Thermal management inside a discretely heated rectangular cuboid using P, PI and PID controllers

Abstract

This study investigates the viability of three different continuous (P, PI, and PID) controllers to meet specific thermal requirements at a desired location in a cooling system with discrete heat sources. The system is a rectangular cuboid with three discrete heat sources placed on the bottom surface at periodic intervals, and the rest of the walls are insulated. A temperature probe is installed in the system's center to monitor the temperature and provide feedback to the flow controllers in a continuous manner. The velocity of air entering from the inlet port varies in response to the controller feedback and discharge through the outlet port at atmospheric condition. The Galerkin finite element technique solves the governing Navier-Stokes and energy equations and the appropriate initial and boundary conditions. The simulations consist of testing the system's response at the probe point using different combinations of proportional (P), integral (I), and derivative (D) controllers with varied gains to analyze and compare the system's steady-state error and transient behavior in terms of overshoot, oscillation, and settling time. The results indicate that the P controller cannot eliminate steady-state error, while the PI controller achieves zero steady-state error and faster settling. However, if appropriately tuned, the PID controller enhances oscillation control and response time.