Non-isothermal flow between rotating disks

Abstract

Consideration is given to laminar axially symmetric flow and heat transfer between two horizontal disks which rotate around a common axis with a common angular velocity. The temperatures of both disks are constant with that of the upper disk being hotter. The centrifugal body force drives a tangential velocity through its coupling with the Coriolis force in a thermal layer near the lower disk. Ekman layers are produced on each disk and heat is convected by the secondary axial flow. Significant convective transport occurs for σβϵ − 1 2 ⪢ 1, where σ is the Prandtl number, ϵ is the inverse of rotational Reynolds number, and β is the product of a temperature difference and the thermal coefficient of expansion. A perturbation solution is carried out for σβϵ − 1 2 ⪢ 1. Some numerical solutions are given for lower rotational rates.