Thermal management of micropolar ferrofluid forced convective flow in a T-shaped vented chamber via a proportional-integral-derivative controller

• The proportional gain is optimized at K p = 0.06 m/sK, ensuring minimal oscillations and faster settling times. • The optimal integral gain is identified as K i = 0.01 m/s 2 K. • The derivative gain achieves its best performance at K d = 0.05 m/K. • Variations in K p , K i , and K d have no influence on the steady-state values of Reynolds number ( Re = 13.54) or Nusselt number ( Nu = 6.67). A two-dimensional T -shaped ventilated chamber under forced convective flow is regulated by a proportional-integral-derivative flow controller in the current research, focusing on improving the hydro-thermal performance. In the complex configurations where heat extraction must adjust dynamically to the fluctuating inflow conditions, preserving effective temperature regulation is vital for several applications, such as compact cooling systems, electronic components cooling, and energy storage units. In this circumstance, a micropolar ferrofluid (Fe 3 O 4 -water) circulates through the vented chamber, entering from the left-side inlet port at a fixed room temperature and leaving through the right-side outlet port under ambient conditions. The bottom surfaces are heated, while the top surface of the chamber remains cold. The inflow velocity is regulated based on the feedback from the continuous flow controller. A boundary temperature probe is placed at the system’s outlet port to measure the ferrofluid temperature frequently and send a feedback response to the flow controller. The governing mass, momentum, and energy equations representing micropolar ferrofluid flow and heat transport are resolved using the Galerkin finite element technique, permitting an inclusive computational analysis of the system’s behavior. Controller performance is assessed in terms of rise time, percentage overshoot, and settling time relative to the desired setpoint thermal condition. Subsequently, the parametric simulations are performed for tuning selected flow controller (proportional, integral, and derivative) gains within their range of operation (0.06 ≤ K p ≤ 0.20 m/sK, 0.005 ≤ K i ≤0.01 m/s 2 K, and 0.0005 ≤ K d ≤ 0.05 m/K) to achieve optimal response characteristics. The discoveries sensibly demonstrate that K p = 0.06 m/sK, K i = 0.01 m/s 2 K, and K d = 0.05 m/K are the optimum settings for the selected flow controller’s gains.