Dynamic Behavior of a Heated Stirred Tank

process time constant

5

heat rate

50

The dynamic behavior of a heated stirred tank obeys the following ODE:

dT

dt

=

F

V

(

T

i

-T)+

Q

Vρ

c

p

,

where

T

is the tank's temperature (expressed in kelvin),

T

i

=300K

is the initial temperature as well as the temperature of the stream flowing into the tank,

Q

is the heating rate (through steam heating) expressed in watts,

τ=

V

F

is the process time constant (in seconds),

V=10

liters is the tank volume,

ρ

is the fluid density (

kg

3

m

), and

c

p

is the heat capacity of the fluid expressed in

kcal/(kgkelvin)

. We take the following assumption concerning the fluid's characteristics:

ρcp=1kcal/liter°C

.

The steady-state temperature of the tank is higher if either

Q

or

τ

is increased. By choosing small process time constants, for any specified value of

Q

the response to added heat is faster (i.e., the time needed to reach the steady-state temperature is shorter). This type of dynamic response is typical of a first-order system.