A growth kinetics model, which assumes that the growth rate is related to the supersaturation of a rate-determining reactant, is developed to study the mechanism of silicon carbide growth by physical vapor transport. To examine the dependence of growth rate on growth temperature and inert gas pressure, two different growth conditions are considered, one with a small axial temperature gradient in the growth chamber, 2 K/cm, and the other with a large axial temperature gradient, 20K/cm. The study is conducted for a range of inert gas pressure as well as the growth temperature. It is observed that the growth rate has an Arrhenius-like dependence on growth temperature except when the growth temperature is high. The low temperature growth is usually associated with a small-scale system that has a larger axial temperature gradient, while the high temperature growth occurs in a scaled-up system. An integrated model that considers the RF induction heating, radiation-conduction heat transfer and growth kinetics, has been developed to predict the magnetic field, temperature distribution and growth rate profile. The model can help in the design and development of large-scale growth systems.