Agriculture Reference
In-Depth Information
that are closed but not so tightly it reaches
several units, and in open greenhouses, 10
or more. The external wind has a large influ-
ence, as well as the temperature differences
between inside and outside and, therefore,
pressure differences.
In a first approach, the leakage losses can
be estimated with the equation (Bordes, 1992):
For an approximate calculation of the
heating, a simplified energy equation may
be applied, for the night when the require-
ments are higher (
R
s
= 0), resulting in:
Heating = Overall losses + Air renewal
Q
c
= K
(
T
i
−
T
e
) ×
S
c
+ m
×
C
p
(
T
i
−
T
e
)
(5.13)
Q
ren
= 0.35 ×
R
×
V
(
T
e
-
T
i
)
(5.11)
R
= Air exchange rate (h
−1
)
V
= Greenhouse volume (m
3
)
Q
ren
= in watts (W)
A.4.7
Specific heat of a body
The specific heat of a body is the amount
of energy that must be supplied to 1 kg of
this body to increase its temperature
by 1°C.
The specific heat of water (at 15°C) is
4.186 kJ kg
−1
°C
−1
and the specific heat of dry
air (at 20°C) is 1 kJ kg
−1
°C
−1
.
A.4.6
Energy balance
Assuming, in a simplified way, that the solar
energy that enters the greenhouse is used only
to heat the greenhouse and for evapotranspir-
ation (neglecting the energy used for photo-
synthesis, among other simplifications) the
instantaneous energy balance would be,
approximately (Montero
et al
., 1998):
Solar radiation - Evapotranspiration
A.4.8
Latent heat of vaporization
The latent heat of vaporization for a liquid
is the amount of energy that must be sup-
plied to 1 kg of this liquid to convert it from
liquid to gas.
The latent heat of vaporization of water
(at 20°C) is 2445 kJ kg
−1
.
+ Heating = Overall losses
+ Air renewals
S
s
×
t
×
R
s
(1 −
t
)
+ Q
c
= K
(
T
i
−
T
e
)
×
S
c
+ m
×
C
p
(
T
i
−
T
e
)
(5.12)
S
s
= Soil surface (m
2
)
t
= Greenhouse transmissivity to solar radi-
ation (expressed as a decimal per unit)
R
s
= Instantaneous external solar radiation
(W m
−2
), or irradiance
t
= Proportion of radiation used for transpi-
ration (expressed as a decimal per unit)
Q
c
= Heat supplied by the heating system
per time unit (W)
K
= Global heat transfer coefficient (W
m
−2
°C
−1
)
T
i
= Greenhouse (internal) air temperature (°C)
T
e
= External air temperature (°C)
S
c
= Greenhouse cover area (roof and side-
walls; m
2
)
m
= Air mass renewed by ventilation or
infiltration (kg s
−1
)
C
p
= Air specific heat (J kg
−1
°C
−1
)
This equation is only approximate, for
standard conditions (in the measurement
of
K
) and with the mentioned exceptions.
A.4.9
Global heat transfer coefficient
The global heat transfer coefficient of a
greenhouse
covering
material
(
K
)
is
(Papadakis
et al
., 2000):
1
11
j
j
K
=
d
hh k
(5.14)
++
∑
i
e
j
K
= Global heat transfer coefficient of a
greenhouse covering material (W m
−2
°C
−1
)
h
i
= Convection heat transfer coefficient
between the inner side of the greenhouse
cover and the internal air (W m
−2
cover
°C
−1
)
h
e
= Convection heat transfer coefficient
between the outer side of the greenhouse
cover and the external air (W m
−2
cover
°C
−1
)
d
j
= Thickness of the element
j
of the green-
house covering material (m)
