The solution of the field equations of the cylindrical Couette flow problem for a rarefied gas is found when the state of equilibrium between the cylinders is perturbed by the following small thermodynamic forces: (i) a pressure difference; (ii) an angular velocity difference; and (iii) a temperature difference. The flow is analyzed within the framework of continuum mechanics by using the field equations that follow from the balance equations of mass, momentum and energy of a viscous and heat conducting gas. These equations are solved analytically by considering slip and jump boundary conditions. The fields of density, velocity, temperature, heat flux vector and viscous stress tensor are calculated as functions of the Knudsen number and of the angular velocity of the rotating cylinders for each thermodynamic force. The asymptotic behaviors of these fields are compared with those obtained from a kinetic model of the Boltzmann equation. The influence of the slip and jump boundary conditions on the solutions is also discussed.
Linear stability of the cylindrical Couette flow of a rarefied gas
