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

• Published in: Finite elements in analysis and design Vol. 42; no. 10; pp. 809 - 820
• Main Authors: Bermúdez, A., Leira, R., Muñiz, M.C., Pena, F.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2006; Elsevier
• Subjects: Analytical and numerical techniques; Axisymmetric enclosure; Computational techniques; Exact sciences and technology; Finite elements; Finite-element and galerkin methods; Fundamental areas of phenomenology (including applications); Heat transfer; Mathematical methods in physics; Nonlocal boundary condition; Numerical simulation; Phase change; Physics; Stefan–Boltzmann radiation condition; Thermal radiation; Finite elements; Numerical simulation; Nonlocal boundary condition; Stefan–Boltzmann radiation condition; Axisymmetric enclosure; Phase change; Transient response; Boltzmann equation; Stefan problem; Phase transformations; Enclosure; Axial symmetry; Finite element method; Cavities; Casting; Thermal radiation; Stefan-Boltzmann radiation condition; Modelling; Silicon; Non linear effect; Iterative methods; Non local theory; Heat transfer
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2005.08.009

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.