Application of Lattice Boltzmann Method for Simulating MGD in a Microchannel under Magnetic Field Effects.

In this paper, magnetogasdynamics with outlet Knudsen of 0.2 is studied in a pressure-driven microchannel. By using a developed code, the effects of changing magnetic field parameters including power and length with implementation of slip velocity at the walls has been simulated numerically. The geometry is a two dimensional planar channel having a constant width through all. The flow is assumed to be laminar and steady in time. In order to analyze the variation of velocity, pressure, Lorentz force and induction magnetic field, the governing equations for flow and magnetic fields have been solved simultaneously using the lattice Boltzmann. No assumption of being constant for parameters like Knudsen and volumetric forces are made. Another feature of this research is to improve the quantity of results which is a major problem in this method and many studies have been done in this area. This study represents the results tending to that of analytical relations by using a second order accuracy for calculation of slip velocity and correction of pressure deviation curve in compare with the past studies if a proper relaxation time is determined. The simulation results show a change in Fx profile to M if the length of external magnetic field length reduces to 40% of the whole. Removing applied magnetic field from both ends of the channel will increase pressure gradient at the intermediate part and displaces the section at which the maximum pressure deviation occurs. Slip velocity and centerline velocity behave different for the reduced magnetic field length.