An integral equation basic to the BGK model for flow in a cylindrical tube

The classical BGK model for describing the flow of a rarefied gas in a cylindrical tube is used as a starting point for developing an equivalent integral-equation formulation of the considered class of problems. While the problems of Poiseuille flow and thermal creep in a cylindrical tube have already been well solved in terms of a pseudo problem obtained from an integral-equation definition of the problems, the development of the relevant integral equation is given here for a larger class of problems. In particular it is noted that a general inhomogeneous source term in the balance equation and a general inhomogeneous term in the boundary condition are both included in the considered model, and, as a special case, the integral-equation formulation for the case of specular reflection at the surface of the tube is also developed.