HVAC SYSTEMS - HFT Stuttgart

Page - 27 -
CHAPTER 02
Two different cases need to be considered in this model, the standstill phase
without mass flow in the tubes and the normal operation case with mass flow in
the tubes. For the standstill phase the problem is similar to that of the fully
mixed hot water storage model without external mass flows. Convection and
conduction effects within the tubes are very complex and difficult to model and
for the regarded application do not influence the accuracy significantly. These
effects are therefore neglected and the problem can be written as:
dT
( U ⋅ l ) ⋅ ( T () t T )
tube C tube − l tube tube tube −
dt
= , (2.2.1-30)
This differential equation can be solved if the initial condition that at t=0 the tube
temperature is given after a phase with mass flow: T = = T , 0
amb
tube t 0 tube
With this condition the temperature in the tube in dependence of the time is
given as:
⎛ U l , tube ⋅ l tube ⎞
T tube ( t ) = ( Ttube
Tamb
) ⎜
t ⎟
, 0 − ⋅ exp
⎜
−
⋅ + Tamb
C ⎟
(2.2.1-31)
⎝
tube ⎠
diso dtube
Δl Δl Δl Δl
Fig. 2-4: Segmentation of a tube with heat isolation
During phases without mass flow no heat transfer is considered between the
fluid and the tube walls. Therefore, both are on the same temperature level and
a common heat capacity is considered, which is defined as:
ltube