Abstract A hydrothermal crystal growth system usually consists of a porous bed of polycrystalline charge, predetermined volume of a solvent, suitably oriented seeds, etc. For preliminary study of flow and heat transfer, the convective system for hydrothermal growth can be considered as a composite fluid and porous layer and the flow in the nutrient bed can be modeled using the Darcy–Brinkman–Forchheimer formulation. A three-dimensional algorithm has been developed to examine the flow and heat transfer in a typical autoclave system, which is partially heated on the vertical wall and adiabatic at the top and bottom. The study presents, for the first time, a transport model for hydrothermal growth and the possible flow structure in an autoclave. The temperature and flow fields are analyzed for a few selected cases.