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

Compressible flow and heat transfer within gas-filled rapidly rotating cyli ndrical cavities is analyzed through a formal analytical solution based on the integral transform method. The axisymmetric continuity, Navier-Stokes a nd energy equations are handled for perturbations over the rigid body rotat ion solution typical of very high angular velocities, aimed at finding the secondary flow pattern induced by the end caps prescribed boundary conditio ns. The resulting linearized formulation in streamfunction-only form is sol ved through the generalized integral transform technique (GITT), and conver ged numerical results are obtained for streamfunction and velocity componen ts, which are critically compared against previously reported purely discre te solutions. The physical flow behavior is also interpreted in terms of th e major governing parameters. (C) 2001 Elsevier Science Ltd. All rights res erved.