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

Abstract

SUMMARYThis paper presents a parallel Galerkin boundary element method for the solution of surface radiation exchange problems and its coupling with the finite element method for mixed mode heat transfer computations in general 3-D geometries. The computational algorithm for surface radiation calculations is enhanced with the implementation of ideas used for 3-D computer graphics applications and with data structure management involving creating and updating various element lists optimized for numerical performance. The algorithm for detecting the internal third party blockages of thermal rays is presented, which involves a four-step procedure, i.e. the primary clip, secondary clip and adaptive integration with checking. Case studies of surface radiation and mixed heat transfer in both simple and complex 3-D geometric configurations are presented. It is found that a majority of computational time is spent on the detection of foreign element blockages and parallel computing is ideally suited for surface radiation calculations. Results show that the decrease of the CPU time approaches asymptotically to an inverse rule for parallel computing of surface radiation exchanges. For large-scale computations involving complex 3-D geometries, an iterative procedure is a preferred approach for the coupling of the Galerkin boundary and finite elements for mixed mode heat transfer calculations.

Three-dimensional global modeling of a unidirectional solidification furnace with square crucibles

“…Otherwise, when at least one of the radiative surface elements in concern is in a non-axisymmetric surface, shown as cases 4-6 in Fig. 2, it is based on an algorithm developed by Cui and Li [13]. This is a general algorithm designed for calculating view factors of any 3D configurations with a 3D discretization.…”

“…Moreover, in the calculation of view factors, the key point is to check whether any obstacles in the furnace block a ray emitting from one surface element to another one and to evaluate how much energy emitted from one surface element can reach to another one. Generally, this task is overwhelmingly time consuming for a complex configuration, in particular, when the configuration is in three dimensions and non-axisymmetric [13]. In our 3D global model in which a 2D/3D mixed discretization scheme is used, we developed an effective and highly efficient algorithm to undertake this task by utilizing the geometric features of a solidification furnace.…”