  This paper reports theoretical and numerical investigations on free molecular
gas flows through micro-channels. Both diffusely and specularly reflective
channel surfaces are considered. Gaskinetic methods are adopted to develop the
analytical solutions for surface and flowfield properties. The crucial steps
include constructing the velocity distribution functions (VDFs) for points at
the plate surfaces and inside flowfield, and then completing the integration
over the related velocity phases. For diffusely reflective surfaces, the VDFs
are related to the densities and temperatures at the two exits and the plate
temperatures. For surfaces with specular reflections, the VDFs at the plate
surface and inside the flowfield are identical, and independent of the surface
temperature ratio and the geometric aspect ratio. Based on the VDFs and
velocity phases, surface property coefficients (e.g., C_p, C_f, and C_q) and
flowfield properties (e.g., density, velocity components, and temperature) are
obtained. For the diffusely reflective surface scenario, the mass flow rate can
be approximated and the results include four non-dimensional parameters: the
aspect ratio, the density ratio, and two temperature ratios. For specularly
reflective surface scenario, the surface and flowfield properties are uniform
everywhere, the channel aspect ratio and plate temperatures do not have any
influence. Particle simulations with the direct simulation Monte Carlo (DSMC)
method are performed, and essentially identical results validate the
theoretical work. This work is heuristic and can be used to investigate less
rarefied micro-channel gaseous flows, for example, aid experimental measurement
design for thermal transpiration flows.
