Solar energy use in buildings - Solar Energy Sciences and Engineering Applications - page 599

transfer coefficients of 10 cm of conventional insulating material with U-values of
0.4Wm − 2 K − 1 .
Just as for the energy balance of windows, an effective U-value can also be defined
for transparent thermal insulation as the difference between losses and solar gains with
efficiency η 0 .

G
T i −

U eff = U wall + TTI − η 0 (18.6.2)

T o

Solar efficiencies η up to 50% with a simultaneous low heat transfer coefficient lead
to low or even negative effective U-values. Given favourable wall orientation, negative
U-values can be achieved, which means the wall produces heat gains for the building.
Weekly averaged measurements of a 10 cm transparently insulated building in the city
of Freiburg, Germany exhibited effective U-values of between 0 and 3.5Wm − 2 K − 1 .

The solar efficiency η corresponds to the total energy transmission factor of a glaz-
ing and consists of the g d -value of the transparent insulating material, the absorption
factor of the absorber α and the proportion of the heat flow inward to the total heat
flow. The heat flow from the absorber inward is calculated from the temperature node
of the absorber at temperature T a to the room air temperature T i via the heat transfer
coefficients of the wall.

−

s wall
λ wall +

− 1

1
h i

U wall =

Q i
A =

U wall ( T a − T i ) (18.6.3)

Q o is calculated via the heat transfer

The heat flow from the absorber outward

coefficient U TTI of the TTI material.
Q o
A

= U TTI ( T a − T o ) (18.6.4)

The solar efficiency is then proportional to the ratio of the interior heat flux to the
total heat flux as the sum of interior and exterior flux.

U wall ( T a − T i )

η 0 = αg d (18.6.5)

U wall ( T a − T i ) + U TTI ( T a − T o )

Assuming identical temperatures inside and outside, a constant solar efficiency can be
defined (as shown in Figure 18.6.2) that is very suitable for material comparisons and
estimates of the energy yield.

U wall
U wall +

η 0 = αg d (18.6.6)

U TTI

With 5 cm transparent capillary tubes, the U TTI value is 1.3 W m − 2 K − 1 at a g-value of
0.67; with 10 cm it is 0.8 W m − 2 K − 1 and g

0.64. The aerogel material shows a U TTI
value of 0.8 W m − 2 K − 1 with a very small layer thickness of 2.4 cm at a g-value of 0.5.
For optimal use of solar heat, one must ensure that transparently insulated rooms
do not overheat. Conventional window areas usually bring sufficiently high solar gains

=