In the literature, the combination of the second order slip and the second order jump conditions was mostly employed with the Burnett and BGK Burnett equations for hypersonic gas flows. In this paper, we will investigate both the first order and the second order slip/jump conditions, in which the combination of the second order slip and the second order jump conditions is implemented to work with the Navier-Stokes-Fourier equations for low speed nano/micro-scale and hypersonic rarefied gas flows such as the pressure driven backward facing step and 90-degree bend nano/micro-channels, the lid-driven micro-cavity, and hypersonic gas flow over the flat plate. The simulation results show that the combination of the second order slip condition and the second order jump condition predicts better surface pressure and gas temperature than those of the first order slip and jump conditions in all cases studied in comparing with experimental and DSMC data.

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