Estimating Temperature Profiles in Agitated Tanks

A common process task involves heating a slurry by pumping it through a well-stirred tank. It is useful to know the temperature profile of the slurry in the agitated vessel. This information can be used to optimize the heat transfer process by performing simple sensitivity studies with the formulas presented below. Defining the inlet temperature of the slurry as Tj, and the temperature of the outer surface of the steam coil as Ts then by a macroscopic mass and energy balance for the system, a simplified calculation method is developed. 

V = Volume of slurry in tank, ft3 p = Density of slurry, lbm/ft3 W = Mass flow rate of slurry through tank, lb/hr CP = Heat capacity of slurry, Btu/(lbJ (°F) 

U = Overall heat-transfer coefficient of heating coil Btu (ft2) (°F) (hr) 

A = Total heat-transfer surface of coil, ft2 t = Time since start of heating T(t) = Temperature of slurry in tank 

Perfect mixing is assumed. The temperature profile of the tank with respect to time is then given by the following expression reported in the literature. 

---