Solar Thermal Heat Utilisation - Renewable Energy: Technology, Economics and Environment - page 126

This results in the following energy balance for the absorber of a collector
(Equation (4.5)).

& & & &

&

= m & − m & + + + +

c θ c θ Q Q Q Q

(4.5) G

p out p in

g,abs

conv,abs rad,abs refl,abs cond,abs

The global radiation on the absorber G . g,abs is defined by the total global radia-

tion G . g on the collector cover and the corresponding transmission coefficient τ cov
(Equation (4.6)).

& & (4.6)
The reflection losses of the absorber Q . refl,abs can be calculated with the radiation
on the absorber and the degree of reflection (Equation (4.7)). It is neglected that a
small part of the radiation reflected by the absorber is again reflected by the cover
back towards the absorber. τ cov is the transmission coefficient of the cover and the
reflection coefficient of the absorber is ρ abs .

=

G G

cov

g,abs g

&

&

refl,abs =

ρ

Q τ

G

(4.7)

cov

g abs

According to the Stefan-Boltzmann radiation law, the radiation losses Q . rad,abs
result from the degree of emission ε , the difference between the absorber tempera-
ture θ abs and the ambient external temperature θ e , to the fourth power (in Kelvin),
plus the Stefan-Boltzmann-constant σ (5,67 · 10 -8 W/(m 2 K 4 )) according to Equa-
tion (4.8). In addition, they are proportional to the radiating absorber area S abs .

(

)

&

4 4

rad ,abs =

εσθ θ − S

Q (4.8)

abs abs e abs

The convective thermal losses of the absorber are initially transferred to the
cover plate. In a steady state (i.e. the temperature changes of the cover plate do
not change) this thermal flow is then transferred entirely to the environment. This

convective thermal flow Q . conv,abs can be assumed to be approximately linear. It
depends on the difference between the absorber temperature θ abs and the ambient
air temperature θ e , and can be described by using the heat transfer coefficient
U * coll that is constant in the first approximation (i.e. temperature-independent heat
transfer coefficient). The corresponding equation is as follows (Equation (4.9)).

&

=

*
coll

( - )

Q U θ θ S (4.9) abs e abs

conv, abs

The thermal flow Q . cond,abs due to the heat conduction from the absorber to the
frame and the insulation is very small compared to the other thermal flows and
can be neglected. The energy balance results therefore in Equation (4.10) for the

heat Q . useful transported by the heat transfer medium.