Exact analysis of Marangoni convection with throughflow

The onset of Marangoni convection with throughflow in a horizontal fluid layer with upper boundary free and insulating to temperature perturbations and the lower boundary rigid and either conducting or insulating to temperature perturbations is investigated. The resulting eigenvalue problem is solved exactly. The Prandtl number arising due to throughflow plays a crucial role in determining the stability of the system. It is found that a small amount of throughflow in one particular direction destabilizes the system depending on the Prandtl number and temperature boundary conditions.