In this section we write the dynamic modeling equations to find the tank and jacket temperatures. This methodology was developed in Chapter 2. We make the following assumptions

- Constant volume and liquids with constant density and heat capacity.
- Perfect mixing in both the tank and jacket.
- The tank inlet flowrate, jacket flowrate, tank inlet temperature and jacket inlet temperature may change (these are the inputs).
- The rate of heat transfer from the jacket to the tank
is governed by the equation

, where U is the overall heat transfer coefficient and A is the area for heat transfer

The notation that we use is presented in Table 1.

**Table 1. Notation**

- Material Balance Around Tank
- Energy Balance Around Tank
- Material Balance Around the Jacket
- Energy Balance Around the Jacket

B. Wayne Bequette, bequeb@rpi.edu