Ghost effect and bifurcation in a gas between coaxial circular cylinders with different temperatures

A gas in a time-independent state between rotating coaxial circular cylinders with different temperatures is considered. The bifurcation of the field in the continuum limit is studied on the basis of the system of fluid-dynamic-type equations and their boundary conditions derived from the Boltzmann system [Phys. Fluids 8, 628 (1996)]. When the ratio of the temperatures of the two cylinders is not close to unity, the bifurcation occurs at infinitesimal speeds of rotation of the cylinders of the first order of the Knudsen number. The temperature field in the continuum limit is determined together with the infinitesimal velocity field, and a bifurcated temperature field, as well as an axially uniform and symmetric field, exists in the absence of the flow velocity (ghost effect). Further, thermal stress, as well as viscous stress, produces a finite effect on the bifurcated temperature field (a non-Navier–Stokes effect). For example, when the ratio of the temperatures of the two cylinders is ten or one tenth, the non-Navier–Stokes effect on the bifurcated temperature field amounts to 10%.