Please only answer if you really know how to solve the question. This issue involves process control and modeling. Need to apply laplace and stuff. It is subject of the Chemical Engineering course.

The system in figure presents a thermal exchange process through an agitated tank, using a solid material inside. Considerations for the system are:

- Tank is perfectly agitated; the physical properties are constants; V and F are constants; the solid material contributes significantly to energy storage, its temperature being uniform.

Use as auxiliary equation UA (T Tm) (heat transferred from liquid to metal); heat losses are negligible.

Data: V = 2 m³; F = 1 m³/h; = 1000 kg/m³; Cp=1.0 kcal/kgC; M= 10 kg (mass of solid); Cpm = 200 kcal/kgC; AU = 1000 kcal/h.C.

Figure. Tank with thermal interaction

For the previous process: Obtain the transfer function between T(s) and T₀(s). Calculate the time constant and process gain. Check whether the system is stable or unstable and oscillating or non-oscillating, justifying your answer.