Facades and Summer Performance of Buildings - Low Energy Cooling for Sustainable Buildings - page 28

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)