Nonisothermal flow of a rarefied gas in a circular cylindrical channel

Non-Equilibrium Thermodynamics off Boundary Conditions of the Burnett Approximation

“…Moreover, in this paper the Burnett correction to the distribution function was found for the BGK model. It is shown in [8,9] that the structure of this correction differs from that found directly from the Boltzmann equation. These factors justify our subsequent analysis of boundary conditions for Poiseuille flows.…”

“…It is known that in this case a parabolic velocity profile results, so that the first and second derivatives of the gas velocity U z with respect to the coordinate χ normal to the surface of the channel walls are non-zero. In accordance with this, the Chapman-Enskog correction φ, taken directly on the surface of the channel walls, has the form [8,9]:…”

“…2), the quantity (A.I) can be specialized to J dx<SK(-e(VJe-%(l-R)SV x *V,B) 9 ρ<"> + ο (A.4) where # is the inversion operator in the velocity space. Now introduce the function ρ τ , which describes the solution of the problem of temperature jump [10]:…”

“…The correction φ in this case appears as in [8,9]: dL where the following notation is introduced ι δυ du\ ι^d lvl '' In the approximation under consideration the forces (13) and fluxes (14) do not exhaust all the thermodynamic variables involved in the entropy production (*).…”