Lattice boltzmann simulations of magnetohydrodynamic slip flow in microchannels

The results of an analytical and numerical investigation into gaseous slip flow with small rarefaction through a long microchannel in the presence of magnetic field are presented. These flows occur in magnetic thin films and other electromagnetic micro-scale devices. In obtaining the microfluidic solutions in the presence of a magnetic field, a number of physical, mathematical and numerical issues need to be considered. These issues deal with the scaling laws for micro-scale MHD flows and the relevant parameters such as Mach number, Reynolds number, Hartmann number, magnetic Reynolds number, and Knudsen number. For planar constant area micro-channel, it is possible to obtain an analytical solution. The numerical solution using Lattice BGK (LBGK) method requires the construction of an appropriate particle distribution function which recovers both the continuum MHD flow equations and magnetic induction equations in low Mach number limit. For the test cases considered, the LBGK results agree well with the analytical solutions for velocity and pressure field. As physically expected, the higher value of the magnetic field (higher Hartmann number) flattens the velocity profile in the channel.