Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 69

Third group losses can be calculated based either on the determination of the
overall entropy growth used in the Guoy-Stodola equation (2.2.10) or determined
from the exergy balance equation for the considered surface in the steady state. The
latter method will be used.
To develop the analysis, an imagined heat source connected to each considered
surface has to be assumed. For each surface, 2 or 3, there are the arriving emissions at
three different temperatures to be taken into account. It is assumed that these emissions
are absorbed by the surface and transferred as heat to the imagined heat source. Then
immediately this heat is taken from the source to generate the emission of the surface
at its temperature.
Thus the exergy balance equation for surface 2 can be interpreted as including:
the input exergy entering the surface 2 and represented by terms due to:

- emission ψ S · Q 1 − 2 arriving from surface 1,

- emission ψ 2 · Q 2 − 2 arriving from surface 2,

- emission ψ 3 · Q 3 − 2 arriving from surface 3,

- heat E 2 · (1 − T 0 /T 2 ) needed for emission of surface 2 and delivered from the heat

source.

the output exergy leaving the surface 2 and represented by terms due to:

- emission Q 1 − 2 · (1 − T 0 / T 2 ) of surface 1 converted as the heat absorbed by the heat

source,

- emission Q 2 − 2 · (1 − T 0 / T 2 ) of surface 2 converted as the heat absorbed by the heat

source,

- emission Q 3 − 2 · (1 − T 0 / T 2 ) of surface 3 converted as the heat absorbed by the heat

source,

- emission E 2 · ψ 2 of surface 2.

The exergy balance equation can be written in form of the exergy loss δB 2 equal
to the difference of the exergy input and output:

E 2 ) 1

T 0
T 2

δB 2 = ψ 3 Q 3 − 2 + ψ S Q 1 − 2 + ψ 2 ( Q 2 − 2 − E 2 ) − ( Q 3 − 2 + Q 1 − 2 + Q 2 − 2 − −

(2.4.63)

Analogically, the exergy loss δB 3 is:

E 3 ) 1

T 0
T 3

δB 3 = ψ 2 Q 2 − 3 + ψ S Q 1 − 3 + ψ 3 ( Q 3 − 3 − E 3 ) − ( Q 1 − 3 + Q 2 − 3 + Q 3 − 3 − −

(2.4.64)

Applying respectively again the formula for the sum of the terms of the infinite
geometric progression, the values or required heat can be determined as follows.