A constant volume tank containing water of constant density $()$ is being heated using steam and the provided rate of heat input is denoted by $Q.$ The tank is subjected to a constant inlet flow rate Fi$,$ which enters the tank at temperature Ti$.$ The temperature inside the tank is uniformly maintained at $T.$ The outlet stream from the tank has the same flow rate Fi$,$ which exits at temperature T$.$ Derive a transfer function model for the tank$-$heater system correlating the input variables $Q$ and $Ti$ with the output variable $T$ expressed in terms of the deviation variables.

$(5$ Marks$)$