  In rarefied gases, mass and heat transport processes interfere with each
other, leading to the mechano-caloric effect and thermo-osmotic effect, which
are of interest to both theoretical study and practical applications. We employ
the unified gas-kinetic scheme to investigate these cross coupling effects in
gas flows in micro-channels. Our numerical simulations cover channels of planar
surfaces and also channels of ratchet surfaces, with Onsager's reciprocal
relation verified for both cases. For channels of planar surfaces, simulations
are performed in a wide range of Knudsen number and our numerical results show
good agreement with the literature results. For channels of ratchet surfaces,
simulations are performed for both the slip and transition regimes and our
numerical results not only confirm the theoretical prediction [Phys. Rev. Lett.
107, 164502 (2011)] for Knudsen number in the slip regime but also show that
the off-diagonal kinetic coefficients for cross coupling effects are maximized
at a Knudsen number in the transition regime. Finally, a preliminary
optimization study is carried out for the geometry of Knudsen pump based on
channels of ratchet surfaces.
