A numerical solution to the problem of a compressible viscous fluid flowing in a heated circular tube

A numerical method for solving the problem of the flow of a compressible viscous fluid through a heated circular tube is presented. The basic equations governing the geometry are derived and written in finite difference form, and a systematic method for solving the governing equations using a digital computer is described. A problem involving the flow of helium is solved, and some conclusions regarding the radial pressure and velocity profiles are made. The method used in checking the equations is given, and some improvements which could be applied to solve the problem on a larger digital computer are enumerated.