Computer‐extended series for a source/sink driven gas centrifuge

We have reformulated the general problem of internal flow in a modern, high speed gas centrifuge with sources and sinks in such a way as to obtain new, simple, rigorous closed form analytical solutions. Both symmetric and antisymmetric drives lead us to an ordinary differential equation in place of the usual inhomogeneous Onsager partial differential equation. Owing to the difficulties of exactly solving this sixth order, inhomogeneous, variable coefficient ordinary differential equation we appeal to the power of perturbation theory and techniques. Two extreme parameter regimes are identified, the so‐called semi‐long bowl approximation and a new short bowl approximation. Only the former class of problems is treated here. The long bowl solution for axial drive is the correct leading order term, just as for pure thermal drive. New O (1) results are derived for radial, drag and heat drives in two dimensions. Then regular asymptotic, even ordered power series expansions for the flow field are carried out on the computer to O (ε 4 ) using MACSYMA. These approximations are valid for values of ε near unity. In the spirit of Van Dyke, one can carry out this expansion process, in theory, to apparently arbitrary order for arbitrary but finite decay length ratio. Curiously, the flows induced by axial and radial forces are proportional for asymptotically large source scale heights, x * . Corresponding isotope separation integral parameters will be given in a companion paper.