The Effects of Gravity and Surface Tension Gradients on Cellular Convection in Fluid Layers With Parabolic Temperature Profiles

The effects of surface tension and buoyancy on the convection stability of fluid layers with a mean parabolic temperature distribution is examined. A variety of free-surface, thermal boundary conditions are used. Quantitative values for the effect on the critical Rayleigh number of the free-surface boundary condition, fluid depth, and physical properties are given. The role of the mean temperature profile is also discussed. The results should be of value in judging experiments where a free surface is used to enhance the flow visualization. The numerical procedure used to find the eigenvalues was effective and easily altered to obtain results for similar stability problems.