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experimentally derived empirical Nusselt correlation for the ventilated gap as well as

a representation of the transient response of the whole fa¸ade system (Fux, 2006).

The main motivation for studying Nusselt correlations in detail was that ventilated

fa¸ades often have large gap sizes, where channel geometries for Nusselt number

calculations do not give correct results and fluid flow over single plates has to be

considered. Furthermore, wind-induced air flow in the fa¸ade as a forced convection

term cannot be neglected, as it is often of the same order of magnitude as the buoyancy-

driven flow rate. A third reason for carrying out an experimental investigation using

particle imaging velocimetry and CFD simulations for parameter studies is that highly

absorbing elements in the fa¸ade such as PV panels produce strongly asymmetric

temperature boundary conditions, for which Nusselt correlations from the literature

cannot be applied. The main results of the heat transfer analysis were:

Nusselt correlations taken from the literature and CFD simulations can reproduce

natural convection situations with small differences in surface temperatures reason-

ably well. For large differences in temperature, the results of the CFD simulation

strongly depend on the operating density used. For plate distances of 20 cm or more,

free convection over a vertical single plate fits the experimental results better than

channel flow.

For forced flow, also both approaches of flow over single vertical plates or flow

between parallel plates were analysed. The best results for measurements and CFD

simulations were obtained by a combination of mixed flow over a heated single

plate (
Nu
H,mix
) and an expression for the fully developed turbulent flow within a

channel (
Nu
H,fd
) which corresponds directly to an equation developed by Petukhov

(see Equation 2.2).

3
Nu
3
H,mix
+

Nu
3
H,fd

Nu
H
=

(2.1)

2
/
3
H

d

d

H

ξ/
8
Re
d
Pr

12
.
7
√
ξ/
8
Pr
2
/
3

Nu
H,fd
=

1

1

+

(2.2)

+

−

1

0
.
18
/Re
0
.
d
and the transforming factor
H/d
must be used

in order to transform the Nusselt number
Nu
d
, which relates to the plate distance
d
,

into the Nusselt number
Nu
H
, which is based on the plate height
H
.

The term
Nu
H,mix
, which includes the Nusselt correlation for a single plate, was

developed for two different flow rates. For
u<
1
.
0ms
−
1

The friction factor
ξ

=

(as the average velocity

between both plates)
Nu
H,mix
is of the form

0
.
32
Re
c
H,res
√
Pr

0
.
32
u
gap

Nu
H,mix
=

−

u
0
+

(2.3)

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