Solar Thermal Heat Utilisation - Renewable Energy: Technology, Economics and Environment - page 127

&

& &

= − −

(4.10)

Q ρ

τ G τ G

cov cov

g abs g

useful

*

U ( − ) − σ (

4

-

4

)

θθ ε S TT S abs e abs abs abs e abs

coll

Considering Equation (4.1), the first two terms of Equation (4.10) can be
joined. Furthermore, the absorber normally has low degrees of emission. If the
temperature difference between the absorber and the environment is kept low, the
last term of Equation (4.10) can be neglected in many cases. The entire heat and
radiation losses can be described, in an approximation using a heat transfer coeffi-
cient U coll , as linearly dependent on the temperature that takes the entire thermal
losses into account. These assumptions result in Equation (4.11).

&

&

useful =

− ( − )

Q

τα G U θ θ S (4.11)

cov abs coll abs e abs

g

In some cases neglecting the 4 th order dependency can be too big of an omis-
sion. The dependency can then be approximated by a 2 nd order term. This is de-
scribed in Equation (4.12). C 1 and C 2 are corresponding auxiliary constants.

&

&

2

useful =

( − ) − ( − − )

Q τα C θ θ S C θ θ S (4.12)

G

cov abs g 1 abs e abs 2 abs e abs

4.1.5 Efficiency and solar fractional savings

The efficiency η of the conversion of solar radiation energy into useable heat in
the collector results from the ratio of the useful thermal flow transported by the

heat transfer medium Q .

useful to the global radiation incident on the collector (Equa-

tion (4.13)).

&

Q

&

η=

useful

(4.13)

G

g

For a collector with given transmission and absorption coefficients, plus a
given thermal conductivity coefficient, the efficiency can be calculated combining
Equations (4.11) or (4.12) with Equation (4.13) (Equation (4.14) and (4.16) re-
spectively). If the energy balance is drawn for a collector area of one square me-

tre, this results in Equations (4.15) and (4.17) respectively. G . g,rel is the global
radiation on an absorber area of one square metre (net collector area). C 1 and C 2
are auxiliary constants to calculate the utilisable heat of the collector.
With given material parameters, the highest efficiency is achieved at the lowest
possible temperature difference between the absorber, the environment and a
maximum radiation.