Environmental Engineering Reference
In-Depth Information
hourly ambient temperature were measured. The other types of meteorological data can
accommodate hourly or daily global solar radiation on horizontal surface instead of tilt
surface as well as hourly temperature or mean-max-min daily temperatures.
9.1.4. Mathematical Models
Mathematical models were developed for the different components in preparation of the
simulation program “SOLDES”. The following models were developed :
1.
Numerical method to estimate solar radiation on a tilted surface
This model calculates the beam and diffuse components of solar ration on a tilted
surface having the same angle as the absorber plate of the solar collectors given as
input the following information:
o
Measured hourly solar radiation on a tilted surface and measured hourly
ambient temperature (MEDT1) as the case in the solar desalination plant.
o
Measured hourly solar radiation on a horizontal surface and measured hourly
ambient temperature (MEDT2),
o
Estimated daily total solar radiation on tilted surface and estimated mean,
maximum and minimum daily ambient temperatures (MEDT3)
o
Estimated daily total solar radiation on horizontal surface and estimated
mean, maximum and minimum daily ambient temperatures (MEDT4)
The solar radiation on tilted surface,
I
t
is estimated from the following equation:
1
1
sin(
h
)
1
1
−
P
1
+
cos(
α
)
(27)
sin(
h
)
0
I
=
I
+
I
=
I
×
P
×
cos(
θ
)
+
×
I
×
sin(
h
)
×
×
t
b
d
0
0
0
2
1
−
1
.
×
ln(
P
)
2
If the atmospheric transmittance,
P
, is given as known data, hourly solar radiation on a tilted
surface can be calculated from the above equation. However, the only data available is the
hourly global radiation or the daily global radiation. Therefore, to proceed with the computer
simulation, it is necessary to convert global radiation to hourly bean and diffuse components.
This is achieved by estimating the hourly
P
values from Eq. 23 knowing the global radiation,
then calculating the beam and diffuse components from the following the following
equations:
1
sin(
h
)
I
=
I
×
P
×
cos(
θ
)
(28)
b
0
0
1
sin(
h
)
1
+
cos(
α
)
1
1
−
P
I
=
×
×
sin(
h
)
×
×
0
(29)
d
0
2
1
−
1
×
ln(
P
)
2
when daily global radiation is available instead of the measured hourly values, the hourly
solar radiation is first estimated using an iterative procedure then the beam and diffuse
components are estimated from Eqs. 28 and 29[5].
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