Compressible magnetohydrodynamic flat plate boundary layer flow with slightly rarefied effects

In this work, the influence of the applied electromagnetic field and rarefied gas effect on the compressible laminar boundary layer flow is investigated using locally self-similar solutions and Computational Fluid Dynamics (CFD) simulations. Firstly, the locally self-similar solutions under a uniform electromagnetic field with load factor $K=1$ are conducted to analyze the flow characteristics of the rarefied magnetohydrodynamic (MHD) boundary layer. Subsequently, CFD simulations with various load factors are performed to study the influence of the electromagnetic field on slip effects. Finally, the induced magnetic field under a dipole electromagnetic field is calculated with the Biot–Savart law to assess the validity of the low-magnetic-Reynolds-number assumption for rarefied MHD flow. The results demonstrate that slip effects under the applied electromagnetic field are weakened at $K=0$ but significantly enhanced at $K=1$ and $K=2$ due to changes in boundary layer profiles. Additionally, the induced magnetic field is found to be strongly affected by the load factor and the magnetic Reynolds number but almost independent of the Knudsen number. This suggests that the criterion for low-magnetic-Reynolds-number assumption in continuum flows can be directly applied to rarefied MHD flows.