The marginal stability of oscillatory Bénard-Marangoni convection with internal heat generation

The onset of oscillatory Benard-Marangoni convection in a horizontal fluid layer with internal heat generation and a deformable free surface is studied using an analytical technique employing the classical linear stability theory. We consider the case when both the Rayleigh number and Marangoni number are linearly dependent. We obtained the analytical result for the expansion of the Rayleigh number in the limit of a very short wave. We found that the internal heat generation factor influences the leading order of Rayleigh number.