Dynamic Thermal Control of Nanofluid Systems: A Numerical Approach to Evaluate Performance of Proportional, Proportional-Integral, and Proportional-Integral- Differential Controllers in Hybrid Cooling Circuits

Purpose – This study numerically investigates the combined effects of a constant cooling circuit and a variable cooling circuit inside a square enclosure having vents with Al ₂ O ₃ -water nanofluid using P, PI, and PID controllers. Design/methodology/approach – The cavity contains two constant inlet ports, two controlled inlet ports, an outlet port, four isothermal cylindrical heat sources, and a temperature probe at the center of the cavity to evaluate the temperature and return feedback to the flow controllers continuously. The surrounding walls are at ambient temperature, and the nanofluid discharge is at ambient conditions at the outlet. The controllers control the inlet flow velocity and the oscillations, overshoot, settling tim e and steady state error in the values of the temperature (θ) taken nondimensionally at the center are analyzed. The governing Navier-Stokes and energy equations are solved through the Galerkin finite element method with appropriate initial and boundary conditions. Simulations were carried out for proportional gain ( K _p = 0.001, 0.002, 0.003 ms ⁻¹ K ⁻¹ ), the integral gain ( K _i = 0.011, 0.013, 0.015 ms ⁻² K ⁻¹ ), and the derivative gain ( K _d = 0.0001, 0.0003, 0.0005 mK ⁻¹ ) for three different controllers. Calibration of different controllers (P, PI, and PID) is done in a systematic manner. Findings − The results illustrate that the PID controller yields the best thermal management. Using only the P controller, there always remains a steady state error, which is eliminated by the PI controller. The PI and PID controllers, on the basis of settling time and overshoot, have similar levels of performance. Originality/value – The evaluation of P, PI, and PID Controllers in Hybrid Cooling Circuits gives useful insights into optimal use of nanofluids and controllers for cooling and the techniques to optimize the controller parameters for enhanced thermal stability and performance commonly seen in microelectronics or bio-electronics.