Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders. (November 2015) - Lopez, Jose M.; Marques, Francisco; Avila, Marc
Highlights: Heat transfer between differentially heated and rotating cylinders is investigated. A criterion determining whether laminar heat transfer is convective or conductive is given. The criterion only depends on the Rayleigh number and geometry. In the conductive case axially periodic boundary conditions can be used in simulations. The interaction of centrifugal forces and buoyancy gives rise to a rich variety of flow patterns. Abstract: The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the cylinders are assumed to be of infinite length or periodic in the axial direction. In these cases heat transfer in the laminar regime occurs only through conduction as in a solid. We here investigate numerically heat transfer and the onset of turbulence in such flows by using both periodic and no-slip boundary conditions in the axial direction. The influence of the geometric parameters is comprehensively studied by varying the radius ratio ( 0.1 ⩽ η ⩽ 0.99 ) and the length-to-gap aspect ratio ( 5 ⩽ Γ ⩽ 80 ). Similarly, a wide range of Prandtl, Rayleigh, and Reynolds numbers is explored ( 0.01 ⩽ σ ⩽ 100, Ra ⩽ 30, 000, and Re ⩽ 1000, respectively). We obtain a simple criterion, Ra ≲ a ( η ) Γ, which determines whether the infinite-cylinder assumption can be employed. The coefficient a is well approximated by a cubic fit over the whole η -range. Noteworthy the criterion is independent of the Prandtl number and appears robust with respect to Reynolds number even beyond the laminar regime.