Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 25

in paragraph 2.4.1.1, example 2.4.1.2, for solar radiation, the difference between
calculated ψ S = 0 . 9333,

(example 2.4.1.1), for black surface at 6000 K is insignificantly smaller because the
solar spectrum is not much different from the black surface spectrum.

0 . 9326 for the considered solar spectrum and the value ψ =

2.2.6 Exergy of radiation flux
In paragraph 2.2.4 the energy u , J/m 3 , of trapped radiation residing within a space
is discussed. Radiation emission density e , W/m 2 , of a surface at known temperature
is discussed in paragraph 2.2.5. However generally, the radiation flux propagating in
space can consist of many emissions from unknown surfaces and of unknown tem-
peratures. Such radiation energy flux, discussed in the present paragraph, can be
categorized as a radiosity j , W/m 2 , of an arbitrary radiation flux of an arbitrary energy
spectrum which can be determined, for example, from measurement.
Now we know that there are many different methods for derivation of the general
formula for exergy of the arbitrary flux of radiation. Each method leads to the same
result which could be also achieved simply e.g. by interpretation of equation (2.2.3)
as shown by Petela (2010):

i b ,0, λ ,min ) T d 2 Cdλ

E → j = ( i b ,0, λ ,max + (2.2.49)

β ϕ λ

i b ,0, λ ,min ) T 0 d 2 Cdλ

E 0 → j 0 = ( i b ,0, λ ,max + (2.2.50)

ϕ

β λ

L b ,0, λ ,min ) T d 2 Cdλ

S → s j = ( L b ,0, λ ,max + (2.2.51)

ϕ

β λ

L b ,0, λ ,min ) T 0 d 2 Cdλ S 0 → s j ,0 = ( L b ,0, λ ,max + (2.2.52)

ϕ

β λ

where:

j , j 0 - radiosity density of considered radiation and environment, W/m 2 ,
s j , s j ,0 - entropy of radiosity density of considered radiation and environment,
W/(m 2 K),
T , T 0 - absolute temperature of radiating surface and the environment, K.

The monochromatic normal directional intensity i b ,0, λ , W/(m 2 sr), for linearly
polarized black radiation propagating within a unit solid angle and dependent on
wavelength λ , was established by Planck (1914):

c 0 h
λ 5

1
exp c 0 h
kλT

i b ,0, λ = (2.2.53)

− 1