Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 28

Exergy of arbitrary, non-polarized and uniform radiation. The formula for such
radiation results from (2.2.60) in which i 0, ν (and L 0, v ) does not depend on angles β
and ϕ :

⎛
⎝ 2
ν

⎞

2 T 0
ν

σT 0
3 π

⎠

b A = i 0, ν dν − L 0, ν dν + cos β sin β dβ dϕ (2.2.61)

ϕ

β

and to utilize formula (2.2.61) the solid angle ω within which the surface A is seen from
point P on surface A, as well as the radiation spectrum as function of frequency, i 0, ν (ν ) ,
(e.g. determined by measurement), has to be known. Again, the formulae (2.2.59) can
be applied.
Exergy of arbitrary, non-polarized and uniform radiation propagating within solid
angle 2π. The formula for such radiation is derived by substituting equations (2.2.57)
into (2.2.61):

2 π 2 πT 0

ν

σ
3 T 0

b = i 0, ν dν − L 0, ν dν + (2.2.62)

ν

To utilize formula (2.2.62) the function i 0, ν ( ν ), has to be known. The total exergy
of the considered radiation arriving to the all points of the surface A is calculated as
follows:

B = bA (2.2.63)

Example2.2.6.1 Figure 2.2.7 shows the measured monochromatic normal radiation
intensity i 0, λ , (solid line) of radiation, as a function of wavelength λ , for the water vapor
layer of equivalent thickness 1.04 m at temperature 200 ◦ C according to Jacob (1957).
The product of the thickness and the partial pressure for the vapor is 10.4 m kPa. The
monochromatic normal intensity i b ,0, λ for black radiation, calculated from equation
(2.2.53), is also shown for comparison (dashed line). For approximate calculation,
instead of the surface area under the solid line, the area of seven rectangles (dotted line)
is taken into account as the integral energy emitted by the vapor upon the hemispherical
enclosure. The areas of these rectangles can be recognized as the absorption bands of
width λ spread symmetrically on both side of wavelength λ , of which values are given
in Table 2.2.1.
Exergy of radiation arriving in 1 m 2 of the enclosing hemispherical wall can be
calculated from formula (2.2.62), in which frequency, with interpretation explained
by formula (2.2.55), is eliminated by wavelength and each integral can be replaced by
the sum of appropriate products:

2 π i 0 λ λ 2 πT 0 L 0 λ λ

σ
3 T 0 +

b = − (2.2.64)