Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 48

Figure 2.4.2 Scheme of concentrated radiation (from Petela, 2010).

The poor concentration of energy needs intensive theoretical studies in order to obtain
acceptable efficiency of energy utilization. Effective method for such purpose could be
exergy analysis.
The concentration possibility of radiation can be illustrated with use of a simple
model shown in Figure 2.4.2. The imagined plane surface (long dashed line) of area
A S represents the black ( ε S 1) solar irradiance IR at constant temperature T S . The

other plane surface (solid line) of area A is gray, at emissivity ε , and its temperature
T is controlled by the cooling heat Q . The vacuum space between the two surfaces
is enclosed by other cone-shape surface (short dash line) which is mirror-like ( ε 0

=

= 0).

The surface areas ratio a S = A S /A . The energy balance of the cooled surface A is:

εσT 4 a S εIR = + k ( T − T 0 ) (2.4.4)

where k is the heat transfer coefficient at which heat Q is extracted from surface A .
The heat rate

q = k ( T − T 0 ) (2.4.5)

can be used to express the total heat Q absorbed by surface A :

A S
a S

Q = q (2.4.6)

The energy efficiency η E of concentration of solar radiation can be measured as
the ratio of absorbed heat Q and the solar irradiance IR :

Q
IR

η E = (2.4.7)

For comparison, exergetic efficiency η B can also be considered based on the
following definition:

B Q
IRψ

η B = (2.4.8)