An improved asymptotic expansion method for fluid flow and convective heat transfer in cone-and-disk geometries with rotating cone

Abstract

In this paper, an improved asymptotic expansion method has been developed to simulate fluid flow and convective heat transfer in a conical gap at small conicity angles up to 4°. Unlike previous works, the improved asymptotic expansion method was applied to the self-similar system of Navier–Stokes equations for small conicity angles. The characteristic Reynolds number varied in the range from 0.001 to 2.0. A detailed validation of the improved asymptotic expansion method compared to the self-similar solution performed for the case of cone rotation with a fixed disk demonstrated its significant advantages compared to previously known asymptotic expansion methods. For the first time, novel approximate analytical solutions were obtained for the tangential and axial velocity components, the swirling angle of the flow, tangential shear stresses on the surface of a fixed disk, as well as static pressure distribution varying in the gap height, which perfectly coincide with the self-similar solution. The accuracy of the improved asymptotic expansion method in the numerical calculation of the Nusselt number in the range of Prandtl numbers from Pr = 0.71 to Pr = 10 significantly exceeds the accuracy of the previously known asymptotic expansion methods. This enables expanding the range of Reynolds and Prandtl numbers, for which the improved asymptotic expansion method has approximately the same accuracy as the self-similar solution. The fact is confirmed that the account for the radial thermal conductivity in the energy equation in the case of small conicity angles up to 4° leads to insignificant deviations of the Nusselt number (maximum 1.5%).