The NACA 0012 airfoil and the sharp 25-55-degbiconic cases are usually considered in evaluating the accuracy of new forms of velocity slip and temperature jump wall boundary conditions in the Navier-Stokes-Fourier equations. These cases have been investigated by many researchers in previous works with the first order Maxwell slip and Smoluchowski jump boundary conditions. Recently, we proposed a new form of the second order temperature jump for simulating rarefied gas flows and obtained accurate results for low speed microflows. The current work is an extension of our previous CFD work where we apply both the secondorder velocity slip condition and the second order temperature jump boundary condition in new forms to simulate rarefied external gas flows for these cases. The second order boundary conditions are implemented into the rhoCentralFoam solver in the OpenFOAM software. The NACA 0012 airfoil case is investigated with angles-of-attack of 0 and 10 degrees and Mach numbers of 0.8 and 2. The sharp 25-55-deg biconic case is simulated at Mach of 15.6. The simulation results obtained for the NACA0012 airfoil show that the combination of the second order slip/jump boundary conditions gives suitable agreements with DSMC for surface gas temperature and drag coefficients in comparison with those of the first order conditions. However, the results of the biconic case figure out that the second order conditions are not superior than the first order conditions.

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