Using transient and stationary mathematical heat transfer models including heat conduction, radiation, and radio frequency (RF) induction heating, we numerically investigate the time evolution of temperature gradients in axisymmetric growth apparatus during the sublimation growth of silicon carbide (SiC) bulk single crystals by physical vapor transport (PVT) (modified Lely method). Temperature gradients in the bulk and on the surface of the growing crystal can cause defects. Here, the evolution of these gradients is studied numerically during the heating, growth, and cooling stages, varying the apparatus design, namely the amount of the source powder charge as well as the size of the upper blind hole used for cooling of the seed. Our results show that a smaller upper blind hole can reduce the temperature gradients both in the bulk and on the surface of the crystal without reducing the surface temperature itself. (c) 2006 Elsevier B.V. All rights reserved.