This article is cited in 31 papers

Heat and Mass Transfer and Physical Gasdynamics

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

I. V. Shevchuk

Institute for Technical Thermal Physics, National Academy of Sciences of Ukraine, Kiev

Abstract: 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.

UDC: 530.24

Received: 26.02.2003

 English version: High Temperature, 2004, 42:1, 104–110