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 which cases heat transfer 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. We obtain a simple linear criterion that determines
whether the infinite-cylinder assumption can be employed. The curvature of the
cylinders enters this linear relationship through the slope and additive
constant. For a given length-to-gap aspect ratio there is a critical Rayleigh
number beyond which the laminar flow in the finite system is convective and so
the behaviour is entirely different from the periodic case. The criterion does
not depend on the Prandtl number and appears quite robust with respect to the
Reynolds number. In particular, it continues to work reasonably in the
turbulent regime.Comment: 25 pages, 9 figure
