ABSTRACT The current research explores mixed convection within a two‐dimensional T ‐shaped mixing conduit holding a centrally placed heated cylinder. The work is motivated by the demand for reliable and efficient cooling strategies in thermal management applications. The computational domains are designed with two inlets, one outlet, and a heated cylinder maintained at a constant temperature. The finite element method solves the governing equations for flow and heat transfer. A proportional‐integral‐derivative (PID) controller regulates the airflow entering from the upper left inlet of the channel to ensure that the average air temperature at the outlet remains close to a specified target. The controller's performance is evaluated by monitoring outlet temperature variations and the extent of overshoot. Numerical experiments are conducted to investigate the effect of different controller parameters on achieving a stable and rapid system response. The results show that lower proportional gain, higher integral gain, and lower derivative gain lead to the most effective control action, resulting in the smallest temperature fluctuations and the shortest settling time. Quantitatively, the optimal setting reduces outlet temperature deviations (maximum overshoot) by nearly 13.4 percent and shortens the settling time to less than half that observed under the lowest integral gain setting.
Saad et al. (Thu,) studied this question.