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

Abstract

The unsteady flow and heat transfer characteristics of a fluid film caused by a time-dependent rotation of the disk are studied. The self-similar solutions 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 (β→∞), the problem reduces to von Karman flow over a rotating disk. For small film thickness, analytical solutions are obtained and they are found to be in good agreement with the numerical results for small parameter λ measuring the unsteadiness in the angular velocity. For a given disk rotation, non-unique solutions exist.