Regulation of mixed convective flow in a horizontal channel with multiple slots using P, PI, and PID controllers

This study numerically investigates mixed convective cooling in a two‐dimensional horizontal channel containing periodically heated blocks by applying proportional (P), proportional‐integral (PI), and proportional‐integral‐derivative (PID) controllers. Three different controller configurations regulate the amount of cold air entering the chamber. The air's non‐dimensional temperature is continuously monitored at the set point to compare the controllers’ performance, and the percentage of overshoot and the steady‐state error are analysed. The investigated chamber comprises one inlet and two exit ports, a temperature sensor, and two heated blocks that are isotherm heat sources. The Galerkin finite element approach computationally solves the equations of continuity, momentum, and energy to analyse the thermo‐fluid phenomena occurring within the chamber. Parametric simulation is carried for different values of the proportional gain (Kp = 0.005, 0.010, 0.050 m s−1 K−1), the integral gain (Ki = 0.05, 0.10, 0.15 m s−2 K−1), the derivative gain (Kd = 10−5, 10−4, 10−3 m K−1) to achieve a consistent and expeditious response. Variations of Reynolds, Richardson, and mean Nusselt numbers with time are plotted to compare the system's performance. The investigation indicates that the PI controller produces a comparable level of performance with the PID controller, reducing the necessity to add a derivative controller.