HVAC SYSTEMS - HFT Stuttgart

T
tube,
i
( t ) =
T
tube,
i
+ T
⎛
⎜
⎜
⎜
⎜
( t −1)
⋅
⎜
⎜
⎜
⎜ m
⎜
⎜
⎝
fluid , in , i
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜ m
⎜
⎜
⎝
⎛
⎜
⎜
⎜
⎜
⎛ Ttube,
i ( t −1)
⎞
+ ⎜
⎟ ⋅
⎜
⎜
T amb −
⎟ ⎜
⎝
2 ⎠
⎜
⎜ m
⎜
⎜
⎝
T
fluid , out , i
=
T
⋅
+
fluid , in , i
tube
tube
tube
⎛
⎜ m&
⋅ ⎜
⎜
m&
⎝
m
, i ⋅c
dt
, i ⋅c
dt
, i ⋅c
dt
tube
, i ⋅c
dt
tube,
i
hc ⋅ A
+ m&
2
tube,
i
tube,
i
⋅ c
⋅ c
−
−
tube,
i
m&
m&
+
m&
⋅c
Page - 29 -
⎛ hc ⋅ A ⎞
⎜ ⎟
⎝ 2 ⎠ hc ⋅ A
−
hc ⋅ A 2
⋅c
fluid +
2
hc ⋅ A ⎛ hc ⋅ A ⎞
− ⎜ ⎟
2 ⎝ 2 ⎠
⎛ hc ⋅ A ⎞
⎜ ⎟
⎝ 2 ⎠ hc ⋅ A U l ,
+ +
hc ⋅ A 2
⋅c
fluid +
2
U
l , tube
2
2
⋅ Δl
2
⎛ hc ⋅ A ⎞
⎜ ⎟
⎝ 2 ⎠ hc ⋅ A U l ,
+ +
hc ⋅ A 2
⋅c
fluid +
2
2
⎟ ⎟⎟⎟⎟⎟⎟⎟⎟⎟
⎛ hc ⋅ A ⎞
⎜ ⎟
⎝ 2 ⎠ hc ⋅ A U l , tube ⋅ Δl
−
+ +
hc ⋅ A 2 2
m&
fluid ⋅c
fluid +
2
⎠
fluid
fluid
fluid
( T ( t ) + T ( t − 1)
)
tube , i
fluid
fluid
tube , i
fluid
fluid
fluid
fluid
hc ⋅ A ⎞
− ⎟
2 ⎟
hc ⋅ A ⎟
+ ⎟
2 ⎠
⎛
⎜
⋅ ⎜
⎜
m&
⎝
fluid
hc ⋅ A ⎞
⎟
2 ⎟
hc ⋅ A ⎟
⋅ c fluid + ⎟
2 ⎠
2
CHAPTER 02
⎞
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⋅ Δl
⎟
2
⎟
⎟
⎠
tube
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⋅ Δl
⎟
2
⎟
⎟
⎠
tube
(2.2.1-37)
(2.2.1-38)
The Equations 2.2.1-37 and 2.2.1-38 are used for the programming of the
model for the case with mass flow in the tubes. For the case without mass flow
in the tubes the heat losses of the tubes are calculated from Equation 2.2.1-31.