2000; Frei and Becker, 2005;
Ghosh et al., 2007). Information regarding design aspects and thermal
performance of GHFP system is very limited. Mathematical modeling is
important tools for determine the energy efficient design as well as predicting
overall system performance (Tiwari and Sarkar, 2007).
Therefore, the objective of the present study is to analyze the thermal
performance of the arch shape greenhouse by developing mathematical model
and to study the effect of greenhouse fish pond related parameters on
water temperature during winter period.
MATERIALS AND METHODS
Description of Greenhouse
The greenhouse experiment was carried out during 15 October, 2006
to Feb, 2007 at Solar Energy Park, IIT Delhi (Latitude28° 35^{/}
N, Longitude77° 12^{/} E and an altitude of 216 m above mean
sea level). The arch shape greenhouse having length 4.5 m, width 3.0 m
and central height of 2.0 m was used for experimental purpose. The effective
floor and water area of greenhouse were 13.5 and 8 m^{2}, respectively.
It had an advantage of being economic and easy to construct. The orientation
of the greenhouse was from east to west direction. The volume of the greenhouse
enclosure was 19 m^{3}. The frame of the greenhouse was constructed
from aluminum flat and is covered by UVstabilized lowdensity polyethylene
film. The view of the experimental greenhouse (Fig. 1).
Principles of Greenhouse
During sunshine hours total solar radiation received by the greenhouse
cover is partly reflected, absorbed and transmitted inside the greenhouse.
A large portion of inside radiation is absorbed by water. This is utilized
in raising the water temperature. The floor absorbs rest part of radiation.
This absorbed thermal energy is conducted and convected into the ground
and room air, respectively. During off sunshine hours, when room air temperature
drops, a process of convective, evaporative and radiative heat exchanges
takes place among floor, water and room air. This heat exchange is a form
of long wave radiation, which is trapped inside the transparent greenhouse
cover and consequently heats up the room air, which in turn leads to the
sudden fall in water temperature (Fig. 2).
Experimentation
Two rectangular ponds of size 4x2 m with depth of 1.1 m were constructed
inside and outside of greenhouse. The effective water volume is 8 m^{3}
with water depth level maintained at 1.0 m. The ponds were stocked with
40 numbers of fish with Indian major carp such as Catla catla
(average weight 2.45±0.27 g; average length 7.4±0.3 cm)
and Labeo rohita (average weight 2.53±0.19 g; average length
7.6±0.28 cm) in the ratio of 3:1 in each pond. The tanks were prepared
as per the recommended practices (APHA, 1985). The fish were fed primarily
with supplementary feed (ground nut oil cake 50% and rice bran 50%) at
the rate of 2% live fish biomass twice a day throughout the 137 days experimental
period. Feeding rates were adjusted periodically for weight gain by fish.
The fish sampling was done at 15 days interval to measure length and weight
for each species. During study period no fish were died in both systems.

Fig. 1: 
View of the experimental greenhouse 

Fig. 2: 
Crosssectional view of the greenhosue 
Data Aquisition
Total solar radiation on a horizontal water surface on an hourly basis
was measured by a dataloger model R10 provided with probes. The average
radiation based on 10 h duration sunshine was taken into consideration.
Water temperature (T_{w}) at surface (0 to 4 cm), ambient air
(T_{a}) and inside greenhouse air temperature (T_{g})
were measured by alcoholfilled glass bulb thermometer having least count
of 1°C on an hourly basis. A digital humidity meter was used to measure
the relative humidity (γ) inside greenhouse with a least count of
0.1%. The air velocity was measured with an electronic digital anemometer
(least count 0.1 m sec^{1}).
THERMAL MODELING
Energy Balance Equations
The energy balance equations for the different parts of the GHFP
are written on the following assumptions:
• 
Absorptivity and heat capacity of air is neglected. 
• 
Heat flow is onedimensional and in a quasisteady state condition. 
• 
Storage capacity of the greenhouse covering materials is neglected. 
• 
Rradiative heat exchange between the walls and roofs of greenhouse
is negligible. 
• 
There is no stratification along the depth of water as we consider
a shallow pond. 
• 
GHFP is east west direction. 
• 
Fish in the tank are very less in number and small in size. 
The energy balance equation for various components like fishpond, greenhouse
air of greenhouse can be written as follow:
a) For fish pond:
Where:
= Attenuation factor (Tiwari, 2002)
b) For greenhouse air:
After simplifying, the Eq. 2 can be written as:
Now, Eq. 3 can be rewrite
Substituting Eq. 4 in the Eq. 1 and simplifying, Eq. 4 can be written
in the following first order differential equation.
Where:
The analytical solution of Eq. 5 can be written as:
Where:
T_{wo}=The water temperature at t = 0
=The
average value of f_{1}(t) for the time interval between 0 and
t
a=Constant during the time
Once the numerical value T_{w} is determined, then the greenhouse
air temperature T_{r} can be evaluated from Eq. 3.
Thermal Performance of the System
Thermal Load Leveling (TLL)
Since the greenhouse air temperature T(r) is a function of time and
ambient temperature. The greenhouse air temperature plays the vital role
on water temperature, which affects the health of the fish in the pond.
The TLL for water of fishpond can be defined as:
TLL gives an idea about the fluctuation of temperature of water in the
fishpond. For the given temperature difference, the denominator should
be as maximum as for fish growth due to the heating in water; therefore,
TLL should be minimum for winter condition (Tiwari and Sarkar, 2007).
Therefore, TLL is an important index for optimizing the parameters of
fishpond while heating with greenhouse.
STATISTICAL ANALYSIS
Coefficient of Correlation (r)
When predicted values are validated with the experimental data then
correlation between predicted and experimental values is presented with
a coefficient known as coefficient of correlation. The coefficient of
correlation can be evaluated with the following expression (Chapra and
Canale, 1989).
Root Mean Square of Percent Deviation (e)
The prediction is done with the help of thermal modeling. The predicted
values are validated with experimental data. The closeness of predicted
values and experimental data can be presented in terms of root mean square
of percent deviation. The expression used for this purpose is as follows
(Chapra and Canale, 1989).
Where:
COMPUTATIONAL PROCEDURE AND INPUT PARAMETERS
The developed thermal model has been solved with the help of MATLAB7.0
software. Numerical calculations were made corresponding to the hourly
variations of water, ambient air, inside greenhouse air, greenhouse cover
temperature, solar radiation, relative humidity and wind velocity for
a typical winter day i.e., is on 17.1. 2007 of New Delhi, India. Since,
17th January was the coldest day during the experimentation. Values of
solar intensity (total and diffuse) recorded on a horizontal surface
Table 1: 
Design parameters used for computation 

outside the greenhouse were converted on each section (i = 1 to 8) on
greenhouse cover with the help of Liu and Jordon (1962) formula. This
was multiplied by its respective area and effective transmissivity of
greenhouse cover in order to obtain solar radiation transmitted inside
greenhouse. While studying the effects of parameters on water temperature
like depth of pond water, transmissivity and number of air changes of
greenhouse parameters were changed and others were kept constant. In order
to verify the accuracy of the model, the predicted values of greenhouse
water and room air temperature were validated against the experimental
results (Table 1).
RESULTS AND DISCUSSION
The hourly variations of average solar radiation and ambient air temperature
have been shown in Fig. 3. The solar radiation varies
from 80470 W m^{2} of the day. Maximum solar radiation was observed
12:00 to 13:00 h of sunshine period. The greenhouse air temperature also
increases proportionately with increase of solar intensity and viceversa.
The greenhouse air temperature was predicted from Eq. 3. The room temperature
reaches maximum at 14:00 to 15:00 during sunshine hours, while minimum
values were shown at night between 4:00 to 7:00 h (Fig.
4). The predicted room air temperature exhibited good agreement with
experimental air temperature with coefficient of correlation (0.91) and
root mean square percent deviation (5.87%), respectively. The predicted
fish pond water temperature has been evaluated by using the developed
Eq. 6. From the Fig. 5, it is noted that the water temperature
reaches maximum between (12:00 to 16:00) during sunshine hours while minimum
values were observed at night between (5:00 to 6:00). From present study,
it was observed that there is an increase of 4.765.83°C (ΔT
= 4.9°C) of water temperature as compared to outdoor pond water. Similar
observations were obtained by Zhu et al. (1998) and Tiwari and
Sarkar (2007). In this study slight variation of water temperature may
be attributed due to the shape of greenhouse and climatic parameters.
There is a good correlation exhibited between predicted and experimental
water temperature with the values of coefficient of correlation (r = 0.94)
and root mean square percent deviation (e = 3.47%), respectively. The
depth of fishpond was varied from 0.5 to 1.0 m with 0.5 m increment, increasing
the pond depth indicates absorbed more solar radiation but less fraction
of solar radiation available in pond water which results lowering water
temperature (Fig. 6). The results also reveal that increasing
depth of water is not suitable towards the thermal gain. However, shallow
pond shows better results for heat gaining. The transmissivity mainly
depends on the property of the greenhouse cover materials. The increase
of transmissivity has a negligible effect on the water mass (Fig.
7). There is slight increase of water temperature with

Fig. 3: 
Diurnal variation of average solar radiation and ambient
temperature on 17.1.2007 

Fig. 4: 
Hourly variations of predicted and experimental room
temperature inside greenhouse 
increasing transmissivity during sunshine hours, but due to availability
of more solar radiation results in increasing greenhouse room air and
simultaneously water temperature. The air change in GHFP is necessary
to provide fresh air and removal of hot air from greenhouse. Number of
air changes in greenhouse affects the variation of air temperature, which
is ultimately affects the water temperature in the pond. The water temperature
decreases with the increase of the number of air changes in greenhouse.
This may occur with the increase of number of air changes, convective
and evaporative heat transfer from pond water surface to the greenhouse
air is enhanced (Fig. 8). The larger the depth of water
gives lower TLL, which is most favorable for fishpond. TLL is declined
from 0.10 to 0.09 with the change of pond water depth from 0.5 to 1.0
m. However, higher thermal performance can be obtained in larger depth
of water (Fig. 9). There are no results available for
comparison. Because most of the previous studies on thermal modeling dealt
with the even span shape greenhouse without TLL.
Table 2: 
Final weight, length and total production in open and greenhouse
pond after 137 days experimental period 


Fig. 5: 
Hourly variations of predicted and observed water temperature
inside greenhouse 

Fig. 6: 
Effect of depth of pond mass on water temperature 
Growth performance revealed that of Catla catla was higher in
both the systems compared to Labeo rohita (Table
2). From present results we can conclude that the fish management
especially the species composition plays a vital role in this respect.
Total fish production in the greenhouse pond

Fig. 7: 
Effect of transmissivity of greenhouse cover on water temperature 

Fig. 8: 
Effect of number of air changes per hour on water temperature 

Fig. 9: 
Effect of depth of pond on Thermal Load Leveling (TLL) 
was about 1.273 kg. On the other hand, the open pond delivers a lower
fish yield of 0.636 kg. This is reflected in the substantially higher
metabolic growth rate in greenhouse pond compared to open pond. The difference
in fish production in both the systems clearly indicates that the better
thermal performance of the greenhouse.
CONCLUSION
The greenhouse fishpond heating has been studied with the help of thermal
modeling. The greenhouse fishpond system can provide 18.5 to 21.5°C
against 13.0 to 15.5°C temperature of open pond water for fish farming
during winter study period. The effects of different parameters on thermal
performance of greenhouse reveal that 1.0 m pond water depth is suitable
to get optimum water temperature during winter period. Greenhouse pond
contributes significantly (ΔT = 4.9°C) more temperature over
open pond during winter period. So, before designing any greenhouse pond,
one should keep in mind that TLL should be minimized for better thermal
efficiency of the pond. Difference in fish production was also greater
in greenhouse pond than open pond due to higher water temperature prevailed
during study period. On the basis of the present study it can be concluded
that the developed thermal model is quite simple and reliable to predict
water temperature for greenhouse fishpond in any location.
ACKNOWLEDGMENTS
The authors acknowledge the financial support provided by the Department
of Science and Technology, Govt. of India. The authors are also thankful
to Dr. (Mrs.) Vinita Sharma, Scientist F and Dr. (Ms.) Usha Dixit, Scientist,
Department of Science and Technology, Govt. of India for their encouragement
and moral support.
NOMENCLATURE
A 
= 
Area (m^{2}). 
C 
= 
Specific heat (J kg^{1} °C). 
e 
= 
Root mean square of percent deviation (percentage). 
h_{i} 
= 
Heat transfer coefficient from greenhouse cover to inside greenhouse
(W m^{2} °C). 
h_{o} 
= 
Heat transfer coefficient from greenhouse cover to the ambient environment
(W m^{2} °C). 
h_{cw} 
= 
Convective heat transfer coefficient from water to greenhouse cover
(W m^{2} °C). 
h_{rw} 
= 
Radiative heat transfer coefficient from water to sky (W m^{2}
°C). 
h_{ew} 
= 
Evaporative heat transfer coefficient from water to greenhouse cover
(W m^{2} °C). 
h_{cw} 
= 

h 
= 
Sum of convective, radiative and evaporative heat transfer coefficient
from the water surface to inside greenhouse room (W m^{2}
°C). 
I 
= 
Solar radiation falling on inclined surface on greenhouse cover
(W m^{2}). 
K 
= 
Thermal conductivity of humid air (W mK^{1}). 
K_{g} 
= 
Thermal conductivity of ground (W m^{1} °C). 
K_{c} 
= 
Thermal conductivity of concrete (W m^{2} °C). 
K_{b} 
= 
Thermal conductivity of brick (W m^{2} °C). 
L 
= 
Length of greenhouse (m). 
L_{g} 
= 
Thickness of ground (m). 
M 
= 
Mass (kg). 
N 
= 
No. of air changes per hour in greenhouse. 
Nu 
= 
Nusselt number. 
r 
= 
Correlation coefficient (decimal). 
T_{w} 
= 
Water temperature (°C). 
P_{w} 
= 
Saturated vapor pressure at water temperature (Pa). 
P_{g} 
= 
Saturated vapor pressure at greenhouse air temperature (Pa). 
t 
= 
Time in seconds. 
T 
= 
Temperature (°C). 
U_{i} 
= 
Overall heat loss coefficient from greenhouse air to the ambient
air through greenhouse cover (W m^{2} °C). 
v 
= 
Velocity of air (m sec^{1}). 
V 
= 
Volume of greenhouse (m^{3}). 
X 
= 
Characteristic dimension (m). 
Greek letters
a 
= 
Absorptivity (decimal). 
γ 
= 
Relative humidity (decimal). 
ε 
= 
Emissivity, dimensionless. 
τ 
= 
transmissivity of greenhouse cover, dimensionless. 
ρ 
= 
Density (kg m^{3}). 
σ 
= 
StefanBoltzmann constant (5.67x10^{8} W m^{2}
k^{4}). 
∞ 
= 
Infinity (ground at larger depth). 
Subscripts
a 
= 
Air or ambient air 
g 
= 
Ground in greenhouse or floor of greenhouse. 
i 
= 
No. of walls and roofs of greenhouse. 
w 
= 
Water. 
r 
= 
Room (greenhouse enclosure). 
gc 
= 
Greenhouse cover. 
APPENDIX A
h_{i} = h_{0} =
5.7 + +3.8v = 5.7 (if velocity of air inside greenhouse is taken
zero) 
(A.2) 
h_{cw} = 2.8 + 3.0v (for
0 ≤v≤ 7 m sec^{1 }(Watmuff et al., 1977) 
(A.3) 