Formalization of the Technological Process of Outlet Temperature Control in a Heat Exchanger

The paper addresses the formalization of the outlet temperature control process in a heat exchanger using a simplified lumped parameter mathematical model. An overall energy balance equation is derived for a constant capacity system, and a first order linear differential equation is obtained that relates the outlet liquid temperature to variations in steam flow rate. By applying the small deviation method around the steady state operating point, the model is linearized and transformed into the Laplace domain to obtain the transfer function between the control input and the controlled output. A numerical example with given heat capacity, heat transfer coefficient, steam temperature, and nominal steam flow is used to compute the process time constant and steady state gain, and to describe the step response of the outlet temperature. The results show that the formalized model can be effectively used for PID controller tuning, stability and performance analysis, and simulation of automatic temperature control loops in industrial heat exchange processes.