Numerical modelling of a transient conductive–radiative thermal problem arising in silicon purification

The objective of this work is to present and numerically solve a mathematical model for the thermal behavior of a casting ladle devoted to purification of silicon. A nonlinear and nonlocal boundary condition is considered for radiative heat transfer in an inner closed cavity of the domain. We also propose a numerical approximation using a finite element method. An iterative algorithm and numerical results are presented.