# Dynamic Behavior of Heated Tanks in Series

Dynamic Behavior of Heated Tanks in Series

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

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 is the temperature of tank (expressed in ), is the steam temperature (expressed in ), is the mass flow rate in , is the overall heat transfer coefficient (expressed in ), is the heat exchange area of each tank in , and is the specific heat capacity of the fluid (expressed in ). Two parameters are introduced: and . This Demonstration plots the temperature of the three tanks versus time for user-set values of the parameters , , and . The blue, magenta, and brown curves correspond to the temperatures of the first, second, and third tanks, respectively.

T

i

i

°C

T

S

°C

W

kg/min

U

kJ/(min°C)

2

m

A

2

m

c

p

kJ/(kg°C)

α=

W

M

β=

UA

M

c

p

α

β

T

S