Finite-Element Formulations for Accurate Calculation of Radiant Heat Transfer in Diffuse-Gray Enclosures

Computer Modelling of Bulk Crystal Growth

“…Radiation heat transfer is particularly important in simulation of Czochralski systems, where small changes in crystal and melt shape have a highly nonlinear effect on radiation [35]. For some materials, particularly oxides, internal radiation transfer can also be important [36,37].…”

The Galerkin boundary element solution for thermal radiation problems

“…Strictly speaking, the correct terminology should be the Galerkin boundary element method, because of the existence of kernel function and the surface integration. Kuppurao and Derby [5] and Minkowycz and Haij-Sheikh [6] have presented numerical solutions for surface radiation problems. The former is based on the finite element formulation and applied it to a simple empty cylinder, while the latter derived the Galerkin method using a variational approach and applied it to a simple 1D geometry consisting of two disks.…”

“…Some of the authors used the terminology of finite element method for such an approach [5]. Strictly speaking, the correct terminology should be the Galerkin boundary element method, because of the existence of kernel function and the surface integration.…”

A parallel Galerkin boundary element method for surface radiation and mixed heat transfer calculations in complex 3‐D geometries

“…Unlike the previous work [3,4], the Galerkin boundary integral is derived from the direct boundary formulation of problems and such a derivation is based on the need to ensure a full detection of geometric blockages or shadowing effects caused by configuration arrangements rather than as an alternative formulation for surface radiation problems. The computational algorithm is enhanced with a creation of appropriate data structure and with the use of some proven hidden line removal schemes for 3-D computer graphics applications.…”

“…The Galerkin formulation for surface radiation exchange calculations has recently been derived within the framework of finite elements [4] and variational calculus [5]. In Reference [4], the surface radiation calculations were performed using the finite element method for hollow cylinder. The kernel function was integrated over a solid angle, instead a surface area usually used in the finite element or boundary element computations.…”