Marangoni Convection in Radiating Fluids

Abstract

The onset of Marangoni convection driven by surface tension gradients in radiating fluid layers is studied. The system considered consists of a fluid layer of infinite horizontal extent which is confined between a free upper surface and a rigid isothermal lower surface. The radiative boundaries of black–black, mirror–mirror, and black–mirror are considered. The critical conditions leading to the onset of convective fluid motions in a microgravity environment are determined numerically by linear stability theory. The perturbation equations are solved as a Bolza problem in the calculus of variations. The results are presented in terms of the critical Marangoni number and optical thickness for a wide range of some radiative parameters, including the Planck number, nongrayness of the fluid, and the emissivity of the boundaries. It is found that radiation suppresses Marangoni convection during material processing in space.