Two-Dimensional Micro-Hartmann Gas Flows

We analyze and simulate a, near continuum MagnetoGasDynamic(MGD) flow inside a two-dimensional microchannel with a low magnetic Reynolds number assumption. Complex physics such as rarefication, electric and magnetic effects are considered in the asymptotic solutions. This work represents an extension from the classical Hartmann flow in a, two-dimensional channel of infinite length to a microchannel of finite length. We obtain a, non-dimensional equation that relates the pressure ratio, Reynolds number, Mach number, magnetic Reynolds number and magnetic force number. We also solved for asymptotic solutions of compressible gas flow based on the velocity-slip and temperature-jump wall boundary conditions while maintaining a consistent quasi-isothermal assumption. Numerical solutions of the same formulation are obtained for validation of the present analytical solutions.