Experiments on centrifugally driven thermal convection in a rotating cylinder

Abstract

Heat-transfer measurements have been carried out in a right circular cylinder of fluid which is heated from above and rotated steadily about its vertical axis. Convection is produced relative to solid-body rotation through the coupling of the centrifugal acceleration and density variations in the fluid. Two silicone oils having kinematic viscosities of 350 cS and 0·65 cS were used in the experiments. In the former case viscous forces are important throughout the cylinder whereas in the latter case Ekman layers form and the Coriolis acceleration controls the interior flow.

With the 350 cS oil the Nusselt number for heat transfer from the top to the bottom of the cylinder is a function of Gr_ω and r₀, where Gr_ω is a Grashof number defined by employing the centrifugal acceleration evaluated at the outer edge of the cylinder in place of the gravitational acceleration, and r₀ is the cylinder aspect ratio.

The behaviour is quite different for the 0·65 cS oil. Ekman layers form on the horizontal surfaces and heat is convected by Ekman suction. The Nusselt number is given by \[ Nu = 4.16\beta^{0.822}\epsilon^{-0.499}r_0^{0.173},\quad Ac\leqslant 0.025,\quad\sigma\beta\epsilon^{-\frac{1}{2}} > 0.7, \] where β is the thermal Rossby number, ε is the Ekman number, σ is the Prandtl number, and Ac is the ratio of gravitational to centrifugal accelerations. This is consistent with previous theories which indicate that the system should depend on the parameters σβε^−½ and r₀ in the limit as ε and β approach zero.