A self-similar solution of Navier-Stokes and energy equations for rotating flows between a cone and a disk

A laminar flow and heat transfer are investigated in a gap between a disk and a cone which touches the disk by its apex. Group analysis is used to reduce the Navier-Stokes and energy equations to a self-similar form which enables one to derive their exact numerical solution. Calculations are performed for cases of cone rotation with a stationary disk, disk rotation with a stationary cone, and simultaneous rotation of the disk and cone at different velocities for several values of the exponent in the power-law radial distribution of the disk temperature and Prandtl number of $0.71$. The calculation results for the case of cone rotation with a stationary disk agree well with the known experimental data.