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In rarefied gases, mass and heat transport processes interfere with eachother, leading to the mechano-caloric effect and thermo-osmotic effect, whichare of interest to both theoretical study and practical applications. We employthe unified gas-kinetic scheme to investigate these cross coupling effects ingas flows in micro-channels. Our numerical simulations cover channels of planarsurfaces and also channels of ratchet surfaces, with Onsager's reciprocalrelation verified for both cases. For channels of planar surfaces, simulationsare performed in a wide range of Knudsen number and our numerical results showgood agreement with the literature results. For channels of ratchet surfaces,simulations are performed for both the slip and transition regimes and ournumerical results not only confirm the theoretical prediction [Phys. Rev. Lett.107, 164502 (2011)] for Knudsen number in the slip regime but also show thatthe off-diagonal kinetic coefficients for cross coupling effects are maximizedat a Knudsen number in the transition regime. Finally, a preliminaryoptimization study is carried out for the geometry of Knudsen pump based onchannels of ratchet surfaces.

Onsager's Cross Coupling Effects in Gas Flows Confined to Micro-channels