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

Publisher Website
Google Scholar
Abstract
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 1980b and references therein). The measurements show that the convective onset near the critical Rayleigh number Rc 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.