Industrial production of glass involves natural convection of viscous fluids heated from above in shallow cavities. This problem is revisited by means of extensive numerical simulations and analytical expansions for a 2D configuration. This approach yields exact and approximate analytical expressions that can be practically used to evaluate the convective intensity and the heat flux in the different regimes. These results also confirm that the control parameter for this problem is the product of the Rayleigh number, based on the height of the enclosure, by the cavity aspect ratio squared whatever the top boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.