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A nonlinear Lyapunov-based boundary control law is proposed for mixing enhancement in a magnetohydrodynamic (MHD) channel flow, also known as Hartmann flow. This flow is characterized by an electrically conducting fluid moving between parallel plates in presence of an externally imposed transverse magnetic field. The system is described by the MHD equations, a combination of the Navier-Stokes equation and the Maxwell equations under the so-called MHD approximation. Micro-jets and pressure and magnetic field sensors embedded into the walls of the flow domain are considered in this work to find a feedback control law that is optimal with respect to a cost functional related to mixing measure.