Thermocapillary convection in an absorbing-scattering medium subjected to irradiation

The criteria for the onset of thermocapillary convection in a horizontal radiating fluid layer heated by an incident thermal radiative energy source are determined. The fluid layer is an absorbing and isotropically scattering medium confined between a free upper surface and an insulated rigid lower surface. Linear analysis is performed on the continuity, momentum, energy, and approximate radiative equations. The resulting disturbance equations are solved using a numerical optimization technique to obtain the eigenvalues governing the onset of convective motion. The influence of thermal radiation on the critical Marangoni number is examined. Attention is drawn to the physical significance of the heat transfer mode, gravitational force, the scattering effect, and the surface radiative properties. The conditions leading to the onset of convection are presented as functions of the optical thickness, scattering albedo, Planck number, surface emissivities, and transmissivities.