Kinetic theory of thermal transpiration and mechanocaloric effect. II

The problem of thermal transpiration between parallel plates and in a cylindrical capillary is considered by using the Maxwellian diffuse-specular reflection at the surface. The relevant integral equations are solved by a simple numerical scheme and results for both the Poiseuille flow and the thermal creep flow rate are obtained. Some recently reported variational results for the Poiseuille flow appear to be inaccurate (off by about 10%–15%), and there is a need for further refinement in the variational calculations. The effect of partial accommodation is found more significant in the free molecule region than in the near continuum region. Thus to minimize the surface effects, the experiments on the thermal conductivity measurements via thermal transpiration would best be conducted in the near continuum region.