Computer extended series for a thermally driven gas centrifuge

Linear multidimensional thermally driven flow in a gas centrifuge can be approximately described away from the ends by Onsager's homogeneous pancake equation. Upon reformulating the general problem we find a new simple and rigorous closed form, analytical solution by assuming a ''special'' separable solution and replacing the usual Ekman end cap boundary conditions with idealized impermeable, free slip boundary conditions. Then the flow is described by an ode with solutions in terms of simple, ''classical'' functions. By identifying a small parameter, say epsilon, we define a semi-long bowl approximation, assume a power series expansion in epsilon and produce a sequence of asymptotic approximations to the master potential. Not surprisingly the leading order term involves the well known ''long bowl'' solution. Using the so-called ''solving'' property of the 1-D pancake Green's function we determine the next higher order solution. This recursive process is carried out on the computer to find all the terms up to O(epsilon4)