Chapter 33 - Lattice Boltzmann simulations of magnetohydrodynamic slip flow in micro-channels

Abstract

This chapter presents results of an analytical and numerical investigation into gaseous slip flow with small rarefaction through a long microchannel in the presence of magnetic field. These flows occur in magnetic thin films and other electromagnetic microscale 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 microscale magnetohydrodynamics (MHD) flows and the relevant parameters such as Mach number, Reynolds number, Hartmann number, magnetic Reynolds number, and Knudsen number. For planar constant area microchannel, it is possible to obtain an analytical solution for pressure-driven flow. The numerical solution using lattice BGK (LBGK) method requires the construction of an appropriate particle distribution function that recovers both the continuum MHD flow equations and magnetic induction equations in low Mach number limit. For the test cases considered in the chapter, the LBGK results agree well with the analytical solutions for velocity and pressure field. The results also show that the higher value of the magnetic field (higher Hartmann number) flattens the velocity profile in the channel.