In this study, direct simulation Monte Carlo (DSMC) method, the Navier-Stokes equations, and the Burnett equations are applied to micro Couette flow to investigate flow and heat transfer characteristics in the slip and transition flow regimes. The unique solutions of the Burnett equations are obtained through determination of additional boundary condition for pressure using the results of DSMC. The effect of rarefaction on velocity, temperature and pressure distributions is analysed. The non-dimensiotial parameter PrE characterizing convective heat transfer in Coutte flow increases as flow becomes more rarefied. The prediction of shear stress and heat flux at wall shows that the solution of the Burnett equations is superior than that of the Navier-Stokes equations at relatively high Kn number in the slip flow regime. But the Burnet equations with the slip boundary condition, which is proportional to Kn number, cannot be extended to the transition flow regime.