Abstract: A numerical procedure for analyzing the MHD flows in theMHD generator of the bypass scramjet engine was developed in the presentstudy by applying a five-equation model associated with non-ideal MHD flowsat low magnetic Reynolds number. In the numerical procedure, an entropycondition scheme was applied for solving the non-homogeneous Navier-Stokesequations and an SOR method for solving the elliptic equation governed theelectrical potential. The Hall effects on the MHD flow in the MHD generatorwere studied numerically. E-beams were shown as the ionizer to provide theeffective and stable conductivity in the MHD flows. The numerical resultsindicated that the Hall effects might make the distortions on the flow andelectric fields in the MHD generator to induce unstable secondary flow, andnon-uniform Joule heating. In addition, The performance parameters of theMHD generator were obtained numerically to reveal that the Hall effects maydeteriorate the performance of MHD generator.