Fluid description of Knudsen layers and applications to the Pirani gauge problem

An attempt is made to extend the validity limit of fluid dynamics toward larger Knudsen numbers. It is effected by employing an 18-moment generating function to incorporate far-reaching wall effect into the Boltzmann function to replace the classical 13-moment expansion, and by formulating molecular continuity condition at a solid wall in the mu-space. Taking moments of each of these equations, from Knudsen layer corrections to the transport formula of the Fourier laws and from boundary conditions governing velocity slip, the temperature jump, molecular reflectivity and population of diffuse reflection at the wall are obtained. These make problems of fluid dynamics under rarefied circumstances well-posed, and problems related to the Pirani gauge heat transfer are solved in this light.