Dynamic Behavior of a Heated Stirred Tank

The dynamic behavior of a heated stirred tank obeys the following ODE:
,
where is the tank's temperature (expressed in kelvin), is the initial temperature as well as the temperature of the stream flowing into the tank, is the heating rate (through steam heating) expressed in watts, is the process time constant (in seconds), liters is the tank volume, is the fluid density (), and is the heat capacity of the fluid expressed in . We take the following assumption concerning the fluid's characteristics: .
The steady-state temperature of the tank is higher if either or is increased. By choosing small process time constants, for any specified value of 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.

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Reference: B. W. Bequette, Process Control: Modeling, Design, and Simulation, Upper Saddle River, NJ: Prentice Hall, 2003.
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