Onset of Benard-Marangoni convection in a rotating liquid layer with nonuniform volumetric energy sources

The criteria for the onset of natural convection in a rotating liquid layer with nonuniform volumetric energy sources from absorbed thermal radiation are determined via linear stability analysis. The linearized perturbation equations are solved by using a numerical technique to obtain the eigenvalues that governs the onset of convection in a microgravity environment. The stability criteria are obtained in terms of the Marangoni number as function of the optical thickness. The influences of the Rayleigh number, Taylor number, Bond number, Crispation number, and Biot number on convection are examined in detail. These parameters provide a relationship between the critical Marangoni number and the Coriolis force, the buoyancy force, the interfacial tension, and the heat transport mechanisms.