Bènard-Marangoni Convection with Free Slip Bottom and Mixed Thermal Boundary Conditions

The onset of cellular convection induced by surface tension gradients in a horizontal liquid layer heated from below is examined by making use of linear stability analysis for mixed thermal boundary conditions with free-slip condition at the lower boundary. We use a combination of analytical and numerical techniques to obtain a detailed description of marginal stability curves. It is established numerically that ‘the principle of exchange of stabilities’ is valid. The numerical results are presented for a wide range of the values of the parameters characterizing the nature of thermal boundary conditions. We investigate for the first time, a situation wherein value of the parameter characterizing the thermal condition at the upper boundary varies inversely to that characterizing the thermal condition at the lower boundary, and obtained distinct ranges in which increasing values of the parameter of the lower boundary lead to formation of convection cells of increasing or decreasing size at the onset of convection.