Exergy analysis of solar radiation processes - Solar Energy Sciences and Engineering Applications - page 67

Analogously to the energy conservation equation, the exergy balance equation
can be applied. When relating all the equation terms to the exergy input, which is the
exergy I ψ S of solar radiation entering the SCPC system, the following conservation

equation for the whole SCPC, can be written:

·

+ + + + + + + + + =

ξ B 11 ξ B 21 ξ B 31 ξ BQ 2 c ξ BQ 2 r ξ Q 3 u ξ Q 3 c ξ B 2 ξ B 3 η B 100 (2.4.49)

where any percentage exergy loss ξ is calculated as the ratio of the loss to the exergy
input, e.g., for the convection heat Q 2, c one obtains ζ Q 2 c =

ψ S ).
In the considered system of non-black surfaces the radiation energy striking a
surface is not totally absorbed and part of it is reflected back to other surfaces. The
radiant energy can be thus reflected back and forth between surfaces many times. To
simplify the effect of further such multi reflections, it is assumed that surface 3 is black,
( ε 3

δB Q 2 c / ( I ·

1),
the only non-black surface in the exergetic analysis of the SCPC system is surface 2,
( ε 2 < 1).
The nine exergy losses appearing in equation (2.4.49) can be categorized in three
groups. The first group contains the exergy losses (external) related to heat trans-
fer, ( ξ BQ 2 c , ξ BQ 2 r , ξ Q 3 u , ξ Q 3 c ). The second group ( ξ B 11 , ξ B 21 , ξ B 31 ) determines the exergy
fluxes (external losses) escaping from the SCPC and the third group contains the exergy
losses (internal) due to irreversible emission and absorption on surface ( ξ B 2 , ξ B 3 ).
First group losses. The exergy loss δB Q 2 c , due to the convection transfer of heat
Q 2, c from the each of the two sides of the reflector to the environment, is equal to the
exergy of heat Q 2, c :

= 1). Thus, as the imagined surface 1 was previously assumed to be black ( ε 1 =

Q 2, c 1

T 0
T 2

δB Q 2 c = − (2.4.50)

The exergy loss δB Q 2 r , due to the radiation transfer of heat Q 2, r from the outer
side of the reflector to the environment, is equal to the exergy of heat Q 2, r :

Q 2, r 1

T 0
T 2

δB Q 2 r = − (2.4.51)

The external exergy loss δB Q 3 u , due to the transfer of the useful heat Q 3, u from
surface 3 through the cooking pot wall to water, is equal to the difference of the exergy
of this heat at temperature T 3 and at temperature T w :

Q 3, u T 3 −

T 0 T w − T 0

δB Q 3 u = − (2.4.52)

T 3 T w

The exergy loss δB Q 3 c , due to convective heat transfer from surface 3 to the
environment, is determined similarly:

Q 3, c T 3 −

T 0 T 0 − T 0

δB Q 3 c = − (2.4.53)

T 3 T 0

where, obviously, the second fraction in the brackets of equation (2.4.53) is zero.