Transient numerical investigation of induction heating during sublimation growth of silicon carbide single crystals

Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace

“…We notice that A ∈ H(div, Δ c ), but we are not going to assume that A ∈ H(div, R 3 ) so the normal trace A · n on Σ may be discontinuous and hence the integral conditions in (22) are not redundant.…”

“…In the past years, induction heating techniques have been widely applied in the metallurgical and semiconductor industry, in processes such as metal smelting [14,16,27], metal hardening [13,28] or crystal growth [15,22]. An induction heating system basically consists of one or several inductors supplied with an alternating electrical current and a metallic workpiece to be heated.…”

“…From the mathematical point of view, and in order to perform a numerical simulation of the furnace, the physical process is expressed as a coupled non-linear system of partial differential equations arising from the thermo-electromagneto-hydrodynamic problem. In the past years several papers have been published dealing with the thermo-electromagnetic problem [5,7,8,14,16,22], with the electromagneto-hydrodynamic problem [18,24] or with the thermo-electromagneto-hydrodynamic problem [17,21], but not fully coupled because materials properties are supposed to be independent of temperature.…”

Modeling and simulation of sublimation growth of SiC bulk single crystals

“…The material data used for the following numerical experiments are precisely the data provided in the appendices of [11] and [12], respectively.…”

“…Recent papers on stationary models include [9,17]. Transient numerical results concerning the heat transfer during PVT are considered in [3,11,16].…”