The cylindrical Couette flow of a rarefied gas is studied in the case when the inner cylinder is rotating while the outer cylinder is at rest. Velocity, density and temperature profiles are investigated by a Direct Monte Carlo Simulation method and a numerical solution of the Navier-Stokes equations for compressible flow is found. The results obtained by both methods are: in an excellent agreement at a small Knudsen number Kn=0.02; in a satisfactory agreement at Kn=0.1 and they vastly differs each other at a moderate Kn=0.5. The comparison shows that the continuum approach can be used successfully for calculations of nonisothermal rarefied gas flows at small Knudsen numbers Kn<0.1. These results are important for applications in non-planar microfluidic problems.
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