Article [12] Time Dependent Study of a Flow of a Gas between Two Coaxial Circular Cylinders Abstract: Time Dependent Study of a Flow of a Gas between Two Coaxial Circular Cylinders made of the condensed phase of the gas is considered where the outer cylinder is suddenly rotating with small angular velocity around their common axis and the inner kept at rest where evaporation or condensation is taking place. The problem is studied analytically on the basis of the Boltzmann equation lay the perturbation method and for small Kundsen numbers. A model kinetic equation of the BGK ( Bhatnager- Gross- Krook) type is solved using the method of moments with a two-side distribution function. The problem is studied from t standpoint of non-equilibrium thermodynamics where the different characteristic properties of the system such as entropy, entropy production, thermodynamic forces, kinetic coefficient and internal energy change are estimate.