Page 186 - Design of Solar Thermal Power Plants

3.3 THERMAL PERFORMANCE OF PARABOLIC TROUGH COLLECTOR 171

In order to eliminate T b from Eq. (3.40), Eq. (3.42) and Eq. (3.43) are
substituted into it, then the two energy balance equations can be com-
bined as
2
d T f C R þ C R þ C R bf dT f T f A a S
b ba
f
ba
f
C C þ þ ¼
b f
ds 2 R bf R ba ds R bf R ba R bf
(3.44)

R ba þ R bf dT fo dT fi T a
_
_ mc f ðT fo T fi Þ C b mc f þ
R R ba ds ds R R ba
bf
bf
Outlet temperature T fo of heat-transfer fluid within the parabolic
trough collector is selected as the lumped temperature of heat-transfer
fluid within the metal absorber tube. Thus Eq. (3.44) is changed into
2
1 þðR þ R Þ _ mc f d T fo 1 þ _ mc R bf R þ R ba ! dT fo
f
bf
bf
ba
T fo ¼ þ
C C R R ba ds 2 C R bf C R R ba ds
f
b bf
bf
b f
_ mc dT fi ðR þ R Þ _ mc f
ba
f
bf
þ þ T fi
C f ds C C R R ba
b f
bf
1 A a
þ T a þ S (3.45)
C C R R ba C C R bf
b f
b f
bf
Based on the above, a differential equation can be deduced
2
d T fo dT fo dT fi
þ A þ BT fo ¼ C þ DT fi þ ES þ FT a (3.46)
ds 2 ds ds
in which
1 þ _ mc f R bf R bf þ R ba
A ¼ þ (3.47)
C f R bf C b R bf R ba
1 þðR bf þ R ba Þ _ mc f
B ¼ (3.48)
C b C f R bf R ba
_ mc f
C ¼ (3.49)
C f
ðR þ R Þ _ mc f
ba
bf
D ¼ (3.50)
C b C f R bf R ba
A a
E ¼ (3.51)
C C R bf
b f
1
F ¼ (3.52)
C C R R ba
b f
bf