Time constant of temperature control

The operating principle of the RC-I has already been presented. The jacket set-point temperature is controlled by a proportional controller by the reactor temperature. In turn, the jacket temperature is controlled by a PI controller by mixing warm and cold oil together. 

The proportional controller affects the estimation of the heat flow rate from the temperature measurements during dynamic experiments, i.e. when some heat may be accumulated. In fact, the accumulation term in the heat equation is 

The question is to know whether the term UA(Tf -Tj) gives a good estimation of the term 0q, and therefore any change in 0 provokes a rapid change in Tji and all the heat is evacuated by the wall and not accumulated. The control of 

The low time constant of the control loop shows that rapid changes in cause rapid changes in Tr 0 can be estimated from the difference between Tr and Tj, and the heat accumulation term will be negligible. 

For a constant 0q the temperature tends to the following steady state value  

---