Mixing enhancement in 2D magnetohydrodynamic channel flow by extremum seeking boundary control

The interaction between electrically conducting fluids and magnetic fields in channel flows generates significant magnetohydrodynamics (MHD) effects, which often result in the need of higher pressure gradients to drive the fluid and lower heat transfer rates due to the laminarization of the flow. Active boundary control, either open-loop or closed-loop, can be employed to overcome this limitation. Open-loop controllers are in general more sensitive to uncertainties of the system, which may result in a poorer performance. Extremum seeking is a powerful tool to tune in real time open-loop controllers, incorporating certain degree of feedback into the control scheme. In this work we combine extremum seeking with a fixed-structure open-loop controller with the ultimate goal of enhancing mixing in a 2D MHD channel by boundary actuation. We show that by carefully tuning the extremum seeking controller the modified open-loop control scheme can be as effective as previously proposed closed-loop control schemes.