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Dynamic Behavior of Heated Tanks in Series

​
α
0.1
β
0.005
steam temperature
250
Consider three tanks in series heated with steam. The initial temperature of the three tanks and the temperature of the feed stream to the first tank are chosen equal to 20°C. The governing equations, obtained by writing the energy balance equation for each tank, are the following:
d
T
1
dt
=
W
M
(20-
T
1
)+
UA
M
c
p
(
T
S
-
T
1
)
,
d
T
2
dt
=
W
M
(
T
1
-
T
2
)+
UA
M
c
p
(
T
S
-
T
2
)
,
d
T
3
dt
=
W
M
(
T
2
-
T
3
)+
UA
M
c
p
(
T
S
-
T
3
)
,
where
T
i
is the temperature of tank
i
(expressed in
°C
),
T
S
is the steam temperature (expressed in
°C
),
W
is the mass flow rate in
kg/min
,
U
is the overall heat transfer coefficient (expressed in
kJ/(min°C
2
m
)
),
A
is the heat exchange area of each tank in
2
m
, and
c
p
is the specific heat capacity of the fluid (expressed in
kJ/(kg°C)
). Two parameters are introduced:
α=
W
M
and
β=
UA
M
c
p
. This Demonstration plots the temperature of the three tanks versus time for user-set values of the parameters
α
,
β
, and
T
S
. The blue, magenta, and brown curves correspond to the temperatures of the first, second, and third tanks, respectively.
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