PATTERN SELECTION FOR RAYLEIGH-BÉNARD CONVECTION IN INTERMEDIATE ASPECT RATIO BOXES

Abstract

The present numerical study examines the pattern selection process in Rayleigh-Bénard convection for boxes with intermediate aspect ratio. The three-dimensional rectangular enclosure has insulated side walls. The top wall is cooled and the bottom wall is heated, both isothermally. The Boussinesq approximation is invoked. Results of numerical simulations are presented and discussed for a Prandtl number of 3.5 and aspect ratios of 10.61 and 5.32. The computations show the exact mechanism of the transition process by a detailed examination of the flow and temperature field for three different cases. The first documents a decrease in the number of rolls from 10 to 8 as the Rayleigh number is increased from 10,000 to 17,000. In the second, the change was from an eight-roll planform to a flow structure with a nonroll polygonal planform as the Rayleigh number was increased from 17,000 to 24,000. A transition from 8 rolls to a T-shaped 4-roll pattern was also documented when the Rayleigh number was stepped up from 17,000 to 20,000.