Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 56

Figure 2.4.8 Plate under a canopy in the environment air, S = 700W / m 2

(left) and S = 1000W/m 2

(right), (from Petela, 2010).

In the thermodynamic equilibrium state of the situation shown in Figure 2.4.6b, the
irradiance S is spent on heat Q extracted at constant plate temperature T p and on
the convective ( E p − a ) and radiative ( E p − c ) heat fluxes from the plate to the canopy.
The plate temperature T p is controlled by the appropriately arranged amount of heat
Q . The canopy temperature T c is constant for the given plate temperature T p and
distributed uniformly over the surfaces of the canopy. The energy balance equation for
the plate is:

S = Q + E p − c + E p − a (2.4.20)

where

σ ( T p − T c )

E p − c = (2.4.21)

= −

E p − a Ak p − a ( T p T a ) (2.4.22)

and where k p − a is the respective convective heat transfer coefficient and T a is the
temperature of air between the plate and the canopy. Simplifying, it is assumed T a = T 0 .

The energy balance of the canopy is:

= + +

E p − c E c − sky E c − 0 E c − a (2.4.23)

where

E p − a = E c − 0 = k p − a ( T p − T 0 ) (2.4.24)

and where k p − a = k c − a are the respective convective heat transfer coefficients. The

harvest of the solar energy in the considered situation can be again determined by
the energetic efficiency η E and exergetic efficiency η B determined respectively from
formulae (2.4.18) and (2.4.19).
For example, assuming k p − a = 5 W/(m 2 K), Figure 2.4.8 shows the cal-

culation results for the two different values of irradiance, S

k c − a =

700 W/m 2

= and

1000 W/m 2 . As in situation (a) also in situation (b), with the increasing plate

S =