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The room considered in the example has dimensions 7.3 m wide by 2.4 m
high and the north-south depth is 6.7 m. The south-facing double-glazed
window area is 11.1 m
2
. The thermal mass is 4 cm thick concrete on the floor
with thermal conductivity equal to 1.8 W/(m
2
·K), density 2242 kg/m
3
, and
specific heat capacity 840 J/(kg·K). The interior lining on vertical walls and
on the ceiling is a 13 mm thick gypsum board. The insulation is 3.5 RSI on
vertical walls, 7.4 RSI on the ceiling and 1 RSI on the floor (connecting to a
basement).
Figures2.8
and
2.9
showthemagnitudeandphasevariation(Bodeplots)for
the two cases of
Z
11
/carpeted floor and
Z
17
/concrete floor, including actual
discrete frequency responses and fitted fourth-order transfer functions.
Figures 2.8
and
2.9
show that the room response can be approximately
separated into a short-term dynamics high-frequency range and a
low-frequency range; in the high-frequency short-term dynamics region the
room air thermal capacitance is significant and the difference between
Z
11
for the concrete floor and the carpeted one is small in both phase and
magnitude. That is, the effect of thermal mass is minimal in this region. The
separation between short-term and long-term building thermal dynamics
begins at frequencies of approximately 35 cycles per day (cpd) or periods
of about 40 minutes. More extensive studies (Athienitis, Stylianou, and
Shou, 1990) for different constructions have produced similar results for
Z
11
, which represents the effects of convective heat gains or losses.
Short-term dynamics are particularly important for feedback control
studies. For lower frequencies such as one cycle per day the magnitude and
phase of
Z
11
and
Z
17
is a strong function of room construction and there
is a significant difference between the response of the massive (concrete)
construction and the nonmassive one (carpet).
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