Stabilization of thermocapillary instability in a fluid layer with internal heat source

The onset of steady thermocapillary (surface-tension-driven Marangoni) instability in a horizontal fluid layer in the presence of a uniform heat generation is considered theoretically using stability theory. The fluid layer, heated from below, is bounded above by a deformable free upper surface and below by a rigid plane boundary. The stability of the fluid layer is investigated and subjected to a feedback control on the temperatures of the boundaries. An exact solution for marginal stability owing to an exchange of stabilities has been obtained. Long wavelength instability may coexist with a finite wavelength instability for certain sets of parameter values, often referred to as frontier points.