Convection in a rotating annulus having sidewalls of height-dependent thermal conductance

Abstract

Thermal convection in a vertically-mounted, rotating annulus of a particular design proposed by Davies and Walin (1977) is investigated. The annulus used in the present study differs from the conventional type in some important aspects: the sidewalls are finitely conducting, and the thermal conductance of the sidewalls is height-dependent. The theoretical model due to Davies and Walin is briefly recounted. The present study aims to verify the theoretical model; we have acquired numerical solutions to the governing Navier-Stokes equations. The numerical results are supportive of the theoretical contentions. The near-linear dependence of the isothermal slope on the parameter D, which is a function of Ω and ΔT, is corroborated within reasonable limits. New data on the vertical and radial structures of the meridional and azimuthal flows are presented. The numerical results also confirm that the shape of the sidewall thickness has a substantial influence on the meridional flow patterns. In the bulk of the interior flow field, the dominant azimuthal flow field and the temperature field are linked by the thermal wind relation.

Key Words:

• Convection
• isotherm slope
• Rayleigh number
• rotating annulus
• thermal wind