Oscillatory magnetogasdynamic slip flow in a microchannel

The problem of pressure-driven magnetogasdynamic (MGD) slip flow with small rarefaction through a long microchannel is considered. The flow is driven by a steady or oscillatory pressure gradient. The study of MGD flows in microchannels is of interest since they occur in many electromagnetic microscale devices. In obtaining the microfluidic solutions in the presence of a magnetic field, some additional physical, mathematical, and numerical issues need to be considered. These issues deal with the scaling laws for microscale MGD flows and the relevant parameters such as Mach number, Reynolds number, Hartmann number, magnetic Reynolds number, and Knudsen number. For planar constant area microchannels, it is possible to obtain the analytical solutions for both steady and oscillatory pressure-driven flows at low magnetic Reynolds numbers. The flow field is assumed to be quasi-isothermal, which is a good assumption in the absence of a strong electric field. As physically expected, at higher values of the magnetic field (that is at a higher Hartmann number) the velocity profile in the channel flattens, and the pressure varies nonlinearly along the channel.