Convective instability of a rotating fluid above a rapidly heated surface

Abstract

/02 convective instability is encountered frequently in natural and industrial processes. A layer of fluid above a rapidly heated surface in a gravitational field ceases to be in equilibrium after a certain time has elapsed from the onset of heating, and the ordinary heat conduction is replaced by convective motion. We know of several studies ~see also the literature cited therein! where the onset of convection is related to the loss of mechanical stability, the effects of random fluctuations, or to a second-order phase transition where the convection velocity was taken as the order parameter. Fluids with different Prandtl numbers and slow rates of heating in the Earth’s gravitational field have been used in previous investigations. In the present paper we investigate the convective instability of a liquid nitrogen layer undergoing rigid-body rotation above a finite extremely rapidly heated surface. One parameter, the angular rotation velocity v , was varied, which as will be shown subsequently, is equivalent to varying only the acceleration due to gravity g with an almost constant ratio of Coriolis force to viscous force ~the Taylor number D). The experiments were carried out using a rotating cryostat with a working cylinder diameter of 0.2 m. The heat-transfer surface was the largest plane of a 5034.7633.2 mm glass plate on which was deposited a 1000 A conducting film whose resistivity was independent of temperature. Paper 15 mm thick was stuck to the film with BF-2 adhesive and five miniature silicon temperature sensors consisting of 0.330.330.5 mm uncased KT324B transistors were stuck to this paper at various distances along the longitudinal axis of the surface. The thickness of the silicon wafer adhered to the heat-transfer surface was 0.1 mm and the total thickness of the film coating was 30 mm. The glass plate was placed on the cylindrical surface of the cryostat working volume along the generatrix, with the heat transfer surface facing the axis of rotation. The liquid nitrogen layer above the plate had a constant thickness of 13.4 mm. At zero time, a direct current was switched instantaneously across the conducting film. Since the p–n junction was sensitive to changes in temperature, the sensors changed resistance in proportion to the change in the average temperature in the 0.015 mm volume. The delay of the sensors did not exceed 50 ms. The resistance of the p–n junction was measured by the four-probe method and the change in resistance was recorded by a storage oscilloscope. The oscilloscope traces for a fixed current through the film and different v were superposed. The combined pattern did not de-