Thermocapillary flows under an inclined temperature gradient

Abstract

The subject of the paper is the stability of the thermocapillary flow generated by an inclined temperature gradient. The investigation is carried out for water (Prandtl number $Pr = 7$ ) in the limit of a vanishing Biot number. By means of the linear stability analysis, the instability boundary of the return flow and the main instability modes have been found. The evolution of the convective regimes predicted by the linear stability theory and arising as a result of a nonlinear interaction has been studied by a numerical simulation of three-dimensional governing equations. Hexagonal cells differently oriented with respect to the main flow have been revealed as well as roll-like and quadrangular patterns. Transitions between different convective patterns occurring under changes of the governing parameters have been considered.