terms of the numerator, which involve the geometric and optical
models of the STSC.
u ¼
R þn
n IðaÞda
R a
a IðaÞda ð2Þ
2.1.1. Geometric model
To develop the STSC model, we propose the integration of the
geometric model, which corresponds to the intercept of a circular
area with a virtual parabola, as shown in Fig. 2. In this geometrical
model, it is necessary to specify the height of the virtual parabola,
the coordinates of the centre of the circular area and the radius.
This model moves the intercept point along the y-axis, which can
be applied to parabolic concentrators, shifting the intercept point
to the origin. The limits of the reflector are given on the y-axis
and are delimited by (yint ± r). Finally, the black-shaded section
represents the differential area increase or the reflector segment,
which corresponds to the area under the normal distribution curve
of the solar image (i.e., the focal point).
The STSC geometric model is obtained by applying the surface
integral for the interception of the two solids [24] and the total energy
intercept, as observed in Eq. (3).
Z þn
n
IðaÞda ¼
Z
n
Z
ðRÞ
IðAÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
@z
@x
2
þ
@z
@y
2
s
dxdy ð3Þ
Fig