Heat exchange enhancement by extremum seeking boundary feedback control in 3D magnetohydrodynamic channel flow

Electrically conducting fluids are generally favored as heat transfer media for their excellent heat conduction and high boiling point. However, 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. In this work we propose an active boundary control to overcome some of these unfavorable MHD effects inside a 3D MHD channel flow. Extremum seeking is used to adaptively tune a fixed-structure boundary controller to maximize in real time a cost function related to heat transfer. The closed-loop controller achieves the ultimate goal of increasing overall heat transfer rate through the channel walls, and therefore enhances the efficiency of the heat exchanger. The velocity dynamics is predicted by a pseudo-spectral solver while the temperature dynamics is predicted by a finite difference solver. Simulation results show the efficiency of the proposed controller.