Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 46

expresses the solid angle ω and is equal to the area of circle of radius R divided by the
square distance L , thus:

R 2 π
L 2

10 − 5 π sr cos β sin β dβ dϕ = = 2 . 16 × (2.4.1)

β ϕ

By substitution of (a) and (2.4.1) into (2.2.66):

68500
π

10 − 5 π 1 . 48 kW / m 2 b b , ω = 2 . 16 × = (b)

The emission e b , ω of black solar radiation arriving in the solid angle ω is:

e b
π

e b , ω = cos β sin β dβ dϕ (2.4.2)

ϕ

β

where e b = 73 . 47 MW/m 2 is determined by formula (2.2.32). The ratio of exergy to

energy of emission is ψ = b b , ω /e b , ω = 68 . 5 / 73 . 47 ≈ 0 . 93.

Example 2.4.1.2 More exact computations of the exergy of solar radiation were
carried out by Petela (1961a) based on the extraterrestrial radiation spectrum deter-
mined experimentally by Kondratiew (1954). Calculations are based on equation
(2.2.61) for non-polarized and uniform radiation. Table 2.4.1 presents some exemplary
Kondratiew data on intensity of radiation i 0, λ (column 2) as a function of wavelength
λ (column 1). The part of the spectrum is shown in Figure 2.4.1 together with three
spectra (dashed lines), for comparison, for black radiation at absolute temperatures
6000, 5800 and 5600 K. The i 0, λ values in Table 2.4.1 are assumed constant for
the respective ranges of wavelengths λ (column 5). Correspondent ranges of fre-
quency ν calculated based on equation dν 10 8 m/s, are

shown in column 6 whereas values i 0, ν in column 4 were determined from equation
i 0, λ =

dλ/λ 2 , for c 0

= c 0 · = 2 . 9979 ·

i 0, ν /λ 2 . The ν values in column 3 were determined from equation λ c 0 .

The L 0, ν values of column 8 are calculated from equation (2.2.54). Columns 7
and 9 are calculated as respective products of columns 4 and 6; ( i 0, ν ·

c 0 · · ν =

ν ), and 6

and 8; ( L 0, ν · ν ).

Formula (2.2.61) is applied in the following numerical form:

2 i 0, ν ν

2 T 0 L 0, ν ν

σT 0
3 π

b A = − + cos β sin β dβ dϕ (2.4.3)

ϕ

β

Assuming the environment temperature T 0 = 300 K, substituting formula (2.4.1)

into (2.4.3) and using data from Table 2.4.1:

2

5 . 6693 × 10 − 8 × 300 4

10 − 5

b A = × 10079300 − 2 × 300 × 2263 . 3 + × π × 2 . 16 ×

3 π

1275 . 8W / m 2

= 1367 . 9 − 92 . 151 + 0 . 0033 =