Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 52

Figure 2.4.4 Simplified scheme of radiation energy (a) and exergy (b), (from Petela, 2010).

emissivity α = ε , thus the body emissivity is ε = 1 − τ . The air layer has temperature T A ,

transmissivity τ S = 0 . 71 for the high temperature solar radiation and τ 0 = 0 . 17 for a

100 W/m 2 arriving
in the air layer is assumed. The Earth's surface is black, does not transfer energy to the
ground, and has temperature T 0

low temperature radiation. The yearly average solar irradiance S =

287 . 16 K (14 ◦ C).
The air layer absorbs: solar energy (1

=

S, radiation from sky and radiation
from earth surface, whereas it releases the energy by radiation and convection to the
sky and the Earth surface:

− τ S ) ·

τ 0 ) σ ( T sky + T 0 ) τ 0 ) σT A +

(1 − τ S ) S + (1 − = 2(1 − k [( T A − T 0 ) + ( T A − T sky )]

(2.4.12)

and the Earth's surface absorbs: solar energy, radiation from the air layer and radiation
from sky, whereas it releases the energy by radiation and convection:

− τ 0 ) σT A + τ 0 σT sky = σT o + τ S S + (1 k ( T 0 − T A ) (2.4.13)

where T sky is the sky temperature representing black space above the air layer, σ is the
Boltzmann constant for black radiation, and k is the convective heat transfer coefficient
assumed equal for all convections. For k

3 W/(m 2 K), from the two equations (2.4.12)
and (2.4.13) the two unknown temperature can be calculated: T A =

=

279 . 6 K and T sky =

267 . 4K.
The global warming effect could be considered based on the influence of changing
the factor τ 0 describing pollution of air, on the change of environment temperature T 0 .
From equation (2.4.12) the partial derivative

T 0 + T sky − 2 T A

∂T 0
∂τ 0 =

= 44 . 087 K / % (2.4.14)

4 T 0 (1

k
σ

− τ 0 ) +