Lattice Boltzmann Simulation 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 microscale devices. It has been shown that the integration of magnetic field in microfluidic MEMS design can enhance the performance of these devices in a variety of applications. 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 microscale MHD flows and the relevant parameters such as Reynolds number, Hartmann number, magnetic Reynolds number, and Knudsen number. For planar constant area microchannel, 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.