Case A Continuous Heating in an Agitated Tank

Liquid is fed continuously to a stirred tank, which is heated by internal steam coils (Fig. 1.21). The tank operates at constant volume conditions. The system is therefore modelled by means of a dynamic heat balance equation, combined with an expression for the rate of heat transfer from the coils to the tank liquid. 

With no heat of reaction and neglecting any heat input from the agitator, the heat balance equation becomes 

This equation is actually equivalent to a first-order delay (Sec. 2.1.1). With the initial conditions 0] = 0i,init and 0 = 0, it has the solution 

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