Hydrothermal synthesis, which uses aqueous solvents under high pressure and relatively low temperature, is an important technique for the growth of crystalline materials such as quartz, bismuth silicate and various kinds of oxides, all of which are difficult to grow. A hydrothermal growth system usually consists of finely divided particles of the nutrient, predetermined volume of a solvent and a suitably oriented crystal seed (Fig. 1) under very high pressures, generally several thousand psi. The nutrient dissolves at a higher temperature in the lower region, moves to the upper region due to buoyancy-induced convective flows and deposits on the seed due to lower solubility if the seed region is maintained at a lower temperature. The system can be modeled as a composite fluid and porous layer using the Darcy-Brinkman-Forchheimer flow model in the porous bed. Since the growth process is very slow, the process can be considered quasi-steady and the effect of dissolution and growth can be neglected. This first study on transport phenomena in a hydrothermal system therefore focuses on the flow and temperature fields without the presence of the seed and mass transfer. A three-dimensional algorithm based on the curvilinear finite volume technique and a non-staggered grid layout has been developed to simulate the flow and heat transfer in a typical autoclave system. An axisymmetric flow pattern at low Grashof numbers and three dimensional flow pattern at high Grashof numbers are predicted. The study is also extended to study the onset of oscillatory flow with a variation in the porous bed height. These results, for the first time, depict the possible flow patterns in a hydrothermal system, that can have far reaching consequences on the growth process and crystal quality.