Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 21

Figure 2.2.4 Radiating parallel surfaces.

also discussed as follows. Simple derivation of the emission exergy of a black surface,
published for the first time by Petela (1961b) in Polish and then repeated in English,
Petela (1964), is based on the balance of the emitting surface according to the model
shown in Figure 2.2.4. The two surfaces A and A 0 which are black, flat, infinite, par-
allel, facing each other, enclose a space without substance (vacuum) and interchange
heat by means of radiation. The model of such two-surfaces-only is often selected for
consideration because the space is enclosed by the simplest possible geometry involving
only two plane surfaces. Each surface is maintained at uniform and constant temper-
atures due to exchange of the compensating heat with the respective external heat
sources. Surface A 0 at temperature T 0 represents the emitting environment whereas
surface A, at arbitrary temperature T , emits the considered radiation. The simplicity of
the model with the black surfaces is that there is no reflected radiation to be considered.
In order to derive the formula on the emission exergy density b b of a black surface,
the following exergy balance for surface A, is considered:

b b 0 + b q = b b + δb (2.2.36)

where the terms in equation (2.2.36) or in Figure 2.2.4, all in W/m 2 , are:

b b , b b 0 - exergy of emission density of surfaces A and A 0 , respectively,
b q , b q 0 - change in exergy of respective heat source,
δb , δb 0 - exergy loss due to irreversibility of simultaneous emission and absorption on
the respective surface.

From the definition of exergy the radiation of a surface at environment temperature
b b 0 =

0. The change in exergy of heat source, based on formula (2.2.4):

q T

− T 0

b q = (2.2.37)

T

where q , W/m 2 , is the heat delivered by the heat source of temperature T . This is the
amount of heat which allows surface A to emit and maintain its constant temperature
T . This is also the heat exchanged by radiation between surfaces A and A 0 , which
with use of formula (2.2.32) can be calculated from the energy balance of surface A:
q ( T 4 T 0 ).

= ( e b − e 0 ) = σ · −