Continuum Mech. Thermodyn. (2000) 12: 379–386 c  Springer-Verlag 2000 Couette flow with slip and jump boundary conditions W. Marques Jr., G.M. Kremer and F.M. Sharipov Departamento de F´ ısica, Universidade Federal do Paran´ a, Caixa Postal 19044, 81531–990 Curitiba, Brazil Received July 10, 2000 The steady plane Couette flow is analyzed within the framework of the five field equations of mass, momentum and energy for a Newtonian viscous heat conducting ideal gas in which slip and jump boundary conditions are considered. The results obtained are compared with those that follow from the direct simulation Monte Carlo method. 1 Introduction A very simple problem of a gas flow in continuum mechanics and kinetic theory of gases concerns the steady plane Couette flow. In this problem a gas is confined between two infinite parallel plates which are at the same temperature but the plates are moving with a constant relative velocity. The fields to be determined depend on the gas rarefaction, or more precisely, on the so-called Knudsen number which is defined as the ratio of the molecular mean free path to a characteristic macroscopic dimension of the flow. Regarding the value of the Knudsen number, we may roughly distinguish two regimes of the gas flow: the continuum (or hydrodynamic) regime and the kinetic (or transition) regime. In the hydrodynamic regime, the Knudsen number is very small so that the gas can be considered as a continuous medium and the hydrodynamic equations can be applied to the gas flow. In the kinetic regime, the molecular mean free path is comparable to the macroscopic dimension of the flow and we cannot consider the gas as a continuous medium. Hence, an exact solution for the Couette flow problem in the transition regime must be derived from the Boltzmann equation that describes the system. One of the most interesting result derived from the Boltzmann equation in the Couette flow problem is the presence of a heat flux parallel to the plates induced by the shear flow, an effect which is absent in the Navier-Stokes regime. We call attention to the fact that this transport of energy along the flow direction can also be observed in molecular dynamics simulation. Recently the non-linear transport [1, 2] and the moment equations [3, 4] of the steady plane Couette flow of a rarefied gas were analyzed and the solutions obtained were compared with the results of molecular dynamic (MD) method [5]. In this work the steady plane Couette flow is studied within the framework of the field equations that follow from the balance equations of mass, momentum and energy of a Newtonian viscous heat conducting rarefied gas where slip and jump boundary conditions are taken into account. The fields of velocity, temperature, viscous pressure tensor and heat flux vector are calculated and compared with the results obtained from the direct simulation Monte Carlo (DSMC) method [6].