Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 49

where ψ is the exergy-energy ratio discussed in paragraph 2.2.5 and the exergy B Q of
heat absorbed by surface A is:

Aq 1

T 0
T

B Q = − (2.4.9)

The reality of the discussed effect of concentration of solar radiation can be eval-
uated by the calculated value of the overall entropy growth , which consists of: the
positive entropies of heat Q , the emission of surface A , and the negative entropy of
absorbed solar radiation:

Q
T +

4
3 σT 3

= Aε − A S εSR (2.4.10)

where SR is the entropy of irradiance IR . It has to be noted that using the energy
emissivity ε in formula (2.4.10) for entropy calculation is not precise and, as discussed
in details by Petela (2010), the smaller is the precision the smaller is the emissivity
ε . The magnitude SR can be evaluated from the assumed ratio SR / IR to be equal the
ratio s / e of the black emission entropy and emission energy, SR / IR = s / e . With use of
formulae (2.2.32) and (2.2.39), the following relation can be derived:

4
3

IR
T S

SR = (2.4.11)

The overall entropy growth determined from equation (2.4.10) should be positive
( > 0). Otherwise, (when

0), the concentration of solar radiation is impossible
as being against the Second Law of Thermodynamics.

≤

Example 2.4.1.3 The concentration of solar radiation can be considered, e.g., at
IR 800 W/m 2 1m 2

= arriving at the imagined surface of area A S = shown in Figure

3 W/(m 2 K) and the environment temperature T 0

2.4.2. Assuming k 300 K equation

(2.4.4) allows for determining the temperature T of surface A as function of the surface
ratio a S . As is shown in Figure 2.4.3, with the increase in a S , the temperature T grows
(thin solid line) and the heat rate q is also increasing (long-dashed line), determined by
formula (2.4.5).
However, according to formula (2.4.6), with growing a S the total heat Q is varying
(short-dash line) with a maximum of about 134 W at about a S

= =

2. The maximum
appears because with growing a S its effect becomes stronger than the effect of growing
heat rate q .
The energy efficiency η E of concentration of solar radiation, based on definition
(2.4.7) is varying as shown with the thick-dashed line in Figure 2.4.3. The efficiency
η E has the maximum of about 16.8% appearing also at about a S ≈

≈

2, correspondently

to the maximum of Q .
Exergy B Q of absorbed heat is determined by (2.4.9) and shown in Figure 2.4.3
with a dash-dot line. The exergy B Q varies and has a maximum of about 45.8 W, which
appears in the surface area ratio about a S ≈ 6. The maximum is a result of two factors

varying with growing a S : one is growing exergy of heat due to growing temperature
T , other is due to diminishing of the absorbed heat Q .