In crystal growth devices, in order to control the growth defects and compositional homogeneity of the crystal, a thorough understanding of the heat transfer characteristics is required. In this effort, the combined natural convection and conjugate heat transfer in an axisymmetric configuration representative of the container used in float zone devices are numerically simulated. The geometry adopted contains two concentric cylinders, the inner one representing the crystal within which heat conduction takes place, and the outer one being the container wall; between them is the domain of a height-to-width ratio of 40, filled with encapsulated argon gas. The main parameters varied in this study are Rayleigh number (Ra) and heating location. Substantial refinement in grid size, from 61 x 81 to 201 x 301 nodes, has been exercised to assess the numerical accuracy of the solutions. For Ra = 1.25 x 10(4), steady-state solutions exist regardless of the heating location. For Rn = 1.25 x 10(5), on the other hand, persistently oscillatory convective patterns appear, exhibiting both co-rotating (buoyancy-induced) cells and contra-rotating (shear-induced) cells. Consequently, the overall heat transfer rates fluctuate in time. The heat transfer fluctuation in the heated region is not as strong as in other regions; however, the magnitudes of the heat flux there are strongly influenced by the heating location, indicating that, in order to maintain a uniform thermal environment, the power level of the heat source needs to be adaptively adjusted according to the heating location. This challenge to the design and operation of the materials processing equipment can be met with the aid of knowledge gained from numerical simulations.