An asymptotic expansion method vs a self-similar solution for convective heat transfer in rotating cone-disk systems

Abstract

This paper compares an asymptotic expansion method and a self-similar solution for modeling Couette flow and convective heat transfer in a conical gap at small conicity angles up to 4°. The cases of rotation of a cone with a stationary disk and rotation of a disk with a stationary cone are considered. The self-similar system of equations provides the best agreement with experiments compared to the asymptotic expansion method. In any case, both methods are applicable only to conicity taper angles up to 4°, while at large conicity angles, the calculation results become significantly inaccurate. Calculations also showed that, at small conicity angles, convective heat transfer can be modeled using the self-similar energy equation in the boundary-layer approximation without considering radial heat conduction. In this study, analytical solutions were also obtained for limiting cases of a stationary fluid in a gap at small conicity angles without and with allowance for radial heat conduction.