Natural convection in an annular fluid layer rotating at weak angular velocity

Abstract

A study is made of natural convection in an annular fluid layer confined between two horizontal cylindrical boundaries rotating at the same angular velocity. The problem is solved for two-dimensional flow with isothermal boundaries, the outer boundary being warmer, using perturbation and numerical methods. The weak rotation regime only is considered, for which centrifugal acceleration is neglected. Governing equations for the flow field are solved in a non-inertial coordinate system rotating with the boundaries, in order to remove uniform, solid-body rotation effects from the pure natural convection flow. Results reveal that a significant mass of fluid far from the boundaries remains tied up to the gravity vector at first, when the angular velocity is small, and thus does not take part in the solid-body rotation. This creates a net circulating flow around the annulus in the rotating system, the intensity of which is shown analytically to be proportional to Ra 2 Re for incipient convection. Perturbation solutions are in good agreement with numerical data for Rayleigh numbers up to several hundreds, depending on the radius ratio. At high Rayleigh numbers, a bifurcation exists between the circulating and solid-body rotation flow regimes, in contrast with the smooth transition observed at lower Rayleigh numbers. Hysteresis effects are observed over a certain range of Reynolds numbers, provided that the Rayleigh number is high enough.