The accuracy of the numerical simulation of rarefied gas flows, in particular the Navier-Stokes-Fourier (N-S-F) equations, depends on the employed surface boundary conditions. In the literature, the combination of the second order slip/jump conditions was mostly used for either the Burnett or the BGK Burnett equations for hypersonic gas flows. In the present work, we suggest the second order temperature jump condition in a new form. The combination of the second order slip/jump conditions is implemented in the framework of OpenFOAM to employ with the N-S-F equations for low-speed nanoscale and hypersonic rarefied gas flows. In this paper, we will investigate both the first and second order slip/jump boundary conditions for low speed rarefied gas flow in the pressure-driven backward facing step nanochannel, and hypersonic gas flows over the flat plate and past a circular cylinder in cross-flow. Simulation results show that the combination of the second order slip/jump conditions predicts better surface properties than those of the first order slip/jump conditions in all cases studied by comparing with the Burnett and DSMC data. Especially the N-S-F simulation results of the cylinder case figured out that the combination of the second order conditions, that the jump condition in new form, capture the Burnett data at Kn = 0.1, while those of the first order conditions do not.

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