Environmental Engineering Reference

In-Depth Information

1
.
0ms
−
1
and the exponent
c
is 0.63 for symmetrical plate temperatures

or plate distances
d>
0
.
4m. For asymmetrical plate temperatures and plate distances

d<
0
.
4m, the exponent
c

where
u
0
=

0
.
61. For higher velocities (
u>
1
.
0ms
−
1
),
u
gap
is fixed

to a maximum permissible value of 1.0m s
−
1
. In this case, the relation
u
gap
/
u
0
is

1.0 and
Nu
H,mix
becomes zero. Consequently, Equation 2.1 will be reduced to

Equation 2.2.

The Reynolds number
Re
H,res
is calculated from both free and forced flow condi-

tions, where asymmetric plate temperatures for the warm and cold side of the fa¸ade

gap can be used.

=

Re
2
H,force
+

Re
2
H,free

=

Re
H,res

(2.4)

Gr
H
/
2
.
5

uH

υ

Re
H,force
=

;
Re
H,free
=

gβ
T
(
WS
)

T
m
H
3

gβ
T
(
CS
)

T
m
H
3

−

−

=

=

Gr
H
(
WS
)

;
Gr
H
(
CS
)

υ
2

υ
2

Gr
H
(
WS
)
represents the buoyancy-driven flow for the warmer plate and
Gr
H
(
CS
)
that of

the colder plate.

The new correlation is able to cover a wide range of boundary conditions for mixed

flowinfa¸ades: namely, plate distances between 5 and 50 cm, inlet air temperatures

between

10 and +60
◦
CandReynolds

numbers
Re
d
(for plates at distance
d
) between 500 and 6500 (corresponding to flow

velocities analysed between 0.06 and about 2.0m s
−
1
). Compared with the simpler

approaches chosen in the European standard DIN EN 13363-2 and the international

standard ISO/DIS 15099, the correlation agrees excellently with experiments and CFD

simulations. While the ISO/DIS 15099 method agrees quite well with the CFD results

for some cases, the simplified DIN EN 13363-2 model usually leads to higher heat

transfer rates.

The dynamic thermal model is based on a numerical solution of the one-dimensional

heat conduction equation applied to both sides of the ventilated fa¸ade. Both sides are

coupled by long-wave radiative heat exchange across the air gap, which can be up to

90% higher than the convective part. After solving the heat conduction equation on

both sides of the ventilation gap in each simulation time step, the determined radiative

heat flow is added as heat gain to the colder surfaces and is subtracted as heat loss

from the warmer surfaces. Then the calculation of the actual time step is repeated

with the new heat gains and the resulting layer temperatures are again determined.

This procedure is repeated several times for each time step. The calculations have

shown that three iterations usually provide a sufficient convergence in temperature.

The model has been implemented both as an independent software tool (TransFact)

10 and +30
◦
C, surface temperatures between

−

−

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