The surface layers of the sun and other stars with similar or lower surface temperatures are convective. Traditionally, the transfer of energy through convective stellar layers is computed parametrically by the so-called mixing-length theory. We do not know how realistic results based on this theory are. The proposed work attacks this problem by a fully hydrodynamic modelling approach, which is possible with modern high-speed computers. Comparisons of the results with mixing-length theory results and observations of the sun are proposed.