Boundary effect on the Benard-Marangoni instability

The conjugate onset instability of a liquid layer with free upper surface and heated from below by a heating coil through a solid plate is studied. The focus is on the effect of the solid plate thickness and its conductivity. It is found that the solid plate with a higher thermal conductivity tends to stabilize the system. In real experiments, it is much more difficult to achieve a perfectly insulating boundary condition than to achieve a perfectly conducting condition for a thermal disturbance. The parallel flow assumption is shown to be valid when the plate thickness and its thermal conductivity are small.