Numerical modeling of the convective heat-mass transport in a hydrothermal autoclave for beryl crystal growth has been performed. The system is considered as a composite fluid and porous layer with a seed placed in the upper part of the autoclave. The numerical solution of the flow model is done using combined Navier-Stokes and Darcy-Brinkman-Forchheimer equations, while concentration profiles are solved through the diffusion-convection equation. The numerical algorithm of the solution is presented. As a result of calculations, flow pattern, temperature and concentration fields for various heights of the porous layer have been determined. (c) 2006 Elsevier B.V. All rights reserved.