The aim of the paper is a steady-state inverse heat transfer problem for plate-fin and tube heat exchangers. The objective of the process control is to adjust the number of fan revolutions per minute so that the water temperature at the heat exchanger outlet is equal to a preset value. Two control techniques were developed. The first is based on the presented mathematical model of the heat exchanger while the second is a digital proportional-integral-derivative (PID) control. The first procedure is very stable. The digital PID controller becomes unstable if the water volumetric flow rate changes significantly. The developed techniques were implemented in digital control system of the water exit temperature in a plate fin and tube heat exchanger. The measured exit temperature of the water was very close to the set value of the temperature if the first method was used. The experiments showed that the PID controller works also well but becomes frequently unstable.

The optimization of finned tube heat exchanger is presented focusing on different fluid velocities and the consideration of aerodynamic configuration of the fin. It is reasonable to expect an influence of fin profile on the fluid streamline direction. In the cross-flow heat exchanger, the air streams are not heated and cooled evenly. The fin and tube geometry affects the flow direction and influences temperature changes. The heat transfer conditions are modified by changing the distribution of fluid mass flow. The fin profile impact also depends on the air velocity value. Three-dimensional models are developed to find heat transfer characteristics between a finned tube and the air for different air velocities and fin shapes. Mass flow weighted average temperatures of air volume flow rate are calculated in the outlet section and compared for different fin/tube shapes in order to optimize heat transfer between the fin material and air during the air flow in the cross flow heat exchanger.