On the Low Rayleigh Number Asymptote for Natural Convection Through an Isothermal, Parallel-Plate Channel

The problem of natural convection through a channel formed by isothermal, parallel plates forms a cornerstone of our understanding of a class of natural convection flows. Following the pioneering study of Elenbaas, it is widely accepted that there is a fully developed re´gime, at low Rayleigh number, in which the Nusselt number becomes directly proportional to the Rayleigh number. This paper gives a detailed analysis of heat transfer in this re´gime. It is concluded that the previous numerical studies, which appeared to confirm this asymptote, used inappropriate boundary conditions, and that the asymptotic behavior should, in fact, not be expected except under very special conditions.