Solving using 3 steps..

What If…

A Stirring Tank..

Stream 1 has A&B, Stream 2 has pure A

Applying 3 steps..

Mass Balance:

eqn (1)

Assume steady state,

Component Balance:

Component A:

Component B:

Energy Balance:

eqn (2)

Transfer Function

Let say want to find,

Assume steady state, eqn (1) & (2) become,

Linearization

Linearized equation yield:

Laplace Transforming:

Assume nominal steady state,

Equation become:

By assuming T2, w1 & w2 are constants,Transfer function can be found to be:

ρ=80 kg/m3, V= 200 m3,

Steady state flow rate:w3=150 m3/s , w1=100 m3/s,

T1 step change from 400C to 500C

Using Simulink..

By substituting given information, transfer function become:

By using Simulink, the results are as follow: