Melting from a horizontal disk rotating with a time-dependent angular velocity

The unsteady flow and heat transfer characteristics of a fluid film caused by a time-dependent rotation of the disk an studied. The self-similar solut ions of the Navier-Stokes equations and the energy equation exist when the angular velocity of the disk varies inversely as a linear function of time. The system of ordinary differential equations is solved numerically. When the film thickness becomes large (beta --> infinity), the problem reduces t o von Karman flow over a rotating disk. For small film thickness, analytica l solutions are obtained and they are found to be in good agreement with th e numerical results for small parameter lambda measuring the unsteadiness i n the angular velocity. For a given disk rotation, non-unique solutions exi st. Copyright (C) 2000 John Wiley & Sons Ltd.