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The purpose of this work is to provide a model in lattice Boltzmann method for D simulating thermal rarified gas flows. The study model is a microchannel with a square cross section. The magnetic field flux was created by the magnets on two facing walls. The electrodes are embedded on the walls adjacent to that of the magnets and DC voltage is applied at both ends. Compressible fluid behavior is compared in slip (Kn =0.15) and transient (Kn =0.1) regimes. There are assumptions of laminar and steady flow. Newtonian fluid is electrically and magnetically conductive. Slip and temperature jump on the microchannel walls are considered and the effects of electric double layer thickness and changes of Hartmann number are studied. Since the ionic process is non-isothermal, energy equation is coupled with that of the velocity and the magnetic field and the effects of interaction forces of Lorentz, electric and electrothermal have been entered into Boltzmann equations in separate terms. The outcomes show the interaction between an axial electric field and a transverse magnetic field results in three-dimensional nature of the flow. Navier-Maxwell second order slip boundary condition imposed on the electromagnetic channel walls plays an important role in the vortices formation and the temperature distribution across the channel goes out of the symmetric state. Mass flow rate loss along the channel, resulting from the fluid rarefaction, and pressure deviation from linearity, across and along the channel axis because of the compressibility, was observed

Keywords: Lattice Boltzmann Method, Slip Boundary Condition, Mixing, Electromagnetic Force, Compressibility

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