Suppression of Cellular Convection by Lateral Walls

Abstract

An analysis is presented showing the effect on the critical Rayleigh number of inserting parallel vertical walls into a fluid heated from below. The walls are rigid (nonslippery) and thermally conducting to an arbitrary degree. Three-dimensional cellular convection between the walls is analyzed to determine the most unstable cell size, and the Rayleigh number for this cell size is calculated. It is shown that critical Rayleigh number based on either height or spacing can be made as large as may be desired by decreasing the spacing between vertical walls. At large height-to-spacing ratio with finite conducting walls a new form of the Rayleigh number is found to govern the stability. Experimental measurements are reported and compared to the analytical results.