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 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 (\beta \longrightarrow \infty), 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 \lambda measuring the unsteadiness in the angular velocity. For a given disk rotation, non-unique solutions exist