Consider a stirred tank heating
process with constant holdup. A liquid enters and leaves the tank
at a mass flow rate of 100 lb/min. The feed and exit temperatures
are 60^oF and 100^oF at steady state. The feed
flow rate and temperature are possible disturbances while the
heating rate Q is a potential manipulated variable. Assume the
liquid has a density of 60 lb_m/ft³ and a heat
capacity of 1.0 Btu/lb_m∙^oF, and the liquid
volume in the tank is 50 ft³. Derive the dynamic model
for the process? Linearize the model and obtain three transfer
functions relating the effluent temperature to the feed
temperature, feed flow rate, and heating rate?