A Process Control Question

You see a transfer equipment consisting of two tanks. The heat of the inner tank is transferred by

convection along the wall.

$-$The volume of each tank; $V=1m^3$

$-$Heat transfer cross$-$sectional area, $A=1m^2$

Flow of heat between tanks heat transfer coefficient ha $=10ca\frac{l}{h}(m^2)C$

Heat capacity between each tank C: $2ca\frac{l}{k}g(C)$

The temperature of the steam fed to the tank and the temperature inside the tank are initially equals.

PID controller is used in the process when a change in heat flow to the inner tank occurs to keep the tank

exit temperature $(T_2)$ at the set value.

a$)$ Write transfer functions.

b$)$ Draw a block diagram for this process using transfer functions.