The hydrodynamics and thermal behaviors of fluid in micro - Couette flows is investigated numerically. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the study. The Effects of Knudsen number Kn, Brinkman number and the pressure gradient on the Couette microchannel hydrodynamics and thermal behaviors are investigated. It is found that as Kn increases the slip in the hydrodynamic and thermal boundary condition increases. Also, it is found that the slip velocity and the temperature jump at the boundaries increases as the Brinkman number and the pressure gradient increases.