Boundary feedback control for heat exchange enhancement in 2D magnetohydrodynamic channel flow by extremum seeking

The heat exchange efficiency of electrically conducting fluids can drop dramatically when they interact with externally imposed magnetic fields. The movement of such fluids under the presence of imposed transverse magnetic fields can generate substantial magnetohydrodynamics (MHD) effects including the need of higher pressure gradients to drive the fluids and lower heat transfer rates due to the laminarization of the flows. Active boundary control can be employed to overcome this disadvantage. We consider in this work a heat exchange process in a 2D MHD channel flow. An extremum-seeking scheme is proposed to tune in real time a fixed-structure boundary controller with the ultimate goal of maximizing the outlet temperature of the electrically conducting cooling fluid, and therefore enhancing the efficiency of the heat exchanger. A heat transfer solver based on finite difference techniques is developed to predict the temperature dynamics within the 2D MHD channel, where the velocity dynamics is predicted by a pseudo-spectral solver. Simulation results show the efficiency of the proposed controller.