Environmental Engineering Reference
In-Depth Information
The solution of the differential equation yields the zone temperature 1 as a function
of time:
e
ψ ( t )
· dt dt
t
τ ( t ) e
1
τ ( t )
1
τ ( t )
· dt
1 , 0 +
1 ( t )
=
(6.19)
0
The equation can be simplified if the time τ is constant:
t
1
τ
ψ ( t ) e τ dt
t
τ
1 , 0 +
e
1 ( t )
=
(6.20)
0
Where the term ψ ( t ) stands for
I ( t )
R 12 2 ( t )
τ
C
1
R e e ( t )
1
ψ ( t )
=
+
+
R e R 12
R e +
τ
=
R ges C
=
R 12 C
If the zone temperature is kept at a user-defined setpoint, the heating or cooling
loads required can thus be determined. The model was validated using VDI 6020.
Inputs are U -values, g -values and air change rates. No details of the construction are
required and there are no numerical stability problems.
The model was implemented in the simulation environment INSEL using a modular
structure. Each zone is calculated with a separate block, and earth-connected parts of
the building and the interaction between zones are calculated separately. Schedules
for air changes, heating and cooling, night lowering of temperature setpoints, etc.,
Heating
Cooling
Gains
1
Φ
Φ e
12
R e
R 12
e
2
Φ
c
Figure 6.38 Temperature nodes, thermal resistances, heat capacity and heat flows in a simple nodal
building model
 
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