Thermocapillary convection driven by a uniform heat flux in an open cylindrical container of unit aspect ratio is investigated by two- and three-dimensional numerical simulations. The underformable free surface is either flat or curved as determined by the fluid volume (V≤1) and the Young-Laplace equation. Convection is steady and axi- symmetric at sufficiently low values of the Reynolds number (Re) with either flat or curved interfaces. Only steady convection is possible at any Re in strictly axisymmetric computations.
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