Étude analytique du régime conductif des écoulements de convection dans un bain d'alliage

We present an analytical study of the structure of the flow of a molten alloy. The alloy is contained in a cylindrical crucible and locally heated on its free surface by an electron beam. Due to the high temperature under the electron beam, local evaporation of alloy components occurs. The difference of volatility of the two components creates a concentration gradient in the melt. The study consists of determining analytically the structure of the flow with the following approximations: the aspect ratio height over diameter of the liquid layer is small and for moderate heat supply. We show that in the first significant order, the flow pattern in the conductive regime is governed by two dimensionless numbers, a Marangoni and a Rayleigh number that measure the relative strengths of the thermal and solutal effects.