Compressible flow and heat transfer in ultracentrifuges: hybrid analysis via integral tranforms

Compressible flow and heat transfer within gas-filled rapidly rotating cylindrical cavities is analyzed through a formal analytical solution based on the integral transform method. The axisymmetric continuity, Navier–Stokes and energy equations are handled for perturbations over the rigid body rotation solution typical of very high angular velocities, aimed at finding the secondary flow pattern induced by the end caps prescribed boundary conditions. The resulting linearized formulation in streamfunction-only form is solved through the generalized integral transform technique (GITT), and converged numerical results are obtained for streamfunction and velocity components, which are critically compared against previously reported purely discrete solutions. The physical flow behavior is also interpreted in terms of the major governing parameters.