Heat transport and temporal evolution of fluid flow near the Rayleigh-Bénard instability in cylindrical containers

First this paper describes in detail an apparatus for heat-transport measurements in shallow horizontal layers of fluid at low temperatures. Then high-precision results of convective heat transport as a function of the Rayleigh number R are presented for cylindrical cells of aspect ratio L = 2.08,4.72 and 57. The present paper concentrates on the long-time behaviour of Boussinesq systems. Non-Boussinesq effects, transient effects near the convective onset, and time-dependent states are described elsewhere (Walden & Ahlers 1981 Ahlers et al . 1981 Ahlers 1980 b and references therein). The measurements show that the convective onset near the critical Rayleigh number R c is sharp within the experimental resolution of about 0.1 % of the Nusselt number N even in laterally finite containers. Values of R and of the initial slopes of N ( R ), are obtained and compared with predictions for different flow patterns. Over a wider range of R and for L = 57 and 4.72, N was found within experimental resolution to be a unique, continuous function of R For L = 2.08, hysteretic transitions are revealed by N ( R ) near R ≈ 3 and R ≈ 10. For L = 4.72, the effect of impulsive heating was studied and revealed complicated, long-lived, but surprisingly repro- ducible transients.