ANALYSIS OF THERMAL-STRESS SLIP-FLOW AND NEGATIVE THERMOPHORESIS USING THE BOLTZMANN-EQUATION FOR HARD-SPHERE MOLECULES

The Grad-Hilbert expansion of the Boltzmann equation is obtained up to the second order in the Knudsen number for a hard-sphere molecular gas. The thermal stress slip condition as well as its associate Knudsen-layer correction, which is second order in the Knudsen number, on the fluid-dynamic type equation so derived is obtained for a hard-sphere molecular gas under the kinetic boundary condition of Maxwell type. From the result it is shown that the negative thermophoresis [Sone Y., 1972, Phys. Fluids, 15, 1418] occurs for a hard-sphere molecular gas under the Maxwell-type boundary condition as well as for the Boltzmann-Krook-Welander model under the same boundary condition. In the course of the analysis the temperature jump problem is studied under the Maxwell-type boundary condition.